by Edwin X Berry, PhD, Theoretical Physics, CCM
Ed Berry LLC, Bigfork, Montana
To read key referenced papers:
- CO2 Coalition paper
- Dia Ato paper
- Bernard Robbins paper
- Eike Roth paper
Click here
Responsiveness of Atmospheric CO2 to Fossil Fuel Emissins
by Jamal Munshi
Ferdinand Engelbeen says Jamal Munshi has not proved absence of correlation.
What do you think? Add your comment below.
A Thermal Acid Calcification Cause for Seasonal Oscillations in the Increasing Keeling Curve
Download this Excel file here: https://edberry.com/Excel-File
Here is table “Berry Carbon Flow Test” for discussion in our comments.
I request Ferdinand and anyone else who is contesting my calcuations to present your calculations for comparison.
We assume that the natural carbon cycle is at constant levels as shown in Figure 3.
With that information, we insert human carbon into the atmosphere at a constant rate of 10 PgC per year. Then we calculate annual time steps to see how much human carbon ends up in each reservoir each year.
This simple calculation is a way to compare our calculations because we keep human carbon inflow constant for each year.
The years run from zero to ten. All the L data are in PgC, and flow data are in PgC/Year.
Lg = land, La = atmosphere, Ls = surface ocean, Ld = deep ocean, L is the total PgC in the carbon cycle for each year. Ntice L increases by 10 PgC each year.
The CO2 ppm column simply converts the PgC in La to ppm.
Here’s how it works.
Year 0: 10 PgC is added to La, but you don’t see it until the beginning of Year 1.
Year 1: the 10 PgC in La produces outflows to Lg and Ls. We see the result in Year 2.
Year 2: the outflows from La have moved some carbon to Lg and Ls. Etc.
Notice that as La gets more PgC, its Outflow to Lg and Ls increase, etc.
While La increased by 7.14 PgC from Year 1 to Year 2, it increased by only 1.49 PgC from Year 9 to Year 10.
Also notice that as Lg and Ls get more carbon, they send carbon back to La.
Adjustment, Residence, E-time Compared
IPCC’s response times fail physics
Physics e-time has a precise definition. The IPCC times do not. In summary:
- Physics: e-time is the time for the level to move (1 – 1/e) of the distance to its balance level.
- IPCC: adjustment time is the time for the level to “substantially recover” from a perturbation.
- IPCC: residence time is the average time a CO2 molecule stays in the atmosphere.
IPCC defines “adjustment time (Ta)” as:
The time-scale characterising the decay of an instantaneous pulse input into the reservoir.
Cawley defines “adjustment time (Ta)” as:
The time taken for the atmospheric CO2 concentration to substantially recover towards its original concentration following a perturbation.
The word “substantially” is imprecise.
Cawley follows IPCC to define “residence time (Tr)” as:
The average length of time a molecule of CO2 remains in the atmosphere before being taken up by the oceans or terrestrial biosphere.
In summary, IPCC uses two different response times where it should use only e-time:
- When the level is far from its balance level (which can be zero), IPCC thinks e-time is an adjustment time because the level is moving rapidly toward its balance level.
- When the level is close to its balance level, IPCC thinks e-time is a residence time because “molecules” are flowing in and out with little change in level.
Figure A illustrates how e-time relates to IPCC’s adjustment and residence times.
Figure A. E-time covers the full range of movement of level to a balance level. IPCC adjustment and residence times apply to only each end of the range.
IPCC, 2001: Working Group 1: The scientific basis. Appendix 1 – Glossary.
Lifetime
Lifetime is a general term used for various time-scales characterising the rate of processes affecting the concentration of trace gases. The following lifetimes may be distinguished:
Turnover time (T) is the ratio of the mass M of a reservoir (e.g., a gaseous compound in the atmosphere) and the total rate of removal S from the reservoir: T = M/S. For each removal process separate turnover times can be defined.
Adjustment time or response time (Ta) is the time-scale characterising the decay of an instantaneous pulse input into the reservoir. The term adjustment time is also used to characterise the adjustment of the mass of a reservoir following a step change in the source strength.
Half-life or decay constant is used to quantify a first-order exponential decay process.
The term lifetime is sometimes used, for simplicity, as a surrogate for adjustment time.
In simple cases, where the global removal of the compound is directly proportional to the total mass of the reservoir, the adjustment time equals the turnover time: T = Ta.
In more complicated cases, where several reservoirs are involved or where the removal is not proportional to the total mass, the equality T = Ta no longer holds.
→Carbon dioxide (CO2) is an extreme example. Its turnover time is only about 4 years because of the rapid exchange between atmosphere and the ocean and terrestrial biota.
However, a large part of that CO2 is returned to the atmosphere within a few years.
Thus, the adjustment time of CO2 in the atmosphere is actually determined by the rate of removal of carbon from the surface layer of the oceans into its deeper layers.
Although an approximate value of 100 years may be given for the adjustment time of CO2 in the atmosphere, the actual adjustment is faster initially and slower later on.
Two quick suggestions, before getting to the content at a later time:
1. Make sure the cover page is labelled as “First Draft”, so that it will be easy to distinguish from subsequent versions.
2. Include in the Introduction a URL link to the document you are countering, so your readers can compare it side-by-side with your own paper as they read your arguments.
Thanks for all your good work!
I could care less about sinks. The measurement of C14 is absolute. If the 50% increase in CO2 was man made, the C14 concentration should be 33% lower today than it was in 1800. Sinks do not matter.
https://royalsocietypublishing.org/doi/10.1098/rspa.1958.0021
Has not been proven wrong. Pre hydrogen bomb the total CO2 emitted was 14% and it was measured at 2.03%+/-0.15%
Since then the atmopspheric testing of hydrogen bombs in 1965 doubled (atmospheric) C14. With a half life of 5740 years this has all gone in 2025. So all the CO2 from 1965 and before 1965 has gone.
And a perfect e-kt curve proves the Bern model is wrong . C14 cannot hide in 60 years, so there is only once place, the ocean. Dilution 50x.
As confirmation the current C14 level is now -2.03%+1/50 =0.0%.
https://i0.wp.com/eos.org/wp-content/uploads/2022/09/bomb-pulse-carbon-curve.png?w=1200&ssl=1
This is open and shut direct measurement. No models required.
(Not argument from coincidence from firn results in ice cores as used by Prof Happer)
The entire history of C14 from 1800 to 2025 is plain. And the horizontal asymptote at 0.0% dilution was expected.
As for C13, the dilution of -8 from the standard of -6 is only explained by ocean CO2 at -12 and not by fossil fuel CO2 at -24. I don’t like these indirect methods. Absolute measurement by radio(active) carbon dating is open and shut.
And the interesting result from Ferguson in 1958 is the question of whether the -2.03% was the static value has been settled. It is still -2.0% in 2025.
Another confirmation is the average age of sea water at -600years, debunking the attempt to argue a surface ocean. 600 years is very close to 50x the e-kt half life of 10 years as agreed in the 36 papers in table 1 of this recent document
https://www.mdpi.com/1099-4300/25/2/384#:~:text=The%20residence%20time%20in%20the,dioxide%20mass%20of%203403%20Gt.
In which he concludes
(1) The adjustment time is never larger than the residence time and is less than 5 years.
(2) The idea of the atmosphere being stable at 280 ppm in pre-industrial times is untenable.
(3) Nearly 90% of all anthropogenic carbon dioxide has already been removed from the atmosphere.
but I would correct (3) to 98%. Only this explains and perfectly explains the fact that C14 levels today are exactly what they were in 1800.
I met Will Happer in Melbourne and made these arguments. He did not counter them, except to refer to ice cores. When pressed he said his view that the CO2 increase was man made was ‘personal’.
I thought it was political, a debate technique of concession and onto this area of expertise, proving the increase was inconsequential, limited and entirely beneficial. All well made and true points.
So I was surprised when he supported an attempt to prove the CO2 was man made. This was rubbish. And a negative on his overall wonderful contribution with the CO2 coalition to argue the massive benefits of CO2.
Another point he misses is the NASA greening. That firstly the CO2 14% increase between 1988 and 2014 was not only related to tree coverage, it exactly matched it. What this means is that the entire cash grab based on legislated carbon credits is nonsense. More CO2 means more trees.
But it was a big effort to make his world tour promoting his excellent work. I was just disappointed that the conceded the idea that CO2 was man made when that is so easily proven untrue in an open and shut C14 measurement. I can only conclude that even good physicists do not understand radio carbon dating. Or they are too anxious to show off their own fields of expertise.
2 typos–Pg 4 1st paragraph, Pg16 2nd to last paragraph.
Thanks for continuing to defend and explain your work. Until others point out logic or math flaws in your work it has to be reckoned with. I think your explanation of equations A,B,C,D could stand some work. I think CO2C correctly state that change in atmospheric CO2 equals inflow(N)+Inflow(H) – outflow(total) but uses N instead of total because there are no human sinks. Their error is thinking of them as sources and sinks and not flows . There are 2 sources (N) and (H) but there is no sink (H) so they leave it out and get it wrong.
All this is very interesting however;
I am an Applied Physicist not a Theoretical one, I suggest that a much simpler approach is needed to convince the non-science population.
To disprove that CO2 caused warming all you need to do is look at the Ice core data and ask one very simple question.
If CO2 causes warming why on all cycles prior to the present; does temperature drop when CO2 is at its highest at the top of each curve?
The answer is also very simple; temperature rise causes CO2 rise by the heating of the oceans, where most of the world’s CO2 is dissolved. If that is true then manmade CO2 emissions are irrelevant.
When the oceans heat they also give off water vapour which increases cloud cover and that causes the cooling cycle. As the cooling progresses cloud cover decreases and eventually that causes another heating cycle.
Also CO2 contributes an insignificant amount to the Green House effect as the mechanism of absorption of radiation is via Atomic absorption (not thermal) this energy is re radiated by the CO2 atom again in a random direction, unless there is water vapour present the scattered radiation is not absorbed as thermal energy.
You asked for input.
1. Don’t spend so much time on Einstein etc. Those who will ever believe that a negative disproves the theory don’t need this.
2. Make your point about the source of CO2 but a. it grows food b. warmth is good for humans c. we’re coming out of an ice age and d. adapting and preparing is more effective than trying to change the whole climate. Don’t give up on these points in your preamble. Otherwise, to use your track team analogy, it’s like a horse race team giving up a jockey because they thinkbthey have a winning horse.
Didn’t Einstein’s Relativity prove that only natural causes and effects influence reality? The German romantics and their successors are attempting to impose the dialectic on empirical science. Locke et al disproved magic as an influence on reality and virtue signalling has no basis in fact. Einstein’s physics is the basis of the peer review process but computer modelling has lowered the standard of proof drastically.
Sorry to sound Luddite but observational physics doesn’t depend on an audience or a consensus.
Abstract
Some folks at a group called the CO2 Coalition (2024) say that the extra carbon dioxide (CO2) in the air comes mostly from human activities, like burning fuel. They call this idea Hypothesis 1, or H(1), and claim they have proof it’s true. But their argument doesn’t hold up because they messed up their math on how carbon moves around in nature, ignored studies that show their idea is wrong, and didn’t follow the basic rules of science. They also used shaky evidence.
A lot of people, including the UN’s climate group and many scientists, agree with the CO2 Coalition that humans are the main cause of rising CO2. They’ve got data and big names backing them up. But science isn’t about who’s loudest or has the most support—it’s about testing ideas to see if they’re wrong. And there’s evidence out there that shows H(1) isn’t correct.
This matters because a group called Our Children’s Trust is fighting in court to challenge President Trump’s climate decisions. They’re using the idea that humans cause most CO2 to push their case. If you support Trump’s climate policies, it’s good to know why this human-caused CO2 idea might not be right, so everyone can be on the same page defending his choices.
Dear Dr Berry,
Thank you for the opportunity to read your draft paper “CO₂ Coalition’s Not-So-Golden Science.” Your rigorous derivation and challenge to Hypothesis H1 present a valuable and much-needed correction to prevailing carbon cycle narratives. In the spirit of strengthening your already compelling argument, I would like to offer the following suggestions for improvement:
1. Clarify Derivations: Some of the core equations could benefit from step-by-step explanatory text or diagrams showing how the terms correspond to physical flows. A flowchart of reservoir dynamics would enhance accessibility for technically literate readers less familiar with differential models.
2. Include Empirical Comparisons: Integrating graphs that compare your model’s output to empirical records (such as the Mauna Loa CO₂ series) would help validate the model visually and reinforce the conclusion that human contributions are minor.
3. Address Isotopic Counterarguments: Given the frequent citation of δ¹³C and ¹⁴C evidence to support anthropogenic dominance, a short, direct rebuttal to these points within the main paper would anticipate criticism and strengthen the self-contained nature of the argument.
4. Neutral Language Tone: While the core message is strong, softening the tone of phrases such as “not-so-golden science” and “fatal error” in select areas could broaden your reach to readers who are open to your analysis but wary of rhetorical framing.
5. Define Key Terms Early: Introducing technical terms such as e-time, Hypothesis H1/H2, and inflow-outflow dynamics upfront would improve flow and prevent confusion as the argument progresses.
6. Strengthen Policy Relevance: The legal and regulatory implications, especially regarding the EPA’s findings and the Lighthizer case, are of high importance. Expanding this section to clearly show how disproving H1 undermines regulatory authority could add significant weight to your conclusions.
7. Offer Reproducibility Tools: Including a supplementary Python or Excel simulation would allow others to run the model themselves, increasing transparency and academic reach.
These suggestions are offered in support of your work and its contribution to restoring correct physical principles in climate-related modelling. I hope they are helpful as you refine and publish this important piece.
Kind regards,
Jack Miller
Matthew,
You are not distinguishing between atmospheric C14 measured as a ratio to C12 (“delta C14”), and atmospheric C14 concentration. The former has returned to near pre-bomb test values; the latter most certainly has not. See https://www.cambridge.org/core/services/aop-cambridge-core/content/view/193CDF1F705B269BC975AF178CEF1AC3/S0033822224000274a.pdf/discussion-presentation-of-atmospheric-14co2-data.pdf. You will be able to understand the detailed behavior of the two measures in Figure 1 (before bomb tests) and Figure 2 (after), only if you appreciate that when an isotopic gradient exists between two reservoirs that are exchanging carbon, the mixing tends to reduce the gradient and leads to a net transfer of C14 towards the reservoir with the lower delta C14 value. Nature is subtle. Even before the bomb tests, C14 free CO2 added to the atmosphere by fossil fuel burning ended up INCREASING the C14 concentration in the atmosphere by this mechanism! Of course, at the same time it lowered the delta C14 value.
Because of this mixing, the present composition of the atmosphere is an unreliable indicator of the source of the CO2 increase.
I met with him too at his Melbourne talk. I concur.
CO2 did not remain at 280ppm until the early 1900s. CO2 rose to 450ppm and 500ppm on many occasions during the Holocene.
We concur with every scientific point made here by Dr Ed Berry, In addition we show from delta 13C measured data that the vast majority of CO2 emissions into the atmosphere have an ocean origin.
Additionally the Pinatubo experiment conducted by Bromley & Tamarkin published in their paper Bromley & Tamarkin 2022 demonstrated quite categorically that human emissions of CO2 are miniscule.
In separate papers Bromley also shows that it is Henry’s Law that controls atmospheric CO2 concentrations and that it is impossible for humans to control atmospheric CO2 concentrations.
All of this along with the 37 pages of references can be obtained in our recently published book:
Climate Truths
Dr Robert Ian Holmes and Brendan Godwin
http://www.climate-truths.com
We cite all of this good work of Dr Ed Berry in this book.
you should get a debate going on this on Whats up with That.
Hi Don,
Thanks, but I am not interested.
A year or so ago, the CO2 Coalition started such a “debate” on WUWT. The discussion became so crowded with nutcase comments that it was impossible to have a rational debate.
The only way to have a focused debate is here.
Hi Jack,
Thank you. I am now going through your suggestions, and I will update this draft accordingly.
Ed
Ed,
1. I understand your intent with your equations (A) and (B), but your notation is poor. There are two different L (level) functions of time which you label through their arguments. It would be clearer to use different names for the functions, perhaps utilizing subscripts instead of inappropriately giving what is apparently the same function two different arguments. Clearer notation might have prevented your further confusion discussed below.
2. There are no errors in the CO2C’s bookkeeping or in that of mainstream climate science. They track total carbon levels, not “human” and “natural” carbon separately as you do, and they do so accurately. They do not say or imply that “human carbon” gets stuck in the atmosphere. The science is dead simple: when we put 100 units of carbon into the atmosphere it gains about 45 units and the rest flows into land/sea reservoirs. That is shown by the uncontroversial empirical fact that human emissions exceed the atmospheric accumulation rate.
3. Neither I nor any reputable scientist contests your conclusion that only a small fraction of the carbon atoms in the current atmosphere were once part of fossil fuel. But so what? The large two-way exchanges between the atmosphere and land/sea reservoirs mix the inventories in about a decade. Therefore you can’t tell the cause of the atmospheric carbon increase from its current composition. You can tell the cause by noting that land/sea carbon inventories have increased as well. The inventories that have decreased are the fossil fuel reserves.
Dear David,
Thank you for your comment.
1. I certainly agree that I must improve my explanation of CO2C’s carbon cycle error. I am working on that.
2. Indeed, CO2C, you, and others track the total carbon level. I am sure we agree that the total carbon level does not measure the individual human and natural carbon levels.
But we disagree on your claim,
“when we put 100 units of carbon into the atmosphere it gains about 45 units and the rest flows into land/sea reservoirs. That is shown by the uncontroversial empirical fact that human emissions exceed the atmospheric accumulation rate.”
That is where this debate must focus. I will revise my draft to address this issue I raise in 1.7 immediately thereafter 1.7.
3. The reason I mentioned the difference between IPCC’s fast and slow carbon cycles is because CO2C seem to have a difficult time trying to explain this difference.
3a. You bring up a second point in your claim “can’t tell the cause of the atmospheric carbon increase from its current composition.” I assume you are referring to my use of Delta14C to derive the relative amounts of human carbon in the atmosphere.
This is a point worth discussing, because I claim today’s Delta14C level is a result of the continuing inflow (and resulting outflow) of human and natural carbon, and these inflows set the balance levels of each component.
I see you raised the same issue with Matthew.
Ed
Dear DMA,
Thank you for your point that I must improve my explanation of ABCD, etc. I will do that in my next draft.
Meanwhile, please help me find the two typos you found. (My addition of the Table of Contents inserted about one new page, so page numbers changed.)
Ed
Hi Peter,
Thank you very much. You can see that this draft includes your suggestions.
Ed
“The science is dead simple: when we put 100 units of carbon into the atmosphere it gains about 45 units and the rest flows into land/sea reservoirs. That is shown by the uncontroversial empirical fact that human emissions exceed the atmospheric accumulation rate.”
Emissions from many sources (termites, tropical ocean) exceed the annual accumulation. Your statement sits on an assumption that all natural emissions are constant and sinks are growing at a rate less than human emissions. That assumption is false. CO2 flow through the atmosphere is independent of its source. The quantity of CO2 in the atmosphere is controlled by natural forces, largely temperature, and the standard gas laws. Curtailing or increasing one minor source will induce an offset reaction in other sources. It is reasonable to treat any source by itself with flow characteristics the same as the total. Dr.Ed has done just that and his work shows that human emissions are only a small part of the rising CO2. The causes of the increase in atmospheric CO2 are changes in nature that allow the atmosphere to hold more.
Sorry I can’t spot them again. You probably got them in your review.
DMA,
The sum of all natural CO2 emissions (including termites, tropical oceans, volcanoes, freshwater ponds, decaying vegetation…) is not well known. The sum of all natural CO2 absorption (vegetation growth, dissolution into seawater as dictated by Henry’s Law, ..) is also poorly known. Nevertheless we can rigorously and accurately compute the DIFFERENCE between all natural absorptions and all natural emissions, a quantity called “Net global uptake” in the literature. By carbon conservation, that difference must equal the quantity of “missing carbon”, the carbon that didn’t stay in the atmosphere after we put it there by burning fossil fuels. That carbon had to have gone somewhere, into one of the natural sinks. See for example Ballantyne, A. P. Alden, C.B., Miller, J.B., Tans, P.P. ,2012: Increase in observed net carbon dioxide uptake by land and oceans during the past 50 years, Nature, vol 488 pp 70-72. doi:10.1038/nature11299. They find that between 1960 and 2010:
Human emissions totaled 350 +or – Pg of carbon
Atmospheric accumulation was 158 + or – 2 PgC
Therefore by subtraction, ocean and terrestrial sinks took in 192 + or – 29 Pg of carbon.
(1 Pg = 1 billion metric tonnes. Note that the analysis applies to the carbon in CO2, not CO2 itself, because it is carbon that is conserved, not CO2.)
Ballantyne et al divide the data into decades and find that, like human emissions, net global uptake increased during those 50 years. You are correct that “increasing one minor source will induce an offset reaction in other sources.” You are also correct that natural forces have an effect. Net global uptake, while definitely positive in the 1990’s, was a bit lower than in neighboring decades. Ballantyne et al attribute that to the cooling effects of the Pinatubo eruption.
There is no assumption in this analysis that emissions are constant. There is no assumption that carbon from one source behaves differently than carbon from another. The only asymmetry in the analysis is that “human absorption” is taken as 0. That would change if Direct Air Capture technology was deployed on a large scale. For Ed’s sake let me emphasize that “human absorption” by Direct Air Capture has nothing to do with what he calls “human carbon”.
You argue “It is reasonable to treat any source by itself with flow characteristics the same as the total.” I think you are saying, as Demetris Koutsoyiannis has, why not pin the blame for the growth on decaying vegetation, whose emissions are growing as the stock of vegetation grows? But the growth in vegetation that the CO2 Coalition praises implies that there is more carbon in vegetation in 2010 than there was in 1960. Similarly the ph decrease of the oceans tells us that there is more carbon in the oceans in 2010 than in 1960. Where is there LESS carbon? There is less carbon in the fossil fuel reserves. Doesn’t that tell you that removing carbon from those reserves is the cause of the increases elsewhere?
“To disprove that CO2 caused warming all you need to do is look at the”- many papers documenting a reduction in clouds during the modern warm period. Three of those papers concluded that all of modern warming can be explained by the increase in solar energy reaching the surface and heating the oceans to depth. All sky down welling IR has trended down also. Some negative feedback is preventing the clear sky increase in CO2’s 15 micron band from producing an enhanced greenhouse effect.
The ice core record is clear proof that CO2 doesn’t correlate to temperature other than as lagging indicator. That it is always at peak values when global cooling begins is proof it doesn’t have enough juice to overcome natural variability.
Hi David,
I just finished updating my point about CO2C’s carbon mass balance error, now in 3.1.
In my view, “Net global uptake” is just plain bad physics. The “Net global uptake” boys have no carbon cycle model to support their conclusions. They assume H(1) is true before they make their calculations.
They don’t get it that there are independent human and natural carbon cycles.
The idea that there is “missing carbon” that they can measure, and the “carbon that didn’t stay in the atmosphere” assumes H(1) is true.
Ed,
As Dave Andrews correctly points out, it’s an empirical fact that human CO2 emissions are greater than the amount of CO2 accumulating in the atmosphere. You don’t need a carbon cycle model to compute the global mass balance of CO2.
The annual increase in atmospheric CO2, which is known with a high degree of certainty, is less than the global annual emissions from fossil fuel burning and cement production alone. The latter two things are more likely than not underestimates because they depend on countries accurately reporting their consumption of fossil fuels.
The difference between CO2 rise and CO2 emissions from fossil burning and cement production is referred to as the so-called “missing CO2”. The scale of engineered CO2 removal from the atmosphere by humans is too small to account for the “missing CO2”. Thus, common sense should tell you that if there is no significant human CO2 sink and the annual increase in atmospheric CO2 is less than that emitted by human activities alone, nature – the oceans and land — must be a net global sink of atmospheric CO2, not a source. I don’t see how it’s plausible to infer anything different.
The mass balance result is partly the basis for IPCC’s conclusion that the rise in atmospheric CO2 is largely due to human emissions rather than from natural sources. There is a substantial body of other evidence that shows both the oceans and land are net sinks of atmospheric CO2.
Your statement that Delta 14C is decreasing because it is returning to
its balance level.” Is a tautology. You are essentially saying Delta 14C is decreasing because it’s decreasing.
You seem not to fully understand the causes of the post-bomb decline in Delta 14C of atmospheric CO2. This is reflected in your incorrect statement that “If human CO2 caused all the CO2 increase, it would have reduced the Delta 14C balance level by 33 percent.”
And you also state that “Berry’s accurate curve fit shows no measurable effect of human CO2 emissions or of a “Suess effect dilution”.” If so, then are you suggesting that net uptake of 14CO2 alone accounts for the post-bomb decline of Delta 14CO2? Your curve fit is to the post-bomb decline of Delta 14C of atmospheric CO2. But it doesn’t account for the isotopic dilution effect on atmospheric Delta 14CO2. It’s simply a curve fit.
And your 33 percent calculation firstly assumes that all of the 14C produced from atmospheric testing of nuclear weapons remains in the atmosphere and becomes isotopically diluted by 14C-free CO2 emissions from fossil fuel burning. This is a false assumption. Moreover, your assumption is at odds with your claim that isotopic dilution was not the cause of post-bomb decline of atmospheric Delta 14CO2.
You overlook the fact that both 12CO2 and 14CO2 are cycled and exchanged between the atmosphere and ocean and land. The magnitude of this CO2 cycling and exchange, which you appear to accept and use in one of your other arguments, is clearly shown in your Figure 3 – IPCC’s natural and human global carbon cycle figure. This carbon cycling and exchange between reservoirs has the effect of lowering the Delta 14C of atmospheric CO2 and increasing the Delta 14C of CO2 in the ocean and of exchangeable/recyclable CO2 in soil and plants in the terrestrial biosphere.
Empirical data clearly show the Delta 14C of CO2 in ocean surface water and in recycled soil and plant carbon in the terrestrial biosphere increased during the post-bomb period as the Delta 14C of atmospheric CO2 declined. I can provide a figure showing this if you would like to see it.
The exchanges of CO2 between the atmosphere and the ocean and terrestrial biosphere that has a lower Delta 14C than the atmosphere partially contributed to the decline of Delta 14C of atmospheric CO2 before isotopic equilibrium was reached between the atmosphere and the ocean and land. The net effect of this recycled CO2 on the isotopic dilution of atmospheric 14CO2 is less than what would have occurred if all of the bomb 14C had remained in the atmosphere. It is the reason why the Delta 14C of atmospheric CO2 has not declined to 33 percent below the pre-bomb level. But the post-bomb decline of atmospheric Delta 14CO2 is still largely due to isotopic dilution. Net uptake of CO2 would not be expected to have a major effect on the Delta 14C of CO2 remaining in the atmosphere because there is only a small isotope effect on uptake of the two isotopes – 12C and 14C.
Because of isotopic dilution, the Delta 14C of atmospheric CO2 is now less than that of ocean surface water. The resulting isotopic disequilibrium of 14C between the atmosphere and ocean surface water is the reason why the concentration of 14CO2 in the atmosphere is now increasing. This was predicted to occur. Dave Andrews has provided empirical data in one his published papers, showing this has happened. Thus, the oceans are now a net global source of atmospheric 14CO2 and a net global sink of atmospheric 12CO2.
The CO2 in ocean surface water and the atmosphere reached isotopic equilibrium in the early 90s, but the Delta 14C of atmospheric CO2 has continued to decline to slightly below its pre-bomb level, most likely due to continued isotopic dilution from emissions of 14C-free CO2 from fossil fuel burning. There is every reason to expect it will continue to decline with continued emissions of 14C-free CO2 from fossil fuel burning.
Thanks for your excellent workings, Ed.
Additional thought: we have been given a very robust self-repairing planet.
IPCC tell us there are 39,000GT of CO2 in the oceans.
There are also 1,386,000,000 cu kms of water = 1386 x 10 to the 15 cu m
Sea water weighs 1024kg/cu m
Total weight of oceans is 1419 x 1 with 18 zeros
Divide the CO2, 39,000 GT, or 39 with 15 zeros, by the size of the oceans and you get 27ppm
Humans produce 38GT p.a. so 100 years of it would increase the CO2 by 2.6ppm.
I was working in the 1970’s when the National Geographic was prophesying the next ice age was about to begin, but CO2 had increased for the previous 30 years! Folks are gullible. God has given us a great planet! (which of course we must not pollute with plastic)
Ed,
It’s time to give it up. You know as well as I do that our positive net global uptake is a consequence of applying dL/dt = Inflow – Outflow to total carbon. There are no mistakes, circular reasoning, or extraneous unwarranted assumptions involved. It can also be deduced from common sense.
Years ago you posted that a bad argument is better than none at all. But the CO2 Coalition, who make plenty of bad arguments themselves, thought otherwise. They knew that between you, Harde and Salby, and Koutsoyiannis, climate skepticism was weakened by obviously bad arguments. Last winter you tried to get bad science into Montana law. Now you want bad science to influence federal science policy. There is enough chaos in Washington DC without your help.
Find another hobby, Ed
New and interesting information which may add to your paper ?
The text below i a copy from a recent article by Charles Rotter in WUWT with following title and introduction ;
Settled Science Springs a Leak: Rivers Reveal the Carbon Cycle’s Dirty Secret.
The recent Nature study titled “Old carbon routed from land to the atmosphere by global river systems” is not only a rigorous piece of scientific work—it’s also a spectacular indictment of the so-called “settled science” of climate change. This 2025 paper is a flaming arrow into the heart of carbon cycle certainty, unearthing yet another inconvenient truth: over half of the CO2 emitted from rivers comes from carbon sources that are hundreds to thousands of years old—not from recent fossil fuel emissions or current biological activity.
Hi David,
You wrote, “our positive net global uptake is a consequence of applying dL/dt = Inflow – Outflow to total carbon.”
But you have never proved your claim in any of your publications. All you do is handwaving. I have proved that your statement is wrong, but you just don’t get it.
So, let me ask you something simpler. Do you understand my argument about a weight on a string? Many PhD’s in physics still argue that the weight speeds up. They just don’t get it.
The argument you make about “positive net global uptake” is a similar physics error.
Dear Jerry,
(Below, I repeat your comments and indent my comments.)
It’s an empirical fact that human CO2 emissions are greater than the amount of CO2 accumulating in the atmosphere.
You don’t need a carbon cycle model to compute the global mass balance of CO2.
The difference between CO2 rise and CO2 emissions from fossil burning and cement production is referred to as the so-called “missing CO2”.
Thus, common sense should tell you that if there is no significant human CO2 sink and the annual increase in atmospheric CO2 is less than that emitted by human activities alone, nature – the oceans and land — must be a net global sink of atmospheric CO2, not a source.
The mass balance result is partly the basis for IPCC’s conclusion that the rise in atmospheric CO2 is largely due to human emissions rather than from natural sources.
There is a substantial body of other evidence that shows both the oceans and land are net sinks of atmospheric CO2.
Your statement that Delta 14C is decreasing because it is returning to
its balance level.” Is a tautology. You are essentially saying Delta 14C is decreasing because it’s decreasing.
You seem not to fully understand the causes of the post-bomb decline in Delta 14C of atmospheric CO2. This is reflected in your incorrect statement that “If human CO2 caused all the CO2 increase, it would have reduced the Delta 14C balance level by 33 percent.”
And you also state that “Berry’s accurate curve fit shows no measurable effect of human CO2 emissions or of a “Suess effect dilution”.”
If so, then are you suggesting that net uptake of 14CO2 alone accounts for the post-bomb decline of Delta 14CO2? Your curve fit is to the post-bomb decline of Delta 14C of atmospheric CO2. But it doesn’t account for the isotopic dilution effect on atmospheric Delta 14CO2. It’s simply a curve fit.
And your 33 percent calculation firstly assumes that all of the 14C produced from atmospheric testing of nuclear weapons remains in the atmosphere and becomes isotopically diluted by 14C-free CO2 emissions from fossil fuel burning.
This is a false assumption. Moreover, your assumption is at odds with your claim that isotopic dilution was not the cause of post-bomb decline of atmospheric Delta 14CO2.
You overlook the fact that both 12CO2 and 14CO2 are cycled and exchanged between the atmosphere and ocean and land. The magnitude of this CO2 cycling and exchange, which you appear to accept and use in one of your other arguments, is clearly shown in your Figure 3 – IPCC’s natural and human global carbon cycle figure. This carbon cycling and exchange between reservoirs has the effect of lowering the Delta 14C of atmospheric CO2 and increasing the Delta 14C of CO2 in the ocean and of exchangeable/recyclable CO2 in soil and plants in the terrestrial biosphere.
Empirical data clearly show the Delta 14C of CO2 in ocean surface water and in recycled soil and plant carbon in the terrestrial biosphere increased during the post-bomb period as the Delta 14C of atmospheric CO2 declined. I can provide a figure showing this if you would like to see it.
The exchanges of CO2 between the atmosphere and the ocean and terrestrial biosphere that has a lower Delta 14C than the atmosphere partially contributed to the decline of Delta 14C of atmospheric CO2 before isotopic equilibrium was reached between the atmosphere and the ocean and land.
The net effect of this recycled CO2 on the isotopic dilution of atmospheric 14CO2 is less than what would have occurred if all of the bomb 14C had remained in the atmosphere.
It is the reason why the Delta 14C of atmospheric CO2 has not declined to 33 percent below the pre-bomb level. But the post-bomb decline of atmospheric Delta 14CO2 is still largely due to isotopic dilution. Net uptake of CO2 would not be expected to have a major effect on the Delta 14C of CO2 remaining in the atmosphere because there is only a small isotope effect on uptake of the two isotopes – 12C and 14C.
Because of isotopic dilution, the Delta 14C of atmospheric CO2 is now less than that of ocean surface water. The resulting isotopic disequilibrium of 14C between the atmosphere and ocean surface water is the reason why the concentration of 14CO2 in the atmosphere is now increasing. This was predicted to occur.
Dave Andrews has provided empirical data in one his published papers, showing this has happened. Thus, the oceans are now a net global source of atmospheric 14CO2 and a net global sink of atmospheric 12CO2.
The CO2 in ocean surface water and the atmosphere reached isotopic equilibrium in the early 90s, but the Delta 14C of atmospheric CO2 has continued to decline to slightly below its pre-bomb level, most likely due to continued isotopic dilution from emissions of 14C-free CO2 from fossil fuel burning. There is every reason to expect it will continue to decline with continued emissions of 14C-free CO2 from fossil fuel burning.
Ed,
dL/dt = Inflow – Outflow, integrated and applied to total atmospheric carbon, means that the amount the total atmospheric carbon level changes in some time period “Cchange” equals the difference between the amount that went into the atmosphere and the amount that left during that period. Are you with me so far?
The amount that went into the atmosphere in that period can be divided into two parts: human emissions from fossil fuel burning “Eh” and natural emissions “En”. The only significant outflow is natural “An”. Putting this all together
Cchange = Eh+En-An. Rearranging
Eh-Cchange = An – En
which is sensibly called “net global uptake”, the amount by which human emissions exceeded the carbon level change, or the net amount of carbon REMOVED from the atmosphere by natural processes. Measurements show that this quantity has been positive during the Industrial era. You had graphs showing this in your earlier papers, but apparently decided to remove it from your current scribblings.
You disrespect your readers, Ed, by thinking that they don’t understand this and pretending that you do not either. If you have further questions you can ask DMA.
David,
You get the wrong answer because you combine human and natural flows and omit an important term.
You claim the only significant outflow is natural “An”. Then you omit “Ah.” You flunk physics.
The rule of physics is never, never, never omit a term in your equations. But you do, and you thereby get the wrong answer. You must include this term and then put in data to prove it is negligible. You have not done this.
I prove this term is very important. In fact, the term you omitted makes all the difference.
We have been over this before in our published papers. You should have learned.
My primary mentor, Winterberg, was the best student of Heisenberg. He wrote years later that I was his best student. (I would have flunked his courses if I made an error like you keep making.)
Ed,
It is easy to find data showing that an “Ah” term is negligible. This would measure human processes removing carbon from the atmosphere and has nothing to do with what you call “human carbon”. (You sometimes seem unclear on that or perhaps purposely want to muddy the waters.)
See the following International Energy Agency report on global carbon sequestration projects. https://www.iea.org/data-and-statistics/data-tools/ccus-projects-explorer The 2025 global CAPACITY is for the removal of 50.9 MEGA-tonnes of CO2/yr. (They don’t say how much of that capacity will be used.) On the other hand, human emissions in 2024 were 41.4 GIGA-tonnes, and net global uptake by natural processes was around 19 GIGA-tonnes. GIGA is 1000x larger than MEGA. So you can correct net global uptake downward by the factor of .997 if you like, though the real correction using UTILIZED capacity would be smaller. Note that while IEA projects a 6-fold increase in sequestration capacity over the coming decade, that will still not be sufficient to make a big impact, though every bit helps.
You like to feign confusion and attack the rock-solid carbon balance calculation but never address the other major criticism of your work. You estimate/calculate that only a small portion of the carbon in the present atmosphere was once part of a fossil fuel. NO ONE DISAGREES WITH YOU! What you get wrong is your inference that the CAUSE of the increase is therefore natural. NO! Mixing between your “human carbon” and much larger stocks of “natural carbon” have fooled you.
Ove,
The Nature paper cited by Rotter is quite interesting. It is open-access, and you should read it. It will not change the measurement of net global uptake by natural processes at all. The models of exchange rates between various reservoirs based on C14 data will need to be adjusted. It is hardly a “flaming arrow into the heart of carbon cycle certainty.” It is a typical small step forward in understanding nature.
Dear David,
You write, “It is easy to find data showing that an “Ah” term is negligible.” There are no such data!
All the “data” you reference ASSUMES in its processing that Ah is zero, making your argument circular. The IEA “data” are junk data.
The burden of proof is on you. You cannot simply list references. You must show your total argument if you wish to make your point.
Do you claim IPCC’s natural carbon cycle data are wrong? If so, then show the corrections you wish to make to IPCC’s natural carbon cycle data.
You cannot legitimately claim that human carbon caused all (or almost all) of the CO2 increase and at the same time agree that IPCC’s natural carbon data are valid.
My papers prove these two positions are not compatible. I used simple deductive reasoning. Therefore, you cannot use data to prove my deductive reasoning is wrong. You must find an error in my deductive reasoning to prove my argument is wrong. You have not done this.
You estimate/calculate that only a small portion of the carbon in the present atmosphere was once part of a fossil fuel. NO ONE DISAGREES WITH YOU! What you get wrong is your inference that the CAUSE of the increase is therefore natural. NO! Mixing between your “human carbon” and much larger stocks of “natural carbon” have fooled you.
David,
You are not debating physics. You are only debating your emotions. I can’t debate your emotions.
My formulation of IPCC’s natural carbon cycle allows deductive proof that the impact of human carbon emissions has negligible effect on the CO2 level.
Nothing you have argued has any effect on my proof, which still stands.
David,
Your net global uptake argument is a confirmation biased fake argument. You said:
““net global uptake”, the amount by which human emissions exceeded the carbon level change, or the net amount of carbon REMOVED from the atmosphere by natural processes. Measurements show that this quantity has been positive during the Industrial era.”
What measurements? Just words. No citation. There are no such measurements. If you are referring to the Global Carbon Budgets. These papers are the biggest waste of tax payers money in the history of science. They are based on assumptions, guesses, estimates and models based on false assumptions. No one has ever measured ocean emissions. That would require thousands of measurement stations over the oceans globally. Emissions are different in every location around the world.
The Pinatubo experiment conducted by Bromley & Tamarkin 2022 demonstrated that human emissions of CO2 are miniscule and almost too small to measure. The oceans are the dominant source and sink for CO2.
“They examined data following the explosive volcanic eruption of Pinatubo on the island of Luzon in the Philippines in June 1991. This eruption emitted large amounts of aerosols into the atmosphere blocking sunlight and reducing SSTs and surface temperatures. This altered the Henry’s Law ratio causing a reduction in oceanic emissions lowering the atmospheric concentrations. There was a large natural movement down in atmospheric concentrations of CO2 post the eruption, followed after that by an even larger natural movement back up.
The large movement down in CO2 concentrations post the eruption occurred despite the fact that during this same period, human emissions of CO2 continued unabated. Natural emissions also continued from, e.g. biosphere decay & ocean emissions. During 1991-1992 there was an El Nino event which caused increased emissions from a warmer Pacific Ocean. On top of that, the volcano itself added large amounts of CO2 gas to the atmosphere. In spite of all these emissions, overall SSTs dropped post the eruption causing a large drop in atmospheric CO2 concentrations.”
Bromley & Tamarkin 2022; Correcting Misinformation on Atmospheric Carbon Dioxide; https://budbromley.blog/2022/05/20/correcting-misinformation-on-atmospheric-carbon-dioxide/ Accessed 28-8-2023
Additionally Bromley showed that it is impossible for humans to control atmospheric CO2 concentrations. This is controlled by Henry’s Law and Henry’s equilibrium ratio which is in turn controlled by sea surface temperatures.
Bromley, Bud 2021; Henry’s Law controls CO2 concentration, not humans; Posted on August 18, 2021; Accessed 25/8/2023; https://budbromley.blog/2021/08/18/henrys-law-controls-co2-concentration-not-humans/
Bromley, Bud 2023 EPA Submission Document; Comment submitted by Clare Livingston “Bud” Bromley III; Posted by the Environmental Protection Agency on Aug 10, 2023; https://www.regulations.gov/comment/EPA-HQ-OAR-2023-0072-0504; Attachment 3 Comment by Bud Bromley on the proposed rule by the Environmental Protection Agency; New Source Performance Standards for Greenhouse Gas Emissions from New, Modified, and Reconstructed Fossil Fuel-Fired Electric Generating Units: Emission Guidelines for Greenhouse Gas Emissions from Existing Fossil Fuel-Fired Electric Generating Units; and Repeal of the Affordable Clean Energy Rule
https://www.regulations.gov/document/EPA-HQ-OAR-2023-0072-0001
Further isotopes clearly demonstrate that the vast majority of CO2 emissions has an ocean origin.
Increase in CO2 Concentrations is coming from the Oceans
Brendan Godwin ; March 2021
DOI: 10.13140/RG.2.2.35445.29923
https://www.researchgate.net/publication/350162788_Increase_in_CO_2_Concentrations_is_coming_from_the_Oceans
The δ13C for the oceans is -10‰ as measured by NOAA, See also the extensive work on isotopes conducted by Philip Mulholland.
Carbon Isotope Ratio Formula 17Jun25
June 2025
DOI: 10.13140/RG.2.2.36123.37920/1
Lab: Philip Mulholland’s Lab
Philip MulhollandPhilip Mulholland
https://www.researchgate.net/publication/392822758_Carbon_Isotope_Ratio_Formula_17Jun25
For more information see http://www.climate-truths.com.
Ed,
I am not emotional about carbon conservation. I am emotional about integrity. The only explanation for “the best student of Winterberg” not being able to figure out and acknowledge the obvious is that you are dishonest, and that you think so little of your followers that you take the chance that they can’t figure it out either. It’s not rocket science, but perhaps you know your followers better than I do.
I was going to point out all your errors with C14, but I see that Jerry Elwood has already done a good job of that, and you have responded with your usual gibberish, so there is not much else to say. I will leave you alone until the next time you try to influence Montana law. There is a good reason you are toxic among the Montana Republicans.
Brendan.
From my earlier post to DMA:
“See for example Ballantyne, A. P. Alden, C.B., Miller, J.B., Tans, P.P. ,2012: Increase in observed net carbon dioxide uptake by land and oceans during the past 50 years, Nature, vol 488 pp 70-72. doi:10.1038/nature11299. They find that between 1960 and 2010:
Human emissions totaled 350 +or – Pg of carbon
Atmospheric accumulation was 158 + or – 2 PgC
Therefore by subtraction, ocean and terrestrial sinks took in 192 + or – 29 Pg of carbon.
(1 Pg = 1 billion metric tonnes. Note that the analysis applies to the carbon in CO2, not CO2 itself, because it is carbon that is conserved, not CO2.)
Ballantyne et al divide the data into decades and find that, like human emissions, net global uptake increased during those 50 years. [DMA is] correct that “increasing one minor source will induce an offset reaction in other sources.” [DMA is] also correct that natural forces have an effect. Net global uptake, while definitely positive in the 1990’s, was a bit lower than in neighboring decades. Ballantyne et al attribute that to the cooling effects of the Pinatubo eruption.”
By the way, while the Henry’s Law coefficient is indeed temperature dependent, the main Henry’s Law effect is that if you stuff extra carbon into the atmosphere, a new balance will push some into the oceans. That is what has happened.
David,
Well done. Your Ballantyne et al 2012 is hidden behind a paywall. But the abstract doesn’t help your cause at all. Look at the first line.
“One of the greatest sources of uncertainty for future climate predictions is the response of the global carbon cycle to climate change”
The whole paper is based on this confirmation bias. Climate change is a non existent problem. As usual for these confirmation biased papers. it is assumed that the climate change is human induced. HICC has never been validated in any scientific real world experiment. There are zero scientific papers in the empirical literature that can show, from observations based on experiment, that human emissions of CO2 cause any change to global temperatures of the climate. No one has ever measured the temperature of the Earth warm and been able to attribute that warming to CO2 molecules in any real world experiment. That means HICC is not a theory and hasn’t even risen to the scientific level of a hypothesis. It is just an idea and one that fails experiment. As Richard Feynman says, if it fails experiment it is wrong. So your paper is based on this line which is a fallacy.
The paper used mathematical illusions (sorry – models), not measurements. It is related to the global carbon budget which is all fake.
In any event, whatever is written in the bowels of this paper is falsified by Bromley & Tamarkin 2022 which is based on only measurements.
DMA is wrong.
David, your comments are toxic, riddled with ad hominem, lacking in any science and provide no value to this discussion. You ignore all inconvenient truths and keep pumping your confirmation biased propaganda.
David,
You said:
“Henry’s Law coefficient is indeed temperature dependent, the main Henry’s Law effect is that if you stuff extra carbon into the atmosphere, a new balance will push some into the oceans”
You called it the “main” effect. That demonstrates your confirmation bias. That is correct but you are talking about only a miniscule amount.
However you are ignoring the inconvenient opposite truth. If humans remove CO2 from the atmosphere, such as burring it underground, the oceans will replace all of that remove CO2 back into the atmosphere.
As proven by Bud Bromley, it is impossible for humans to control atmospheric CO2 concentrations.
This is an attempt to explain TOTAL C14 something which is very different and nothing to do with the basic concept of radio(active) CO2 dating. The very concept of the equilibrium in which the ratio of C14/C12 is a constant is being attacked as wrong even prior to 1965! That’s the end of radio carbon dating then.
What was true prior to 1965 is still true. C14/C12 in 1958 proved the fossil fuel CO2 level was 2.03% +/-0.15%. At that point the growth in total atmospheric CO2 was 14%. If the source of the CO2 was fossil fuel without C14, the dilution MUST have been 14%. It was not.
The WHOLE POINT of radio carbon dating is that you measure the RATIO so that it is independent of fluctuations in total atmospheric CO2. It is only the ratio which matters. Total C14 in the atmosphere can go up and down as CO2 goes up and down. It’s irrelevant. With a half life of 5740 years, it is total C14 in the system which is constant. All sinks are relatively short term. CO2 in the atmosphere could double and C14 the atmosphere would double but the equilibrium ratio would remain unchanged.
Again I read your comments correctly, you are saying that Ferguson was wrong and fossil fuel CO2 was increasing the amount of C14 in the atmosphere ‘through this mechanism’. That’s rubbish.
The idea of an ‘isotopic gradient’ is rubbish. C14O2 is only one atom in a trillion. It cannot move independently of the C12O2 in which it is embedded. The difference in absorption of C14O2 and C12O2 is under 1% and it is accommodated in the calculation of delta.
It also does not explain the perfect e-kt behaviour in C14/C12 nor the horizontal asymptote of 0.0% in 2025. If you project these theories to 2025 they are incorrect.
C14O2 in the atmosphere was doubled in 1965. Ten half lives later 98% of all 1965 CO2 is now in the water and 98% of the extra C14O2 is in the ocean. The total then is -2.03%+1/50th = 0.03% in the ratio. It all fits perfectly.
These new theories of the independent behaviour of TOTAL C14 after the bomb blast need examination. I have seen a few now try to reproduce the C14/C12 bomb curve and the failure if you project past 2020.
I am amazed that such a simple concept is so hard for people.
Dear Ed,
It is difficult to react on a lot of allegations on one’s work, if nobody did warn the authors that these allegations even existed…
My co-worker, David Burton, and I have commented in the past on the “model” that you used to describe the carbon cycle. To no result, as you still use the “classic” model that assumes that the CO2 level in the atmosphere is caused by the sum of all CO2 inputs and that the level in the atmosphere causes the height of the outputs. We call that the “lake” model. Every flow is one-way from river inputs to lake outputs.
The real CO2 world is quite different: 95% of all CO2 fluxes are just cycling in and out, completely independent of the CO2 level/pressure in the atmosphere. Only 5% is directly pressure difference (with the ocean surface and plant alveoles) dependent, not even depends on the absolute pressure of CO2 in the atmosphere…
Take what happens in spring/summer: a lot of new leaves are formed and together with increased sunshine and temperature, lots of CO2 are sucked out of the atmosphere, even so much that the atmospheric CO2 levels get lower! Despite that at the same time the warming oceans are releasing lots of CO2 from their surface.
That means that hardly any extra CO2 is absorbed, due to the CO2 pressure in the atmosphere. In reality: 2.5 PgC/year extra absorbed in vegetation by the extra CO2 pressure, while fossil emissions are about 10 PgC/year.
That are the largest carbon cycles within a year, completely reversing in other seasons.
That is what we call the “fountain” model: lots of water are cycling over the fountain, but if some worker opens the small valve of the water supply, only then the level in the water basin will increase, completely independent of how much water circulates over the fountain.
Which model then is right? In your “classic” model, the ratio of “markers” in the lake (atmosphere) never can exceed the marker ratio in the total inputs. In the “fountain” model, a marker (like a green color at St. Patrick”s day in Chicago) can asymptotically go up to 100% of the fountain water…
A good marker is the ratio between 13C/12C which is a lot lower in fossil fuels. While vegetation has a similar ratio, the O2 balance and the greening of the earth shows that vegetation is a net absorber of CO2, thus enriching the remaining atmosphere in 13C/12C ratio. Ocean releases also are slightly higher in 13C/12C ratio than in the current atmosphere.
While the human input in the years 1958-2024 increased from about 1.5 to 5% of all inputs, the observed drop in 13C/12C ratio shows that already over 10% of the current atmosphere (and 6% in the ocean surface) is from fossil fuels.
Thus your “classic” model is completely refuted by the observations…
That includes that your equation (2) is already good for the waste bin and all the other allegations against our work are not based on real world observations…
Best regards,
Ferdinand Engelbeen, lead author of the CO2 Coalition’s work on the origin of the CO2 increase in the atmosphere.
Dear Ferdinand,
Thank you for commenting here to support your CO2 Coalition paper.
You addressed more than one point in your comment. I will reply in separate comments to avoid confusion. And you are welcome to add other points later.
Regarding your 13C/12C ratio, let’s call it R.
RealClimate says R for human CO2 is about 98 percent of the ratio in natural CO2, and R has declined about 0.15 percent since 1850 as of about 2004.
To calculate the effect of human CO2 let L13 = the level of R. We calculate L13 by combining the natural R with the human R by multiplying their levels by their R’s:
…… L13 = Ln Rn + Lh Rh …………………………… (1)
where:
…… Ln = the natural R level = 1.000
…… Lh = the human R level = 0.980
…… Rn = the natural CO2 fraction = 0.92 for 8% human and 0.68 for 32% human
…… Rh = the human CO2 fraction = 0.08 for 8% human and 0.32 for 32% human
The IPCC says human CO2 is 32%, meaning H(1) is true.
Inserting this into (1) gives:
L13 = 0.680 + (0.980) (0.320) = 0.9936 = 1 – 0.0064 …………………………… (2)
The Berry Model says human CO2 is 8%, meaning H(1) is false. This gives:
…… L13 = 0.920 + (0.980) (0.080) = 0.9984 = 1 – 0.0016 …………………………… (3)
RealClimate says the human-caused R is:
…… L13 = 1 – 0.0015 …………………………… (4)
Therefore, the R data (4) support the Berry model (3) and contradict the IPCC model (2).
Even with slightly different data, it is clear that the Berry model is consistent with the R data, and your model is not.
Your paper mentions that the R data are not very good and should not be the final decision on H(1). So, you have a basis for considering other data like the 14C/12C ratio.
Dear Ferdinand,
Let’s talk about models.
My model is fully described by mathematical equations and physical assumptions. That’s the way physics and engineering work.
Your model has no equations or stated assumptions. Yet, you make conclusions without being able to calculate anything from your model.
Your argument for your fountain model is simply imaginary. Such models are a dime a dozen and they prove nothing.
A model is a simplified description of a physical problem that explains the overall problem and allows calculation that make predictions.
So, your fountain model is not really a model. It is your personal feeling about how nature works.
My equation (2) that says Outflow = Level / Te
It is a description of how the overall carbon cycle works. It does not attempt to describe every carbon atom.
My model replicates IPCC’s natural carbon cycle and shows how nature could have remained constant at a level of 280 ppm.
Your model can’t explain how nature might have stayed constant.
If your model can’t explain a constant carbon level, your model can’t explain anything. It is purely a product of your imagination.
My model follows Dalton’s Law of Partial Pressures. Yours does not.
My equation (2) applies to the carbon cycle but it does not apply, for example, to how fast water flows out of a spout at the bottom of a bottle. There is a different equation that describes that.
Similarly, my model does not apply to how fast water flows over a dam. Another equation describes that.
My lake analogy is merely to help people understand how a higher level produces a higher outflow.
My model also follows standard systems engineering models, where levels define outflows and outflows change levels.
This is a very important issue. The validity of my model is supported by how my model also works for electric circuits.
Without this formulation, you have no model. Your model is vaporware.
Your criticisms of my model are hand waving after you reject what is already known in physic and engineering.
When you reject my equation (2) which is IPCC’s equation, you have nothing. You have no substitute for (2).
Your personal feelings about nature that you cannot describe with a model are not a valid criticism of my model.
Dear Ferdinand,
You wrote:
“You still use the “classic” model that assumes that the CO2 level in the atmosphere is caused by the sum of all CO2 inputs and that the level in the atmosphere causes the height of the outputs. We call that the “lake” model. Every flow is one-way from river inputs to lake outputs.”
Your description does not match my model. See my Figure 3, page 10. It shows IPCC’s data for its natural and human carbon cycles.
Carbon flows in both directions, not one. The level in the atmosphere is NOT “caused by the sum of all inputs.”
The rate of change in a level equals the Inflow minus the Outflow. This is my equation (1) which is the standard continuity equation.
The natural carbon level in the atmosphere sets the natural carbon outflow to land and surface ocean. Similarly for human carbon.
When the outflows equal the inflows, the level remains constant as the flows continue.
From your description, you do not understand my carbon cycle model at all. Which means you don’t understand my simple equations based on (1) and (2). No wonder you have no math in your model. You don’t understand simple math.
Your “Lake model” criticisms do not apply to my carbon cycle model because your Lake model is not my carbon cycle model.
Congratulations, real science wins!
Cees.
I guess I can’t see the difference between the fountain and the lake. Both have inputs and outflows but the fountain recycles some of the out as in. The amount flowing out of the fountain is still set by the inflow.
Dr. Ed, congratulations on your win! Your next assignment, if you choose to accept it, is to apply your reasoning to the revenue flow budget problem congress doesn’t seem to know how to cope with.
I started reading comments today and made note of some points people make that indicate they may not fully understand your essential argument, one that is shared by many others that you have referenced. I believe the argument in simple terms is that amount of human-sourced CO2 remaining in the atmosphere is far less than your detractors claim, because the annual addition of human CO2 is mixed with as much as twenty times more CO2 from so-called natural sources. Absorption of CO2 does not discriminate whence it came, therefore the amount of human-sourced CO2 remaining in the atmosphere is closer to 5% rather than the 33% claimed by your detractors.
One commenter implied that removing carbon from fossil fuel reserves is the cause of carbon increases elsewhere. Well, it is “a” cause, of course, but it’s the magnitude of both fossil fuel and natural sources and their contributions to the sinks that is being contested. As that same commenter noted, we don’t know the magnitude of all the natural carbon sources.
Another commenter writes, “nature – the oceans and land — must be a net global sink of atmospheric CO2, not a source.” Maybe, but this obscures the fact that natural sources annually contribute about twenty times more carbon to the atmosphere than do human sources. One has to do a rigorous analysis such as yours to estimate how much more of a sink nature is, if in fact it is. Now that I understand how “net global uptake” has been defined, I think global uptake (sinks – sources) could easily be negative with respect to natural carbon flows. I have a spreadsheet model based on math similar to yours that indicates human-sourced carbon would have to be less than 2% of the atmosphere for natural sinks to outweigh sources.
I was stunned to read that David Andrews agrees with you that “only a small portion of the carbon in the present atmosphere was once part of a fossil fuel.” How could he perceive “Ah” to be negligible in that circumstance?
Are you still inviting criticism of your article above? Having read some of your previous papers, I skipped down to the comments assuming you were done editing.
Dear Jim,
Thanks for your great summary. Yes, anyone can still add their comments.
Dear Ed,
Sorry for the late reply. My browser (Firefox) didn’t show your replies, neither did my comment show up for several other users… Now I use the Microsoft browser and everything looks normal.
So let’s start with the main difference: the use of the about 4 years residence time, which according to you is the only time of importance.
The 4 years residence time is the time that any CO2 molecule in average stays (“resides”) in the atmosphere. Whatever its origin. There we do agree. Even the IPCC agrees with us.
No problem at all there…
Then we have the continuity equation for the conservation of carbon mass:
Formula (1) shows that:
dL/dt = Inflow – Outflow (1)
Again, I don’t think that anybody disagrees with that, not even the IPCC.
The problems start with Formula (2):
Outflow = L / Te (2)
You insist that the outflow is proportional to the absolute height/pressure of CO2 in the atmosphere and you insist that Te is equal to the about 4 years residence time as defined by the IPCC. So be it. That is your choice.
The real world formula for the CO2 outflow into the oceans is:
F = k•s•ΔpCO2
Where:
k is the velocity coefficient (wind speed mixing)
s = the solubility coefficient (composition)
and ΔpCO2 the CO2 pressure difference between atmosphere and ocean surface.
See: https://www.pmel.noaa.gov/pubs/outstand/feel2331/maps.shtml
Thus the outflow is directly proportional to the CO2 pressure difference with the ocean surface (and similar in plant alveoles water), not the absolute pressure of CO2 in the atmosphere in your formula (2).
Thus in reality:
Outflow = [pCO2(atm) – pCO2(ocean)] / Tau
Where Tau is the exponential decay rate to reduce a disturbance (like the addition of extra CO2 from whatever source) to 1/e of the initial disturbance.
For any linear process (where the outflow is directly proportional to the height of the disturbance) that is a quite simple formula:
Tau = disturbance / result
Which is independent of the length of the period over which Tau is calculated.
With the above formula, one can calculate Tau for the oceans, because the “disturbance” is known: that is the pCO2 of the atmosphere minus the equilibrium pCO2 of the oceans for the average sea surface temperature. Which is currently around 295 μatm (μatm is similar to ppmv, the latter is in dry atmosphere the former in the atmosphere “as is”). That gives following results in graph form:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.jpg
Which gives a calculated real world Tau of around 50 years.
The influence of temperature on the pCO2 of the sea surface is calculated with the formula of Takahashi, based on near one million seawater samples:
∂ln pCO2/∂T=0.0423/K
See: http://www.sciencedirect.com/science/article/pii/S0967064502000036
Then your use of the residence time as “base” for the reverse formula (2):
The mostly used formula of the residence time is:
Te = L / Outflow
Which is true when Inflow = Throughput = Outflow, although Te = L / Throughput is more accurate if there is a disequilibrium between inflows and outflows.
One may reverse that formula if and only (!) if all fluxes are unidirectional from input(s) via the atmosphere to output(s). Thus with the “classic” model of a container where the inputs dictate the liquid height/pressure in the container and that dictates the outflow.
When cycles are involved, one never, ever, may reverse the formula of the residence time, as that gives false results.
Take the outflow into vegetation: in spring/summer some 120 PgC as CO2 gets absorbed by plants, when temperatures and sunshine go up, largely independent of the current CO2 levels in the atmosphere. To the contrary, the amount of CO2 sucked out of the atmosphere is so large that the CO2 levels in the atmosphere drop with strongly increasing uptake, despite a huge supply of CO2 out of the warming oceans.
The observed influence of the extra CO2 pressure in the atmosphere is only 2.5 PgC/year, based on the oxygen balance. Thus only some 2% of the outflow is caused by the extra CO2 pressure in the atmosphere above the internal CO2 pressure of the plants. 98% of the CO2 outflow into vegetation is completely independent of the CO2 level in the atmosphere…
That implies that formula (2) is completely at odds with reality.
BTW, no need to show lots of formula’s to “define” the real world. If the result of all these formula’s is at odds with simple math like the carbon mass balance, then the simple math wins the contest…
That is part 1…
Dear Ed,
Here follows part 2, about the 13C/12C levels, expressed as δ13C…
No problems at all with your calculations of what remains as low-13C fossil fuels in the atmosphere.
The problem again is with your interpretation of the results of the calculations.
The IPCC indeed says that the full increase of 32% (meanwhile near 50%) of the CO2 as mass in the atmosphere is caused by the human input of fossil CO2.
They don’t say that all the fossil fuel CO2 molecules still reside in the atmosphere. That is your interpretation of what the IPCC says.
What you forgot is that about 25% of all CO2 in the atmosphere is exchanged each year with CO2 from other reservoirs. That is the 4 years residence time. That doesn’t remove one gram of CO2 out of the atmosphere, only replaces fossil fuel low-13C CO2 with 13C richer CO2 from other reservoirs.
How much is exchanged? While both the ocean surface and the biosphere have a rather limited amount of fast-exchanging CO2, the crux of the matter is in the much slower exchange rate, but much larger reservoir of the deep oceans. The point there is that what goes into the deep oceans (especially via the THC near the poles) is the isotopic composition of today, but what comes out near the equator is the composition of some 1,000 years ago.
BTW the IPCC’s Bern model assumes that not such direct exchanges between atmosphere and deep oceans exist.
If all fossil emissions remained in the atmosphere, the current drop in δ13C would be three times deeper than observed. With the calculation of different exchange fluxes between atmosphere and deep oceans, one estimate the real exchange rate of CO2 between atmosphere and deep oceans:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg
The graph can be better (is already some 20 years old) and needs a recent update, but that is not important for now.
What is important is, while only some 10% of the current CO2 in the atmosphere is originally from fossil fuels, the rest of the near 50% increase of CO2 mass in the atmosphere is fully caused by the release of fossil fuel CO2 at near twice that increase, but about 2/3 of the original fossil CO2 molecules now reside in the (deep) oceans and vegetation.
Moreover, with your Figure 4 and Equation 4, you definitely show that the model you used is the classic “lake/bathtube” model, where inputs define the level and the level defines the outflow, without any recycling.
That model implies that the level of a “marker” in the reservoir never can exceed the ratio of that marker in the inputs.
For the fossil fuel content in the atmosphere (and ocean surface), that rule is completely overblown by the facts: over 10% in the atmosphere, over 6% in the ocean surface, with an input between 1.5% and 5% from 1958 to today…
Ferdinand
Dear Ferdinand,
Welcome back and thank you for your detailed comments.
Sorry for your browser problems. I have found Microsoft’s Edge to be by far the best browser out there, and I have tried them all. Edge lets me save over 1000 tabs distributed among five workspaces, all quickly accessible, with no problems, and it saves all these tabs when it reboots Edge.
I will reply to your comments soon.
Ed
A small teasing in between the discussions:
Question: if there was very little inputs of CO2 at all, where will the level of CO2 in the atmosphere end?
Answers:
– According to Equation (2) at near zero CO2 in the atmosphere.
– According to Henry’s law (calculated with Takahashi) at 295 ppmv for the current average SST.
Dr. Berry,
While working on suggestions for your article, I thought these comments might be applicable to your ongoing debate with Mr. Engelbeen.
Flux is a general term for transfer processes that are very specifically defined in the fields of electricity, heat transfer, chemical diffusion and reaction kinetics. In the latter, for example, chemical reactions are classified as, zero order, first order, second order, etc. depending on how many reactants affect the rate of reaction. One AI source puts it this way, “Essentially, with first-order, more reactant means a faster reaction, while with zero-order, the reaction proceeds at the same pace regardless of how much reactant is present.” In the context of the atmosphere, this means that natural CO2 “flows” in and out of the atmosphere in direct proportion to the concentration of CO2 in the various reservoirs. This is completely opposite to characterization of CO2 “fluxes” as “completely independent of the CO2 level/pressure.” On the other hand, fossil fuel emissions are essentially zero order, independent of the concentration of CO2 in any reservoir.
At the risk of belaboring the point, flow is also subject to possible misconceptions. Flow through a pipe has units of volume/time, whereas flow of a molecule from one reservoir to another has units of amount/time. Chemical diffusion flux is more specifically defined as amount/(area x time). It may be helpful in these discussions to use language that appropriately discriminates between the specific type of mass transfer being described. I think it useful to replace flux or flow with a more specific term when referring to mass transfer from one reservoir to another with undefined surface areas.
The way Mr. Engelbeen refers to pressure in his June 24 comment makes me wonder if he is conflating atmospheric or PV=nRT pressure with a Henry’s-Law-type concentration difference between reservoirs. He writes, “95% of all CO2 fluxes are just cycling in and out, completely independent of the CO2 level/pressure in the atmosphere. Only 5% is directly pressure difference (with the ocean surface and plant alveoles) dependent, not even depends on the absolute pressure of CO2 in the atmosphere…” That is a grossly false characterization of CO2 fluxes in the atmosphere, which are mostly, if not completely, concentration dependent.
Ferdinand Engelbeen, 6/27/2025, “BTW, no need to show lots of formulas to “define” the real world. If the result of all these formula’s is at odds with simple math like the carbon mass balance, then the simple math wins the contest…” Dr Berry’s formulas are not at odds with simple math if the result of simple math is ambiguous. The simple math assumes no growth in non-fossil fuel CO2 and, as pointed out earlier by others, contains no significant human absorption term. Engelbeen’s argument comprises handwaving assertions devoid of a rigorous proof. It reflects his view of the world, not necessarily the real world. I will gladly invite correction if my view conflicts with the real world.
Once again, “You insist that the outflow is proportional to the absolute height/pressure of CO2 in the atmosphere….” Neither height or pressure have appropriate units to describe mass transfer of amount/time such as Pg C/year or ppm CO2/year between reservoirs. I recommend Mr Engelbeen confirm whether or not the height/pressure he refers to is akin to the “disturbance” of two reservoirs whose concentrations are out of equilibrium.
Dear Ferdinand,
Thank you for your comments. My reply below shows your relevant comments as quotations.
You write:
No, I state (2) as a hypothesis. That means it is OK for you to challenge this hypothesis.
No, I derive Te for the atmosphere from IPCC’s own data. The result is Te = 3.5 years.
It is safe to say that the 2007 IPCC carbon cycle data has considered this 2001 noaa data in its published data for the average flow of carbon from the surface ocean to the atmosphere.
Your discussion of wind and solubility details does refute my formulation of IPCC’s carbon cycles. My formulation can easily accommodate these effects by changing the e-times.
However, you have made a critical error in your formulation for carbon flows for use in a systems model of the carbon cycle.
You formulate your flows as a difference of flows in each direction between reservoirs. That is not valid for a systems model and it gets the wrong answers.
In systems models, we must calculate the flows in opposite directions independently.
Each flow is a function of the level of carbon in its reservoir divided by its e-time. It is an error to combine the flows (or pressures) in opposite directions to get a formula for net outflow.
To integrate a systems model over time, we must first use the carbon levels in each reservoir to calculate outflow from each of the six nodes (in the four-reservoir model).
Then, we calculate how these six flows change the four levels.
You write,
No. That is the net outflow. Now try to calculate how your “net outflows” change the six levels. Good luck.
The only way to calculate the change in a level is to use my continuity equation (1) for each reservoir independently – for any selected time step.
You write,
Your graph shows only the delta pressure. This is not sufficient information to correctly calculate the flows in a systems model.
No, it does not. Not only is your calculation faulty but your definition of Tau does not apply to the six Te’s in my carbon cycle model.
In addition, you changed your definition of Tau from Te to something else.
The only time constants that matter in a systems model are the individual time constants for each node in the model. With that information, we can calculate how the system responds, which I do correctly in my published papers.
Temperature can change Te in my formulation.
You have said nothing that disputes my carbon cycle formulation. But I have shown errors in your formulation.
Dear Ferdinand, you are making a big error.
Outflow in (2) is NOT Throughput. Outflow is the flow in only one direction. To get Throughput, you need to add the flows in opposite directions, and these flows do not have the same Te.
I can reverse (2) because it does not depend on other flows, as you incorrectly assume.
The only correct way to calculate the evolution of a systems model is to first calculate each flow from each reservoir. Flows are rates.
Then we use (1) for each reservoir to calculate the rate of change of each level.
Then we integrate the level changes over a chosen time step.
This gives the information to calculate any existing cycles.
Your method is simply wrong mathematically.
My model can use one-month time-steps to simulate flow changes due to vegetation changes.
By the way, CO2 is not “sucked out of the atmosphere.”
My carbon cycle formulation shows all the changes in flows and levels that result from proper physics. My formulation solves all of your problems.
You have not shown there is any error in my formulation. But you have shown that you do not understand my formulation. My formulation follows the standard for systems models, and your formulation does not.
Can you reduce your formulation to an electric circuit?
Dear Ferdinand,
You do not understand my model, even though I explained it.
I show what happens when we combine my (1) with my (2).
The result is Inflow sets a balance level. If inflow is constant, the level moves to the balance level. At the balance level, the outflow equals the inflow, so there is no longer any change in the level.
I did not “forget that about 25% of the carbon in the atmosphere is exchanged each year.” Rather, I fully accounted for that change in my formulas.
Human carbon inflow, if constant, sets a constant human carbon balance level. Natural carbon inflow, if constant, sets a constant natural carbon balance level.
Forget about all your “exchange” arguments because they are wrong. So long as the human and natural inflow remain in the same proportion, their balance levels remain in the same proportion. Thus, I calculated the effect of 13C correctly.
Your problem is that you do not understand my carbon cycle mode.
IPCC’s carbon cycle data that I refence fully accounts for your claims. The outflow of human or natural carbon from the deep ocean equals the level of human or natural carbon in the deep ocean divided by an e-time that is the same for human and natural carbon.
IPCC has properly accounted for all this within the limited accuracy of the available data.
The Bern model is flawed because is assumes H(1) is true.
Well, they don’t remain in the atmosphere. They flow through the atmosphere, setting a balance level equal to their Inflow * Te (4).
Your calculations are in error because you are not using a correct carbon cycle model.
Your statement that I bolded is not supported by any data or model, and it violates IPCC’s natural carbon cycle data.
You misunderstand my figures.
Figure 4 is simply my way to illustrate how inflow sets a balance level and level sets outflow. It should be obvious that I did not intend Figure 4 to illustrate my formulation of IPCC’s carbon cycle model.
For an illustration of IPCC’s carbon cycle, see Figure 3. It shows IPCC’s data for levels and outflows found in Figure 2.
Figure 6 shows the e-times I calculated for IPCC’s natural carbon cycle at equilibrium. Notice the flows in opposite direction are equal, so the net flows between the reservoirs are zero, which is the definition of equilibrium.
An important part of our discussion is to notice that my formulation exactly reproduces IPCC’s natural carbon cycle at equilibrium. That shows it is a basis to calculate IPCC’s carbon cycle out of equilibrium.
Neither you, nor anyone else, has a carbon cycle model that can replicate IPCC’s data at equilibrium. Therefore, neither you nor anyone else has a model that can calculate IPCC’s carbon cycle out of equilibrium.
In other words, my formulation of IPCC’s carbon cycle model, so far, is the only game in town.
Look at Figure 6. This shows IPCC’s natural carbon cycle at equilibrium.
Now look at Figure 7. This shows the percent of natural carbon in IPCC’s natural carbon cycle at equilibrium. 1.4% is in the atmosphere and 2.2% is in the surface ocean. 90.3% is in the deep ocean.
Your data is simply wrong according to IPCC’s own data.
Answer to your question:
If all carbon inflow into the atmosphere stopped, and outflow continued, the carbon level would go to zero.
But that is impossible because we cannot stop the carbon inflows into the atmosphere from land and surface ocean.
Takahashi’s calculation assumes there is an inflow of carbon into the atmosphere that sets the balance level at 295 ppmv.
In summary, your arguments are wrong because:
• You violate required systems model math and structure.
• You misunderstand my formulation of IPCC’s carbon cycle.
• You misunderstand how inflows produce balance levels.
Thank you very much for your input and arguments.
Sincerely,
Ed
Jim,
You would not have been stunned at my “only a small portion of the carbon in the present atmosphere was once part of a fossil fuel” if you had read and understood either Jerry Elwood’s comments or Ferdinand Engelbeen’s comments on the mixing between the atmosphere and the other reservoirs. You need to understand what is technically called a “disequilibrium isoflux”, which tends to balance the isotopic composition of reservoirs even when no net carbon is exchanged. Ed’s “human carbon” is like an isotope, one depleted in C14. Perhaps it would help if you just imagine our emissions are adding total carbon to the fast cycle ocean and land reservoirs as well the atmosphere, carbon which has been removed from slow cycle fossil fuel reserves. We have added a lot to the fast cycle. We haven’t put much carbon back into the empty coal mines.
Ed has been told about this for years, but feigns ignorance.
I don’t understand why you think this has anything to do with the amount of carbon humans remove from the atmosphere, the negligible “Ah”.
As explained before, it is an empirical fact, not a model, that net global uptake is positive in the current era. How else do you explain that atmospheric accumulation rates are but half of emission rates? It was sometimes negative in the geological past.
Jim,
You write “The simple math assumes no growth in non-fossil fuel CO2 and, as pointed out earlier by others, contains no significant human absorption term.”
1. If I say net global uptake in some defined period equls Human Emissions – Atmospheric Accumulation, and that quantity is measured to be positive, where have I assumed no growth in non-fossil fuel CO2?
2. Describe what you mean by the “human absorption term” and give a significant example. [If you start talking about Ed’s “human carbon” you haven’t understood the carbon conservation (mass balance) argument.]
David,
In response to your first post addressed to me earlier, JUNE 27, 2025 AT 4:37 PM, I am not familiar with “disequilibrium isoflux” and, frankly, not good at interpreting isotopic carbon data. But I don’t think that necessary to see a deficiency with your simple math compared to Dr Ed’s rigorous model. I did some modelling myself and found results in line with those he presents. His physical model is consistent with my understanding of the first order processes I based my calculations on.
You wrote, “it is an empirical fact, not a model, that net global uptake is positive in the current era. How else do you explain that atmospheric accumulation rates are but half of emission rates? It was sometimes negative in the geological past.” In cooling periods, I can understand negative global uptake. We are in a warming period now. Questioning the relative contribution of human emissions versus natural emissions seems reasonable to me. I don’t think simple math resolves the problem. Perhaps my answers to your later post will help explain.
In response to 2., the human absorption term is the “Ah” that evolved from your comment on JUNE 21, 2025 AT 4:54 PM. You wrote the simple math formula, Cchange = Eh+En-An. Dr Ed pointed out it should be Cchange = Eh+En-An-Ah. Based on your other comments, I inferred that you view Ah as an insignificant quantity attributable to sequestration or other methods of human efforts to remove CO2 from the atmosphere. Correct me if that is wrong. No, what I mean by human absorption is that quantity of fossil fuel carbon that is removed by the same processes that remove any carbon from the atmosphere according to Dr Ed’s Climate Equivalence Principle (2.1). I think this may be Ed’s “human carbon” that you are accusing me of talking about. Quite frankly, I don’t see why you seem to think that me thinking huge amounts of fossil-fuel-sourced CO2 can be removed from the atmosphere by natural processes implies I misunderstand your simple-math mass-balance argument. In simple terms, fossil fuels have gone into the atmosphere, with some remaining there, but most having been removed by natural processes, the land, surface and deep ocean reservoirs. Did it occur to you that, if we stopped burning fossil fuels, most of that carbon would eventually end up on the bottom of the ocean floor never to be heard from again?
In response to 1., suppose nature had emitted blue-labeled CO2 molecules at the same rate as, but instead of, fossil fuels burned by humans. Would you then conclude that blue carbon caused all the positive “net global uptake?”
David,
An additional thought on the “Ah” term. Whereas emissions from nature and fossil fuels can easily be distinguished as En and Eh, “An” might be mistakenly perceived as a conflation of both natural-sourced and human-sourced carbon absorbed only by the available natural processes. To be clear, I consider “Ah” as that fraction of atmospheric carbon removed naturally that was originally a fossil fuel. So if At is the total amount removed in a given time interval, At = An + Ah, where An is the non-fossil fuel carbon removed by natural processes.
Ed,
(Below, I repeat your responses that warrant a comment to my comments followed by my responses to yours.) Your responses are indicated by “Ed-” at the beginning of each.
Ed – Yes, but that is completely irrelevant, as my equations show.
Me – I find your response that its completely irrelevant startling. You simply refuse to acknowledge that it tells you nature isn’t a net global source of atmospheric CO2. You have a cognitive bias against accepting that reality.
Well, you have not computed global mass balance. In fact, you have no equations or math at all and you have not identified any errors in my math. Your equations and math don’t match reality.
First you say I have no equations or math, and then you say my equations and math don’t match reality. Here’s the reality.
As Cawley (2011) and others since then have demonstrated with empirical data, the rate of change in the mass of carbon in the atmosphere, dC/dt, equals the sum of global human emissions and global natural emissions of carbon from the oceans and land combined minus global environmental uptake into the oceans and land. As I mentioned in my previous comments, the human sink of atmospheric CO2 is not large, so it’s not a significant factor in the global uptake of carbon.
This relationship between the changes in the mass of atmospheric carbon and the flows of carbon in and out of the atmosphere is an approximation of the global atmospheric carbon mass balance budget. The net global environmental flux of carbon, which is the difference between the mass of carbon emitted globally from the oceans and land combined and the mass of carbon taken up globally by the oceans and land combined, is simply calculated from the difference between the rate of change in the mass of carbon in the atmosphere and human emissions of carbon, both of which are known with a high degree of certainty. And contrary to what you believe and others have contended, this calculation does not require knowing the uncertain estimates of the natural emissions and uptake of carbon to and from the atmosphere. The mass balance analysis using long-term data on global human carbon emissions and changes in the mass of carbon in the atmosphere unambiguously shows that nature has acted as a net global sink of atmospheric carbon over the past 60+ years, not a source. If you don’t accept this reality, then it isn’t because the mass balance of carbon doesn’t show it to be real. That your model conflicts with this reality demonstrates your model is wrong. Natural carbon emissions are not the cause of the increase in atmospheric CO2.
Ed – That’s because the IPCC scientists forgot to account for the outflow of human CO2. I accounted for that outflow using IPCC’s own data and thereby proved there is no “missing CO2.”
Me – It’s unfortunate that you persist in misrepresenting what IPCC reports say. The scientists who wrote the carbon cycle portion of IPCC reports didn’t forget to account for the outflow of human CO2 from the atmosphere. They didn’t account for it because, as you well know, it’s impossible to distinguish between naturally-sourced and human-sourced CO2. For this reason, the outflow of CO2 is reported by the IPCC without regard to the emission source or sources. You have repeatedly reminded readers in your posts that it’s impossible to distinguish between natural- and human-sourced CO2. But you still ignore and instead, pursue your misguided effort to separately model the cycling of human-sourced and naturally-sourced carbon. You have to model the total carbon in the cycle, regardless of its source. Once CO2 is emitted, it’s impossible to know and track its source.
Ed – As I have shown, human CO2 flows out of the atmosphere following the same rules that determine how natural CO2 flows out of the atmosphere. IPCC’s own data show how natural CO2 flows out of the atmosphere. If natural CO2 did not flow out of the atmosphere, then natural CO2 could not have stayed at 280 ppm as IPCC assumes.
Me – You misrepresent what IPCC’s data show and misunderstand my point and what I mean by “human CO2 sink”. The only part of the human carbon cycle shown by the IPCC is the human-sourced CO2 emitted from fossil fuel combustion, cement production and land use and land cover changes. It doesn’t show any human-sourced carbon outflow from the atmosphere for the very reason stated above. What the IPCC has done is show the contribution of the equivalent of human-sourced CO2 emissions on the natural carbon cycle, which is the cycling of both natural and human-sourced CO2. Secondly, “human CO2 sink” doesn’t mean atmospheric CO2 that originated from human activities, such as fossil fuel combustion. It refers to the direct removal of CO2 from the atmosphere by engineered means, e.g., CO2 scrubbers. The global magnitude of direct carbon removal by humans is not large enough to account for a significant fraction of the missing CO2.
Also, I wasn’t suggesting or implying that CO2 from human sources flows out of the atmosphere at a different rate than CO2 from natural sources. I agree that naturally-sourced and human-sourced CO2 are identical and flow in and out of the atmosphere following what you call the same rules. But you still haven’t explained how nature can be a net global source of atmospheric CO2 when the rise in it is less than what is being emitted into it globally from human activities. And I never questioned whether carbon emitted from natural sources flows out of the atmosphere. Your comment seems to suggest that I have claimed it doesn’t. It flows out at the same rate as human-sourced carbon. The fact that the pre-industrial level of atmospheric CO2 was around 280 ppm and had remained relatively constant simply shows the global emissions and uptake of atmospheric CO2 were roughly in balance. But that is no longer the case.
Ed- That so-called “IPCC’s conclusion” is a result of IPCC’s assumption of this conclusion, therefore circular reasoning.
Me – IPCC’s conclusion is based on a vast body of independent lines of scientific evidence, including the mass balance of carbon in CO2. And there is consilience of the multiple lines of independent evidence that has come from unrelated sources. That evidence has held up over time and has only grown stronger. For example, the estimated change in the inventory of CO2 stored in the world’s oceans over the period from 1994 to 2007 by Gruber et al. (2019, published in Science ) shows a net increase of almost 124 Gt CO2. It is equivalent to an average net uptake rate of 9.5 Gt CO2 per year going into the oceans globally from the atmosphere. The estimate of the net ocean uptake of CO2 globally over this 13-year period represents 34% of the global CO2 emissions from human activities over the same period. These results, which are based on direct measurements of changes in the inventory of CO2 in the world’s oceans, are further evidence that the oceans are a net global sink of atmospheric CO2, not a source.
Ed- That so-called “evidence” is a result of assuming H(1) is true. Circular reasoning.
Me – If you bother to look at the evidence, you will find it isn’t based on that assumption. It’s based on published and peer reviewed results of research intended to develop a quantitative and predictive understanding of the cause of rising atmospheric CO2, including where all of the CO2 emitted globally is going and how much human emission sources are contributing to the global increase.
Ed – Delta14C has decreased since 1970 and has approached its original balance level of zero (that I call 100 percent for public understanding). But you miss the key point, which is that the curve of Delta14C shows its original balance level has remained the same (as least within a few percent). And that shows the amount of human CO2 in the atmosphere is between zero and a few percent.
Me – I don’t understand your insistence on calling the pre-bomb ∆14C levels of atmospheric CO2 a balance level. The pre-bomb ∆14C values were declining, not constant, which means ∆14C wasn’t in balance before nuclear weapons testing began in the 40’s.
You have previously claimed that nature maintains a balance level of ∆14CO2 at or near zero. But you offer no theory or explanation of how nature maintains such a balance level. The natural production of 14C is independent of the cycling and natural emissions of carbon. Moreover, published paleo records of ∆14CO2 show that it has varied widely before humans were around and has seldom been at or near zero over the past 500,000 years. If nature maintains a balance level of ∆14C at or near zero, then please explain why has it varied so widely in the past when nature was doing its’ things? The only plausible way for a balance level of ∆14C to exist is to have extended periods when the natural production of 14C happens to coincide with a constant level of CO2 in the atmosphere. But that would only occur under coincident circumstances, not because of natural processes that maintain a constant level.
Thirdly, It is impossible to understand the basis for your claim that the because the ∆14C has remained near its “balance level of zero” proves that the human balance level of CO2 in the atmosphere is less than 2 percent of total CO2 in the atmosphere. The ∆14C of atmospheric CO2 is still declining in the northern hemisphere, not remaining near what you call “its balance level of zero”. Data in a figure in a 2023 paper by Graven et al.(Radioisotope Dating: Going Back in Time) published in Nature shows this. If you can’t access the paper online, you can find the figure on the Scripps CO2 Program Isotope Data Gallery website.
The fact that ∆14C has still declining in the atmosphere and declining to less than zero in the northern hemisphere doesn’t tell you the fraction of CO2 in the atmosphere that originated from human sources. And given that it’s impossible to know that fraction at any point in time, your claim to have proved what it is, based on the ∆14C data or on any empirical data or model for that matter, is simply not credible.
By “human balance level”, I assume you mean the fraction of CO2 in the atmosphere resulting from human emissions at any point in time, which, of course, is impossible to know.
Lastly, that the ∆14C of atmosphere CO2 in the southern hemisphere has not yet declined to levels observed in the northern hemisphere is likely a result of the lag in inter-interhemispheric mixing of CO2. Most of the human-sourced global CO2 emissions occur in the northern hemisphere, and it is well established that the CO2 concentration in the southern hemisphere in the same year is consistently less than in the northern hemisphere due to this lag in inter-hemispheric mixing of atmospheric CO2.
Ed- You may not fully understand this because you are not thinking in term of balance levels, which I define in my equations.
Me – Your fixation on balance levels is nonsense. Neither CO2 or ∆14C are in balance or have been for a long time.
Ed- Inflows set balance levels and levels approach their balance levels. The human CO2 inflow sets a balance level that would be 33 % of the CO2 in the atmosphere if H(1) were true. Meanwhile natural CO2 inflow sets its own balance level and Delta14C tracks this natural inflow. This simple reasoning about two independent inflows includes isotropic dilution, which is simply the ratio of the human CO2 balance level to the total of natural and human balance levels.
Me – Again, your argument is senseless for several reasons which I have addressed above. Also, please explain your statement that “∆14C tracks this natural inflow”. Are you assuming this or asserting that natural CO2 inflow alone accounts for or explains the observed changes in ∆14C? Below, you assume, albeit incorrectly, that the decline in ∆14C is due to both wash out of 14C from the atmosphere and isotopic dilution from inflow of CO2 that has a “natural ∆14C” level. Your claim and the assumption below are inconsistent and both are false.
Ed – I assume only that the high Delta14C caused by the bomb tests flows out as natural Delta14C CO2 flows in. This, in time, washes out the high Dela14C and lowers the Delta14C level to the balance level set by the new inflow. This assumption is independent of any human CO2 inflow with its Delta1C of -1000 (that I refer to as zero percent for public communications).
Me – But Ed, the outflow of 14C (which is also outflow of ∆14C) from the atmosphere has no impact on the ∆14C of CO2 remaining in the atmosphere. It only reduces the 14C concentration in the atmosphere. You forget that ∆14C is the ratio of 14C to total C. So, your assumption that ∆14C flows out of the atmosphere, washes out the high ∆14C, and lowers it to a balance level set by a new inflow is nonsense. The ∆14C of CO2 in the atmosphere is affected by the ∆14C of CO2 flowing into the atmosphere from natural and human sources, not by the outflow of 14C from the atmosphere. That you can curve-fit an exponential function to the post-bomb decline in ∆14 is not evidence that your model explains the cause of the decline.
Ed – I explained my only assumption above, that new natural CO2 inflow gradually replaces the high Delta14C caused by bomb testing. My carbon cycle equations explain how this happens. If there is a claim that isotopic dilution follows different rules, then such rules are wrong.
Me – As I stated above, isotopic dilution is the only explanation for the decline. Natural CO2 inflow contributes to the isotopic dilution, but it alone doesn’t fully account for the decline. It isn’t necessary to assume a “new natural CO2 inflow” to explain the decline. And if not by isotopic dilution, then please explain what you mean by “new natural CO2 inflow gradually replaces the high ∆14C”. Isotopic dilution reduces the 14C:total C ratio of atmospheric CO2 by increasing the amount of CO2 with a lower ∆14C. It doesn’t replace anything. .You simply make things up to explain things and make untestable assumptions to fit your narrative. By the way, what is the source of this “new natural CO2 inflow” and what is its’ ∆14C?
Ed- It sounds to me that you agree with my carbon cycle model. I think what you are saying is what I describe with my equations.
Me- But you are assuming a “new natural CO2 inflow” and rejecting human CO2 inflow as a contributor to the isotopic dilution of ∆14C. You are having trouble keeping your story straight.
Ed- I agree that this would happen because the high Delta14C natural carbon would flow into all carbon reservoirs. This does not conflict with any of my descriptions.
Me – I don’t know what you mean by “high Delta natural carbon. The high delta carbon is certainly not natural. It was produced from nuclear weapons tests. And, as I previously stated, the flow of high ∆14C out of the atmosphere has no impact on the ∆14C of CO2 that remains in the atmosphere. Don’t you understand this. You’ re misinterpreting data to fit your narrative. I don’t believe you really understand what you’re writing about.
Ed – My equations describe how the carbon flow between the reservoirs. My description is simpler (and more accurate) than yours because I treat the human and natural carbon cycles independently and let them follow the same rules.
Me – Being simple doesn’t make it either correct or accurate. Your equations don’t reflect the actual reasons for the observed post-bomb decline of ∆14C. As to your claim of your description being “more accurate”, it amazes me that you would assert this when, with the exception of the gross emissions of human-sourced carbon, it’s not possible to distinguish between carbon flows from natural and human sources.
Ed – I disagree with your conclusion and David Andrews’ conclusion on this. My explanation is much simpler. The reason 14CO2 has increased is simply because the inflow of natural CO2 has increased while it Delta14C has remained at or near its zero value (that I call 100%). The reason Delta14C is a useful measure of carbon age is because Delta14C has remained almost constant as the CO2 level has changed. If the CO2 increase since 1850 is indeed almost all natural, we would expect the Dela14C to remain near zero, causing 14CO2 to increase in the same proportion as 12CO2. This is exactly what has happened. My explanation wins by Occam’s Razor.
Me – Wow! You have to resort to Occam’s Razor as the decider? But your explanation simply doesn’t hold water because it’s not a credible explanation of the source of the increased 14CO2 in the atmosphere. The source is bomb 14C that is being reemitted from ocean surface water and terrestrial systems to the atmosphere caused by a change in sign of isotopic disequilibria of 14C between the atmosphere and both ocean surface water and the terrestrial biosphere.
There is a significant effect of isotopic disequilibria of 14CO2 on isotope exchange between the atmosphere and ocean by influencing not only the rate and extent of exchange, but also its direction. When the ∆14C disequilibrium between ocean surface water and the overlying atmosphere is large, such as during the peak testing of nuclear weapons, the isotope uptake and exchange is rapid. As the ocean and atmosphere approach isotopic equilibrium, the exchange slows and will eventually stop when equilibrium is reached. It can even be reversed if ∆14C of atmospheric CO2 is driven below that of CO2 in the atmosphere. A paper by Levin, et al. 2021. (Radiocarbon in Global Tropospheric Carbon Dioxide. Radiocarbon, Vol. 64 (3): 781-791) shows the annual rate of change in ∆14CO2 in the global troposphere during and after the period of nuclear weapons tests in the 50s and early 60s. The annual rate of decline is greatest immediately after the peak. It then varies as it approaches, but never reaches zero, indicating that, according to the last data points, isotopic equilibrium had not yet occurred between the two global carbon sinks (ocean and land) and the troposphere. As I previously indicated, more recent data show the ocean and atmosphere have reached isotopic equilibrium. This is shown in a 1996 paper by Nydal and Gislefoss (Further Applications of Bomb 14C As a Tracer in the Atmosphere and Ocean. Radiocarbon, Vol. 38 (3): 389-406.).
But this has since changed. The ocean and atmosphere and are now back in isotopic disequilibrium of ∆14C as a result of isotopic dilution of atmospheric CO2 from emissions of 14C-free CO2. It has pushed atmospheric ∆14C below that of ocean surface water, causing the ocean to now become a net source of atmospheric 14CO2, rather than a sink. It is why the concentration of 14C in the atmosphere is increasing rather than decreasing.
Me – Your story lacks both explanation and an empirical basis; mine does not. And when Occam’s Razor doesn’t apply, you have to accept Hickam’s Dictum.
Ed – As I explain, I don’t buy David’s explanation because my explanation is better.
Me – Better because it fits your belief, not because it’s supported with empirical data, logic, and sound inductive and deductive reasoning.
Ed – That is a nice bed-time story, but it does not fit the data.
Me – Sorry Ed; it’s fully consistent with empirical data.
By the way, a belated Happy 90th Birthday! They say wisdom comes with age; sometimes age shows up all by itself.
Jim,
Progress! What you call “At” has always been “An” to me (and to Ballantyne, et al. and many others), the removal rate of carbon FROM ANY SOURCE from the atmosphere by natural processes. Go through my earlier argument again, with that understanding in mind. Now you should agree that natural processes are on balance removing carbon from the atmosphere, not adding it, because emissions are 2x accumulation rates. Now you should see that mainstream science never treated “human” and “natural carbon” differently, as some allege. (Only Ed tracks them separately, and that caused him to miss the carbon conservation insight.) Now you should see that no assumptions about the constancy of natural emissions are necessary to determine the sign of net global uptake. All you need is good data, which is in hand. And the data says that despite the warming which you think should make net global uptake negative, it is without doubt positive.
The question of the rate at which carbon in the atmosphere and surface ocean equilibrates with carbon in the deep ocean is an interesting and important one. Some analyses claim it takes “centuries”. I am influenced by a recent paper by Schwartz to think it is closer to one century. I agree we should have a more definitive answer on this, to know the consequences of “net zero”.
I don’t understand the point of your blue carbon question.
Let me take another stab at explaining “disequilibrium isofluxes” with a little model:
• Suppose annual human emissions represent 1 unit of carbon.
• Suppose annual atmospheric accumulation is .45 units
o Then net global uptake would be .55 units
• Suppose natural emissions are 20x bigger than human emissions, or 20 units
o Then An (your At) is 20.55 units.
With these numbers, which are reasonable, natural processes could be described as transferring .55 units out of the atmosphere PLUS EXCHANGING 20 UNITS IN EACH DIRECTION. While the balanced exchange does not move any net carbon, it certainly can change the isotopic compositions if one reservoir starts with an excess of an isotope (or of “human carbon”) compared to the other. The flow out of, say, the high C14 reservoir would contain more C14 than the flow into it, and its C14 content would drop even while its carbon content did not change. Note that using C14 as a “tracer” doesn’t work here. The exchange effectively erases differences. This is why I say, “so what?” when Ed points out the present atmosphere does not have much “human carbon” in it. That by no means says that human emissions are not the cause of the rise. We know they are from the mass balance argument.
Jim, the net mass transfer of CO2 between the atmosphere and the ocean surface is defined as:
F = k•s•ΔpCO2
Where:
k = the transfer coefficient, which mainly depends of wind speed, which is far more important for the mass transfer between air and water or reverse than any chemical reaction or diffusion speed for in average some 100 meter of ocean surface.
s = the solubility parameter, which depends of the concentrations (of different chemicals) in the seawater.
If both are more or less constant for a certain area of the oceans, then the mass transfer only depends of the local pCO2 difference between the atmosphere and the ocean surface.
See: https://www.pmel.noaa.gov/pubs/outstand/feel2331/exchange.shtml and following sections, very interesting and clear reading…
Their global overview is at:
https://www.pmel.noaa.gov/pubs/outstand/feel2331/mean.shtml
And shows the CO2 transfer as moles/m2/year.
The partial pressure of any gas in the atmosphere is directly proportional to its concentration, at least for an ideal gas, but even for non-ideal gases like CO2 quite similar, as long as the concentrations are low.
Thus for e.g. 420 ppmv CO2 in the atmosphere and 1 bar atmospheric pressure, that gives 420 μatm partial pressure of CO2 in the atmosphere. Parts per million by volume are constant for any gas for their molecular weight, so for a constant molar mass, the volumes of a gas and its partial pressure are equal.
Not exact, as one need to take into account that ppmv is expressed in dry air and μatm is “all in”, thus including water vapor. The sea surface CO2 exchanges by Feely and many others, of course did include water vapor in their calculations.
For the ocean surface the pCO2 is measured from samples by getting the sample in equilibrium with the atmosphere and measuring the resulting pCO2 of the atmosphere. Even continuous (on commercial sea ships): spraying seawater in air and measuring the pCO2 of the air, or bubbling air through the water…
That all means that Berry’s formula (2) can’t be true, as that implies that the outflow is directly proportional to the absolute CO2 pressure in the atmosphere (pressure directly proportional to “level”/concentration), while it is only proportional to the CO2 pressure difference between atmosphere and ocean surface.
To show the difference between the ocean surface – atmosphere CO2 cycle and the influence of pressure:
The IPCC estimates the seasonal CO2 exchange between ocean surface and atmosphere at about 50 PgC/year. That is based on the same measurements and calculations as for the above CO2 transfers.
That is caused by temperature: the ocean surface warms in spring/summer and cools in fall/winter, where the pCO2 of the ocean surface follows the temperature, independent of the CO2 pressure in the atmosphere.
The influence of the increased pCO2 in the atmosphere, is measured (!) as 0.5 PgC/year in the ocean surface. That is 1% caused by the extra (!) CO2 pressure in the atmosphere, 99% caused by the sea surface temperature. Thus the influence of the CO2 level/amount/pressure in the atmosphere on the CO2 output is very modest and stops when atmosphere and ocean surface are in equilibrium, according to Henry’s law, which is at about 295 ppmv for the current average SST.
The upper 100 meter or so of the oceans are called the “mixed layer”, which is in close contact with the atmosphere. The CO2 exchanges between atmosphere and mixed layer are very rapid (half life less than a year) and the carbon mass is not much more than in the atmosphere: around 1,000 PgC, in the current atmosphere some 900 PgC at present.
Another important point is that the ocean surface buffer capacity to absorb CO2 from the atmosphere is limited to about 10% of the changes in the atmosphere. That is called the Revelle/buffer factor.
Why that? According to Henry’s law, a 100% increase of CO2 in the atmosphere should give a 100% increase of dissolved CO2 in the ocean surface. That indeed is the case, but… Pure, dissolved CO2 is only 1% of all inorganic carbon species in the ocean surface. Thus a CO2 doubling in the atmosphere gives an increase of pure CO2 in seawater from 1% to 2%… Of course, there it doesn’t stop, and the following chemical reactions make bicarbonates and carbonates from that CO2, but at the same time H+, making seawater less alkaline. The net result is that a 100% increase of CO2 in the atmosphere is followed by some 10% increase in the sea surface:
See: https://tos.org/oceanography/assets/docs/27-1_bates.pdf Table 2 for the increase of nDIC (DIC = CO2 + bicarbonates + carbonates) and compare that to the increase of CO2 in the atmosphere.
Despite these restrictions, seawater contains orders of magnitude more CO2 than fresh water…
Dear Dr. Ed,
To start with, late congratulations with your 90th birthday!
Then about your formula (2):
Outflow = L / Te
where Te = 4 years.
As already said, the largest CO2 (seasonal) flux is the absorption of lots of CO2 by vegetation in spring/summer. That is about 120 PgC/year of the total 210 PgC/year carbon that cycles in and out the atmosphere, as estimated by the IPCC.
Thus in spring/summer, over half the total output is removed by one process, near completely independent of the amount of CO2 that at that moment resides in the atmosphere. Only dependent of sunlight and temperature. Half of equation (2) already refuted by reality.
I don’t see any reason to calculate CO2 fluxes in both directions between the different reservoirs, when the net difference between these two fluxes is quite exactly known. The height of the fluxes is of zero interest, even if these double or halve over time, only the difference between them affects the levels in a reservoir…
Moreover, both the net increase of carbon (derivatives) in the ocean surface and vegetation are either measured (ocean surface DIC) or calculated (vegetation, via de O2 balance). So, no need to calculate any individual CO2 flux in or out between the atmosphere and the two main reservoirs.
The essence of this debate seems to be the kind of “model” that you have in mind of the real world.
In every part of your work, it Is clear that you use the “classic” one-way container with unidirectional inputs going into the container and outputs out of the container, where the inputs set the balance level within the container. That is the “lake” or “bath tube” model.
In that case, and only in that case, the residence time (Te) of about 4 years and the adjustment time (Tau) are equal and only then one may reverse the formula for the residence time in equation (2) as you have done. Your classic model is reflected in your Figure 4.
I have a similar view on this classic process, as that is quite common in chemical engineering, here made clear in the “lake model”, I used for a similar discussion last September in Athens:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/classic_view.png
In reality, large parts of the carbon cycle are just cycling in and out of the atmosphere, largely independent of the CO2 level in the atmosphere. In that case, the residence time Te and the adjustment time Tau are completely independent of each other, as also can be calculated from the observations.
Te for CO2 in the atmosphere still is about 4 years, Tau gets about 50 years.
The around 50 years adjustment time was already calculated by Peter Dietze in 1997 in a discussion with Fortunat Joos, the inventor of the Bern model which the IPCC uses:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/Dietze_1997.png
And repeated by several skeptics like Lindzen, Spencer and myself over the years.
That is what happens in the real world and largely is reflected in the “fountain model”:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/real_view.png
The opening of a small supply of a few liters per minute determines the height in the basin and that determines the overflow.
The input to the fountain of the cycle at 1000 liter/minute has zero influence on the overflow and doubling the circulation by adding a second cycle pump only halves the residence time without affecting the overflow.
In the real world, the calculated residence time Te of 4 years and the calculated adjustment time of 50 years, both based on real world observations, are completely independent of each other.
That is the essence of our differences.
Further, besides the cycles which move lots of CO2 back and forth between atmosphere and oceans/vegetation, independent of the CO2 pressure in the atmosphere, there is zero extra inflow or outflow caused by the CO2 pressure in the atmosphere when that is equal to the CO2 pressure in the oceans or vegetation.
If the partial CO2 pressure (pCO2) in the atmosphere is higher than of the oceans, then there will be an extra outflow beyond the cycling flows. If the pCO2(atm) is lower than in the ocean surface, then the extra CO2 flow will be reverse.
Your formula (2) should be adjusted to the CO2 pressure difference between atmosphere and ocean surface and to the pCO2 difference between atmosphere and plant alveolars water, not the absolute CO2 pressure in the atmosphere.
David,
I never thought net global uptake negative and I am not questioning that net global uptake has been positive since the beginning of the industrial era. I was only interpreting your statement, “It was sometimes negative in the geological past.” I am questioning the relative contribution of human emissions versus natural emissions. You are arguing a black and white, all or none scenario, where any increase in atmospheric carbon must be blamed totally on fossil fuel emissions. I will try to explain how a potential growth in natural emissions competes with that of fossil fuel emissions. I challenge you to provide the data, not a mass balance assertion, to support a counter-argument.
Let me demonstrate how simple math can be used to disguise the facts and mislead. Your math balance equations do not constrain the magnitude of the natural emissions and absorptions, because they don’t take into account additional equations that do. You started going there by including the fact that natural emissions are 20 times human emissions. I will address this alternatively using the additional known annual estimates of total CO2 absorbed. Based on your 2024 numbers quoted [June 22, 2025 at 11:15 am] for human emissions (41.4 GtCO2 = 5.30 ppm) and net global uptake (19 GtCO2 = 2.43 ppm), the simple math, Cchange = Eh – (net global uptake), becomes Cchange = 5.30 – 2.43 = 2.87 ppm. In 2024, I estimate CO2 in the atmosphere was 430 ppm. If about a fourth of that was absorbed that year, based on an e-time of 4 years and the corresponding rate constant of 0.25, that equals a gross uptake (An) of 107.5 ppm. With net global uptake = An – En, then En = 107.5 – 2.43 = 105 ppm. If the atmosphere contained 5% of human-sourced carbon in 2024, then the amount of human-sourced carbon would have been about 5.4 ppm, slightly more than was emitted. In the same year, the non-human-sourced carbon absorbed could be estimated to be 102 ppm (95% of An), which is even less than the natural emissions that year. Your normalized human emissions = 1 scenario gives virtually the same results, i.e., terrestrial sinks remove annually slightly more human-sourced carbon from an atmosphere which contains about 5% of human-sourced carbon than is emitted into that atmosphere. Likewise, slightly less “natural” carbon is removed annually compared to the source emissions. Natural emissions exceeding what is absorbed annually contributes to the accumulation of CO2 in the atmosphere.
As I admitted, I’m not equipped to judge isotopic arguments. However, I’m not at all moved to take you seriously with statements like “the exchange effectively erases differences” and “We know [human emissions are the cause of the rise] from the mass balance argument.”
Dear Ferdinand,
We should dispense with a part of your claim that is mathematically wrong. You wrote
“That all means that Berry’s formula (2) can’t be true, as that implies that the outflow is directly proportional to the absolute CO2 pressure in the atmosphere (pressure directly proportional to “level”/concentration), while it is only proportional to the CO2 pressure difference between atmosphere and ocean surface.”
Let’s just do some basic math.
My formulat (2) indeed says outflow is directly proportional to level.
Your formula merely combines two of my outflows to get a net flow.
For example, in my terminology:
F12 = flow from Land to Atmosphere
F21 = flow from Atmosphere to Land
Therefore:
F21 – F12 = NET flow from Atmophere to Land.
Please stop claiming my (2) is wrong because you are looking for net flows. As I already described this in my last comment. My formulation easily calculates net flows.
Dear Ferdinand and everyone,
At the top of these posts, I put my test calculation for the effect of human carbon emissions on atmospheric CO2.
I made the calculation simple by setting the human carbon inflow to 10 PgC per year for ten years.
Now, I request Ferdinand, and anyone else who wishes, to put your calculations in the same Excel format. Make an image of your boxes like mine, and send it to me by email. I will post it below my calculations.
This is the only way to resolve these discussions. Anyone who is a player, who is serious, who knows how to do calculations can particpate. This is easy to do in Excel.
This is where the “rubber meets the road” as they say. If you cannot show your calculations for this simple test, then you are not a player in this game.
Dear Ferdinand, I expect to see your calculations for the same assumed data. Only then, can we compare our calculations and methods.
Ed
Ferdinand,
Thank you for the discourse on mass transfer of CO2 between the atmosphere and the ocean surface. I assume you are responding to my objections to your use of height/pressure terminology and my concerns that you don’t appreciate the concentration differences that I allege govern transport processes involving mass transfer to and from the atmosphere and its sinks and sources. I see now that our disagreement will not likely be over terminology in that you seem quite familiar with the processes involved.
The equation, F = k•s•ΔpCO2, can be expressed in another form, dC/dt = ks*(Cs – Ca/K). The latter equation better reflects bidirectional transport and that the ratio of the concentrations at equilibrium equals K. Note that equilibrium does not mean transfer between the reservoirs stops, only that no net transfer occurs. CO2 continues to exchange between the reservoirs in proportion to its respective concentrations in the reservoirs. One of the misstatements you make in this regard is “[Net mass transfer of CO2 between the atmosphere and the ocean surface] means that Berry’s formula (2) can’t be true, as that implies that the outflow is directly proportional to the absolute CO2 pressure in the atmosphere (pressure directly proportional to “level”/concentration), while it is only proportional to the CO2 pressure difference between atmosphere and ocean surface.” That is wrong. Outflow from the atmosphere IS proportional to its CO2 concentration and, likewise, outflow from the ocean (inflow to the atmosphere) is proportional to the ocean CO2 concentration.
Another misleading statement follows soon after, “[seasonal CO2 exchange between ocean surface and atmosphere] is caused by temperature: the ocean surface warms in spring/summer and cools in fall/winter, where the pCO2 of the ocean surface follows the temperature, independent of the CO2 pressure in the atmosphere.” Of course, temperature initiates mass transfer, because Henry’s Law constant K is affected by temperature and disequilibrium results when the equilibrium temperature changes. But it is wrong to claim the resulting mass transfer is independent of CO2 concentration. Mass transfer will proceed in proportion to concentration. This is readily seen by imagining how much faster transfer will occur if the density of molecules near the air/reservoir interfaces is concentrated compared to being relatively dilute.
IPCC estimates at least 80 PgC/year exchanges between oceans and the atmosphere. I would like to know how an “influence” of 0.5 PgC/year is measured and how that relates to the current model Dr Berry presented. As I explained earlier, net transfer will stop at equilibrium, but the gross transfer continues. While CO2 is readily being absorbed in areas turned cold, outgassing abounds in the warming areas elsewhere. In both cases, mass transfer occurs in proportion to concentration differences. I don’t think it’s unreasonable to say that equilibrium is the exception, not the rule, year-round.
I looked into the effect of the Revelle factor some years ago. I think it varies widely from warm to cold waters and is based on carbonate equilibria. I don’t think it translates directly into transfer rates. It’s worth revisiting, however, thank you.
The fact that adding CO2 to the atmosphere (by humans) increases the amount of CO2 in the atmosphere should not be confusing.
tl;dr:
It’s really very simple:
● Mankind is adding CO2 to the air, mostly by burning fossil fuels.
● Nature (the net sum of all natural sources and sinks) is removing CO2 from the air.
● The amount of CO2 in the air is increasing because mankind is adding CO2 faster than nature is removing it.
The fact that some skeptics of climate alarmism are confused about such a simple concept surely encourages many other people to dismiss all skeptics of climate alarmism as unserious. That is unfortunate.
Here are the requested calcuations (tl;dr + numbers):
● Mankind is currently adding CO2 faster than nature is removing it, so the amount of CO2 in the air increasing. Measurements show that it is increasing by about 2.5 ±0.1 ppmv/year. (1 ppmv CO2 = 7.8024 Gt CO2 = 2.12940 PgC.)
● Mankind is adding 4.7 ± 0.5 ppmv/year of fossil CO2 to the atmosphere, plus 0.5 ±0.3 ppmv/year CO2 from “land use changes” (clearing forests and draining swamps). That increases the amount of CO2 in the air by 4.4 to 6.0 ppmv/year. (The fossil CO2 figures are calculated from economic data: the amount of coal, oil & natural gas produced and burned.)
● The difference between those two numbers is the rate at which nature is removing CO2 from the atmosphere: (5.2 ±0.8 ppmv/year) – (2.5 ±0.1 ppmv/year) = 2.7±0.9 ppmv/year.
Note #1: there are three different units in which atmospheric CO2 is commonly specified: ppmv (ppm), Gt CO2, and PgC (Gt carbon). 1 ppmv CO2 = 7.8024 Gt CO2 = 2.1294 PgC.
Note #2: I’ve conservatively chosen to add uncertainties linearly, since it is unclear whether we would be justified in adding them in quadrature
Note #3: other than the models used to roughly estimate the minor contribution from “land use change emissions” (from clearing forests and draining swamps), there’re no models used or needed for these calculations.
Note #4: Calculations of human CO2 emissions start with economic data on production/use of coal, oil & natural gas. CO2 is (12.0107/44.0095) = 27.29115% carbon by weight, so, for example, if you fully burn 1 tonne of 94% carbon anthracite coal, 0.94×44.0095/12.0107 = 3.444 tonnes of CO2 are emitted.
Note #5: The justification for using annually averaged Mauna Loa measurements of CO2 is that they’re quite close to the global average, and what we’re interested in is the total amount of CO2 in the atmosphere, which can be calculated from the global average CO2 concentration. The fact that annually averaged Mauna Loa CO2 measurements track very closely with measurements from other locations means that, except near sources and sinks, CO2 is a “well-mixed gas.” The average CO2 level at Mauna Loa (northern hemisphere) in 2024 was 424.61 ppmv. At Cape Grim (southern hemisphere) it was 420.01 ppmv. That’s only about a 1% difference. (The difference offers a clue to the rate at which wind currents mix CO2 emitted mostly in the northern hemisphere into the southern hemisphere’s atmosphere.) That’s pretty well-mixed.
The fact that nature (the net sum of natural carbon sinks and sources) is removing CO2 from the air obviously means that mankind, not nature, is responsible for the ongoing (beneficial) increase.
There’s no question about the fact that nature is removing CO2 from the air; as I’ve just shown, that fact is proven by measurements and simple arithmetic. But you might wonder why nature is currently removing CO2 from the air.
The answer is that the higher atmospheric CO2 levels go, the faster natural “carbon sinks” absorb it from the air. That is a powerful “negative feedback,” which helps to stabilize the Earth’s climate.
The two most important of those sinks are marine uptake and terrestrial “greening” / soils. They both accelerate approximately linearly as the CO2 level rises.
W/r/t absorption of CO2 by water, the linearity is probably obvious: the more CO2 molecules there are in the air, the more frequent are their collisions with liquid water. (It’s more complicated than that, because of chemical and biological processes, but it’s nevertheless approximately linear.)
Terrestrial biosphere uptake is less obviously linear, but it we know from agronomists’ studies that “CO2 fertilization” enhances C3 plant growth nearly linearly to above 1000 ppmv, and the plants that sequester most carbon (trees, sphagnum moss) are C3 plants, so that, too, is approximately linear:
https://sealevel.info/C3_and_C4_Pflanze_vs_CO2_Konzentration_en_1750_2023_linearity_highlighted3.png
The sum of two linear functions is also linear, so the net rate of natural CO2 removals from the atmosphere must also be an approximately linear function of the CO2 level in the atmosphere.”
And that’s what the data show. In fact, the rate of natural CO2 removal from the atmosphere accelerates by about 1 ppmv/year for every 50 ppmv rise in the atmospheric CO2 level (about 1/50 = 2%), as you can see from this plot:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
(That’s Fig. 1 here; here’s the spreadsheet.)
That 2% slope means the effective atmospheric lifetime (“adjustment time”) of CO2 added to the atmosphere is about 50 years. (Note: do not make the mistake of confusing the adjustment time with the “turnover time,” a/k/a “residence time,” which is only about 3-5 years.)
That short (≈50 year) adjustment time is highly inconvenient for climate FUD, but the IPCC’s Second Assessment Report nevertheless acknowledged it, in a roundabout way. It reported that, “Within 30 years about 40-60% of the CO2 currently released to the atmosphere is removed.” [SAR WGI TS B.1 p.15] That implies a half-life of 23 to 41 years, which implies an adjustment time (effective atmospheric lifetime) of halflife/ln(2) = 33 to 59 years. That means the rate of annual natural CO2 removals accelerates by 1/59 to 1/33 of the increase in CO2 level, which is 1.7% to 3.0% per year. (Unfortunately, subsequent IPCC Assessment Reports have failed to mention that fact, presumably because it torpedoes the “climate crisis” narrative.)
Roughly the same result has also been reported by many other researchers, including:
Spencer, Roy W. (2023). ENSO Impact on the Declining CO2 Sink Rate. J Mari Scie Res Ocean, 6(4), 163-170. https://doi.org/10.33140/jmsro.06.04.03
Dr. Peter Dietze: http://www.john-daly.com/carbon.htm
Engelbeen, Ferdinand (2022). The origin of the increase of CO2 in the atmosphere, http://www.ferdinand-engelbeen.be/klimaat/co2_origin.html (section 3)
Berrien Moore III and B. H. Braswell (1994). The lifetime of excess atmospheric carbon dioxide. Global Biogeochem. Cycles, 8(1), 23–38. https://doi.org/10.1029/93GB03392
Excerpt: “The single half-life concept focuses upon the early decline of CO2 under a cutoff/decay scenario. If one assumes a terrestrial biosphere with a fertilization flux, then our best estimate is that the single half-life for excess CO2 lies within the range of 19 to 49 years, with a reasonable average being 31 years.”
Those very strong negative feedbacks, which lead to the relatively short (fifty year) adjustment time, mean the atmospheric CO2 level cannot rise indefinitely unless the emission rate does, too. The CO2 level is currently rising by about 2.5 ppmv/year. So if anthropogenic emissions were to continue at the current rate for the long term, the atmospheric CO2 level would plateau at just 2.5 × 50 = about 125 ppmv above the current level.
That’s a mere 37% of a doubling. For comparison, the Earth has already seen 60% of a doubling since the “preindustrial” 1700s, with only benign effects, so there’s no reason to suppose that another 37% would be harmful.
That’s one of the many reasons that the “net zero” campaign is unscientific.
BTW, you can cite the CO2 Coalition investigation of the carbon cycle like this:
Engelbeen F, Hannon R, Burton D (2024). The Human Contribution to Atmospheric Carbon Dioxide. CO2 Coalition. https://doi.org/10.31219/osf.io/het6n
I hope you find this helpful.
Jim
Along with mass balance, the isotope arguments are an essential part of the analyses. You will not understand atmospheric carbon, and the flaws in Ed’s work, without understanding them.
Think of the disequilibrium isofluxes as simply mixing the carbon in two reservoirs. By analogy, if one reservoir started with 20 proof whiskey and the other with 30 proof, balanced exchanges between them would tend to erase the difference. Ed has also struggled to understand this, and a couple of years ago a flawed Health Physics paper by Skrable also overlooked the process. That paper correctly pointed out that the present atmosphere’s C14 content was way too high for the CO2 increase from pre-industrial levels to all be C14-devoid human emissions. If you like, it was an experimental confirmation of Ed’s calculations. But the continuous mixing means that the present composition is not a definitive quantity. The Seuss effect (look it up) is much smaller than naively inferred without considering disequilibrium isofluxes.
Dear Ed,
I will work on it tomorrow, with a slight change in Figure 3 of the IPCC, as we disagree with the IPCC about the isolation of the deep oceans by the ocean surface. That is based on the IPCC’s Bern model, which doesn’t reflect the real world, because there is a direct connection between the atmosphere and the deep oceans with the THC (thermohaline circulation) of about 40 PgC/year.
That will not affect the overall picture for the atmosphere, only remove the F34 and F43 links and add F24 and F42 links…
Dear Ferdinand,
Thank you for your comment. Don’t feel pressured to reply to my comments instantly. We all have lives to live, me included.
What I am looking for is how you would calculate the annual change in levels of the four reservoirs according to the IPCC data set I use AND my test assumption that annual human carbon inflow equals 10 PgC per year.
After that, you can show your proposed F24 and F42 links and show how they change your calculations.
If your added links are defined well enough, then I can do a second calculation that includes those links.
The overall goal in my request is so we can see and compare any differences in our calculations.
Dear Jim,
Thank you for your comments that show you understand the human carbon cycle much better than David
Andrews does.
My post above properly describes how to interpret the flow of carbon-14 isotopes. David does not get it. So, don’t let him confuse you.
Ed
Dear Dave.
Thank you for your comment, and especially for your updated reference to your publication. I will update my post accordingly.
In the following, I am going to be quite critical of your reply. Please understand that I am not judging you personally in my critiques.
My Reply:
You wrote:
We agree with your (1) but your (2) is ambiguous because you do not follow the path of human carbon through the carbon cycle. You merge human carbon with natural carbon in an undefined manner and this makes your statement and all your following statements that depend upon your (2) wrong.
Your (3) is also wrong. The proper description is to say (a) we assume the flows of natural carbon into and out of the atmosphere are equal and stay constant, so the natural carbon level stays constant and (b) that we keep separate track of the human carbon that flows into the atmosphere and then flows into the other carbon reservoirs.
THIS IS THE CRUX TO THIS WHOLE ISSUE. THE CO2 COALITION DOES NOT PROPERLY DEFINE THE PROBLEM.
(I did not receive your test calculation to compare it with my table above. if you have it, please email it to me.)
BOTTOM LINE: THE CO2 COALITION DOES NOT KNOW HOW TO CALCULATE THE EFFECT OF HUMAN CARBON EMISSIONS ON ATMOSPHERIC CO2.
Your continued explanations are simply handwaving and contradict simple physics:
THAT IS QUITE AN ADMISSION THAT THE CO2 COALITION HAS NO USE FOR CALCULATIONS THAT DISAGREE WITH ITS LEADERS’ EMOTIONAL NEEDS. WHAT HAPPENED TO PHYSICS?
THE CO2 COALITION CANNOT CALCULATE THE TRUE EFFECT OF HUMAN CO2, SO IT REJECTS MY CALCULATIONS WITHOUT FINDING ANY ERRORS IN MY CALCULATIONS AND MAKES A SWEEPING UNJUSTIFIABLE CLAIM THAT IT CALL “FACT”.
YOUR REFERENCE TO “NATURE” IS NOT A SCIENTIFIC STATEMENT BECAUSE YOU DO NOT PROPERLY DEFINE “NATURE”.
THE GOAL OF THIS SUBJECT IS TO CALCULATE HOW MUCH HUMAN CARBON INCREASES THE CO2 LEVEL. THE CO2 COALITION FAILS TO ACHIEVE THIS GOAL.
THAT IS WHAT MY EQUATION (2) DOES BUT THE CO2 COALITION REJECTS MY (2) AND ALL THE CORRECT CALCULATIONS THAT (2) PRODUCES.
TO PUT IT AS POLITE AS I CAN, THAT SENTENCE IS JUNK SCIENCE. THE ADJUSTMENT TIME IS NOT RELEVANT TO THE PROBLEM WE ARE DISCUSSING.
All your references fail to do proper physics. So, using these references further degrades your argument. ARE YOU TRYING TO ARGUE THAT YOUR REFERENCES ARE A CONSENSUS THAT PROVES YOU ARE CORRECT?
But you did not do the simple test calculation that I requested.
THERE IS NO MATH IN YOUR ARGUMENT. ALL YOUR ARGUMENTS ARE HANDWAVING. BY CONTRAST, I CALCULATE REAL NUMBERS THAT THE CO2 COALITION REJECTS.
BOTTOM LINE: THE CO2 COALITION DOES NOT KNOW HOW TO CALCULATE THE EFFECT OF HUMAN CARBON EMISSIONS ON ATMOSPHERIC CO2.
The CO2 Coalition is severely negligent in its use of physics to calculate the effect of human carbon emissions on the level of atmospheric CO2.
Dear Ed,
Thank you for your perceptive, untiring efforts to see that this outrageous, faked-science scandal will finally be laid exposed. I do poems.
A Tripping Point
More carb in the sky makes it hotter
The Greenhouse Effect says it’s gotta
But by Henry’s Law
Hotter oceans add more
and more carb in the sky makes it hotter
and hotter and hotter and hotter . . .
Since you’re referring to my three bullet points by number, here’s the “tl;dr + numbers” version of the three bullets, with numbers added to match yours, and minor clarifications in [brackets]:
Ed wrote:
It is not ambiguous, it is calculated mostly from real, reliable data: high quality measurements, and economic statistics. It is not from hypothetical models, except for the minor contribution of “land use emissions”.
Carbon is fungible, so it makes no sense to try to “follow the path” of emitted carbon. The natural sinks which remove carbon from the atmosphere do not distinguish between “natural carbon” and “human carbon.”
Ed wrote:
All human and natural CO2 emissions go into the air, where they mix. There’s nothing undefined about it, that’s the physical reality. I don’t merge them, the atmosphere does!
Many climate alarmists think some percentage of our emissions are magically teleported to the oceans & biosphere. They are wrong, but it’s widely believed, and even implied in parts AR6. Lots of alarmist sources make that mistake. For example, here’s the UN saying, “The ocean… absorbs 30 percent of all carbon dioxide emissions”. It is nonsense.
Ed wrote:
None of that is correct. It is not true that “flows of natural carbon into and out of the atmosphere are equal and stay constant,” nor is there a “natural carbon level” which “stays constant.” Carbon is fungible, and CO2 from all sources is mixed in the atmosphere.
There are no pipelines for “separate[d] human carbon that flows into the atmosphere and then flows into the other carbon reservoirs.” That is unphysical.
Contrary to your “Figure 3,” which erroneously shows a separate “human carbon cycle” removing carbon from the atmosphere to the land and ocean, there are no major anthropogenic carbon sinks. There are only natural removal processes.
There are small differences between isotopes for the speeds with which various processes proceed, but that merely introduces slight isotopic fractionations, and it does not affect the calculations I’ve showed you.
The amount of carbon in the atmosphere is increasing because the additions to it exceed the removals from it, by about 2.5 ±0.1 ppmv/year. (1 ppmv CO2 = 7.8024 Gt CO2 = 2.12940 PgC.)
We know that the anthropogenic CO2 additions are about 5.2 ±0.8 ppmv/year, and the anthropogenic removals are about zero.
That means the net sum of all other processes (which we call “nature”) is a removal rate of (5.2 ±0.8 ppmv/year) – (2.5 ±0.1 ppmv/year) = 2.7±0.9 ppmv/year.
Ed partially quoted me writing:
To which Ed replied:
The field of “climate science” is overrun with people who think their unrealistic models trump measured physical reality. That’s a major reason it is such a mess. At the CO2 Coalition, we deal in measured reality.
Ed wrote:
The true effect of emitting 5.2 ppmv of CO2 into the atmosphere is a 5.2 ppmv increase in the atmospheric CO2 level.
How is that not obvious?
If, when we (humans) add 5.2 ppmv of CO2 to the atmosphere, the measured increase in the atmospheric CO2 level is only 2.5 ppmv, that means something else removed a not total of 2.7 ppmv of CO2 from the atmosphere.
That “something else” is what we call “nature.”
Ed wrote:
I told you, “Nature [in this context is] the net sum of all natural [CO2] sources and sinks.”
Is that unclear?
Ed wrote:
As I’ve already showed you, human carbon emissions increase the atmospheric CO2 concentration by 5.2 ±0.8 ppmv/year.
Nature (the net sum of all natural sources and sinks) reduces the atmospheric CO2 concentration by 2.7±0.9 ppmv/year.
The difference between those two figures is the measured average annual increase in the atmospheric CO2 concentration: 2.5 ±0.1 ppmv/year.
Ed wrote:
The measurement-derived adjustment time, of about 50 years, is the “CO2 lifetime” which determines the duration of effect for contemporary CO2 emissions. It is the only lifetime which is relevant to the problem we’re discussing.
I urge you to abandon your “models,” and focus on measured reality.
Dave,
You wrote:
“The field of “climate science” is overrun with people who think their unrealistic models trump measured physical reality. That’s a major reason it is such a mess. At the CO2 Coalition, we deal in measured reality.”
And:
“I urge you to abandon your “models,” and focus on measured reality”
You have no measurements, just words. Show us where you measured CO2 being emitted from the oceans. You claim you’ve measured human emissions, you haven’t. The global carbon budget is not measurements, that is all based on guesses and estimates and models based on false assumptions.
You’ve got nothing but words.
Dear Dave,
You make your science life difficult because you do not separate concepts and formulations from data.
As Einstein said, formulation of a problem is more difficult and important than solving the problem.
I omitted your irrelevant data from your paragraphs because your data are not needed to illustrate the formulation. Yet, you go and add the data back again.
POINT #1: You have not produced a simple 10-year calculation to compare with mine. That means you are either ignoring this or incapable of doing this.
I wrote:
“Your (2) is ambiguous because you do not follow the path of human carbon through the carbon cycle.”
You replied,
Everything you write is about your unstated imaginary model. You do not recognize your own assumptions. You think data is everything. It’s not.
Data has only two functions in science: (a) used to formulate a hypothesis that can be tested, and (b) to test the predictions of hypotheses. You are bypassing the scientific method.
You call my work, “hypothetical models.” You don’t realize that my “climate model” is an accurate description of IPCC’s carbon cycle. My “model” is based on my (1) and (2). Everything else is deductive math.
My deductive “model” shows how to correctly calculate the effect of human carbon on the CO2 level, based only on (1) and (2) and IPCC’s own data.
I clearly stated my two assumptions, my equations (1) and (2). You don’t dispute these equations. You seem to not get it that all my equations and calculations are deductions from these two equations.
If you understood my simple math, you could insert your own data into my mathematical model to calculate the effect of your data on the outcome.
All your data is useless unless you have a means to calculate the effect of your data on how human carbon adds to the CO2 level.
You are unable to use your data to calculate a result because you have not formulated a way to do your calculations, and you don’t know how to insert your data into my mathematics.
Above these posts, I show you an example of how I calculate the effect of human carbon on atmospheric carbon. My calculation is not a model. It is a math that any good scientist or engineer should be able to do.
You don’t get it that my equations apply to human and natural carbon equally and independently. Yet, that is the key to calculation the effect of human carbon on the carbon in the atmosphere.
Without such equations, you cannot follow the separate paths of human and natural carbon through their carbon cycles.
You say that “nature” removes human carbon from the atmosphere. Your statement is irrational and incorrect. You assigned the outflow of human carbon to the outflow of natural carbon.
You say:
Unless you can describe nature in equations, you can’t calculate what nature is doing. You reject my description, which leaves you with nothing but handwaving.
Your (3) is also wrong. The proper description is to say (a) we assume the flows of natural carbon into and out of the atmosphere are equal and stay constant, so the natural carbon level stays constant and (b) that we keep separate track of the human carbon that flows into the atmosphere and then flows into the other carbon reservoirs.
You wrote:
I did not say such a thing. I said your hypothesis of carbon flow must be able to replicate the situation where the natural carbon level stays constant because this is the assumed environment where human carbon flows.
You must use the Climate Equivalence Principle to calculate what human carbon will do in that environment.
You wrote:
Nonsense. Every place natural carbon goes human carbon will go. With more carbon, trees grow.
You wrote:
I deleted your numbers because they are distracting you. In theoretical physics we first write our equations to formulate a solution to our problem. Only then do we add numbers. You are modifying your equations because you assume human carbon outflow. First, get your equations correct, and then deal with the data.
You wrote:
I replied:
“THAT IS QUITE AN ADMISSION THAT THE CO2 COALITION HAS NO USE FOR CALCULATIONS THAT DISAGREE WITH ITS LEADERS’ EMOTIONAL NEEDS.”
You wrote:
I do not have an “unrealistic model.” Anyone who claims that is not a good physicist. I simply do my time step calculations using a standard systems model. You imply that my calculations are like a climate model, all of which are disasters.
You are not dealing in “measured reality.” I am surprised no one in the CO2 Coalition has tried to help you like I have.
I wrote:
“THE CO2 COALITION CANNOT CALCULATE THE TRUE EFFECT OF HUMAN CO2.”
You wrote:
Dave, your examples are wrong because you do not calculate how fast human carbon flows to the other carbon reservoirs. You assume incorrectly that the human carbon inflow sticks in the atmosphere.
You must follow my example calculation and let human carbon flow out of the atmosphere each year.
YOUR REFERENCE TO “NATURE” IS NOT A SCIENTIFIC STATEMENT BECAUSE YOU DO NOT PROPERLY DEFINE “NATURE”.
Your belief is clear, and wrong. It just proves you never learned how to do theoretical physics. You have shown me that you cannot do physics.
THE ADJUSTMENT TIME IS NOT RELEVANT TO THE PROBLEM WE ARE DISCUSSING.
You wrote:
Adjustment time is not mathematically related to calculating the effect of human carbon on the CO2 level. Even you have not shown such a relationship.
You wrote:
Now, you have made this discussion personal.
To call my calculations “models” is a fallacy, especially when you cannot do any calculations to support your illusions.
Dave, did you and your co-authors write your crazy ideas on climate science all on your own?
Did someone in the CO2 Coalition review and approve your paper?
Did Will Happer or Richard Lindzen or anyone approve your outright decimation of physics, math, and logic in your paper and your comments?
Salby discusses the Bern modal in this video (https://www.youtube.com/watch?v=rohF6K2avtY) at 1 hr and 1 min.
He concludes that it is not compliant to basic physics.
David Andrews,
I am studying the isotopic issues applicable to the current discussions. I started reading a Skrable paper: https://cdn-links.lww.com/permalink/hp/a/hp_2022_05_31_skrable_22-00080_sdc1.pdf
In the first paragraph under “Derivation of equations for Pathway 1,” I read “The sign of DCNF(t) can be positive or negative depending on whether or not there is a net change in the activity per unit volume of the atmosphere in any year since 1750, which is proportional to the product C(t)
.”Does this make sense to you?
Jim,
I am home after several days of travel and can focus and be more responsive to the first and second paragraph of your June 28 post. (As it happens, I was in Calgary, Alberta at the NW American Physical Society meeting, and my trip home yesterday took me through Big Fork, MT, Ed’s home. I considered looking him up to see if any birthday cake remained but didn’t.)
I agree there are issues in attributing the “full cause” of atmospheric CO2 rise to human emissions. I usually just describe the mass-balance argument as showing that natural processes are removing more carbon from the atmosphere than they are adding. My example of some ambiguity comes from the Ballantyne paper that I have referred to previously. This paper plots net global uptake from 1960 to 2010. There is a clear increasing trend, roughly proportional to human emissions, that is not surprising. The more CO2 we put into the atmosphere, the more nature redistributes elsewhere. But there are deviations from the trend. The largest appears to be associated with the 1991 eruption of Mt Pinatubo when a temporarily cooler world showed an increase in net global uptake. We cannot say how much natural emissions went down (because of less hot water), or absorption went up (because of more cold water). Presumably both changed. In this case, a natural event reduced the rate of increase. I would submit, however, that perturbations like this should not change our conclusion about the cause of the dominant trend, even if other factors are at work on the details.
I do not dispute your numerical calculations which show a large fraction of “human carbon” being removed from the atmosphere and net “natural carbon” being put into the atmosphere by natural processes. In fact, these calculations are a good illustration of what I have been trying to explain to you. Your mistake is in the sentence “Natural emissions exceeding what is absorbed annually contributes to the accumulation of CO2 in the atmosphere.” Perhaps surprisingly, no they do not. You will notice that “human carbon” is leaving the atmosphere, where its concentration was no doubt higher than in land/sea reservoirs. You will notice that “natural carbon” is also going from a higher concentration reservoir to a lower concentration one, i.e. towards the atmosphere. This should remind you of disequilibrium isofluxes, which can change the type of carbon in a reservoir without changing the amount. The total carbon level changes are determined by the net global uptake. The balanced exchanges only modify the composition.
Dave A, I’m very interested in hearing about what you think are the “bad arguments” made by the CO2 Coalition (of which I’m a member). You have my email address.
Warmest regards,
Dave B
Jim,
Here is a link to my comments on the Skrable paper. Their derivations of specific activity dilution formulae were fine. But like Ed, they don’t appreciate the effects of balanced exchanges between reservoirs which can change isotopic composition without changing levels.
https://pubmed.ncbi.nlm.nih.gov/36719939/
DMA,
Murray Salby also thought …
Murray Salby and Hermann Harde .. ….
Murray Salby was ….
Murray Salby relied on …..
If Murray Salby said it….
Skeptics like yourself claim to reject authority, but all you do is accept without question people who tell you what you want to hear. Either think for yourself, DMA, or if you are unable to do that, make better choices of authorities.
David Andrews June 30, 2025 at 8:50 pm
David,
I deleted your remarks that attack Salby from your above refrenced comment. I will otherwise leave the comment.
My reasons are (a) personal attacks are not part of a science debate, (b) Salby is not here to defend himself, (c) your attacks have no references, (d) your attacks make no contribution to this discussion, and (e) if I leave your attack on Salby, it will set a bad precedant to the discussions on my website.
We are here to discuss and debate climate science. Whatever a person has done in the past, or even accused to have done, is not relevant to the discussion of what the person has published or otherwise presented to the public.
Ed as administrator
David,
You wrote, “I usually just describe the mass-balance argument as showing that natural processes are removing more carbon from the atmosphere than they are adding.”
I think this is the crux of the whole problem. What data actually nails that down? In any given year, about 20 times more natural carbon goes into the atmosphere and a similar amount (+/-) natural mixed with a little industrial carbon comes out. I use the term industrial carbon, because I found it defined in a “old” Keeling paper and it sounds better to me than fossil fuel or human-sourced carbon, but it’s meant to mean basically the same thing. Getting back to the relative amounts transferred question, how do you know the natural source is sometimes, or even often, more than the natural amount removed when corrected for the “industrial” share removed?
You addressed this with the Mt Pinatubo example and then you concluded, “I would submit, however, that perturbations like this should not change our conclusion about the cause of the dominant trend, even if other factors are at work on the details.” The problem is that statement is conjecture and devoid of proof that in almost every year since 1750, natural emissions have not been increasing above the previous year.
In the next paragraph, you denied that natural emissions exceeding natural carbon removed would cause any accumulation and asserted that, “The total carbon level changes are determined by the net global uptake.” Before industrial carbon began being introduced, the nominal CO2 concentration was about 280 ppm. Supposing natural carbon began exceeding the previous years emissions. Wouldn’t you agree that net global uptake in those years was negative and natural carbon was causing an accumulation?
Due to the lateness of the hour, I will review your Skrable comments and reply tomorrow.
David,
Please see section 2.8 of my draft post at the top of these comments for the truth.
This section is my summary of the Delta14C data.
It proves you are wrong about the effect of human CO2, and you have never been able to properly rebut my proof.
This reminds me that you also have not been able to show your version of the simple ten-year test calculation that I put at the top of these comments.
If you can’t calculate how human carbon moves through the carbon cycle, your handwaving rants mean nothing.
But you do provide nice entertainment for the readers.
Dear Dr. Ed,
Here are my responses to your challenge:
https://www.ferdinand-engelbeen.be/klimaat/klim_doc/Ed%20Berry_challenge.docx
and the accompanying Excel sheet with the calculations is here:
https://www.ferdinand-engelbeen.be/klimaat/klim_xls/Berry_fluxes.xlsx
The Excel sheet is made very flexible, so that any change in fluxes, starting conditions and Tau is immediately calculated.
I did return the favor by asking for your calculations for the 2010-2020 period with realistic figures…
Best regards,
Ferdinand
Brendan,
Not only the fluxes between ocean surface and atmosphere are measured,
See: https://www.pmel.noaa.gov/pubs/outstand/feel2331/maps.shtml
but the resulting increase of inorganic CO2 in the ocean surface, in equilibrium with the atmosphere (with some small delay) is measured too:
https://tos.org/oceanography/assets/docs/27-1_bates.pdf
See Figure 3 and Table 2 of that work for the increase in DIC.
If the warming ocean surfaces were the source of increasing CO2 in the atmosphere, then DIC would decrease and the pH increase. Because the net flux of CO2 is reverse, DIC increases and pH decreases in all ocean surface waters where is measured…
DMA, Salby was right on that point: the Bern and similar models are wrong, because they assume an uniform ocean surface that isolates the deep oceans from the atmosphere. In reality there is a huge sink/source that directly connects both via the THC, bypassing the ocean physical and chemical restrictions.
For the rest, Salby was completely wrong on so many points (ice core CO2 migration, increase of CO2 by integration of temperature, etc.) that he simply was unreliable as source of good information.
BTW, he never was involved in discussions about his work, not a real sign of reliability…
David,
In your letter to Health Physics, commenting on Skrable’s Table 2a, you correctly note (in 1.) that cumulative industrial emissions exceed the atmospheric increase in CO2, but incorrectly infer 1) that ocean and land reservoirs could not partially have contributed to the rise in CO2 and 2) that industrial emissions are the total source of the rise. In fact, your admission, that ocean acidification (etc.) are consequences of overflow of anthropogenic carbon out of the atmosphere, explains why the industrial emissions do not accumulate to the degree you imagine. According to your Table 1, the amount of industrial carbon sinked (1,590-322) was 1,268 GTons CO2.
In the following paragraph (note 2.), You wrote, “The dilution from earlier decades’ emissions has largely been erased by mixing.” But the specific activity shown in 2000 on Skrable’s Table 2a, 12.80, is significantly less than the original 14.00 in 1750. That’s a far cry from largely being erased, no? Equating Skrable’s present day “fossil component” with only the most recent industrial emissions swaps the dilution which occurred in the years prior to 2009 with a relatively minor amount of dilution that has occurred since. Your handwaving argument seems like sleight-of-hand.
“What happens in the atmosphere does not stay in the atmosphere.” That seems more descriptive of the Skrable and Berry accounting than the scenario you promote.
Sorry for the delay… Have been working hard on the Excel flow sheets for the “Berry Challenge” and missed this in between comment.
Let us start with your first equation:
“dC/dt = ks*(Cs – Ca/K). The latter equation better reflects bidirectional transport and that the ratio of the concentrations at equilibrium equals K.”
Yes, but that reflects to concentration and thus pressure of CO2 in the atmosphere and only CO2 concentrations in water, not bicarbonates and carbonates, per Henry’s law. Pure, dissolved CO2 in seawater is only 1% of all inorganic carbon species…
The other 99% of the inorganic carbon species also play a role in the equilibria and not exactly linear. But the pCO2(aq) dependence of temperature can be calculated with the formula of Takahashi: some 4.3%/°C up or down, no matter the initial conditions of temperature or concentration.
Of course, I should have said that the formula of Feely was for the net transfer, no matter the direction, but that formula does not depend of the height of the absolute CO2 pressure in the atmosphere, only of the pressure difference with the ocean surface.
The exchange rate between atmosphere and ocean surface is so fast that the average sea surface pCO2 follows the increase in the atmosphere with only 7 μatm difference…
Dr. Ed made it clear that he calculated the absolute transfers in both directions, resulting in the net transfer between the different reservoirs. The only error left then is the use of Te of 4 years, which is completely at odds with the calculated Tau of 50 years, based on real life measurements.
That difference is caused by the fact that the main (seasonal) fluxes are not one-way from input to output, but simply reverse from output to input half the year, moreover, near completely independent of the CO2 level in the atmosphere, as ocean surface and vegetation simply switch position as source/sink.
See it as a lake where two pumped hydro power stations are at work: each pumping water up to a higher lake at the same time that the other power station uses its own higher lake water to make power. And then reversing the flows. That is hardly influenced by the water level in the lake, and the simultaneous in/outflows hardly influence the water level in the lake… Even so, the residence time, Te, is much shorter than for a lake without power stations as the outflows to the upper lakes is also brought into the equation.
Te, the residence time, is completely independent of the direction of the CO2 flows. Every outflow is counted for.
Tau, the adjustment time, highly depends on the direction of the fluxes, as only the sum of all inputs and outputs is what is of interest for the result: the net change in overall flows, caused by some disturbance in the dynamic system.
Two quite different definitions and calculations, which may give the same result, if and only if, all fluxes are unidirectional, what they absolutely not are in the real world…
The outflow of 0.5 PgC/year into the ocean surface is measured in the ocean waters as DIC, the sum of all inorganic species in the sea surface.
See: https://tos.org/oceanography/assets/docs/27-1_bates.pdf Figure 3 and Table 2 for the increase in DIC over time and compare that to the increase of CO2 in the atmosphere. DIC increases with about 10% of the increase in the atmosphere. With the about 5 PgC/yr increase in the atmosphere, DIC increases with about 0.5 PgC/year as the current atmosphere and ocean surface have near equal carbon content…
About 2.5 PgC/year is absorbed by vegetation, based on the oxygen balance.
5 PgC/year remains (temporarily) in the atmosphere and the remainder (~2 PgC/year) goes into the deep oceans. The latter is near impossible to measure directly, but tracers like CFC’s, bomb spike 14C do support these figure.
With near
Dear Ferdinand,
Thank you for your reply.
In return, I added at the top of these comments, a link to my Excel file so everyone can download it. I put the instructions in the file.
Later, I will dispute your Tau, but let’s first see how far we can go where we agree on these calculations.
That is why I made my TEST tab in my Excel file simple so we can see if we agree on the first ten years of simulated human carbon. I am using human carbon inflow of 10 PgC/year for each years. Later, after we agree on the calculations, we can use real data.
In my first test Excel image, I did not make my instructions clear enough, so you did not match my test numbers.
We are assuming that the natural carbon cycle is in equilibrium at 280 ppm. Since it does not change, we do not calcuate it here.
Here, we calculate only the human carbon cycle starting with the Year 0 bins empty. That way we can more easily compare our numbers.
In my Excel file, I show my six Te in the top three lines. After we get the same numbers in this simple calculation, then you can change the six Te in the top green cells to your numbers. The second and third green lines are not part of the calculations. They are there so we can save other Te. Let’s save the third line so we can recover my Te easily.
Then we can see how your calculations differ from mine due to the Te alone.
I am sure we will have some discussion at that point. But at least we will then know exactly what we are discussing.
Everyone is welcome to download my Excel file and then participate in the calculation discussions.
Also, the Bern model is wrong because it assumes human carbon causes all the CO2 increase. This assumption is built into its calculations.
Dear Jim,
Thank you for catching those errors. I fixed them in my word file and will update my pdf above by tomorrow.
Dear Ferdinand,
We will discuss this as we proceed through my Excel file. You will have an opportunity to show how you use this information in your carbon cycle calculation.
Ed
Jim,
Explain to me how net sinks can have “partially contributed to the rise in CO2”. In your earlier numerical exercise, you showed that natural processes could raise the quantity of “natural carbon” in the atmosphere, but only when a larger quantity of “human carbon” left the atmosphere. The only amount of carbon that matters is the total carbon. I hope you are beginning to understand that analyzing these two quantities of carbon separately is a fool’s errand. When the equivalent of disequilibrium isofluxes exchange human carbon for natural carbon without changing the levels, who cares? If the level of “human carbon” in the atmosphere today is small (and it is) that tells us very little.
You have referred vaguely to an increase in ocean outgassing with temperature, while ignoring the rising influx of carbon to the ocean simply from higher CO2 partial pressures. We agree, I think, that like the atmosphere, the surface ocean has more carbon in it now than 75 years ago. We haven’t discussed biomass, but the literature says it has grown, and there is more carbon in terrestrial biomass than 75 years ago. A recent Science article tabulated other caches of carbon : in landfills, behind river dams, etc. Where is there LESS carbon now than 75 years ago? Obviously in depleted fossil fuel reserves. Tell me if you have another hypothesis on where all the carbon is coming from.
Ferdindand,
Thanks for your reply. This discussion is reviving science I haven’t used for a while and it’s enjoyable to discuss with someone looking at things from a different point of view.
With regard to the DIC being 99% of carbon in seawater, their reactions are essentially instantaneous compared to the pCO2 [CO2]aq exchange. I don’t see how that obviates the applicability of my “expanded” Feely equation. Also, I not comfortable with your statement, “[Feely’s] formula does not depend of the height of the absolute CO2 pressure in the atmosphere, only of the pressure difference with the ocean surface.” From my PChem days, I recall partial CO2 pressure as proportional to mol fraction. Gemini says “Partial Pressure of CO2 (pCO2) = (CO2 concentration in ppm / 1,000,000) * Total Atmospheric Pressure (P_total). Feely’s net flux or mass transfer rate is proportional to ΔpCO2 which equals pCO2/Kh – [CO2]aq. As I wrote previously, mass transfer does not stop at equilibrium, only the net transfer. Therefore, mass transfer continues across the interface in proportion to the respective concentrations on both sides.
I’ll pass on commenting about Tau vs a four-year Te for now. The latter seems obvious given the recycling of about 100 ppm/year in the 420 ppm atmosphere. That’s 4.2 years. It follows logically from Dr. Ed’s model. I will continue to investigate why you and others are entertaining a 50-year Tau.
Neither I nor Dr. Ed, I presume, assume that exchanges between the reservoirs are one way. That should be obvious from his model and from my description of the air-sea transport process earlier and how it is physically similar to Feely’s equation. You seem to be stuck on the idea that this process is “near completely independent of the CO2 level in the atmosphere.” On the contrary, what drives mass transfer if not concentration gradients? Seasonal fluxes occur simultaneously on opposite hemispheres. While a warming North Atlantic is outgasing, the Southern Pacific is absorbing and vice-versa.
The lake model seems completely inappropriate to me, especially in the case of the oceans, because the “pump” is nearly totally concentration dependent. The land processes are not so clearly first-order, but surely you can appreciate the CO2 Coalition’s pictures showing the growth rate amplification due to the increasing concentration of CO2. Rather than lakes and fountains, I recommend you envision the basic diffusion model between two volumes separated by a porous membrane. With initially a greater concentration on one side, molecules diffuse across to the less concentrated side. Even before the concentrations are equal, some molecules will diffuse “up stream.” Eventually, at equilibrium, the same number of molecules on each side continue to cross the membrane. Dr. Ed’s four-reservoir model is simply an extension of this situation using the appropriate rate constants between reservoirs to account for the various interfacial barriers and material composition of the reservoirs. The only well-mixed reservoir is the atmosphere, which makes possible estimation of the average yearly inflows and outflows made available by the IPCC, which in turn allows calculation of an e-time of about four years agreed upon by just about everyone.
Your summary of the net mass transfers seems generally consistent with results of Dr. Ed’s model, based on IPCC data, with the exception of the 0.5 PgC/year outflow to the surface ocean. Does the modest 0.5 PgC/year DIC increase allow for the possibility that the majority of the 2 PgC/year going to the deep ocean came from being passed through the surface ocean?
Ed,
Jerry and Ferdinand have done a good job rebutting your confused C14 analysis in Section 2.8. But you seem to be asking for my comments and I will comply. I will be referring to figures in a recent Radiocarbon https://www.cambridge.org/core/services/aop-cambridge-core/content/view/193CDF1F705B269BC975AF178CEF1AC3/S0033822224000274a.pdf/discussion-presentation-of-atmospheric-14co2-data.pdf
The Seuss effect is easily observed prior to atmospheric nuclear testing. See Figure 1a in the above link for a falling Delta14C between 1900 and 1950. Your so-called “balance level” is nowhere to be seen. Also see Figure 1b for the C14 concentration increase during the same period. Jim can explain to you how disequilibrium isofluxes made that happen. Nature is subtle. Adding C14 devoid carbon to the atmosphere increased the C14 concentration in the atmosphere, because of those balanced exchanges!
Figure 2 shows the “bomb pulse” plotted both in terms of DeltaC14 (as you do) and in terms of concentration. You might remember that back when you thought DeltaC14 and concentration were the same thing, and I showed you a true concentration curve similar to that shown here, we both wondered what caused the concentration increase after about 2000. I know now; do you? Hint: think disequilibrium isofluxes due to balanced exchanges. Where is DeltaC14 lowest in 2020?
Figure 4 shows the usefulness of plotting concentration instead of Delta14. You can visually add up the contributions from different reservoirs. Study it and see how the bomb carbon got spread around among the various reservoirs, just as industrial carbon gets spread around today. Notice that the bomb carbon is still with us 65 years later.
David,
Ocean and land reservoirs are both sources and sinks to some degree. Depending on the magnitude in any given time period, they may be net one or the other. An obvious example is that of outgassing during a particularly hot summer in the southern Pacific Ocean. Gradually warming oceans likely mean greater outgassing year to year. Deforestation and other plant decomposition are two sources that could contribute to a rise in CO2 in any given year that the corresponding sinks are less in magnitude. But I will never convince you by these anecdotal arguments. The only way you will see how nature is contributing to the growth in CO2 is to investigate a mathematical model, input the known emissions and rate constants, and try to match the observed Mauna Loa data. I could only get a good correlation by including a growth in natural emissions or a declining sink rate. There is no physical reason to expect the latter. The former is easily explained by a warmer world and an exponentially increasing population.
You ask, “Where is there LESS carbon now than 75 years ago?”
There isn’t, at least not than can be measured quantitatively. Apparently, we both agree that the industrial carbon is not largely left in the atmosphere. Your terrestrial biomass growth is one sink. The oceans are an obvious second. The deep ocean is basically an infinite sink. We also agree on where the extra carbon is coming from. The only disagreement is on how much of the observed increase in atmospheric CO2 is caused by industrial carbon or an additional natural component.
Jim, indeed it is a matter of model…
I was looking at Ed’s model in figure 3 and that is the “classic” model of a container where all fluxes go one-way into the container, increase the level in the container and the level in the container determines the outflow. When outputs equal inputs the level remains the same.
That is the classic “lake/bath tube” model.
The most used formula for the residence time is:
Te = mass / output
For the current atmosphere:
Te = 890 PgC / 215 PgC/year = 4.1 years.
Everybody (including the IPCC) agrees on a Te of around 4 years.
The formula for the adjustment time is:
Tau = disturbance / effect
Where Tau is the time needed to reduce the disturbance to 1/e (~37%) of the initial disturbance.
That formula only is true, independent of the time period over which is measured, if the effect is directly proportional to the disturbance. That is the case for both the net uptake in oceans and vegetation.
Where the disturbance can be a one shot extra CO2 or a continuous increasing source of extra CO2, that doesn’t matter. Tau only depends of the distance of a process to the (dynamic) equilibrium of that process without disturbance.
For the “classic” one-way model, Tau is equal to Te and never can exceed Te. That is what Dr. Ed used.
If there is a cycle at work, which recycles CO2 from the outputs back to the inputs, completely independent of the level in the container, the situation is completely different.
That is the “fountain” model, where lots of water are cycling over the fountain, completely independent to the level in the basin and opening a small supply valve determines the water level in the basin.
The real world is far more like the fountain than the lake: 95% of all CO2 is just cycling in and out, largely independent of the CO2 level in the atmosphere. Only 5% is directly affected by the CO2 pressure difference between atmosphere and ocean surface waters or plant alveoles water.
How much is cycling is only of interest for the residence time Te, but doesn’t affect Tau at all, as that only depends of the net outflow into the other reservoirs and the difference in pCO2 between the reservoirs.
In the case of the “fountain” model, Tau and Te are completely independent of each other…
My colleagues and I are working on a clear overview of the differences between Te and Tau and the results for the different fluxes, including on isotopic decays and the IPCC’s Bern model.
Meanwhile, you can download the sheets that I have made for a similar discussion at a Clintel workshop in Athens last September, where things were worked out already:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/on_the_co2_residence_time.ppsx
——-
Then a few short reactions:
– One can split the Feely equation, but the difference is that the net transfer between atmosphere and oceans can be calculated from observations, while the individual in- and outfluxes are rather estimates with large error margins.
– The same for the transfer between atmosphere and vegetation: individual CO2 fluxes are very hard to obtain, but the overall net transfer is easily calculated from the O2 mass balance.
– The difference between uptake by the ocean surface and the deep oceans…
That is where the IPCC goes wrong: the Bern model assumes an uniform ocean surface at average 7 μatm below the pCO2 of the atmosphere, following the atmospheric increase very rapidly (half time less than a year).
That is true for 95% of the ocean surface, except at the main sink places near the poles, where the cold surface waters are at ~ 150 μatm and the atmosphere currently at ~425 μatm. The opposite happens at the upwelling places near the equator: ~750 μatm for water, ~425 μatm in the atmosphere. That is what drives far more CO2 into the deep oceans than in the ocean surface.
Because of the small average difference in pCO2, the large ocean pCO2 changes due to SST changes over the seasons give near the same CO2 fluxes in and out for the ocean surface, mainly in the mid-latitudes.
Further, watch the absolute CO2 transfer calculations that will follow at the end of this discussion…
Sorry, see a “Not Found” error when clicking the reference to the Excel file…
Thus can’t (yet) see what you have exactly done and how to match what you have done…
Please try this link:
http://edberry.com/excel-file/
Ten people have downloaded my file, so far.
The Bern Model assumes half the human CO2 moves out of the atmosphere with an e-time of 4-5 years but half the human CO2 has a very long e-time, many many decades. And, it assumes all the natural CO2 has an e-time of 4-5 years. I ask people if it is possible for a long e-time CO2 to become a short e-time CO2? If not what natural mechanism partitions the long e-time CO2’s and the short e-time CO2’s? And, how does one human CO2 have a different e-time than another human CO2? How can nature tell one human CO2 molecule from another human CO2 molecule? Is there a law of nature we don’t know about? How do you write a differential equation with the Bern Model as the solution?
The Bern model assumes that the different reservoirs get saturated.
That means that the uptake is quite fast, until saturation is reached and then it stops, and another (slower) reservoir must take over.
That is only true for the ocean surface, which is saturated at about 10% of the change of CO2 in the atmosphere.
That is not true for most of vegetation, that increases its growth for 93% of all (C3-type) plants up to 1,000 ppmv and more.
That is absolutely not true for the deep oceans, which are far from saturated. If all human emissions up to now ultimately get into the deep oceans, that would increase its carbon content with 1%. That would lead to 1% increase of CO2 in the atmosphere in equilibrium, or 3 ppmv. That is all.
The Bern model simply is wrong…
BTW, the Bern model and most models and our calculations look at the increase of total CO2, not at “human” CO2 alone. No matter what caused the increase of CO2 in the atmosphere…
Ferdinand,
Dr. Ed uses that simple model to illustrate what pharmaceutical scientists call a one-compartment model with intravenous infusion, dC/dt = Io/V – keC . Io is constant infusion into a constant volume V. The constant, ke, represents the “elimination” rate constant. The sign is negative, because at equilibrium, Io/V = keC representing the situation where inflow equals outflow at the constant level C. Obviously, it doesn’t apply to the multiple compartment Earth, but it illustrates the physical first-order process that governs most mass transport processes occurring in nature. Rearranging Io/V = keC gives 1/ke = CV/Io which is analogous to Te = mass/Io = mass/inflow = mass/outflow. So far so good.
Here is where you lose me. I understand disturbance can be a one-time injection or a continuous input that may or may not be constant. Tau is defined as time to reduce the disturbance to 1/e. What is e? Also, what is the “effect” that is required to be proportional to the disturbance? Finally, what are the equations that show how Tau only depends on the “distance of a process to the (dynamic) equilibrium of that process without disturbance.” I don’t understand what distance means. I interpret dynamic equilibrium as the same situation I described in my two-reservoir diffusion model where the flux is equal, but not zero, on both sides.
Dr. Ed’s simple model uses the equivalent of ke = 1/Te for explaining the concepts involved (at least I presume he does). But the full blown Berry Model uses around six rate constants to demonstrate why, using IPCC’s own estimates, H1 is false.
Using lake or fountain analogies is fine for people to get a feel for what you’re doing, I need more. What are the underlying equations? I completely reject the 95% cycling fountain model, simply because raising the water level should affect the rate of circulation. That doesn’t happen with the fountain model unless you install a feedback mechanism that adjusts the circulation to maintain the level. That is what nature is doing automatically by increasing mass transfer rates in response to the increase in concentration gradients (disturbance).
I wish you well on your progress toward a clear overview of the differences between Te and Tau.
My responses to your short reactions in same order: 1) Of course. 2) Yes, but using Berry-type models, one can draw conclusion about the individual fluxes. 3) You should be rewarded, if not applauded, for working on surface and deep ocean interactions.
Meanwhile, I will review Tau model literature.
The difference: the out that is recycled has zero influence on the water level in the lake.
The water that that gets the overflow of the basin is removed out of the lake, thus influences the water level…
Sorry, but that is not what Figure 3 shows. Figure 3 shows all fluxes in one direction: from ins to container to outs.
Neither is the calculation of the real adjustment time based on Figure 3, but on the net removal of CO2 out of the atmosphere, which is around 50 years. The residence time of about 4 years is based on the sum of all outflows together, not the net outflow…
Jim,
With all respect, I think a program to add up all the natural emissions AND THE NATURAL ABSORPTIONS OF ALL CARBON TYPES is hopeless. The indirect measurement of absorption – emissions, deduced from industrial emissions – atmospheric accumulation and appropriately called “net global uptake”, is the best that we can hope to do. The data on that is solid; see the previously referenced Ballantyne et al. Nature article and the tight constraints on this quantity, especially when integrated over 50 years.
I am puzzled by your statement “We also agree on where the extra carbon is coming from [ fossil fuel reserves]. The only disagreement is on how much of the observed increase in atmospheric CO2 is caused by industrial carbon or an additional natural component.” If we agree that moving carbon previously sequestered in oil/gas/coal reserves into the atmosphere, and from there into ocean and biomass stocks, (i.e. into the fast cycle), aren’t we done? Apparently, you think that the industrial carbon content of the present atmosphere is relevant, even though you understand that equilibrium isofluxes (essentially mixing) erases past differences without effecting carbon levels. Yes, I am puzzled.
Dear Uncle Bert,
You said “the fluxes between ocean surface and atmosphere are measured”
Your PMel reference cites Feely et al which states 940,000 measurements of surface water pCO2. This is pCO2 not CO2. And they are not measurements. pCO2 is estimated/calculated for the entire ocean using actual CO2 measurements from land based stations. This is politicised junk science, just what I expect from you. A wild goose chase.
Then you get carried away with the DIC. The only scientists that I see researching DIC are those pushing climate alarmism. What’s happening in the DIC is microscopic compared to what’s happening with the dissolution of CO2 in the ocean waters. Most CO2 in the ocean is CO2Aq. Your discussion on the DIC is nothing more than a side show waffle.
The hydration equilibrium constant for carbonic acid at 25 °C is Kh = [H2CO3]/[CO2] = 1.70 × 10−3. Hence, the majority of the carbon dioxide is not converted into carbonic acid, but remains as CO2 molecules. In the absence of a catalyst, the equilibrium is reached quite slowly.
https://www.sciencedirect.com/topics/chemistry/carbonic-acid
R.C. Ropp, in Encyclopedia of the Alkaline Earth Compounds, 2013
5.1.1 Carbonic Acid
Indeed there are about 2,000 CO2 molecules for each H2CO3 (carbonic acid molecule) in water
“Aquatic Chemistry Concepts” by James F. Pankow.
In reality, the conversions between the three forms of Dissolved Inorganic Carbon, CO2 or H2CO3, HCO3- and CO3– are almost instantaneous (less than one minute)
Veyres, C., Maurin, J. Cl. Revisiting the carbon cycle International Journal of Earth Sciences Vol. x, No. x, 2021, pp. x-x. doi: 10.11648/j.xxx.xxxxxxxx.xx.
When I pop the top off my 20 year old Dom Pérignon I don’t have to wait for an eternity for the CO2 to fight it’s way out of the DIC, the CO2Aq bubbles out instantly.
Your comments are specious waffle.
David,
People have been working on mathematically accounting for all the carbon for a long time. Skrable and Berry are not the first. Simple math is not “the best that we can hope to do.” As I wrote before, simple math is ambiguous.
Here are a couple papers in my “file” on carbon dioxide models. “A box diffusion model to study the carbon dioxide exchange in nature,” H Oeschger et al., 1974. Even earlier, “Changes in the Carbon Dioxide Content of the Atmosphere and Sea due to Fossil Fuel Combustion,” Bolin and Eriksson, 1959.
“…aren’t we done?” We can quit anytime as long as you admit defeat! (Just kidding). Communication is a miracle, one of my mentors used to say.
This whole discussion is about how much of the increase in CO2 since the beginning of the industrial era has been CAUSED by industrial emissions. Some, like you I gather, think all 33% was caused by them. Dr. Ed is claiming only 8% percent. I have tried to explain how the growth in natural emissions since 1750 may account for the other 25% of the rise by increases in ocean out gassing and extra decomposing vegetation due to population growth. In other words, in 1750, I estimate natural emission recycling was on the order of 136 PgC/year. Today it could be 204. Let me know if you are still puzzled.
Jim,
The simple math shows unambiguously that natural processes remove more carbon from the atmosphere than they add. Your calculation showed that in the process of LOWERING total carbon in the atmosphere, natural process can add “natural carbon” at the expense of “industrial carbon”. So what? Both are greenhouse gases.
Now you say “extra decomposing vegetation” is a source of atmospheric carbon growth. You must be a disciple of that crazy Greek hydrologist, Demetris Koutsoyiannis, who says the same thing. Do you think trees make carbon? No, they do not. They remove it from the atmosphere when they are growing and return it to the atmosphere when they die and decay. The little formula defining “net global uptake” incorporates carbon conservation. You need to ask yourself in all the instances where you identify possible emitters, what the source of the carbon they emitted was. That too enforces carbon conservation. If you discipline yourself to do that you will be a step ahead of Ed and Demetris.
David,
“So what, both are greenhouse gases” is not the topic of this discussion, which is H1. Whether or not increasing CO2 causes global warming would be H2.
I haven’t seen the work of Koutsoyiannis, but I’m going to add him to my todo list, because I need to be able to document reality to support my speculations. Thank you for that. Compared to 1750, today there are 8 times more people in the world cutting down trees and plowing fields, which may prematurely release CO2 into the air. Thus adding more CO2 than would otherwise be if nothing had changed since 1750.
Asking myself what the source of the carbon was from all of the emitters is the discipline of carbon cycle modelers. I’m way behind Ed and others and trying to catch up. I encourage you to get in the game. It’s hard, but fun.
Dave A, that’s all very obviously correct, but who is “DMA”?
Jim,
Please read some peer-reviewed science too. I am sorry I put you on to Kousoyiannis.
Dave B,
I do not know who DMA is; just somebody who follows Ed. My middel initial is E.
The CO2 Coalition’s cavalier attitude towards the rest of climate science bothers me. Celebrating atmospheric CO2 as plant food and ignoring its warming effects bothers me. I do not think that our present atmosphere is necessarily “optimal” for humans, but change can be very costly even if we are not facing an “existential” threat. I am more conversant on the carbon cycle issues than on radiative forcing, etc., but I see flaws in Happer’s saturation argument. “Extreme weather” problems, especially involving the increased water content of tropical storms, seem to me very likely real and linked to CO2. The poor quality of the denier arguments that I have focussed on, ever since stumbling on the Berry/Harde/Salby confusion between deltaC14 and concentration, makes me very skeptical of other skeptics and inclined to believe the consensus. After all, predictions made 25 years ago turned out to be quite accurate. (Predictions were on the high side for awhile, with the warming perhaps masked by sulphur aerosols, but not any longer.)
Brendan, I have no idea who Uncle Bert is, but what part of the formula:
F = k•s•DeltapCO2
don’t you understand?
From Feely: http://www.pmel.noaa.gov/pubs/outstand/feel2331/maps.shtm
From the next section:
“This map yields an annual oceanic uptake flux for CO2 of 2.2 ± 0.4 PgC/yr.”
And dissolved CO2 + H2CO3 together are only 1% in seawater, 90% are bicarbonates and 9% are carbonates. High time to refresh your chemistry. Learn here about the Bjerrum plot:
https://en.wikipedia.org/wiki/Bjerrum_plot
My thoughts on Tau vs Te after considering comments provided by Ferdinand Engelbeen. Tau equals disturbance / result (outflow) which means, when applied to ocean atmosphere fluxes, Outflow = [pCO2(atm) – pCO2(ocean)] / Tau. Generalizing this formula to carbon distribution between the atmosphere and its adjoining reservoirs requires a huge assumption which I believe is untenable. The assumption used by some researchers seems to be that the disturbance is proportional to the level difference, or pressure difference, between the existing level or pressure and what that level or pressure was in pre-industrial times. In other words, pCO2(now) – p(CO2)then. Roy Spencer writes, “[My] model assumes an anthropogenic CO2 source, and a constant yearly CO2 sink rate proportional to the excess of CO2 over a baseline equilibrium value determined by the Mauna Loa data.” https://www.opastpublishers.com/open-access-articles/enso-impact-on-the-declining-co2-sink-rate.pdf
Dr Spencer obtains a best fit to the Mauna Loa data using a “net” sink rate, 0.02/year, of the difference in the CO2 concentration in a given year compared to a fitted 1750 “baseline” value. That “net” amount is actually the relatively small difference between yearly input and outputs that are two orders of magnitude greater than their difference. The flaw in any model using a “baseline” is that the atmosphere does not remember what its “baseline” value was. It is extremely likely that pCO2(atm) and pCO2(ocean) may never return to their pre-industrial values. The only levels nature remembers are the ones they experience in the present time and places. There is no going back to the way things were in 1750 or 1850 or any other year in the distant past.
How does this affect calculations of Tau? If new baseline equilibrium levels were to be estimated today based on the current magnitude of inflows and outflows, assuming no further perturbations from fossil fuel emissions, then two possible situations remain. Either the baseline remains unchanged from some pre-industrial date, or a new baseline results at greater levels of inflows and outflows. I don’t think lesser levels are realistic given the growth in world population. In the former case, Tau would remain about the same as Dr Spencer predicts at 50 years, i.e. (420 – 280) ppm * 0.02/year = 2.8 ppm/year. But what if the baseline equilibrium is greater than 280? For example, a baseline of 320 ppm makes Tau = 1/0.028 or about 36 years. Therefore, Tau is overestimated if baseline equilibrium conditions have evolved due to increasing natural flows.
It makes sense that estimations of Tau vary widely among researchers. No one really knows what the current equilibrium level is or will be.
More specious waffle from Uncle Bert.
Ferdinand Engelbeen reminds me of the singer Engelbert Humperdinck who I always called Uncle Bert for short. I always shorten long names.
Uncle Bert previously said CO2 over the oceans was measured now he agrees that it is calculated and based on CO2 measurements over land.
And he’s dived back into the DIC for another wild goose chase.
Jim Silverly
You said:
“It is extremely likely that pCO2(atm) and pCO2(ocean) may never return to their pre-industrial values. The only levels nature remembers are the ones they experience in the present time and places. There is no going back to the way things were in 1750 or 1850 or any other year in the distant past.”
CO2 rose to 450ppm twice during the last 200 years from instrumental measurements accurate to 1%-3%
See the chart at https://www.researchgate.net/publication/366823612_Lunar_Forced_Mauna_Loa_and_Atlantic_CO2_Variability/figures?lo=1
which is Figure 2 from:
Yndestad Harald, 2022b: Lunar Forced Mauna Loa and Atlantic CO2 Variability; Science of Climate Change, Vol. 2.3 (2022) pp. 258-274; https://doi.org/10.53234/scc202212/13 ; https://scienceofclimatechange.org/wp-content/uploads/Yndestad-2022-Lunar-Forced-CO2-Variability.pdf
CO2 also rose to 400ppm 12,000 years ago based on Stomata proxy measurements.
Steinthorsdottir 2013
The ice core proxy is very monotonic and does not show all the up and down extremes in CO2 measurements.
I just finished reading Koutsoyiannis, Demetris & Johnson, Mark. (2024). The superiority of refined reservoir routing (RRR) in modelling atmospheric carbon dioxide. https://tinyurl.com/bdd4fhyb
Their equations in Annex A. explain in detail the difference between Tau and Te; they support my view that a sink rate proportional to [pCO2(now) – p(CO2)then], although empirically based, “may be a result of the coincidence of increasing human and natural CO2 emissions. The latter, caused by the biosphere expansion, are totally neglected in this relationship.”
My thanks to David Andrews for introducing me to this work. It seems to support Dr. Ed’s multi-compartment analysis and the conclusion that H1 is false.
Happy Fourth of July, all.
Brendan, a calculated flow, based on quite good observations is as valid as direct observations. These observations were over all oceans: some 960.000 to be exact.
And all you have demonstrated is your complete lack of understanding chemical equations.
And please, shouting at someone only shows that you have no real arguments.
Jim,
Indeed here we are at the crux of the matter. Thanks for your insight!
You have noticed the right difference between Te, used by several skeptics and Tau as used by several other skeptics and most “mainstream” scientists, including the IPCC.
Now the main remaining point is what happened with the equilibrium in current times.
From the past (ice cores) we know that the equilibrium changed with Antarctic temperatures at about 8 ppmv/°C or for global temperatures somewhere between 15-20 ppmv/°C. CO2 are direct measurements, be it averaged over 560 years (Dome C) and 600 years (Vostok), while T is derived from dD and D18O and mainly reflect the temperature where the snow was formed, thus near Antarctica.
https://www.ferdinand-engelbeen.be/klimaat/klim_img/vostok_t_co2.png
The discrepancies with the trend are largely caused by the (very) long lags of CO2 changes after T changes, especially during cooling periods, for which is not compensated.
Higher temperatures on land in general increase vegetation (more land available), that is a negative feedback for CO2.
For recent temperatures, we have the formula of Takahashi to calculate the change of CO2 as result of SST changes.
That gives not more than 13 ppmv since the LIA and 3 ppmv since 1958. The real increase since 1958 is over 100 ppmv together with 170 ppmv human emissions over the same period…
Then the possible increase of the equilibrium over the past decades.
That is completely true for about 90% of the sea surface: the pCO2 of the ocean surface follows very closely the pCO2 of the atmosphere. That means that the ΔpCO2 remains about the same (currently at ~7 μatm) and, together with chemical restrictions, that is reflected in the small increase of DIC at about 10% of the change in the atmosphere. For the current increase of about 5 PgC/year in the atmosphere, most of the ocean surface absorbs ~0.5 PgC/year.
That is not what happens at the extremes of the oceans: at some 5% of the ocean surface, the waters are sinking directly into the deep, due increased density from to low temperatures and salinity. That is at the edge of the sea ice, where SST is slightly negative. pCO2 there reaches ~150 μatm, far below the atmosphere. Moreover, that hardly changes over time, as long as there is sea ice. The same at the other 5% of the ocean surface, where deep ocean waters are upwelling, the temperature hardly changes (thanks to clouds!), thus the pCO2 remains high at around 750 μatm. That means that the equilibrium pCO2 between atmosphere and deep oceans hardly changed over the past few millions of years…
The difference between ocean surface and deep oceans is demonstrated by the difference in CO2 uptake: with only about 5% of the sea surface, the deep oceans absorb some 2 PgC/year, 90% of the surface absorbs only 0.5 PgC/year…
See: https://www.ferdinand-engelbeen.be/klimaat/klim_img/bern_balance.png
Thus, besides the straight forward linear uptake by vegetation, the ocean uptake also remains linear with the “old” equilibrium…
Jim,
Further, the rather stable equilibrium pCO2 of the oceans (and vegetation) is demonstrated by the small changes in Tau over the period 1958-current.
The total emissions are known, these are the cause of the CO2 increase in the atmosphere, but play no role in the pCO2 difference between atmosphere and the rest of nature.
The only assumption is that the base equilibrium since 1850 changed with SST with the formula of Takahashi. If one disagrees with that base, one can start with SST and CO2 in 1958, which makes hardly any difference:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
Where [A] is the sum of all FF emissions (without land use changes), the observed increase in the atmosphere, the calculated influence of SST on the pCO2 of the oceans and the resulting ΔpCO2 between atmosphere and oceans.
[B] is the observed net sink rate and
[C] is the calculated Tau, based on the polynomial through the net sink rate, to avoid the influence of short time SST variations.
Jim,
In recent discussions with Koutsoyiannis (last September during a workshop in Athens for Clintel) he used temperature anomaly as the base for his calculations of the CO2 increase/year. Temperature(anomaly) is of a different order than the CO2 increase/year, but has the same variability as temperature change/year, with a pi/2 shift. T(anomaly) has a slope, while T(change)/year has not:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/wft_T_dT_dCO2_trends.jpg
WfT has the emissions not in their database, but the slope is about twice the slope of the CO2 increase in the atmosphere…
Not the first to use T(anomaly) as base and use its slope to calculate the increase in the atmosphere, while ignoring the twice as fast increasing slope of human emissions…
The net effect of his calculations violate the carbon mass balance, but can be corrected by increasing the natural sinks:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/demetris_1b.png
The increase in the atmosphere may be between 100% natural and 100% human. In the latter case, the net natural contribution is the net sink rate in nature. In the former case, the total sinks remove every gram of what humans have added (as mass, not the only the original FF molecules) out of the atmosphere. Quite remarkable.
In that case, net natural sinks are twice the net natural addition in the atmosphere. So how can nature be the cause of the atmospheric increase?
Then, have a look at table 4:
He calculates the residence time from both the change in temperature over the seasons, and from the year by year variability: both between 3 and 4 years. Except that the seasonal change of CO2 is negative for temperature and the year by year change positive… That makes no difference for the residence time, but makes a huge difference for the adjustment time…
Then in equations [66] and [67] he calculates the remaining human CO2 in the atmosphere. He gets around 6%, Harde found about 10%, based on the 13C/12C ratio. While Harde is right, that only shows the remaining FF molecules in the atmosphere, not what the IPCC says as “airborne fraction” which is about the remaining total mass of CO2, caused by FF emissions (the difference being exchanged with CO2 molecules from other reservoirs).
And how can he explain that only 1.5 to 5% of FF in the supply 1960-2020 causes over 10% FF in the atmosphere in the same period with his one-way supply?
Below equation 48 he writes:
“Proposition 1. The IRF equals the probability density function of the residence time for the case
that the input is an impulse function.
Corollary 1. The mean and median response time equal the mean and median residence time for
the case that the input is an impulse function”
Which is only true for a one-way “classic” input-container-output (“lake/bad tube”) model.
Completely at odds with the real world, where 95% of all CO2 fluxes are independent of the pCO2 in the atmosphere…
Dear Ferdinand,
Thank you very much for your many explanations of your hypothesis that says human CO2 caused all or most of the CO2 increase.
Thank you also for your response to my request to show your calculations in my suggested Excel format. My two takeaways are:
(a) that you acknowledge that this method of doing a time-step calculation is valid (and not an Invalid “model” as Dave Burton has called it) and
(b) Your numbers indicate that our major difference is in the Te that we insert for our calculation.
Of your many links, I recommend this one as your best summary of your argument in 42 slides:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/on_the_co2_residence_time.ppsx
With all your work, you deserve a thorough reply to your argument, so I will try to do that in my next comment and in an update in my draft post above. I will show that your arguments, as summarized in your 42 slides — that conclude the true Te equals a tau of 50 years — will not fly.
After that, I will get back to the comments of David Andrews and others. But since your work is the focus of my post, you deserve my priority to recieve my best repies to your comments.
Ed and Jim,
The net effects of the differences between Te and Tau demonstrated for the past 175 years…
For the current atmosphere:
Dynamic equilibrium: for the current average SST, the equilibrium pCO2 between ocean surface and atmosphere would be around 295 ppmv. Can be calculated with the formula of Takahashi [1], if an equilibrium of the past is known. Some 13 ppmv since the LIA (worse case for the largest T increase reconstruction). Some 10 ppmv since 1850 and a few ppmv since 1958, if one doesn’t trust ice cores…
Situation in 1850 (IPCC, 2013):
628 PgC in the atmosphere
Sum of outputs: 168,4 PgC/year.
Net output: 0 PgC/year.
Te = 628 / 168.4 = 3.7 years
Tau = N/A
Situation in 1960:
673 PgC in the atmosphere
Sum of outputs: ~180 PgC/year [2]
Net output: 1.0 PgC/year
Te = 673 / 180 = 3.7 years
Tau = (673 – 628) / 1.0 = 45 years
Situation in 2020:
880 PgC in the atmosphere
Sum of outputs: ~236 PgC/year [2]
Net output: 4.7 PgC/year
Te = 880 / 236 = 3.7 years
Tau = (880 – 628) / 4.7 = 53 years
Looking for the zero net output (that is the equilibrium):
CO2(eq) = CO2(2020) – [CO2(2020) – CO2(1960)] / [Fnet(2020) – Fnet(1960)] * Fnet(2020)
CO2(eq) = 880 – [880 – 673] / (4.7 – 1.0) * 4.7 = 617 PgC
or about 290 ppmv. Not far from the situation in 1850. Not bad for a rough calculation.
The same calculations were done by Peter Dietze (1997!), Lindzen, Spencer and myself years ago…
My colleague, David Burton, used all recent figures to calculate the zero-net-sink equilibrium CO2 level at:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Then what is the real CO2 outflow caused by the absolute CO2 pressure in the atmosphere?
Also easy to calculate even with only two observations at 1960 and 2020:
F(abs) = 880 / (880 – 673) * (4.7 – 1.0) = 15.7 PgC/year.
Some 16 PgC/year of the CO2 outputs from the atmosphere into oceans and vegetation together is caused by the absolute CO2 pressure in the atmosphere. The rest of the over 200 PgC/year outputs are completely independent of the CO2 level in the atmosphere…
[1] (pCO2)seawater @ Tnew = (pCO2)seawater @ Told x EXP[0.0423 x (Tnew – Told)]
http://www.sciencedirect.com/science/article/pii/S0967064502000036
[2] Assuming that the outflows increase with the increase in the atmospheric, but also the inflows, thus only speeding up the cycles.
According to the IPCC, that is true for the ocean surface (but haven’t seen any explanation why that should be), but the expansion of the biosphere, and thus the expansion of the short seasonal bio-cycle, is a lot slower than the increase in the atmosphere, about half of it…
Thanks Ed,
Only one remark:
Te and Tau are completely different things:
Te is how long a single CO2 molecule (of whatever origin) resides in the atmosphere, before being completely removed (as mass) or exchanged with a CO2 molecule of another reservoir (no change in mass).
Tau is how long it takes to reduce a (one-shot or continuous) extra injection of CO2 as mass (of whatever origin) out of the atmosphere, back to (dynamic) equilibrium.
Tau is <= Te only if all in- and outflows are unidirectional (that is the "lake / batch tube" model)
Tau is completely independent of Te if cycles are involved that bring back CO2 from the outputs to the inputs (that is the "fountain" model).
I am working further on the spreadsheet to put it in about the same form as you have made…
Brendan,
I have had years of discussions with the late Ernst Beck about the historical measurements, until his untimely death in 2010.
The historical measurement methods were not too bad (+/- 9 ppmv), but where was measured was a mess. Midst of towns, forests,… completely unsuitable to know the real “background” CO2 levels of that time.
The late Ernst Beck lumped them all together: the good, the bad and the ugly. The real range of measurements was from near the bottom of the graph to (far) over the ceiling.
When one did choose only the measurements over the oceans or at the coast, with wind from the seaside, all these measurements are on or below the ice core measurements:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/beck_1925_1955.jpg
With one exception: at a slope of the Alps where was measured in the morning and extreme CO2 values were found.
To show the problem: there is a modern station at Linden/Giessen (Mid-West Germany) at a few km of the historical station that makes the largest influence on the CO2 “peak” around 1940.
Here for a few days under inversion, compared to the same (raw) data of Barrow, Mauna Loa and the South Pole:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_background.png
Stomata data are local proxies which are calibrated to ice core values. If the average differs from the ice core values over the resolution of the ice core, then the stomata data must be recalibrated. Not reverse…
See further my comment of Beck’s latest, posthumous published work:
https://scienceofclimatechange.org/ferdinand-engelbeen-about-historical-co2-levels-discussion-of-direct-measurements/
Ferdinand,
I appreciate your kind remarks and responses to my suppositions.
At JULY 4, 2025 AT 1:42 AM, with regard to 90% of the sea surface you wrote, “ΔpCO2 remains about the same (currently at ~7 μatm)” and, for the other 10%, “equilibrium pCO2 between atmosphere and deep oceans hardly changed over the past few millions of years.” With respect, those are arguments by assertion. The obvious rebuttal is the fact that the surface ocean contains about 10% more carbon than it did pre-industrial. Somewhere recently I read where terrestrial mass is also increased, in other words, more vegetation to decompose. In the words of Koutsoyiannis and Johnson, the result is biosphere expansion. Therefore the “disturbance” decreases with time, but the amounts sourced and sinked increase yearly due to the always increasing driving force of extra carbon in the air. You could call my comments just assertion also, but I worked on a spreadsheet that I copied from Dr Spencer modified by changing Tau to Te and adding in realistic sources and sinks. It accomplishes the same results as models based on Berry, Skrable, Bolin & Erickson, and many others. Those models work, because the flow rates in nature stay relatively constant while the reservoir concentrations evolve. There is no need to explain why Tau wanders all over the place.
JULY 4, 2025 AT 2:54 AM you wrote, “Further, the rather stable equilibrium pCO2 of the oceans (and vegetation) is demonstrated by the small changes in Tau over the period 1958-current.” What stable equilibrium? The anomalous disturbance that ebbs and flows all the time everywhere? I propose small changes in Tau are an artifact of your flawed model.
“The total emissions are known, these are the cause of the CO2 increase in the atmosphere, but play no role in the pCO2 difference between atmosphere and the rest of nature.” I assume by this you mean the remaining industrial emissions playing a negligible role? This makes no sense. The addition of industrial carbon and possible incremental increases in natural emissions CREATE the pCO2 difference that causes nature to return to a new equilibrium. Perhaps you could summarize the equations that produce graphs A, B, and C. I’m working on a way to demonstrate how the simple math you and David Andrews rely on can give ambiguous results based on somewhat arbitrary choices of variables.
Ferdinand,
Apparently, Koutsoyiannis’ Research Gate article is not the one you referenced above. I’ll try to locate it and explain why you may have incorrectly concluded, “The net effect of his calculations violate the carbon mass balance….” Different models can account for the same mass balance data. What is important is using equations that employ the correct physical processes involved.
DEAR Dr. Ed
The carbon dioxide molecule excited by the IR photon loses its charge in max. 1 secundum and is capable of absorption again. This is a fact! So what are the prominent representatives of climate science arguing about?
Csaba Huszar
If the total emissions is the sum of each of the individual emissions: Et= E1+E2+E3…., and Quantity (Q) in the atmosphere is what is there now plus the total emissions minus the total sinks. It seems very reasonable to say that sink rate for the total would match the rate of sink for each individual emission source.
The crucial point of this discussion is: If we reduce our emissions will it cause the growth in Q to stop?
Dr. Ed’s approach says NO, only slow slightly. The opposition approach says YES. Both sides here seem to agree that growing CO2 concentration is not a problem but if Dr. Ed’s work is correct and it would certainly be a huge hurtle for those that espouse Net Zero.
The irony is that all this fuss about burning fossil fuels (CO2 increase) is a huge mistake. The only greenhouse gas that has a significant effect on climate is water vapor. Global WV is measured by NASA/RSS and the trend has been increasing about 1.4% per decade which is substantially faster than possible from just temperature increase of the planet (net effect of all forcings and feedbacks). WV has increased more than 3 molecules (more than 5 at ground level) for each molecule of CO2 increase. The WV increase is substantially more than possible from just planet warming (more than twice as fast). The WV increase can account for all of climate change attributable to humanity with no significant net contribution from CO2. https://watervaporandwarming.blogspot.com
The atmospheric process that partially explains why CO2 increase has no significant effect on climate is documented at Theory of Redirected Energy: https://energyredirect3.blogspot.com
Ferdinand,
I looked briefly at the parts of https://www.mdpi.com/2073-4441/16/17/2402 that relate to your critique of Koutsoyiannis’ model.
“…he used temperature anomaly as the base for his calculations of the CO2 increase/year.”
Including a temperature factor in one’s analysis makes sense, although I suspect he doesn’t use that to conclude all of the rise in CO2 is due to temperature. That would be the equivalent of saying nature causes all of the rise.
A “twice as fast increasing slope of human emissions…” compared to the temperature anomaly slope is arguing causation by correlation.
“So how can nature be the cause of the atmospheric increase?”
What my primitive model (converting Roy Spencer’s Tau spreadsheet to Te version) indicates is that natural emissions since 1750 have been increasing logarithmically from about 70 ppm in that last pre-industrial century to about 90 ppm today. Almost all of that is sinked each year. However, the net gradually increases each year. The explanation is, as we have discussed, an expanding biosphere. The oceans contain more CO2 and they are warmer. People have prematurely cut down trees and them decomposing and being burned creates extra emissions that otherwise wouldn’t have been without human’s influence.
Skipping down to your last point, a Proposition 1 and Corollary 1 being “only true for a one-way ‘classic’ input-container-output (‘lake/bad tube’) model [and] completely at odds with the real world, where 95% of all CO2 fluxes are independent of the pCO2 in the atmosphere…”
Koutsoyiannis’ model seems to be along the same lines as the multi-component models of Dr. Ed and others like that. Again, they are using rate constants applicable to real world flows/fluxes in each direction. They account for the amounts and concentration of CO2 in each reservoir. There is no need to deal with an adjustment time, because no one knows what the future holds as far an unsure of changes in industrial emissions and probably natural sources too.
“Large parts of the carbon cycle are just cycling in and out of the atmosphere, largely independent of the CO2 level in the atmosphere.”
This is the Bern Model. This makes no sense. The carbon cycle is CO2. Nature cannot differentiate CO2 molecules. As Dr. Berry described in his first paper, it violates the Equivalence Principle. Te is “e folding time.” Tau is “Bern Time” for a sink that doesn’t exist.
I agree CO2 in and out Sets a balance that varies over the years however for me the argument is CO2 has a diminishing effect on heat as concentration increases. The only method of transferring energy through space is radiation and this decreases on a log base after the first 20ppm. It’s written up by the university of Pensylvania that over 340ppm no measurable heat was found, ergo more CO2 has an insignificant effect on temperature. That being so net zero will have no appreciable effect CO2 is not a problem. I understood from Prof Happer that CO2 has little effect as concentration increases. Perhaps his point is that even if man converts oils or coal any increase is without importance on Global temperatures?
Ed, you keep insisting that we err by ignoring anthropogenic removals of CO2 from the air. But that’s not an error, it just reflects what the data show: that anthropogenic removals are negligible.
Approximately 59 kt (= 0.059 Mt = 0.000059 Gt) of CO2 per year are removed from the atmosphere by Direct Air Capture projects, worldwide. That’s about 0.00015% of anthropogenic emissions. That’s obviously negligible. Those projects are scams.
Approximately 50 Mt (= 0.050 Gt) of CO2 per year is captured and stored by operational CCS facilities, but 99.9% of that is captured at the sources, so it’s really avoided emissions, not removals. But I suppose you could make the case that if estimated emissions are calculated from fossil fuel use then carbon capture at sources should be counted as removals. Still, that’s less than 0.2% of anthropogenic emissions, which is insignificant compared to the error bars.
What else? Cement carbonation?
According to GCB (2024), cement carbonation is estimated to remove about 214 MtC from the atmosphere per year, globally, which is about 0.784 Gt of CO2. (The claimed uncertainty is something like ±20%, but that’s surely optimistic.)
That’s conventionally considered a natural removal process, but you could make a good case for calling it anthropogenic removal. But it’s only about 2% of anthropogenic CO2 emissions, so even that is still much smaller than the error bars on anthropogenic emissions.
What else? Lumber?
Lumber production is roughly 2 billion cubic meters of wood per year, which contains about 2 PgC. That’s equivalent to the carbon in (2 × 3.66419 =) 7.3 Gt CO2. That’s a lot, but it’s carbon which was already removed from the atmosphere by trees (nature). That is, it’s carbon moved from a different “carbon reservoir” (the terrestrial biosphere), not from the atmosphere.
What else? Other agriculture?
Crops remove a great deal of carbon from the air. On a windless, sunny day, a healthy cornfield can almost completely deplete CO2 from the air at ground level by noon! But the nearly all of carbon removed from the air by crops (other than lumber) is soon returned to the air, through decay and digestion.
The bottom line is that anthropogenic CO2 removals from the atmosphere are roughly zero. Or, more precisely, they’re much smaller than the uncertainties in anthropogenic emissions of CO2, so they can be ignored in our calculations.
If you think that’s wrong, then tell me: what other anthropogenic processes do you think remove CO2 from the atmosphere?
Data references:
https://sealevel.info/Global_Carbon_Budget_2024_v1.0_with_ten_yr_avgs2.xlsx
https://www.perplexity.ai/search/globally-how-much-carbon-did-c-sWWftiSbTrqTCQyc8S2sfQ
Stephen,
The Bern model is as bad as Ed’s model, both are completely at odds with reality.
Ed’s model assumes that all CO2 inputs together cause the level in the atmosphere and the level in the atmosphere causes the outputs. That is the “classic” lake/bath tube/container model, where all inputs are unidirectional through the container to the outputs.
Te then is the time that any molecule of CO2 resides in the atmosphere, before being removed out of the atmosphere.
Te = mass / output
Te = ~4 years
In the real atmosphere 95% of all CO2 flows are just cycling between oceans – atmosphere – vegetation in spring/summer and back in fall/winter. These move large amounts of CO2, but remove zero CO2 mass out of the atmosphere, as long as the fluxes from oceans to vegetation and back are equal.
That is the “fountain” model: huge masses of water cycles over the fountain, but the level in the basin only changes when the small supply valve is opened by the maintenance man.
These are not equal anymore: humans add increasing amounts of CO2 directly into the atmosphere, one-way, without appreciable human induced sinks. That adds to the overall level of the atmosphere. The increase in CO2 level pushes more CO2 into oceans and vegetation and reduces the ocean output to the atmosphere.
These amounts are much smaller than what the temperature and sunlight do for the natural fluxes: that is the difference between all huge natural influxes + human influx – (natural + human) outflux. Where one can fight over what the “human outflux” is, but that is completely unimportant.
What is important, is that the net total outflux is smaller than the total influx. The increase in the atmosphere is smaller than the human input, thus the mass balance (and any bookkeeper worth his money) shows that the small increase in the atmosphere is from the human input.
That difference between inputs, outputs and what remains as mass in the atmosphere forms the “adjustment” time, that is the time to bring any extra CO2 (of whatever source) in the atmosphere above the “old” equilibrium (for the current average SST around 295 ppmv) back to 1/e (~37%) of the original extra CO2.
The formula for adjustment time (Tau) for a linear process is:
Tau = disturbance / effect
Where the disturbance = the distance to the equilibrium and effect = the net removal rate of CO2
And is currently around 50 years.
See: https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
The Bern model assumes different Tau’s for different reservoirs, which combined gives the right answer at the start, but then assumes saturation of all reservoirs at different levels, which is only true for the ocean surface, not until over 1,000 ppmv for vegetation and non-existing for the deep oceans. That makes that the alarmists speak about “hundreds to thousands of years” to remove any extra CO2 above equilibrium.
Dr. Ed,
Was (and still am) busy with the calculation sheet and did just read your reply to David.
Sorry, but you are getting much too personal, while simply ignoring what David wrote.
Our work was read by a lot of people, including Will Happer and many others, before being published.
The adjustment time of near 50 years is exactly what happens with the extra mass of CO2 in the atmosphere and that was found by Peter Dietze, already in 1997, in a discussion with the inventor of the (faulty) Bern model, Fortunat Joos:
https://www.john-daly.com/carbon.htm
and the discussions with Joos and others:
https://www.john-daly.com/dietze/cmodcalc.htm and
Many others, including known skeptics like Lindzen and Spencer found similar adjustment times.
Your calculations are about the 4 years residence time which only shows how long an individual CO2 molecule “resides” in the atmosphere, before being removed or swapped with a CO2 molecule from another reservoir. In the latter case, that doesn’t remove one gram of CO2 out of the atmosphere, as long as ins and outs are equal. 95% of all CO2 fluxes just swap molecules, 5% is what humans add and only 2.5% is what the fluxes do remove as mass out of the atmosphere…
Jim,
I know of the difficulty of dealing with huge cycles and small one-way additions…
There is indeed one and only one possibility that the natural fluxes are the cause of the increase in the atmosphere: if, and only if, they increased in exact the same ratio as the human emissions.
If that is not the case, then you violate the equivalency principle for any CO2 molecule in the atmosphere.
Human emissions increased a 4-5 fold between 1958 and current. Total flows (natural + human) increased maybe 50% or 1.5 times for the ocean fluxes (for which I didn’t find any explanation) and some 20% in vegetation. Thus the only possibility for a natural caused increase is rejected.
Indeed the biological cycle moves a lot of CO2 in and out and increased a lot, but as said before:
1. It removes first and releases only what was first removed out of the atmosphere, most of it diurnal and seasonally and a little bit over longer periods (mostly 1-3 years and the rest longer).
2. A cycle doesn’t net remove anything, only the difference between ins and outs does change the content of a reservoir.
3. The total biosphere since about 1990 is increasingly removing more CO2 than adding to the atmosphere.
Then all one-direction models like that of Koutsoyiannis and many others, have one point against them: any marker in the inputs never can exceed the ratio in the inputs in the further flows: the containers or the outputs.
Human FF emissions were 1-5% in the inputs 1958-2020, but are over 10% in the atmosphere and over 6% in the ocean surface. One-way model completely rejected.
Further, there is little doubt that the “equilibrium” CO2 level did not change a lot over time. One can shift it somewhat higher or lower, but a range of 30 to 60 years for the adjustment time still is an order of magnitude higher than de residence time of 4 years. Even the “thinned” levels of 14C (14-20 years adjustment time) or of the 13C/12C ratio adjustment time of around 15 years is way higher than the residence time.
Last but not least, with a residence time of 4 years, the table in Ed’s spreadsheet (tab: Test) shows the human caused increase in the atmosphere of 2020 at 72.47 PgC or an increase in the atmosphere of 40,71 ppmv.
The basic natural CO2 level was/is (IPCC) 589 PgC or 276 ppmv. Together some 337 ppmv.
Observed for 2020 is 414 ppmv???
From where comes the difference? Both the oceans as vegetation increased in carbon level, thanks to the short residence time…
Jim,
Sorry should have been more clear: the (larger) human emissions play no role in the calculation of the adjustment time…
The simple math is in play in both the residence time as in the adjustment time.
In the case of the residence time, the math is always simple, whatever the direction of the flows.
In the case of the adjustment time that is only simple of the decay rate is in linear ratio with the distance between pCO2 of the atmosphere with the pCO2 of the oceans and plants. Which for both is the case.
As good as the carbon mass balance is simple bookkeeping of ins and outs…
Have a view on the (rough) carbon balance of the different flows (PgC/year) and net changes seen from the atmosphere side:
Human emissions: 10 in, 0 out; net change in the atmosphere: +10 (calculated from FF sales)
Atmosphere: 215 in, 210 out; net change in the atmosphere +5 (measured as increase)
Vegetation: 120 in, 122.5 out; net change in the atmosphere: -2.5 (measured via the O2 balance)
Ocean surface: 50 in, 50,5 out; net change in the atmosphere: -0.5 (measured as DIC in the surface)
Deep oceans: 40 in, 42 out; net change in the atmosphere: -2.0 (not directly measured, difference between total ins and outs of the atmosphere and difference with total for the oceans minus ocean surface, see Feely et al.).
All known other sources and sinks either much smaller or much slower in exchange rate…
The cycles give you the residence time, but even if these double, that doesn’t change the adjustment time with one year, only halves the residence time…
But please show me your calculations…
Not my best knowledge, but as far as I know, the opposite may be happening too: high energy O2 and N2 molecules may excite CO2 to emit IR by collisions:
I asked Google:
“can high energy O2 and N2 excite CO2 molecules to emit IR radiation”
And their AI responds with:
“Yes, high energy O2 and N2 molecules can indirectly excite CO2 molecules to emit IR radiation. While O2 and N2 don’t directly absorb or emit infrared (IR) radiation themselves, they can transfer energy to CO2 molecules through collisions, causing them to vibrate and emit IR radiation”
Dr. Ed,
On page 5, there is an indented paragraph with a quote by “Robert.” The end quote is inside the period rather than, by custom, outside.
Another nit pick on page 16, 4th to the last paragraph, “It also says each individual gas flow independently.” Should be “flows,” no? Or “It also treats each individual gas flow independently.”
The 4th paragraph on page 18 is “IPCC’s true human carbon cycle shows human CO2 causes only 8% of the CO2 in the atmosphere. This proves IPCC’s H(1) that claims human CO2 is 33% of the CO2 in the atmosphere is wrong.”
Shouldn’t it be “…8% of the increase of the CO2…” Also in the next sentence, “…human CO2 is (or causes) all of the 33% of the increase of the CO2…”
Where is 8% calculated? I see the 8% shown in Figure 9, but it isn’t specifically explained previously, unless I’m mistaken. The present article does not suffer from brevity, but perhaps adding that explanation or a reference to it in past papers would be appropriate.
David A wrote, “It is easy to find data showing that an ‘Ah’ term is negligible. This would measure human processes removing carbon from the atmosphere…”
Ed replied, “There are no such data!”
David A. is right. I included the data in a comment, here:
https://edberry.com/co2coalition/#comment-112419
Ed, your “Ah,” i.e., the anthropogenic processes which deplete the CO2 from the air, are negligible. More precisely, they are much smaller than the error bars on anthropogenic emissions, so they can be ignored in “mass balance” arithmetic. Even if you count cement carbonation, anthropogenic CO2 removals are still only about 2% of anthropogenic CO2 emissions.
Ed wrote to David A, “You are not debating physics. You are only debating your emotions.”
That’s untrue. The only part of what David A. wrote which is not rock-solid science is his expressed belief that removing CO2 “helps.” That’s a value judgement with which I disagree, but it is not our topic here.
Fredinand,
I don’t think natural fluxes have to increase in the same ratio as human emissions. The latter are zero order and the former first order. No violation of the equivalency principle.
Regarding 1., the biological cycle doesn’t remember when it recycled itself. Whether is was diurnal, yearly, or from fallen trees hundreds of years old.
As for 2., cycling is everything, otherwise nothing moves in and out.
“3. The total biosphere since about 1990 is increasingly removing more CO2 than adding to the atmosphere.”
Yes, but if you figure in a fraction of the removal was industrial sourced, the natural sink minus source eventually flips negative as the industrial content of the atmosphere increases.
I fail to understand why you claim the compartmental models are unidirectional. The only unidirectional model I can imagine is molecular escape from the atmosphere to space. In other words, the sentence “any marker in the inputs never can exceed the ratio in the inputs in the further flows: the containers or the outputs” is incomprehensible to me.
“Further, there is little doubt that the “equilibrium” CO2 level did not change a lot over time.”
That is totally argument by assertion and circular logic. You are using assumptions about an unvalidated Tau model as evidence against the Te models which suggests an expanding biosphere.
“From where comes the difference?”
Well, you explained it yourself. From the increasing ocean and terrestrial carbon levels. 276 ppm seems a bit low, but makes 414 ppm a 50% increase. Of that, the 41 ppm contributed by humans is 29%, leaving 71% or 97 ppm contributed by the growth in natural emissions. Unless proven otherwise, the null hypothesis on H1 stands.
Jim,
“Shouldn’t it be “…8% of the increase of the CO2…” Also in the next sentence, “…human CO2 is (or causes) all of the 33% of the increase of the CO2…”
Is exactly where it goes wrong: 8% (meanwhile over 10%) of all CO2 in the atmosphere (and over 6% of the ocean surface water CO2) is from fossil fuel origin, as the decrease in 13C/12C ratio shows and the other possible main source of low-13C, vegetation is growing, this leaving more 13C behind in the atmosphere…
That doesn’t disprove that FF is the cause of the 33% increase in the atmosphere, only that some 2/3 of the original FF molecules were exchanged with CO2 molecules from the deep oceans, “thinning” the FF “fingerprint”:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg
Dr. Ed,
This page was linked to as a source for “Fig. 11” however, there are only 10 figures!
Also, the historic evidence is all we need to prove CO2 is NOT a climate change force!
Using the geologic evidence going back 550 million years, correlation coefficients can be computed for the relationship between CO2 and Climate (temp) and changing CO2 and changing Climate. The former calculates to 0.29 (uncorrelated). The latter to a mere 0.10 (highly uncorrelated).
No correlation means causation is impossible. Q.E.D.
That is correct. I first learned about this from Prof. Will Happer, when I met him for the first time in 2014, when he taught a colloquium in the Physics Dept. at UNC in Chapel Hill.
I arrived uncharacteristically early for the colloquium, and was surprised and disappointed to learn that the UNC Physics Department had made no arrangements to record it. So I took the middle pair of seats on the front row and used my phone to record the audio. Prof. Happer kindly gave me his PowerPoint slides, and I combined the audio with the slides to make a usable video, which I posted on YouTube.
The sound quality is mediocre, and we don’t get to see his smiling face, but it is a lot better than nothing. You can find the PowerPoint slides and a link to the video here:
https://sealevel.info/Happer_UNC_2014-09-08/
Afterward, I exchanged emails with Professor Happer, and he generously answered my questions. That email exchange is on my website, and it is instructive:
https://www.sealevel.info/Happer_UNC_2014-09-08/Another_question.html
At temperatures and pressures normally found in the troposphere, air molecules, including CO2, are continually and very rapidly colliding with one another, and thus trading energy back and forth. Those collisional transfers are far more frequent than radiative emissions of photons (the other way that CO2 molecules have of giving up energy), so those collisional energy transfers keep the various constituent gases of the atmosphere in local thermal equilibrium.
When a CO2 molecule has been vibrationally excited with 82.66 meV of energy (which is the energy of a 15 µm photon), on average it takes about one full second(!!) before the molecule will emit a 15 µm photon! In contrast, the time before a CO2 molecule in the troposphere would lose that energy by collisional transfer to another air molecule is measured in nanoseconds, though it depends on altitude and temperature.
So even if a particular radiatively active gas in the atmosphere is absorbing lots of radiation, the effect of that absorbed radiation will be simply to warm the bulk atmosphere. It really doesn’t matter which gases absorb the radiation, nor what wavelengths the absorbed radiation was, the effect is just to warm the air. The N2, O2 & Ar are warmed to the same extent as the “GHGs” which absorbed the radiation.
The very rapid collisional energy exchanges (compared to radiative emissions) do NOT mean that emissions from CO2 are small or inconsequential. But they do mean several interesting things:
1. There are MANY energy transfers, back and forth between air molecules, for each emitted LW IR photon.
2. A CO2 molecule is far more often vibrationally excited with 82.66 meV of energy via collision with another air molecule than via absorption of a 15 µm IR photon, even if there’s a lot of incoming IR.
3. In the lower atmosphere, the constituent gases of the atmosphere all stay at almost exactly the same temperature, even though some of them are absorbing and/or emitting IR, and others are not.
4. The amount of IR emitted by the CO2 in a volume of air is determined by just two factors: the amount of CO2 it contains, and the temperature.
5. The amount of IR absorbed by the CO2 in a volume of air is NOT one of those two factors!
It is the temperature of the air (and the amount of gas) which determines the intensity of radiative emissions. Notably, the strength of radiative emissions from CO2 (or another GHG) is almost completely unaffected by the amount of radiation absorbed by that GHG (except indirectly, as the absorption of radiation warms the air).
As it happens, the Earth’s LW IR emission band peak is similar to the molecular bending mode energies of some gases, including CO2. But only triatomic (and higher) molecules have bending modes, so only molecules with three or more atoms can be “greenhouse gases.” That’s why, for example, O3 (ozone) is a GHG, but O2 (diatomic oxygen) is not a GHG.
Ferdinand,
My operating system is no longer compatible with dropbox where I used to share access to files. I’m thinking of not sharing publicly anywhere anymore anyway. I will try to include all the necessary information for you to understand my calculations. They come from modifying a spreadsheet shared by Roy Spencer some four or five years ago at drroyspencer.com. The concept is similar to Dr. Ed’s “test” spreadsheet except, like Dr. Spencer, I’m only considering the atmosphere with all the other reservoirs combined into one.
I added a column to Dr Roy’s spreadsheet between column C, (anthro CO2 INFLOW), and column D, (“anthro” OUTFLOW), naming it Natural inflow. That column accumulates yearly based on the formula = 64 ppm + 1.3*(1E-17)*EXP(0.02*year). That formula calculates the value of natural inflow for all of the values for each year from 1750. It is an artifact of fitting the Mauna Loa data. Instead of Dr Roy’s 0.02 (1/Tau) and 295 ppm value for 1750 CO2 level, I used 0.23 (1/Te) and 280 ppm. The formula for each successive new value of total atmospheric CO2 (Cn) is Cn-1 + EHn + ENn – Cn-1 / Te.
This results in 2018 values of 4.74 ppm industrial in (from Boden et al.), 91.9 ppm natural in, 94.1 ppm total output. The calculated CO2 is 411.6 ppm compared to the actual 408.5 ppm, but the overall correlation with the Mauna Loa data is, if I don’t say so myself, better than Dr Roy’s. You can find his spreadsheet here: https://www.drroyspencer.com/2019/04/a-simple-model-of-the-atmospheric-co2-budget/
I learned that I can maintain a good correlation even with other values of initial CO2 and Te, but never without some increasing increment from other than the industrial source.
Dear Jim,
Thank you for finding more English errors in my draft, which are now fixed in the next update I will post. Regarding you final suggestion, my text now is:
Berry (2019, 2021, 2023a) derived IPCC’s natural carbon cycle as explained above. Since IPCC’s human carbon cycle must use the same e-times as IPCC’s natural carbon cycle, according to the Climate Equivalence Principle, Berry calculated IPCC’s “true” human carbon cycle.
IPCC’s true human carbon cycle shows human CO2 causes only 8% or 33.6 ppm of the 420 ppm of CO2 in the atmosphere. This proves IPCC’s H(1) that claims human CO2 is 33% or 140 ppm of the 420 ppm of CO2 in the atmosphere is wrong.
Dear Dave,
If you tie a weight to a string, and whirl the weight around, then stop whirling and let the string wind up on your steady finger… what makes the weight speed up?
Ed
Ed,
As I have said many, many times before, neither me, nor Ferdinand, nor Dave Burton, nor Jerry Elwood, nor the IPCC has claimed that your “human carbon” is 140 ppm of the present atmosphere. We all know it is much less. I have told that to Skrable, to Koutsoyiannis, to Harde and Salby, to Ato and to others in the parade of deniers that has come through [junk] Science of Climate Change. I have told that to Jim on this thread. I explicitly told you in our “debate” in SCC in 2023. If you read the Seuss paper from the 1950’s, you will see that he was well aware that balanced exchanges (aka “disequilibrium isofluxes”) between the atmosphere and land/sea reservoirs would dilute his effect. I provided a link on this thread to a Radiocarbon paper showing the (diluted) Seuss effect, measured before atmospheic nuclear testing complicated things in the 1950’s. You continue to either willfully misunderstand, or intentionally misrepresent, good science.
That good science leaves no doubt where the atmospheric carbon increase is coming from : Us.
That’s a remarkably random question, Ed. (And I think you meant angular velocity, rather than “speed,” right?)
What does that has to do with anthropogenic CO2 uptake (your “Ah”)? And, what anthropogenic processes do you think remove CO2 from the atmosphere?
(Never mind; I see that “DMA” is the handle of one of the participants here.)
In addition to what David Andrews said (and many skeptics endorse)…
Take an example:
In Europe, each country that uses the Euro has its own 1 and 2 euro coins. One side is the same with the value, the other side is different for each country. Coins from small “countries” like Andorra (between France and Spain) and the Vatican are very rare and real collectors items.
See:
Now, one day, I bring 300 Andorran one euro coins to the local bank. Coins are not that frequently used anymore in the bank transfers, so they have only 600 coins of different countries in stock. Together that gives a sudden increase to 900 coins in total, of which 300 from Andorra.
There are a lot of transactions of coins each day in the bank, which exchange some 180 one euro coins per day. Exchange, not remove.
While at the start 33% of the coins going out are from Andorra, few will come back, as the total number of one euro coins outside the bank is enormous and doesn’t contain much Andorran coins. So the number of one euro coins in the local bank will get reduced very fast with a “residence” time of about 4 days.
At the start there is a 50% increase of all one euro coins in the local bank, that number will slowly get reduced to the “normal” local level of 600 coins at a much slower speed of about 50 days “adjustment” time for any increase of coins from any country.
That results in following graph:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/andorra_decay.jpg
As you can see: the part of Andorran coins is dropping very rapidly, while the number of total coins only slowly get reduced.
Or the difference between the residence time and the adjustment time.
Just replace FF CO2 for Andorra and all CO2 for total coins and make it years for days…
The number of observed FF molecules remaining in the atmosphere is what the input and the residence time caused.
The amount (pressure) of total CO2 in the atmosphere above equilibrium and what is net changing, is reflected by the the adjustment time, independent of the residence time.
First graph:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/andorra_euro.jpg
Dear Dave,
It has nothing to do with the effect of human CO2 on atmospheric CO2.
It is just a simple question to you to see if you can answer a simple question, simply, without making it very complicated with stuff that is irrelevant.
At least two meteololgy books I have read answered this question and related it to what makes the wind in hurricanes speed up as the air gets closer to the eye wall.
Just thought you were up on this simple physics.
Dear David,
Well, let’s review what we are talking about in this post. The CO2 Coalition’s special document we are discussion says in its abstract:
“Since the beginning of the Industrial Revolution in the late 1700s, the average concentration of Earth’s atmospheric carbon dioxide (CO2) has increased by about 140 parts per million by volume (ppmv) to the current amount of about 420 ppmv. This is much higher than concentrations of the past 800,000 years, which rarely exceeded 300 ppmv, according to ice core data. In this document, the CO2 Coalition presents multiple lines of scientific evidence demonstrating conclusively that the modern increase in CO2 is mainly due to anthropogenic emissions.”
And in its introduction:
“That is, nature is removing CO2 from the atmosphere rather than adding to the total. Since nature is removing large amounts of the gas nearly every year, it follows that the rise in atmospheric CO2 cannot be from natural causes.”
“We use multiple lines of scientific evidence to demonstrate that nearly all the increase in
atmospheric CO2 is from human emissions, most of which are from fossil fuel use.”
So, David, do you agree with these CO2 Coalition statements, or do you disagree?
Do you agree or disagree with the arguments by the authors of this special document?
Dear Ferdinand,
David Andrews tried a similar stunt to your in our 2023 debates. Andrews boasted that the solution could be found in Monte Carlo calculations. He was trying to dump on my equation (2). So, I showed David how the balance levels that I derive from (2) produce a quick and more accurate solution than a Monte Carlo calculation.
Your challenge is similar and easily answered by my (2). So, thank you for supporting (2) and thereby all of its derivations.
Ed,
What’s odd about your argument is that you are telling us what we think. You did the same when you wrongly told us that our “natural absorption” term left out the natural absorption of industrial carbon. WE, not you, get to define what OUR terms mean. You consistently try to create straw men by misrepresenting valid arguments.
Dear David,
Amazing. I ask you two questions, that are normal for a debate, and you refuse to answer them:
“So, David, do you agree with these CO2 Coalition statements, or do you disagree?”
“Do you agree or disagree with the arguments by the authors of this special document?”
Further, you claim:
“What’s odd about your argument is that you are telling us what we think.”
Have you truly lost your mind?
Dear Dave,
Here’s my point.
You claim my equation (2) is wrong and that your (and Ferdinand’s) tau is correct.
Yet, nothing you say contradicts (2).
So, your argument are meaningless.
But your tau cannot explain how inflows set balance levels. Your tau cannot explain how nature held a CO2 level before human carbon had any influence on the CO2 level.
Therefore, you tau is a product of your imagination. It adds nothing to your explanations of anything relevant to how carbon flows through the carbon cycle.
You do not have any equation that might substitute for (2). You don’t even realize that you must provide such and explanation to justify all your handwaving about more data that is nice but proves nothing relevant to the core of your message or to the core of our debate.
So, where is your replacement equation for my (2)?
Dear Dave,
Surely, you are not saying that Will Happer supports your irrational arguments in your special document and in your claims in these comments.
I can’t believe Happer would support such nonsense.
Dear Ed,
Your equation (2) only shows how many Andorran coins are left over time, the increase in total coins from 600 to 900 coins anyway was caused by the supply of 300 Andorran coins, no matter how fast these in the next days were replaced by equation (2) by coins from other countries.
That is completely irrelevant for the cause of the increase in coins and how fast the extra number of coins about the “equilibrium” of 600 coins are removed.
The decline of the total number of coins (of whatever country) or the “adjustment time” of the total number of coins back to 600 is all what is of interest…
Exact the same points as for CO2 in the atmosphere…
Dear Ferdinand,
This is in reply to one of your comments far above in these comments.
Your definition Tau is meaningless because you define Tau not as a (level / outflow) but as a (difference in levels / an unspecified and invalid outflow).
You have not provided a substute for my (2). Therefore, you have no rational model. You have no way to calculate how nature could have produced an equilibrium in the levels before we assume human carbon interferred with this equilibrium.
You have not proved there is any need for a Tau that differs from Te, or that your Tau brings anything to the table to explain how carbon flows in the carbon cycle. In other words, your Tau does not even describe nature, let alone the effects of human carbon.
Your use of “removal” rate is not physics or even science. Removal rates have physics backwards. The only way to structure a carbon cycle model is to use the equation (2) Outflow = Level / Te.
You tell your story about how flows continue without changing levels but you do not realize that this is properly explained by (2). Your story does not justify using a Tau to replace Te.
You claim for 2020 that the total carbon outflow from the atmosphere is 15.7 PgC/year.
Even the IPCC recognizes the carbon outflows (as of 1750) were about 108 PgC to Land and 60 PgC to Ocean, for a total of 168 PgC/year outflow.
Your CO2 Coalition-approved model is one of the biggest frauds in climate history. The CO2 Coalition is way left of the IPCC’s position on climate.
You reference other publications (Dietze, Lindzen, Spencer) in your attempt to prove your claims, without realizing that these publications are also wrong.
How can the people in the CO2 Coalition get science so wrong?
Your Tau model cannot explain how D14C, after 1970, declined back to its original balance level of zero.
This D14C decline may be the most important accidental set of data relevant to our discussion of the effect of human carbon on the observed CO2 increase.
Yet, you do not address this subject in a manner supported by physics.
Your formulation does not recognize or calculate balance levels. Because of that omission in your model, you misinterpret the data. (Same for David Andrews, by the way).
Perhaps your most glaring error of all, is your twice-repeated claim in these comments:
“Where Tau is the exponential decay rate to reduce a disturbance (like the addition of extra CO2 from whatever source) to 1/e of the initial disturbance.”
You don’t get it that only my (2) properly explains the 1/e decrease (found in the D14C data) and which properly explains how carbon flows in the carbon cycle.
So, your argument has come full circle.
You allow that (2) expains the initial D14C decrease, but then you claim (2) does not explain this D14C decrease when D14C gets closer to its balance level.
You then claim you need Tau to explain the decrease closer to the balance level. Yet, you don’t even know what a balance level is, or how to define it.
Then you claim:
“Where Tau is the exponential decay rate to reduce a disturbance (like the addition of extra CO2 from whatever source) to 1/e of the initial disturbance.”
Which means you are recognizing, without knowing it, that (2) indeed explains the complete approach of a level to its balance level.
All your CO2C claims are delusional junk science because, in the end, you indeed recognize, in your 1/e claim, that (2) is the correct explanation of carbon flow.
Dear Ferdinand,
You better stick to the carbon cycle. Your attempt to make your point using coins fails.
You have not shown in any of your arguments that your tau produces a more valid explanation of the carbon cycle than (2).
Dear Dave,
I am looking for ANY calculations that you have done properly. That’s why I gave you the chance to answer a simple physics question that is at the freshman level of physics.
For example, you calculated the e-time of D14C to be 20 years.
https://sealevel.info/Graven2020_nofossil_logscale_1970-1995_annot6.png
You used data for about 1972 to 1986 from a log plot of D14C. You further claim others are wrong and you are correct.
There are two key problems with your calculation:
(a) The log plot does not give the correct answer because it does not relate to a balance level that D14C is decaying to.
(b) You are not using the full range of available data.
See Figure 9 of my paper above. It shows a proper curve fit to the D14C data using (8) that is derived from (2), and which shows that a proper curve fit to the D14C data must use two parameters: e-time and balance level. The curve fit in Figure 9 shows Te = 16.5 years and a balance level of zero. And it uses all the available data after 1970.
Figure 9 proves your calculation is invalid. In fact, Figure 9 supports (2), which proves just about everything you are claiming about the carbon cycle is wrong.
Common Dr. Ed, have you never heard of an exponential decay rate for a disturbance of a process in equilibrium? Or Le Chatelier’s principle?
Te and Tau have completely separate definitions.
Te indeed is the residence or “turnover time” that can be expressed with the simple formula:
Te = mass / output
That shows how long a single molecule of CO2 (of whatever origin) in the atmosphere resides in the atmosphere before either being removed, with or without a change in total mass in that reservoir, or being swapped with a CO2 molecule of another reservoir, thus without a change in total mass within that reservoir.
Wiki gives a nice definition for the residence time:
https://en.wikipedia.org/wiki/Residence_time
Tau is how long it takes for a process in equilibrium that is disturbed by an extra input of one of the reactants to get back to 1/e of the original disturbance.
Again from Wiki for an exponential decay:
https://en.wikipedia.org/wiki/Exponential_decay
and of Le Chatelier’s principle:
https://en.wikipedia.org/wiki/Le_Chatelier%27s_principle
These two, Te and Tau can be equal if, and only if, all flows are unidirectional.
The real world shows that 95% of all CO2 fluxes are bidirectional: half the day or half the year CO2 inputs get outputs and reverse that in the other half.
That is our model, which reflects the real world.
Many before me have calculated the equilibrium between the ocean surface and the atmosphere as 280-300 ppmv for the current average sea surface temperature. That is where Tau is based on: the effect of the difference between the CO2 pressure (pCO2) in the atmosphere and that equilibrium. That gives a small real NET output of only half human emissions in both oceans and vegetation together. No matter how much CO2 circulates through the atmosphere. No matter how high the CO2 outflows (thus Te or your formula (2)) get. Completely unimportant for the NET outflow, which is the only part in the total ins and outs that changes the CO2 level in the atmosphere and other reservoirs.
Your model includes a 3.5 years decay rate for all CO2 molecules and for all isotopes alike.
The decay rates for 14C in the atmosphere are calculated between 12 and 20 years.
The decay rate for the 13C/12C ratio is about 15 years.
The decay rate for 12CO2 and 13CO2 mass, back to equilibrium at around 295 ppmv is about 50 years.
Completely independent of and much slower than your residence time…
Thus your formula doesn’t calculate what the observations show.
The only reason for a faster decay rate of the 13C/12C ratio or the 14C of the bomb tests, compared to the mass of 12/13CO2 is that the isotopic ratio’s are redistributed over all reservoirs and a lot of “old” seawater from the deep oceans from long before the use of fossil fuels or atomic bomb tests is coming back with the old isotopic composition.
With your residence time of only 3.5 years, your calculated increase in the atmosphere gets far lower than what is observed. In your spreadsheet (tab: Test) the human caused increase in the atmosphere in 2020 is 72.47 PgC or an increase in the atmosphere of 40,71 ppmv.
The basic natural CO2 level was/is (IPCC) 589 PgC or 276 ppmv. Together some 337 ppmv.
Observed for 2020 is 414 ppmv.
From where comes the difference? Both the oceans as vegetation increased in carbon level, thanks to the short residence time, thus can’t be the source of the increase in the atmosphere…
Then a few points as direct answer:
“Your definition Tau is meaningless because you define Tau not as a (level / outflow)”
The whole world defines Tau as the time needed to reach 1/e of a disturbance of a process in equilibrium…
“You claim for 2020 that the total carbon outflow from the atmosphere is 15.7 PgC/year. ”
I did claim, based on observations, that the part of the outflows caused by the absolute pressure of CO2 in the atmosphere is 15.7 PgC/year. The rest of the outputs is NOT caused by the absolute pressure of CO2 in the atmosphere. These are caused by temperature, photosynthesis, life and pCO2 differences, largely to completely independent of the CO2 pressure in the atmosphere. I did not claim that all carbon outflow from the atmosphere is 15.7 PgC/year.
“Which means you are recognizing, without knowing it, that (2) indeed explains the complete approach of a level to its balance level. ”
Except that the real speed to reach the balance level is 50 years for any excess CO2 in the atmosphere, not 3.5 years. You simply don’t see the difference between the residence time of an individual molecule CO2 (of 3.5 years) based on the sum of all outflows and a mass removal time (of 50 years) which is based on the NET outflow, that is the difference between all inflows and all outflows.
Dear David,
Replying to your comment on July 1, 2025 at 10:25 pm
Your reference https://www.cambridge.org/core/services/aop-cambridge-core/content/view/193CDF1F705B269BC975AF178CEF1AC3/S0033822224000274a.pdf/discussion-presentation-of-atmospheric-14co2-data.pdf
does not in any way “rebut” my papers.
My section 2.8 discusses the Suess Effect because it is part of my calculations. I note
The Suess Effect is not a cause. It is a result of human CO2 inflow that dilutes natural CO2. Berry’s accurate curve fit shows human CO2 causes no significant “Suess effect dilution.”
Your referenced Figure 2 indeed shows a Suess effect of a few percent. That agrees with my calculations of the expected Suess effect. It shows human CO2 in the atmosphere is about 8%. In other words, your Figure 2 supports my (2) and its calculations using IPCC’s data and my Figure 9.
Even the IPCC knows its carbon cycle data is not perfect, so no one expects perfection in carbon cycle calculations. I notice that your D14C data extends to 2020 whereas my data ends in 2015. So, I will upgrade my data and make some minor revisions to my calculations. But we are not looking at any data that will substantially change my conclusion that human carbon emissions have little effect on the CO2 level.
But your paper is lacking something very important, as shown in my Figure 10, which shows the likely reason 14C increased since, say, 1955 is because 12C inreased while the D14C balance level remained near zero.
The balance level is the critical factor because it represents the continuing inflow of natural carbon (or CO2) into the atmosphere.
Since the D14C balance level has remained near zero even while the bombs increased 14C, the balance level is the best measurement we have of the effect of human carbon on atmospheric carbon. And it clearly shows the inflow (and balance level) of human carbon is somewhere between zero and 8% of the total carbon in the atmosphere.
Seems to me that you agree with (2) even though you cannot bring yourself to admit it.
Sometimes my English is too phonetic… Common is of course Come on Dr. Ed…
No problem, there, Ferdinand. Your English is excellent.
Dear Ferdinand,
I put your comments in quote.
The only definition of Te that is important is equation (2).
Te (2) and the continuity equation (1) fully explain the carbon cycle.
No other definition matters because equation (2) governs the carbon cycle model.
Te explains the real world and Tau does not.
The many before you were wrong. We now have a new carbon cycle generation defined by (1) and (2).
Tau is irrelevant because Net output is irrelevant to a carbon cycle model.
No, my “model” which is (1) and (2) does not specify any value for Te.
IPCC’s data for its natural carbon cycle show the overall Te for carbon in the atmosphere is 3.5 years.
However, carbon isotopes 14 and 13 have a larger Te. For example, D14C data show the Te for 14CO2 is close to 16.5 years.
NO. Data reject your claim.
No, the isotopes follow their own independent carbon cycles with their own Te. Otherwise their carbon cycle are the same.
NO. You have no basis in data to make that claim.
My carbon cycle exactly replicates IPCC’s data for its natural carbon cycle at equilibrium. Your model cannot do this.
Therefore, the data reject your model and accept my model.
My Test spreadsheet used in inflow of 10 PgC/year which DOES NOT represent real data.
There’s no difference because these were not real data.
YES. But only Te repesents the 1/e value. Tau cannot. Case in point: D14C data.
You refuse to recognize that (2) produces the equilibrium that matches real data.
Figure 5 shows that Te is the time it takes for the level to move 63% toward its balance level, no matter where we start. Te properly defines the “speed” to reach the balance level.
You simply have not measured the speed to balance level correctly.
Nonsense. Forget about your “individual molecule” thing. Te fully describes how fast a level moves toward its balance level. Your Tau adds nothing but confusion and errors.
Einstein said we must keep things as simple as possible to explain a physical system. You are adding complexity that is not needed.
To Everyone,
The dark side uses clever ways to promote its invalid claim that H(1) is true.
Figure 11 (in my paper above) is a replot of a figure in CO2C. It has a logical error in the way its data are plotted.
CO2C does not catch this error, which means the CO2 Coalition reviewers are not very concerned about republishing junk science.
I could have explained the error in Figure 11, but I thought I would give you a chance to find it on your own.
Will you be the first to find the error in Figure 11?
Ed, it is ironic that in your quiz question, to evaluate my freshman-level physics chops, YOU got it wrong: you said that the spinning weight speeds up, but it does not. Only its angular velocity increases.
Hopefully your mistake was just sloppy wording, rather than an actual misunderstanding. So I asked whether that’s what you meant—but you didn’t answer. So, again: Is that what you meant?
Regarding the atmospheric lifetime of “bomb spike” 14C, 15-17 years is what you get if you forget to take into account Suess Effect dilution. The log-linear plot is useful because that produces a straight line from an exponential decay process, such as the approximately constant-rate mixing of atmospheric carbon with other major carbon reservoirs, which is the dominant process decaying the radiocarbon bomb spike. But you needn’t use a log-linear plot to reach that conclusion. Here are two examples, using two datasets, which yield (approximately) the same result; one of them is linear, and the other is log-linear:
https://sealevel.info/ndp057_Fruholmen_d14CO2_hairlines3.png
https://sealevel.info/logc14_two_half-lives2.png
The reason for preferring the earlier 14C measurements is that there are two different processes shrinking the 14C bomb spike: one is dilution by mixing, through carbon exchanges between the atmosphere and other carbon reservoirs (mostly oceans and terrestrial biosphere). The other is Suess Effect dilution, due to the addition of 14C-depleted fossil carbon to the atmosphere.
The former process is the one we’re trying to characterize.
In the years immediately following the cessation of atmospheric H-bomb tests, dilution by mixing was the major process contributing to the bomb spike decay. But as the years passed, and anthropogenic CO2 emissions accelerated, Suess dilution became a bigger and bigger contributor.
What’s more, the quantification of Suess dilution is dependent on models, which I, frankly, don’t really trust.
So, by confining our analysis to the first couple of half-lives, we maximize the portion of the decay which is due to the process that we’re interested in, and minimize the portion due to Suess dilution and the possible modeling errors.
When you do that, you find a 14C lifetime of about 20 years.
Now, back to the question at hand: What anthropogenic processes do you think remove CO2 from the atmosphere?
Ed,
Of course I agree with the CO2 Coalition’s conclusion that the rise in atmospheric CO2 is anthropogenic. But we are all also on record as saying that does not for a minute imply what you seem to think it implies, that today there should be ~140 ppm of C14 devoid “human carbon” in the atmosphere. We all understand disequilibrium isofluxes. You quite obviously either do not understand, or do not want to.
I have to say that it is rather sad that you spent such an effort over the years showing that “human carbon” is not abundant in our atmosphere, when all you had to do was have a conversation with Hans Suess some 70 years ago to anticipate it would not be.
Dear Dave,
You get a blue ribbon for your answer on the weight on a string. But my wording was meant to trap you. However, your answer is not perfect. You should have mentioned that energy is conserved, therefore. the speed of the weight cannot increase because that is the more fundamental reason the speed cannot increase.
Check my website menu: About/Adventure in Physics – Weight in a String.
https://edberry.com/an-adventure-in-physics-an-untold-story/
You will see that I published the first paper on this subject in the American Journal of Physics in 1963. I corrected the Scienfic American and two books on meteorology. After my publication, at the encouragement of one of my advisors, I did a simple experiment to further prove my point that the speed of the weight is constant.
Back to calculating the Te for Delta14C and for 14C.
My curve fit using (8) automatically takes into accout the Suess effect dilution because it requires setting the balance level as well as the curve fit. If the dilution were 10%, the balance level would have been -100 rather than zero. My figures 9 and 10 explain my point.
The D14C data show the Seuss effect is only a few percent at best. This means the human carbon is only a few percent of the total carbon in the atmosphere. Therefore, the human CO2 emissions add only a few percent to atmospheric CO2.
Your argument that claims the real amount of human CO2 in the atmosphere is much larger than that indicated by the Suess effect is junk science. It is not backed by data or testable hypotheses. It it imaginary handwaving that contradicts physics.
My curve fit with (8) follows the Delta14C data very closely, leaving little room for controversy or an alternate hypothesis.
Ed wrote, “…the human carbon is only a few percent of the total carbon in the atmosphere. Therefore, the human CO2 emissions add only a few percent to atmospheric CO2.”
It has been explained to you over and over why that is wrong. Exchanges of carbon between reservoirs do not change the amount of carbon in those reservoirs, but they change the distribution of 14C-depleted fossil between those reservoirs.
Ed wrote, “Your argument that claims the real amount of human CO2 in the atmosphere is much larger than that indicated by the Suess effect is junk science.”
Please don’t put words in my mouth. I haven’t said that. In fact, that doesn’t even make any sense, because the Suess effect does not “indicate” how much human CO2 remains in the atmosphere.
Using just GCB (2024) best estimates, ignoring CIs for economy of expression…
From 1750 (roughly the start of the Industrial Revolution) through 2023, human emissions added roughly 232 ppmv of fossil CO2 to the atmosphere + very roughly 105 ppmv of CO2 from land use changes, a total of 337 ppmv. Over the same time period, the amount of CO2 in the atmosphere increased by a net total of about 143 ppmv. Over that time period human removals of CO2 from the air were negligible (even if you count cement carbonation as anthropogenic, it was at most 3-4 ppmv). That means that nature removed (337 – 143) = roughly 194 ppmv of CO2 from the atmosphere.
But that does not mean that “the amount of human CO2 in the atmosphere” is 337 ppmv, or 232 ppmv, or 143 ppmv. The amount of anthropogenic CO2 remaining in the atmosphere is far below 143 ppmv, because of exchanges of carbon between the atmosphere and other carbon reservoirs, which reduce the amount of “human CO2” in the air without reducing the amount of CO2 in the air.
Now, Ed, will you PLEASE answer the question about your “An”? What anthropogenic processes do you think remove CO2 from the atmosphere?
So, you still think that the 4% human carbon inflow can cause 33% of the CO2 level in the atmosphere even as you agree that the Suess effect has never been greater than 8% and likey never greater than 4%.
Good luck with that one, David.
Brendan, average sea surface temperatures (SST) are believed to have risen only about 0.5 °C over the 2/3 century since 1958 (when precise CO2 measurements began). Yet over that same 2/3 century period atmospheric CO2 levels rose by 35% (110 ppmv):
https://sealevel.info/co2.html
Now, consider the relative effect of a 0.5 °C SST increase (since 1958) and a 35% atmospheric CO2 level increase (since 1958) on the CO2 fluxes between ocean and air. We know from the temperature dependence of Henry’s Law that a 0.5°C water temperature increase will reduce CO2 solubility in water by about 2%:
https://sealevel.info/CO2_solubility_in_water_vs_temperature_showing_effect_of_1C_warming5.png
But a 35% increase in CO2’s partial pressure in the atmosphere will increase CO2 dissolution into the ocean by 35%. Since 35% > 2%, it is correct to call the “35%” the “main effect.” That’s not confirmation bias, it’s just what the numbers show. It means that the net effect of the two changes (temperature and atmospheric CO2 level) must be an acceleration in ocean uptake of CO2.
Also, note that global temperatures and presumably sea surface temperatures (SSTs) declined in the 1950s, 1960s, and early 1970s. Yet CO2 levels nevertheless kept on rising. Obviously rising water temperatures didn’t contribute to rising CO2 levels when water temperatures were falling.
https://sealevel.info/newsweek_old.htm
The socialists have an agenda that relies on all CO2 emitted in the last 150 years came from humans and that CO2 never rose above 300ppm until humans started burning fossil fuels. Any evidence to the contrary has to be somehow destroyed at all costs, no matter what the costs.
I said that CO2 rose to 450ppm twice during the last 200 years from instrumental measurements. I never mentioned Beck. But Uncle Bert immediately went on the attack against Beck.
Beck compiled some 200,000 instrumental CO2 measurements from 901 different locations from many dozens of highly qualified and notable scientists. Beck never made any measurements, he just collected them. He is the messenger. Yet the socialists choose to attack him vigorously. Don’t attack the science or the measurements, shoot the messenger.
Uncle Bert has just written more totally unverifiable specious waffle including false statements. Harro Meijer and Ralph Keeling have tried to falsify the 1812 to 1961 instrumental record and failed miserably. Now Uncle Bert’s having a crack. The socialists never give up when their narrative is in jeopardy.
Uncle Bert said:
“When one did choose only the measurements over the oceans or at the coast, with wind from the seaside, all these measurements are on or below the ice core measurements”
False.
Figure 7 from:
Yndestad Harald, 2022b: Lunar Forced Mauna Loa and Atlantic CO2 Variability; Science of Climate Change, Vol. 2.3 (2022) pp. 258-274; https://doi.org/10.53234/scc202212/13 ; https://scienceofclimatechange.org/wp-content/uploads/Yndestad-2022-Lunar-Forced-CO2-Variability.pdf
Shows CO2 in a range from 370ppm to 300ppm from 1820 to 1960. 50% of these measurements were over the ocean.
Nothing in all of his comment or links on July 4, 2025 at 3:04 pm did anything to falsify the 1812 to 1961 instrumental record. He’s done much the same as Meijer and Keeling, cherry pick one or two locations and claim these measurements can’t be correct, therefore all the remaining 900 locations are all wrong too. In his attack on the measurements in the supplied link he keeps referring to a background layer. Charles Keeling demonstrated with his measurements that there was no difference between CO2 measurements at the surface to 4,300 metres up on mountain tops.
I.e. His measurements demonstrated there was no such thing as a background layer. There was only a difference if the measurement location was in the middle of a forest. Out of the 901 locations in the 1812 to 1961 instrumental record, Charles Keeling only found one. The 1812 to 1961 instrumental record demonstrated the same as Keeling’s own measurements.
There was no difference over the oceans. Keeling falsified his own background layer nonsense. The background layer is a red herring.
Uncle Bert tried to say that Beck did not interpret the measurements correctly. You can’t interpret measurements. A measurement is a measurement.
Uncle Bert, along with Meijer and Keeling, are all saying the measurements are wrong and the proxies are right. There is complete ignorance with the monotonic ice core record. It shows an average and does not show the up and down extremes in the record. To see the extremes you need to look at Stomata proxies. Then Uncle Bert comes out with the astonishing comment that “Stomata data are local proxies which are calibrated to ice core values”. What a load of nonsense. This comment demonstrates just how desperate Uncle Bert’s specious waffle has become. In addition, CO2 rose to 400ppm in 500 AD. See Figure 14 in:
Mixing Proxy and Measured Data
DOI: 10.13140/RG.2.2.19788.95360/1
https://www.researchgate.net/publication/354144035_Mixing_Proxy_and_Measured_Data
This is CO2 from plant stomata for the past 1,800 years. Chart adapted from Kouwenberg et al 2004 by Dr Robert Holmes in his video presentation The Ice CO2 Record is “Probably Wrong” Too.
Holmes, (2019b) https://www.youtube.com/watch?v=WNEQo6lk9ko&t=2s “The Ice CO2 Record is “Probably Wrong” Too YouTube video with many references to the literature, accessed 20/11/2023.
Uncle Bert, along with Meijer and Keeling, are trying to falsify a measurement because it is an inconvenient truth and destroys the socialist narrative. A measurement is a measurement. You can’t re-interpret it or falsify it to suit your predetermined narrative.
Finally, Figure 2 from:
Yndestad Harald, 2022b: Lunar Forced Mauna Loa and Atlantic CO2 Variability; Science of Climate Change, Vol. 2.3 (2022) pp. 258-274; https://doi.org/10.53234/scc202212/13 ; https://scienceofclimatechange.org/wp-content/uploads/Yndestad-2022-Lunar-Forced-CO2-Variability.pdf
is the average from 901 locations from all over the world, most were over the oceans. Many locations were on mountain tops, one even higher than Mauna Loa. Many along beaches. The key to the accuracy of these measurements is the 3 year overlapping period of 1958, when Mauna Loa began and 1961 when the 1812-1961 instrumental record ended. For that 3 year period the two different measurements mirrored each other and were almost identical.
I’ll probably be locked out of this discussion yet again for another week. I anticipate this will be my final comment. Good luck to those with the patience to sift through Uncle Bert’s specious waffle. I’ve had the experience before and it is not pleasant. The socialist political activists are 24/7 in their political endeavors. We normal people have lives to live.
Dear Ed,
With an input of only 1 to 5% FF in total inputs, the observed ratio of FF in the atmosphere is already over 10% and over 6% in the ocean surface. The rest of the FF molecules gets into vegetation and the deep oceans, where it is more difficult to measure. The speed at with the FF molecules are exchanged is caused by the residence times. No problem with that. That is about CO2 molecules.
The speed at which the total mass in the atmosphere get reduced to the equilibrium with the ocean surface is of a complete different order: an observed year by year increasing NET removal of CO2 mass (of whatever origin) out of the atmosphere. NET removal. That is observed (!) as only half the current human emissions. Or a Tau of around 50 years.
Moreover, the sum of all FF emissions over time is near twice the observed increase in the atmosphere:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_mlo_t_1960-cur.png
Thus nature removed about half of the FF emissions as mass (and 2/3 of the FF molecules were replaced by molecules from other reservoirs). Thus nature is not the cause of the CO2 increase in the atmosphere. Human emissions of FF CO2 are.
Each year the calculated (quite exactly known from taxes!) FF emissions are average twice the observed increase in the atmosphere over a year, be it with huge year by year variations in net sink rate (not net source rate!):
https://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em2.jpg
With the exception of a few borderline (El Niño) years.
Any bookkeeper worth his/hers money will tell you that FF emissions are the cause of the increase in the atmosphere. No matter your formula (2)…
Dear Ed,
I don’t see any error in that plot:
All what was plotted at the left part of the curves, is the observed combination of O2 and CO2 measurements.
Observed.
At the right side there is a plot of the calculated drop in O2 by burning FF for each type of fuel and the sales for that type and the increase in CO2 if all that FF derived CO2 remained in the atmosphere.
Then one subtracts the calculated O2 release by plants, that is the difference between the above calculated O2 use and what was observed, which is caused by their CO2 uptake, which gives a stoichiometric release of O2 for each CO2 molecule absorbed.
Then one subtracts the calculated CO2 uptake by plants from the FF drop. The remaining gap in CO2 uptake is what the oceans did absorb.
The graph has the ocean and vegetation uptake in reverse order for clarity of the graph, but anyway, without ocean uptake, it would end at the same height as the observed O2 level, with a minor difference, caused by the out-gassing of O2 by the warming oceans. Maybe you have a different sink available than the oceans, but as DIC measurements in the ocean surface show: the oceans are net sinks for CO2.
So I am very curious what the “glaring error” could be, as I don’t see any error in that graph.
Dear Ed,
Only one remark, which is at the essence of our dispute:
Me: ” In your spreadsheet (tab: Test) the human caused increase in the atmosphere in 2020 is 72.47 PgC or an increase in the atmosphere of 40,71 ppmv. ”
You: “My Test spreadsheet used in inflow of 10 PgC/year which DOES NOT represent real data.”
It does for the years after 1800, but in your tab “HumanBB” anyway you use the real data of FF emissions and the calculated increase in the atmosphere, caused by these emissions, according to your formula (2) for all flows.
For the years 2010 and 2020 your calculations show:
Year Lg La Ls Ld Total La ppm
2010 154.35 57.05 29.98 112.77 354.14 26.91
2020 196.10 70.18 37.95 147.32 451.55 33.11
The observed CO2 levels were:
2010: 390 ppmv
2020: 414 ppmv
Or an observed increase in La vs. 1750 of:
2010: 114 ppmv
2020: 138 ppmv
Your calculations with formula (2) don’t match the observations and give much too low results for the observed total increase of CO2 in the atmosphere… That is because your individual Te’s are about a factor 4 too fast…
The tabs in the results disappeared…
Anyway, your results from equation (2) in human ppmv increase are:
2010: 26.29 ppmv
2020: 33.11 ppmv
The observed increases are:
2010: 114 ppmv
2020: 138 ppmv
Equation (2) doesn’t reflect reality…
Dave A wrote, “The poor quality of the denier arguments that I have focussed on, ever since stumbling on the Berry/Harde/Salby confusion between deltaC14 and concentration, makes me very skeptical of other skeptics and inclined to believe the consensus.”
I quite understand, and you didn’t even mention Principia Scientific‘s crackpottery. But why doesn’t the abundant nonsense from climate alarmists also make you very skeptical of alarmists and their claims?
For instance, you say that “‘Extreme weather’ problems, especially involving the increased water content of tropical storms, seem to me very likely real and linked to CO2.” But, as I trust you know, those problems are merely predicted, and there’s been no detectable increase in extreme weather, thus far.
Hurricanes & tropical cyclones have not worsened:
Graph: https://sealevel.info/global_major_freq_hurricanes_2022-02-28_ryanmaue_1941x1017_annot1.png
References: https://sealevel.info/learnmore.html?0=hurricanes#hurricanes
Nor have tornadoes:
Graph: https://sealevel.info/tornadoes-1955-2024.png
References: https://sealevel.info/learnmore.html?0=tornadoes#tornadoes
Nor have nor’easters, droughts or floods, or any other class of extreme weather:
Graph: https://www.ncdc.noaa.gov/temp-and-precip/uspa/wet-dry/0
References: https://sealevel.info/learnmore.html?0=droughts#droughts
Do you know where the prediction of worsening “extreme weather,” and, in particular, worsening tropical storms, came from? It was from this book:
https://www.amazon.com/Storms-My-Grandchildren-Catastrophe-Humanity/dp/1608195023
Storms of My Grandchildren: The Truth about the Coming Climate Catastrophe and Our Last Chance to Save Humanity, by Dr. James Hansen, “the world’s leading climatologist.”
In 2011 Dr. Hansen did a publicity tour to promote his book, and on the Dave Letterman show he explained why global warming will cause worsening storms. He said that AGW would warm the tropics more than high latitudes, and the resulting “increasing temperature gradient” [between high & low latitudes] would “drive stronger storms.” Listen to it here:
https://www.youtube.com/watch?v=SOKBOFLhgqM#t=7m25s
I trust you know that the “increasing temperature gradient” between high & low latitudes is nonsense. The temperature gradient is decreasing, not increasing. (Aside: “Arctic amplification” is the happy fact that “global warming” isn’t really very global, because it disproportionately warms chilly high latitudes, especially in winter. The tropics and summers are affected less—which is nice, because they’re warm enough already.)
That’s just as Arrhenius predicted over a century ago.
Hansen’s mistake was not minor, it was the basis of his book! Yet, as far as I know, not a single prominent climate activist or alarmist institution criticized Hansen’s error, or suggested that the decreasing temperature gradient between high & low latitudes could drive weaker storms. Not even one.
THAT is the most striking difference between climate alarmists and skeptics of climate alarmism. As you’ve seen, prominent skeptics and lukewarmers devote considerable time and effort to debunking things like the Berry/Harde/Salby confusion about CO2. But nobody on the alarmist side of the debate bothers to debunk nonsense like Hansen’s confusion about storms.
That’s because the driving motivation of the leading scientists who’re skeptical of climate alarmism is that, like you, we are passionate about scientific integrity, and that generally isn’t the case on the other side.
If you doubt it, then explain why people like Hansen and even Guy McPherson generally get a free pass from other climate alarmists? Why doesn’t anyone in the alarmist community put as much effort into debunking Hansen’s errors as the CO2 Coalition puts into debunking the Berry/Harde/Salby confusion about CO2?
This has gotten long, so I’m going to defer discussion of “saturation,” the inaccuracy of alarmists’ predictions several decades ago, and the supposed “consensus,” to another day.
Dear Brendan,
You will not be locked out of these discussions. So, keep commenting.
I am not blocking any opinions from these comments because I want this to be an open discussion.
Sometimes, WordPress does not recognize a commentor’s email address. So, it holds a comment until I approve it.
I am not at my computer 24 hours a day, so sometimes a comment gets put on hold until I arrive. I always approve comments.
It is important that WordPress filters comments because the internet is literally flooded with website comments that insert bad code into a website and take down the whole site.
Thank you for your comment.
Ed
Dear Brendan…
Again a lot of allegations with little real meat…
As I already said, I have had a lot of direct discussions with the late Ernst Beck and therefore I am very reluctant to discuss his work, as he can’t defend his work anymore.
For a good idea how he worked: he did dig out lots of historical data, which was an enormous work and that really is where he should applauded for. The problem is his non-selection and use of all available data, the good, the bad and the ugly.
One can criticize the criteria that Calendar used to select or deselect the historical data for his compilation, but at least he had stringent criteria, including not using any data that were used for agricultural purposes.
That should have excluded the two main series (Giessen/Germany and Poona/India) which are at the base of his 1940-1942 “peak”, which doesn’t exist in any other measurement or proxy.
A peak of some 80 ppmv in only 5 years is only possible if you burn down a lot of forests and regrowth in 5 years simply is impossible.
That are the bad data. The ugly data: in Figure 1 of Yndestad (directly copied from Beck’s work) you see the “atmospheric” CO2 measurements. The northern Atlantic air was really measured and below the average of the ice cores. The mid- and south-Atlantic pCO2 was only measured on the seawater samples at different depths, including at the surface, noticed as 0 meter depth. According to Beck, that were atmospheric measurements, but… from the same samples the pH was measured… Nevertheless, he used these data in his latest work.
Then we have Figure 2 in Yndestad: the peak in temperature around 1940 may have caused the peak in CO2, but that implies a 120 ppmv peak for only 0.6°C change. Or 200 ppmv for only 1°C sea surface increase. Wow.
Moreover a similar increase and decrease after 1950 does not lead to any detectable increase of CO2. Very strange behavior of CO2: it stops its huge reaction on temperature at the exact moment that accurate direct measurements in the atmosphere start…
What makes all the historical measurements suspicious is that in about every year one can find any CO2 level one likes: from below the ice core measurements to 500-600 ppmv in the same year at the same place on earth or at different places.
There is a modern CO2 (and other gases) station at Linden/Giessen at a few km of the historical station that is the main source of the 1942 peak. Here a few days of measurements under inversion, compared to Barrow, Mauna Loa and the South Pole. All raw, uncorrected data:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_background.png
The historical measurements were three times a day, two at the flanks of the peaks:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_background.png
So that are the measurements that caused the “peak” around 1941…
About the calibration of the stomata data: these indeed are calibrated against ice core measurements over the period 1900-1990:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/stomata.jpg
For the same stomata index (SI) of 7%, the CO2 level may vary between 315 and 365 ppmv. I think that the ice core values are somewhat better…
And even in the stomata data, there is no “peak” around 1940:
According to the ice cores, the CO2 level in 1940 was around 310 ppmv. If the “real” CO2 level was at 380 ppmv, according to Beck, then the stomata index would be at the bottom of the graph near 5%. Nothing special can be seen in the calibration around 1940…
See further my opinion of already from 2008 about Beck’s compilation:
https://www.ferdinand-engelbeen.be/klimaat/beck_data.html
Again, stomata data are calibrated against ice cores for local bias over land for the period 1900-1990. But what happened hundreds of years ago with the local bias? That may have changed due to land use changes in the main wind direction over the centuries or even the main wind direction may have changed as was probably the case between the warm MWP and the cold LIA in Europe. In that case, the stomata data need to be recalibrated to match the averages of both over the same period. Not the other way out…
And I have followed the video. What a bunch of nonsense is that. Good to fill a whole page in reaction. He uses the unreliable stomata proxy data to refute the ice core records (while that should be in reverse!) and he uses the remarks of the late Jaworowski, which were already refuted point by point in… 1996 by the work of Etheridge et al. on three ice cores at Law Dome.
See my comment on Jaworowski, again of 2008:
https://www.ferdinand-engelbeen.be/klimaat/jaworowski.html
And please let politics out of the debate: I am very interested in politics, but don’t mix a debate about data with a debate about who is politically biased in your own eyes…
Dear All,
The essence of the arguments, for or against (H1), centers on what the correct equations are that describe the true physical processes governing mass transfer between the global reservoirs. Ed Berry uses Outflow = Level / Te and related equations which embody the first-order nature of Fickian diffusion. Ferdinand Engelbeen adheres to a Tau “model” which ascribes Outflow proportional to disturbance / Tau where disturbance equals the difference between the current atmosphere concentration of CO2 and some equilibrium level that would be restored on suspension of industrial emissions.
Mathematically, both models begin with the math balance equation (1):
(1) dC(t)/dt = Eh(t) + En(t) – Sn(t)
where C is the concentration of CO2, and E, S, h, and n represent emissions, sinks, human, and natural, respectively. Demetris Koutsoyiannis describes Tau model adherents as “lumping” emissions and sinks together by equating [Sn(t) – En(t) to net sinks, NS(t), defined as in (2):
(2) NS(t) = k* [ C(t) – C* ]
where C* represents a value of C(t) at some hypothetical equilibrium. The Te model also starts with equation (1), but expresses net sinks, SN, as in (3):
(3) SN(t) = ke [ S(t) ]
Which of (2) or (3) properly reflects the true physical processes at work in carbon cycling?
According to Koutsoyiannis, “The proponents of the above ‘sceptic’ [Tau] approach may have difficulties to accept this relationship, preferring [Equation (2)], but [Equation (2)] is for the net sink NS(t) = Sn(t) – En(t), while [Equation (3)] is for the natural sink Sn(t) without subtraction of the emission. It would be absurd to assume that Sn(t) would be related to a portion of the atmospheric storage, such as the surplus above the assumed equilibrium state.
The crucial difference between the two models, other than the question of which equations best describe the realistic physical principles at play, is the fact that the Tau model assumes the equilibrium value of S* has not changed since pre-industrial times. The Te model allows for the possible expansion of the biosphere and a potentially larger S*. This would have the effect of shortening Tau.
Unfortunately for the Tau model camp, this dilemma will never be resolved with simple math. We are going to have to rely on more rigorous analysis such as presented here by Dr. Ed or that of Demetris Koutsoyiannis. See Annex A, page 20, https://tinyurl.com/bdd4fhyb
Dr Ed
Thank you.
Brendan
Jim,
In an earlier note to Ferdinand you said “I’m working on a way to demonstrate how the simple math you and David Andrews rely on can give ambiguous results based on somewhat arbitrary choices of variables.” You seem to have been distracted from that goal or maybe have given up. My goal here is to keep you focused on it.
I think we agree on all of the following data-driven conclusions:
• The present atmosphere contains little “industrial carbon”, carbon that once resided in a fossil fuel. (That is Ed’s key result, but it is old news and unimportant.)
• The (fast cycle) carbon content of the atmosphere, oceans, and biomass have all increased since 1950.
• Natural emissions of carbon into the atmosphere from processes such as ocean outgassing and vegetation decay exceed emissions from fossil fuel burning by an order of magnitude.
• Data and “simple math” allow the further conclusion that natural transfers from the atmosphere to land and sea reservoirs (of ALL carbon types of course) exceed natural emissions. This is equivalent to the statement that “net global uptake” is positive. Repeating relevant data from Ballantyne: between 1950 and 2010, integrated human emissions were 350 +_29 PgC, atmospheric accumulation was 158 +-2PgC, making net global uptake 192 +- 29 PgC.
I know you are struggling to accept the consequences of the final bullet point.
You have argued that the larger natural emissions from decaying vegetation in 2025 compared to 1950 (because there is more vegetation to decay) means they are a cause of the atmospheric rise. This is what Koutsoyiannis has also argued, which is why I put you on to him. Several months ago I told Demetris I would nominate him for the Nobel Prize in Alchemy, if he could demonstrate in a laboratory setting how decaying vegetation managed to emit more carbon than it had taken in from the atmosphere while it was growing. He has not responded to me.
I don’t know how your spreadsheets are structured, but as the biomass example illustrates, it DOES make sense to link various emission and absorption processes and focus on net changes in individual caches of carbon, no matter what Demetris says. Stock changes over a defined period are presumably better known than emission and absorption rates. A larger biomass in 2025 compared to 1950, combined with carbon conservation, precludes biomass growth as a source of atmospheric carbon rise. Simple math is not wrong just because it is simple.
So once again I am puzzled how you can look at the 350 PgC hole in fossil fuel reserves made between 1950 and 2010 and have any doubt whatsoever where all the carbon is coming from. But if you have a coherent rebuttal, by all means bring it. Ed has none. Demetris has none.
And good luck to you convincing people net global uptake is negative.
Dear Jim,
I must make one correction to your review comment:
My equation (1) is not as you wrote it. My equation (1) is:
(1) dL/dt = inlfow – Outflow
This applies to any definable set of carbon atoms, including their total.
I apply it separately to natural 12C and to human-produced 12C. I could also apply (1) to the total of natural and human carbon but this has no advantage.
This (1) is the continuity equation designed to keep track of specific atoms (in our case). Your (1) destroys this necessary continuity.
I disagree with your (1) because it does not include -Sh(t), and therefore it assumes the sinks for human carbon outflow are the same as the sinks for natural carbon outflow.
This assumption destroys the intended continuity, messes up the carbon cycle calculations, and messes up the minds of those like Andrews who can’t keep track of what is in their carbon cycle calculations.
The proper physics way to formulate this problem is the way I suggest, e.g., to do the natural and human carbon cycles separately using my (1). We can add them up later, if we wish.
This may be the most important point of disagreement in these discussions.
Ed
Dear Uncle Bert,
More specious waffle. You are obviously running scared from the 1812 to 1961 instrumental record because it thwarts your political narrative. All you have to offer on this occasion is a list of excuses. You can’t falsify anything with excuses and you can’t falsify measurements. They are what they are.
You said:
“That should have excluded the two main series (Giessen/Germany and Poona/India) which are at the base of his 1940-1942 “peak”, which doesn’t exist in any other measurement or proxy.”
I have already falsified this in my previous comment.
Additionally your list of excuses are confusing. You refer to a figure and then talk about something else.
You said:
“A peak of some 80 ppmv in only 5 years is only possible if you burn down a lot of forests and regrowth in 5 years simply is impossible.”
You’re making the same stupid mistake as Ralph Keeling. You are ignoring the oceans. All your excuses are falsified by Bromley & Tamarkin 2022.
Bromley & Tamarkin 2022; Correcting Misinformation on Atmospheric Carbon Dioxide; https://budbromley.blog/2022/05/20/correcting-misinformation-on-atmospheric-carbon-dioxide/ Accessed 28-8-2023
They examined data following the explosive volcanic eruption of Pinatubo on the island of Luzon in the Philippines in June 1991. This eruption emitted large amounts of aerosols into the atmosphere blocking sunlight and reducing SSTs and surface temperatures. This altered the Henry’s Law ratio causing a reduction in oceanic emissions lowering the atmospheric concentrations. There was a large natural movement down in atmospheric concentrations of CO2 post the eruption, followed after that by an even larger natural movement back up.
The large movement down in CO2 concentrations post the eruption occurred despite the fact that during this same period, human emissions of CO2 continued unabated. Natural emissions also continued from, e.g. biosphere decay & ocean emissions. During 1991-1992 there was an El Nino event which caused increased emissions from a warmer Pacific Ocean. On top of that, the volcano itself added large amounts of CO2 gas to the atmosphere. In spite of all these emissions, overall SSTs dropped post the eruption causing a large drop in atmospheric CO2 concentrations.
“According to the results of this study, the second derivative (i.e., the acceleration) of CO2 concentration dropped precipitously in the 2 years following Pinatubo to its lowest point in the pre-Pinatubo Mauna Loa record, despite the CO2 additions by humans, natural sources, a volcano and an El Nino. Nature rapidly absorbed the added CO2 and then more rapidly accelerated again to reset its CO2 concentration to trend.
there is no other known, logical or physically possible sink for such a large amount of CO2 to be absorbed so rapidly other than ocean surface.
The environment, mostly ocean surface (since ocean about 71% of Earth’s surface,) demonstrated rapid CO2 absorbance capacity which is 239 times larger than maximum possible net human emissions. We conclude that net human emissions are trivially minor, negligible, and absorbed and re-emitted along with the 239 times larger change in natural CO2.
In the 2 years following the June 15, 1991 eruption of the Pinatubo volcano, the natural environment removed more CO2 than the entire increase in CO2 concentration due to all sources, human and natural, during the entire measured daily record of the Global Monitoring Laboratory of NOAA/Scripps Oceanographic Institute (MLO) May 17, 1974 to June 15, 1991. Then, in the 2 years after that, that CO2 was replaced plus an additional increment of CO2.”
You said that Beck copied good and bad data. What you meant is that Beck should have cherry picked his data to make it look like your ice core record.
Then you follow Keeling and blame an inversion. Like an inversion occurred at all 901 locations at the precise time they were all taking sample measurements. Even a grade 5 child can see through this.
Then you doubled down on calibrating stomata against ice core proxies. Only you do that. I have a chart that I can’t show you as I have no web link to the chart. You can find it. It is Figure 7-13 in the book Climate Truths. You’ll have to buy the book. http://www.climate-truths.com. We have charted Stomatal birch CO₂ vs Antarctic ice core CO₂ after Steinthorsdottir, 2013. We did not calibrate CO2 to the ice core data but merely charted them together. It shows CO2 going up and down and the ice core flat lining it’s way through the middle like an average.
Then there’s the flimsy excuse that the instruments were too close to vegetation and the plants were expiring CO2. This conveniently ignores that fact that readings were taken during the day when the plants were taking in CO2 and not expiring.
Patrice Poyet points out.
Poyet, Patrice 2021 in ResearchGate Discussion.
Global Warming (Part 1): Causes and consequences of global warming, a natural phenomenon, a political issue, or a scientific debate?
https://www.researchgate.net/post/Global_Warming_Part_1_Causes_and_consequences_of_global_warming_a_natural_phenomenon_a_political_issue_or_a_scientific_debate#view=5ce771de3d48b7330442d974
“A typical example where one confuses measurements (IR spectroscopy since 1959, or chemical since 1812 the accuracy of which we discussed before) with proxies delivering reconstructed values that are the result of a model applied on data coming from a low pass filter (firnification=convolution) that changes both the resolution and the dynamic of the records.
You can only compare ice-records with ice-records.
“Ice cores furthermore are low-pass filters on the temperatures themselves because of the “firnification” process.” [Poyet, P., 2021. The Rational Climate e-Book: Cooler is Riskier. The Sorry State of Climate Science and Policies. Final First Edition, April 19th, 125 Figures, 185 Equations, 473 pp., e-ISBN 978-99957-1-929-6, DOI: 10.13140/RG.2.2.28648.80640
(Ch. 5 Glaciers, Ice-Cores, Arctic and Antarctic, Page 182 on Page 189; Also page 110.)] “It takes decades, sometimes centuries before the air is completely trapped in the ice (before that, slowly decreasing exchanges remain with the atmosphere) and the composition of it is a complex sort of “mixed average” over the time during which the firnification process operates. In fact, ice core data, though providing some information, are not accurate proxies of the atmospheric composition (they depress, for various reasons, CO2 content that leaks when there is drainage during the firnification – and there is – as this gas is very soluble) nor of the temperature. They are just a better than nothing proxy. You can compare them between each others (e.g. Arctic versus Antarctic searching for the location of a volcanic eruption), but mixing apple, oranges and cabbages does not deliver any scientific result.””
Even your precious ice core record is fake. Ice core records have regularly gone over 300 ppm and as high as 500 ppm 3,000 years ago. The Byrd Core, e.g., has undergone intense attacks that really don’t stand up to any scientific scrutiny. Referring to the chart from Poyet 2021 of proxy measurements shows Camp Century Core in Greenland and the Byrd Core in the Antarctic going above 400 ppm.
This is Figure 15 from:
Mixing Proxy and Measured Data
DOI: 10.13140/RG.2.2.19788.95360/1
https://www.researchgate.net/publication/354144035_Mixing_Proxy_and_Measured_Data
which is taken from Figure 75 in Poyet 2021. The Rational Climate e-Book: Cooler is Riskier. The Sorry State of Climate Science and Policies. Final First Edition, April 19th, 125 Figures, 185 Equations, 473 pp., e-ISBN 978-99957-1-929-6, DOI: 10.13140/RG.2.2.28648.80640
Pre-Industrial CO2 concentrations from Antarctica and Greenland ice cores of up to 500ppm that were rejected by authors of various papers because they did not fit with the “man-made climate warming” theory. Poyet 2021.
Byrd Core has come under general attack, including from you above, by stating that the core samples were contaminated with drilling fluid. It has been said that everything Jaworowski said regarding the Byrd Core was refuted by Etheridge et al 1996 by the three ice cores drilled by Etheridge et al in 1996. Yet Etheridge never mentioned Jaworowski or the Byrd Core or drilling fluid in his paper. Etheridge did not refute anything.
Etheridge et al 1996 ice cores were for the last 1000 years and did not cover the 500 ppm period from Neftel et al 1982 which was 3,000 YBP. He was specifically looking at the last 200 years when CO2 increased. His CO2 measurements from his ice cores were based on assumptions and models. His CO2 growth was attributed to humans burning fossil fuels by way of assumption, not measurements.
Jaworowski points out that this criticism of contaminated core samples is valid for all other ice cores from the Antarctic since 1985.
There is no valid criticism of Neftel et al 1982 or Jaworowski 1992a. Both the Camp Century Core and the Byrd Core are valid CO2 proxy measurements.
As pointed out by Poyet, Callendar cherry picked the so called “Gold Standard” Ice Core Record leaving out all data showing CO2 proxy measurements above 300 ppm. Every time data is presented that shows CO2 above 300 ppm before 1750 it gets attacked by those supporting the IPCC’s narrative. These attacks don’t stand up to scrutiny.
And as for politics. The strategy employed by the socialists is infiltration and subversion. Subversion is where they say they are not who they actually are and are not doing what they are doing. Actions speak loader than words. You are actively pushing the global socialist agenda. You have infiltrated the CO2 Coalition.
Dear Ferdinand,
Perhaps to give you some perspective, please look at my Figure 7. The top row shows the natural distribution of natural carbon among the four IPCC reservoirs. Only 1.4% is in the atmosphere. 90% is in the oceans. This is the equilibrium distribution for the fast carbon cycle.
Human carbon has added about one percent to the total carbon in the carbon cycle. If humans ever stop emitting carbon to the atmosphere, the human carbon cycle would move to the same equilibrium percentages as the natural carbon cycle. At that equilibium, human carbon would all only 4 ppm to the atmosphere.
My calculations do perfect carbon accounting because I keep human carbon atoms separate from natural carbon atoms. No one else, to my knowledge, is keeping the human and natural carbon atoms entirely separate in their carbon cycles. Not even you.
My one specific objection to your comment is there is no Tau of around 50 years. My figure 5 shows e-time s the time for a level to move 63% of the way to its balance level. You claim your tau does the same thing. Therefore, you tau is really my Te. There is no difference. Te explains everything you use to justify your use of Tau.
Figure 5 shows how the level approaches its balance level seemingly very slowly as it gets closer to its balance level. You have use that “very slowly” feeling to invent a tau but your tau is still Te.
I think the other weakness in your argument is that you do not yet understand balance levels.
Dear Ferdinand,
In reply to your comment: July 8, 2025 at 4:25 am
You are correct that my calculations in HumanBB show a much smaller increase in CO2 that the total measured CO2.
That is because my HumanBB calculations are only for human CO2. Notice, those calculations begin with zero levels in the reservoirs and only human carbon gets added each year.
The difference is the amount that natural carbon has added to the atmosphere.
You have discovered how I calculated the effect of human CO2 by using IPCC’s own data.
Thus, my conclusion that according to IPCC’s own data, human carbon adds very little to the CO2 in the atmosphere.
Ed,
The mass-balance formula we have long discussed only makes sense when the natural absorption term includes aborption of ALL types of carbon. Jim discovered what you and I already knew and maybe even Brendan has figured out. You are motivated to confuse the issue because correct analysis proves that your separate anaylsis of industrial and natural carbon hid from you an important insight: natural processes are removing substantially more carbon from the atmosphere than they are adding. That makes it very tough for Jim to argue natural processes are a significant source of the rise, but he is trying. I do not expect him to be successful. You might want to look at graphs of human emissions and atmospheric accumulation in your own earlier papers, which you have omitted from the current one.
Your conclusion that industrial carbon levels in the present atmosphere are small is old news, was anticipated in the 1955 Seuss paper, and is not relevant to the question of why atmospheric carbon levels have been increasing.
David,
Thinking only of net sinks obscures the possible increase in atmospheric carbon due to increasing natural sources. Keep in mind that yearly emissions from natural sources are twenty times more than industrial emissions. Your simple math will never distinguish the sign of the difference between annual natural sources and sinks. That’s why I’m working on a method of determining it. The main thing I know is Mauna Loa data cannot be fitted by my model without allowing for an increase in emissions. That is why I agree with Dr Ed’s rejection of H1.
If decaying vegetation wasn’t at least as much as previous amounts absorbed, there would begin to be a deficit.
You miss the point by focusing on where the carbon is coming from, or at least by assuming it’s all from fossil fuel. The problem is determining how it’s being distributed and to what degree fossil fuels have contributed to the rise in CO2 in the atmosphere.
The second reference for the modern CO2 measurements at Giessen (Germany) should be:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_2005-07-14.png
The historical measurements were at 7 AM, 2 and 9 PM.
That already gives a bias of about +40 ppmv, compared to the ice cores.
Even the modern average at still rural Linden/Giessen is good for average +40 ppmv, together already +80 ppmv for the historical measurements.
Calendar was completely right to reject all historical measurements for “agricultural purposes”…
Jim,
You write “If [carbon from] decaying vegetation wasn’t at least as much as previous amounts [of carbon] absorbed…” You seem to be implying it could be more! Are you vying with Demetris for the Nobel Prize in Alchemy?
Dear Dr. Ed,
With respect, I’m on your side. My equation one,
(JS1) dC(t)/dt = Eh(t) + En(t) – Sn(t)
is exactly your equation,
(EB1) dL/dt = Inflow – Outflow
with Inflow = Eh(t) + En(t) and Outflow = Sn(t) = SN(t) = [ Sh(t) + Sx(t) ] where Sx(t) equals that fraction of total carbon sinked that was not derived from human sources. I could have included that earlier, but there was no need to clutter up the math with variables that can’t be derived from simple math. In other words, we know Eh(t) and dL/dt from the available data, but calculation or estimation of the relative amounts of Sh(t) and Sx(t) are not possible without model approaches like yours. My primary interest is in resolving the question of which model most appropriately describes the physical processes involved. Although probably a fool’s errand, I would like to see everyone get on the same page here.
You wrote, “I disagree with your (JS1) because it does not include -Sh(t), and therefore it assumes the sinks for human carbon outflow are the same as the sinks for natural carbon outflow.”
Sink rates for human carbon outflow are the same as the sink rates for natural carbon outflow, because of the equivalence principle. I hope my explanation of Sn(t) = [ Sh(t) + Sx(t) ] clears that up.
Dear Jim,
I had only an older version of his RRR approach and couldn’t load your reference in Firefox. But now loaded in the MS browser…
Koutsoyiannis wrote:
“1. The notion of the equilibrium state is incompatible with the recent biosphere expansion, which was documented in the main part of this essay and elsewhere [1,9,25].”
The main effect of temperature on short term is on vegetation at about -5 ppmv/°C for seasonal changes and +3 to +4 ppmv/°C for year by year changes. Over periods longer than a decade the influence of expanding vegetation is near zero and the oceans take over as the main level of equilibrium. Visible as +8 ppmv/°C for Antarctic temperatures and 15-20 ppmv/°C for global temperatures over the past 800,000 years.
That the expansion of the biosphere plays little role can be seen as a very stable 13C/12C ratio of -6.5 +/- 0.4‰ δ13C, until humans start to emit FF. The level today is below -8‰, while vegetation is a net sink of CO2, preferable of 12CO2, leaving relative more 13CO2 behind, thus increasing the 13CO2 level in the atmosphere…
What Koutsoyiannis and many others forget is that a cycle doesn’t add or subtract anything from the atmosphere, only the difference between the ins and outs changes the level of CO2 in the atmosphere. Even if the natural cycle of vegetation doubles (as was at least during interglacial periods), that halves the residence time, but doesn’t change Tau with one second.
“2. The idea that human emissions are the only or the main agent of change is incompatible with the ever-changing Earth’s states, including the atmosphere and climate”
We never said or implied that. Over the past 800,000 years, the changes were huge, but all caused by huge changes in temperature over very long time periods. The warming from a glacial period to an interglacial needed 5,000 years for a change of some 100 ppmv CO2, or some 0.02 ppmv/year…
Even shorter periods like the MWP-LIA cooling don’t show more than 10-20 ppmv/°C.
The current change in the atmosphere is 2.5 ppmv/year, with 5 ppmv/year of FF emissions and suddenly over 100 ppmv//°C. Which violates Henry’s law (maybe +13 ppmv since the LIA…)
According to Koutsoyiannis the FF emissions are not the cause of the increase in the atmosphere…
“3. The importance given to human emissions is disproportional to its share in total (4%).”
Again the idea of the “classic” reactor with unidirectional flows through the container… Indeed, in that case, FF ratio’s in the container and output never can exceed the FF ratio in the input.
But the observed FF level in the atmosphere is already over 10% and in the ocean surface over 6%…
Koutsoyinannis “lake model” is herewith rejected.
Our model more resemples the “fountain model”, where a small input is the only cause of the level and overflow of the basin, no matter how much water flows over the fountain itself… The latter gives the short residence time of 4 years for CO2 in the atmosphere. The former the small net outflow rate of 50 years…
“4. While the proportionality relationship in Equation (A3) has an empirical basis (see below), it may be a result of the coincidence of increasing human and natural CO₂ emissions. The latter, caused by the biosphere expansion, are totally neglected in this relationship. ”
The human input increased a factor 5 between 1958 and today. The biosphere expanded some 20% over the same period. Quite a difference.
As said before: only if both expanded at the same rate, the natural fluxes might be the main cause of the increase.
So, the whole appendix A of Koutsoyiannis fails to reject our approach…
It could be more. If there was an equilibrium before the world population grew from negligible to 9 billion people, a lot of old growth forest has been cut down since.
Brendan,
I agree that data from around the time of the Pinatubo eruption demonstrates that natural processes can affect atmopheric carbon levels. Note that in this case, net global uptake INCREASED because of the cooler weather. That is, atmospheric carbon levels were LOWERED (did not rise as fast) because of the event. This is hardly a convincing demonstration that natural processes are raising atmospheric carbon levels as they remove carbon from the atmosphere.
Jim, about the formula’s:
Koutsoyinannis says:
“It would be absurd to assume that Sn(t) would be related to a portion of the atmospheric storage, such as the surplus above the assumed equilibrium state.”
Well, I suppose that Koutsoyiannis never has heard of the Le Chatelier’s principle?
That shows that Sn(t) – En(t) changes from zero to some value that tries to counter the “disturbance”, that is the change in one of the components of a dynamic equilibrium…
That is exactly what Tau does: with some extra CO2 in the atmosphere, Sn(t) will increase in ratio to the extra CO2 pressure and En(t) may be reduced (in the case of the oceans) or not (or even slightly increase, in the case of vegetation). Thus Sn(t) and possibly En(t) of course change with the extra CO2 in the atmosphere.
95% and more of Sn and En are completely independent of the CO2 level in the atmosphere. The 5% depends of the pCO2 difference between atmosphere and ocean surface. That will go to zero if there were no human emissions or stop increasing if we would halve our emissions, but there is no reason to do that at all…
The math still remains very simple: human emissions are straightforward into the atmosphere, for 100%.
The removal of the extra mass (no matter the original FF molecules) only depends of the total extra CO2 in the atmosphere (not that from one year human emissions) above the long standing dynamic equilibrium with the ocean surface, only with a small change in equilibrium over time caused by SST changes. The observed Tau is around 50 years and has nothing in common with the residence time… Even if all vegetation on earth doubled over time, that does about double S(t) and E(t) and thus halves Te, but doesn’t change S(t) – E(t), thus doesn’t change Tau…
ADMIN NOTICE:
I don’t know if you have the same difficulty as I do, trying to find previous comments that I wish to reply to, and trying to find if there is a new comment that is a reply to a comment days ago.
Because of the large number of comments on this post, I find it difficult to reply to comments that are embedded in comments way above the new comments at the bottom of this list.
So, I am going to try an experiment that is reversible:
WordPress allows me to set the number of sub-comments. it is presently set at the default of 4.
As a test, I am going to reset this to 0.
After this reset, all comments will be reorganized into cronological order rather than in reply order.
This will force us to state the author, date, and time of the comment we are replying to.
But I think it will help us to find the comments we wish to reply to, and help us review all NEW comments since we last looked at this page because they will all be at the bottom of the comment list.
So, if you don’t like this chronological order setup, tell me. It is easy for me to reset the WordPress replies back to 4.
We lose nothing by trying this experiment.
Here we go. Refresh your browser to see the comments in chronological order.
Jim,
It was probably more source than sink until about 1980, due to expanding population and following land use changes. Since at least 1990, the biosphere is a net sink, as can be deduced from the oxygen balance: If there is a net CO2 uptake, then extra O2 is produced or reverse. By measuring the O2 balance, one can calculate the net uptake or release of CO2 by the global biosphere.
Only since about 1990, we have O2 measurements that are accurate enough (less than one ppmv in 21,000 ppmv…) to calculate the net uptake or release of CO2 by the global biosphere. Here reflected in the work of Bender et al.:
https://tildesites.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
The partition of the net CO2 sinks between oceans and vegetation can be seen in Figure 7 at the last page.
From 1994 to 2002 the net uptake by the biosphere was 1.0 +/- 0.6 PgC/year. With the exception of the 1998 El Niño, the biosphere was always a net sink for CO2…
It really is that simple: human emissions are directly, for 100% in the atmosphere. They increase the CO2 level with the full emissions and decrease the δ13C and Δ14C levels for all what they supply.
All what nature does is removing about half what humans added as mass and replace 2/3 of all original FF molecules with CO2 molecules from other reservoirs…
Dr. Ed – July 9, 2025 at 9:52 am
Good idea, I probably missed several comments and reactions, due to the local replies…
Ferdinand Engelbeen July 9, 2025 at 9:33 am
Of course:
“Even if all vegetation on earth doubled over time, that does about double S(t) and E(t) and thus halves Te”
only is true for the biosphere part of the natural CO2 fluxes.
As that is about halve the total natural CO2 flux in and out, then Te is reduced by app. 25%…
Dr. Ed, July 8, 2025 at 9:45 pm
Dear Dr. Ed,
The main question remains:
Human emission are redistributed between atmosphere, biosphere, ocean surface and deep oceans.
The increase in the atmosphere is only a fraction of the observed increase.
What is then the source of the observed difference, as both the biosphere and the oceans increased in carbon content?
Ed, in the comment below addressed to “Dave,” were you talking to me, or to Dave A? In it you complained about my (his?) “tau,” but I’ve said nothing about “tau.”
The model you depicted in your “Figure 3,” labeled “IPCC’s natural and human carbon cycles,” is based on a misunderstanding of Fig. 6.1 from AR5, and it is strikingly unphysical. It shows “human carbon cycle” distinct from a “natural fast carbon cycle,” which is nothing like physical reality, and certainly not what the IPCC’s diagram meant. Notably, your model diagram shows various “human carbon cycle” flows between the atmosphere and both “Land” and “Surface Ocean,” which have no basis in reality. It also shows unbalanced “human carbon cycle” flows from the atmosphere into & from both “Land” and “Surface Ocean,” yet shows zero “human carbon” accumulated in both, which obviously makes no sense.
I’m uninterested in analyzing that model, or the equations based on it. I prefer to focus on the real world.
You claimed that human processes removing carbon from the atmosphere (your “An”) are not negligible. So I discussed those processes, one by one, here:
https://edberry.com/co2coalition/#comment-112419
I showed you that your “Ah,” i.e., the anthropogenic processes which deplete the CO2 from the air, are negligible. More precisely, they are much smaller than the error bars on anthropogenic emissions, so they can be ignored in “mass balance” arithmetic. Even if you count cement carbonation, anthropogenic CO2 removals are still only about 2% of anthropogenic CO2 emissions.
● If you now understand that that is correct, then please acknowledge your error, so that we can move on.
● Or if you still think that’s wrong, then please demonstrate that. Please answer the question I keep asking: What anthropogenic processes do you think remove CO2 from the atmosphere?
“If an honest man is wrong, after being shown his error he either stops being wrong or stops being honest.”
– unknown (related by Andre Bijkerk)
Ed wrote, “So, if you don’t like this chronological order setup, tell me. It is easy for me to reset the WordPress replies back to 4. We lose nothing by trying this experiment.”
One thing you’ve lost is the “reply” button.
IMO, 10 would be better than 4, which was better than zero.
However, it would be better yet if there were a user option to choose to view the comments either in “tree view” (with replies shown immediately following the comments to which they reply), or “chronological.” The default should always be “tree view,” but an option to switch to chronological, to find any new comments, would be helpful.
Ideally, each comment would also show a link to the comment to which it’s replying.
As long as we’re wishing for things, it would be nice if references to .jpg and .png images like this produced scaled, inline copies of the image:
https://sealevel.info/1612340_Honolulu_thru_2025-04_vs_CO2_annot1.png
An “edit” button would be nice, too.
Ferdinand,
“Even if the natural cycle of vegetation doubles (as was at least during interglacial periods), that halves the residence time, but doesn’t change Tau with one second.”
The kinetics of mass transfer of molecules between two reservoirs towards their return to equilibrium (or relaxation) after a sudden modification of the conditions, such as a jump of temperature or of pressure is analogous to how Tau and Te are related by 1/Tau = (K+ + K-) where K+ and K- are the individual rate constants for the forward and reverse directions of flow. A change in either individual rate constants will affect Tau. Making Tau independent of Te is a function of your incorrect model.
“Which violates Henry’s law (maybe +13 ppmv since the LIA…”
Henry’s Law expresses an equilibrium condition where the concentration of gas dissolved in a liquid is directly proportional to its partial pressure. It says nothing about the time to come to equilibrium after an imbalance.
“But the observed FF level in the atmosphere is already over 10% and in the ocean surface over 6%…”
Yes, and therefore “classic reactor” and “lake” simple math models can be rejected.
“The human input increased a factor 5 between 1958 and today. The biosphere expanded some 20% over the same period. Quite a difference.”
The simple math difference between 20% of 100 ppm of natural emissions is 5 times larger than the 4 ppm increase in industrial emissions. Even simple math shouldn’t require any correlation between the two fluxes. Koutsoyiannis hasn’t failed to reject your approach. He led you to water, but he just couldn’t make you drink.
Brendan Godwin July 8, 2025 at 8:32 pm
Brendan, I am pretty sure that you are against measuring temperature in the middle of towns, near airco outlets, asphalt parkways, on asphalted rooftops etc. for the global temperature record.
Then it wonders me why you insist to use CO2 data which are highly contaminated by local CO2 sources. As like the alarmists for bad temperature data, because you like the results?
I do contest both: contaminated data are bad data and should not be used for any record.
There is no need to use contaminated data like these of Giessen and Poona, as there is a quite reliable source of average data over the same periods: ice core CO2 levels, with only one drawback: its resolution, which depends of the local snow accumulation.
For 2 out of 3 ice cores at Law Dome, the resolution is less than a decade. with data over the past 150 years, thus including the 1940 “peak” in the contaminated CO2 measurements of Giessen and Poona. The same ice cores have a direct overlap 1958-1978 with the direct measurements at the South Pole:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/law_dome_sp_co2.jpg
Equal within +/- 1.2 ppmv (1 sigma).
If they correctly reflect the atmospheric data over 20 years, I don’t see any reason that they will not correctly reflect the data of 20 years before 1958. That is for the period 1938-1958, thus including the non-existing peak in the global CO2 data.
And again: stomata data are local data over land. They have the advantage of reflecting local changes very rapidly. Local changes, not global changes.
The historical Giessen data were three times a day, of which one in the middle of the day and two at the much higher levels at the flanks of the nightly degassing. Bias of the measurements: +40 ppmv. Bias of the location (in modern measurements) +40 ppmv. Overall bias, compared to global levels: +80 ppmv. That is your 1940 “peak”…
Have further a read of our specialist in ice core and stomata data: Renee Hannon:
https://co2coalition.org/wp-content/uploads/2024/06/Measurement-of-CO2-Concentrations-Through-Time-2024-June.pdf
Bud Bromley has some strange ideas of what Henry’s law implies. The effect of SST on the CO2 pressure of the ocean surface (in equilibrium with the atmosphere) is only some 10-20 ppmv/°C.
Or for the Pinatubo, only a smaller increase in CO2 than before or after the Pinatubo.
A smaller increase, not a decrease!
In January, compared to the previous year January:
1991: 1.1 ppmv
1992: 1.4 ppmv
1993: 0.8 ppmv
1994: 0.9 ppmv
1995: 1.9 ppmv
Moreover, the reduction of the CO2 increase was mainly caused by increased vegetation growth, thanks to the scattered sunlight by the Pinatubo induced aerosols, giving more light to leaves, normally part of the day in the shadow of other leaves…
How do we know that? Because the 13C/12C ratio increased while the CO2 increase dropped. If the oceans were responsible, the CO2 changes and 13C/12C changes would parallel each other:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_dco2_d13C_mlo.jpg
And I have seen the Byrd contaminated data. Well they did show the whole range of data they have measured at the same depth. For uncontaminated data the spread is about 1.2 ppmv for modern drilling and extraction methods.
If you find drilling fluid, that gives an enormous range, which has nothing to do with the real CO2 data of that time. I should have rejected all these data, the authors only retained the lowest data, as these were probably the real background CO2 of that time. But Poyet (and you) like the high, contaminated data, so the rejection must be wrong…
Then the late Jaworowski.
Indeed Etehridge didn’t refute his objections by using his name, he refuted them point by point, whithout naming him. But everybody knew that Jaworowski’s objections were the target. Except Jaworowski himself, who repeated his objections years later…
Further I confronted him in a personal mail with the fact that he had looked at the wrong column in Neftel’s ice core record: the ice age data vs. the gas age data.
He replied that there was no difference, as there are frequent melt layers in the ice of Siple Dome. In reality Neftel encountered only one melt layer and adjusted the ice age – gas age difference accordingly.
And if you believe Jaworowski, how can one measure 200-300 ppmv in the ice cores when the outside CO2 is over 400 ppmv and in the labs where is measured probably a lot higher, if there is a lot of exchange through “cracks in the ice”?
Let the good old Dr. Jaworowski rest in peace, together with his wrong ideas of CO2 in ice cores…
And how much liquid water do you think remains between the ice crystals at -40°C at the inland cores like Vostok and Dome C?
Ferdinand
To Ferdinand Engelbeen, from July 9, 2025 at 9:33 am
“95% and more of Sn and En are completely independent of the CO2 level in the atmosphere.”
That is completely wrong and utterly opposed to the forces at work between transport across interfaces. Study the derivation of the kinetics of the reaction of A B, which is analogous to interfacial transport. http://brussels-scientific.com/?p=7724 . The transport rates are proportional to the concentration at all times even at equilibrium when the forward and reverse rates are equal. Until equilibrium, the concentrations are constantly changing. There is no static concentration to which the disturbance is heading, such as in the case of your Tau model where the rate is proportional to the current level minus the equilibrium level. That old equilibrium level may never be achieved because of the new equilibrium created by additional carbon added to the system.
Jim Siverly, July 9, 2025 at 11:43 am
Jim,
If I have understand it correctly, both Dr. Ed and I use bidirectional flows to calculate Te or Tau alike. No problem there, except that the time constants of Dr. Ed are based on the total outflows as if these were caused by the absolute CO2 level/pressure in the different containers, while 95% of all outflows (especially from atmosphere into vegetation and back) are completely independent of the CO2 level in the atmosphere. Which makes that his increase of total CO2 mass in the atmosphere is way lower than observed.
I am aware of the time constant for Tau, as that is an observed 50 years. Not 4 years, or there wouldn’t be such an increase in the atmosphere.
Your calculation of the 5 times higher increase of the vegetation inflow violates the equivalency principle for CO2: for nature to be the main cause of the CO2 increase in the atmosphere, it should have increased all in- and outflows a 5-fold between 1958 and today, not 20%…
Koutsoyiannis, Harde and many others use the one-way input – container/lake/bath tube – output model and are completely at odds with reality, thus their results make no sense at all.
Jim Siverly, July 9, 2025 at 1:05 pm
Jim,
“The transport rates are proportional to the concentration at all times”
Yes, for those processes that depend of the CO2 concentration. The calculated output based on the absolute CO2 pressure in the atmosphere is some 16 PgC/year in total into both oceans and vegetation together.
Take the output form the atmosphere into vegetation in spring/summer: 120 PgC absorbed by the biosphere with increasing temperature and sunlight, due to photosynthesis. Going from near zero to 100% in a few months time, near completely independent of the pCO2 in the atmosphere. Even reducing the pCO2 of the atmosphere with some 10 ppmv in the NH. If there was no emission of 60 PgC from the same biosphere at night and 50 PgC from the warming ocean surface, the drop would be 120 PgC or 60 ppmv…
Reverse, there may be some influence of the CO2 pressure in the water of the leaves that respire CO2 at night, but for all other releases by bacteria, molds, animals, including humans, there is zero influence of the pCO2 of the atmosphere in the quantity that is released from decaying organics…
From Ferdinand Engelbeen, July 9, 2025 at 1:21 pm
Ferdinand,
Again you repeat the assertion that “95% of all outflows (especially from atmosphere into vegetation and back) are completely independent of the CO2 level in the atmosphere.” This cannot be supported by experimental data. If so, please present it. Look at the anecdotal data from the CO2 coalition where they subjected trees to several levels of CO2 with arguably a proportional increase in growth rate. If the growth was independent of CO2 level, no significant growth would have been observed.
You completely misunderstand my comparison of your five-fold increase in human emissions and my 20% increase in natural emissions. There is no violation of equivalence principle which applies to first-order uptake. Human emissions are zero order. They don’t follow the rules that must be applied to first order natural emissions and uptake.
“Koutsoyiannis, Harde and many others use the one-way input – container/lake/bath tube – output model and are completely at odds with reality, thus their results make no sense at all.”
Dr. Ed is right. You do not understand his model and the others. You have yet to develop a rigorous model that refutes theirs. Their models are not at odds with reality as they all explain the data and use proper physical principles in doing so. It’s your devotion to a simple math coincidence model that prevents you from understanding their models.
GENERAL QUESTION TO THOSE COMMENTiNG ON PHYSICS:
How familiar are you with the following concepts:
Lagrangian, Hamiltonian, Principle of Least Action, entropy, equilibrium, systems formulation and mathematics, time-step numerical integration, Markov Chains, probability, the significance of stastistical non-correlation, scientific method, and the philosophy of science?
This is not a test and you don’t have to answer this question. But the reasoning you learn in these subjects does help people understand my simple deductive model that is entirely based on (1) continuity equation and (2) outflow proportional to level divided by an e-time.
To Ferdinand Engelbeen, from July 9, 2025 at 1:49 pm, and also from July 9, 2025 at 9:33 am
I may be incorrect in claiming all “transport rates are proportional to the concentration.” You gave examples such as releases by bacteria, molds, animals, including humans, etc. I will give some thought to what degree that would effect a Te model. But certainly, the ocean processes are first order in both directions.
From July 9, 9:33 am
“The math still remains very simple: human emissions are straightforward into the atmosphere, for 100%.”
You are likening human emissions to a “disturbance” and characterizing Tau as relaxation time. That is not an appropriate model in that continually accumulating human emissions, rather than a one-time “dose,” conflated with additional “excess” natural emissions give rise to your ambiguous Tau values. Your estimates of Tau are a consequence of using a flawed model.
“The removal of the extra mass (no matter the original FF molecules) only depends of the total extra CO2 in the atmosphere (not that from one year human emissions) above the long standing dynamic equilibrium with the ocean surface, only with a small change in equilibrium over time caused by SST changes.”
That is assertion based on what equation NS*(t) = K* [ S(t) – Se* ] predicts. Since there will never be cessation of burning fossil fuels in our lifetime, you won’t have any way to verify it.
“The observed Tau is around 50 years and has nothing in common with the residence time… Even if all vegetation on earth doubled over time, that does about double S(t) and E(t) and thus halves Te, but doesn’t change S(t) – E(t), thus doesn’t change Tau…”
Do you have any actual evidence of that?
Jim Siverly quoted Ferdinand saying, “The observed Tau is around 50 years and has nothing in common with the residence time…” and asked, “Do you have any actual evidence of that?”
The roughly 50 year “adjustment time” (a/k/a the 35 year effective first half-life) of CO2 added to the atmosphere is determined from measured data, as I discussed here (section 2):
Burton, D. A. (2024). “Comment on Stallinga, P. (2023), Residence Time vs. Adjustment Time of Carbon Dioxide in the Atmosphere.” OSF Preprints. https://doi.org/10.31219/osf.io/brdq9 (and there’s supplementary material here)
It also cites five other sources reporting approximately the same result: Spencer 2023, Engelbeen 2022, Dietze 2001, IPCC SAR WG1 TS B.1 p.16, Moore & Braswell 1994:
1. Spencer, R. W. (2023). ENSO Impact on the Declining CO2 Sink Rate. J Mari Scie Res Ocean, 6(4), 163-170. https://doi.org/10.33140/jmsro.06.04.03
2. Engelbeen, F (2022). The origin of the increase of CO2 in the atmosphere, http://www.ferdinand-engelbeen.be/klimaat/co2_origin.html (section 3)
3. Dr. Peter Dietze: http://www.john-daly.com/carbon.htm
4. The IPCC’s Second Assessment Report: WG I Technical Summary, section B.1, p.16:
https://archive.ipcc.ch/ipccreports/sar/wg_I/ipcc_sar_wg_I_full_report.pdf#page=29
https://sealevel.info/SAR_TS_p15_50yr_adjustment_time_highlighted.png
Excerpt:
“Within 30 years about 40-60% of the CO2 currently released to the atmosphere is removed.” That implies an adjustment time of 33-59 years, and a half-life of 23-41 years.
5. Moore, BIII, &Braswell, B.H. (1994). The lifetime of excess atmospheric carbon dioxide. Global Biogeochem. Cycles, 8(1), 23–38. https://doi.org/10.1029/93GB03392
Excerpt:
“The single half-life concept focuses upon the early decline of CO2 under a cutoff/decay scenario. If one assumes a terrestrial biosphere with a fertilization flux, then our best estimate is that the single half-life for excess CO2 lies within the range of 19 to 49 years, with a reasonable average being 31 years.”
Also, Prof. Richard Lindzen mentioned it during the Q&A (3rd video) of this excellent(!) lecture:
● Part 1: https://www.youtube.com/watch?v=hRAzbfqydoY
● Part 2: https://www.youtube.com/watch?v=V-vIhTNqKCw
● Part 3 (Q&A): https://www.youtube.com/watch?v=69kmPGDh1Gs (including discussion of CO2 adjustment time / effective atmospheric lifetime):
Dear Ferdin
I am responding to your “Fountain Model” that you described in response to my comment. Your Fountain Model is nothing that exists in nature. When water enters a fountain, it doesn’t cascade over a stagnant pool of water that is only released if a small valve opens from the bottom. The water mixes with all the water in the fountain, and the thoroughly mixed water cascades over the side. Nature doesn’t segregate CO2. Dr. Ed’s hypothesis is that outflow is proportional to level or concentration. This makes sense because as the concentration of CO2 increases in the atmosphere, according to the gas law, CO2 partial pressure increases, and the number of collisions with its surroundings increases. These surroundings include other gases, matter, etc. Some of these collisions are with sinks, thus increasing outflow. A hypothesis has to be derived from logic. Your hypothesis that there is some carbon cycle that exists in nature that is partitioned from the human carbon cycle violates the Equivalence Principle and all manner of logic and common sense that the scientific method derives from. Your notion that there are human sinks and natural sinks has no observable basis. You will need to explain in detail how nature does this.
Dear Uncle Bert,
Re: Your comment July 9, 2025 at 12:47 pm.
You’re looking at ice core data for the last 150 years. You can’t take ice core proxies until firnification is complete. That takes centuries. Take that same data that you’ve presented and conduct a proxy measurement in another 200 to 300 years and it will show the same flat line.
You said: “stomata data are local data over land . . . Local changes, not global changes”. You also say CO2 is a well mixed gas the same everywhere. You say it’s not well mixed if it is measured from stomata. Ice core data is local to the poles and is not global. You thinking is scrambled.
Your Giessen hysteria is based on nothing except your specious waffle, excuses and a wing and a prayer.
You said: “Bud Bromley has some strange ideas of what Henry’s law implies”. Bud Bromley is a world renown expert on Henry’s Law. He worked with Henry’s Law his entire working career. It is his profession. He knows a lot more than you do. You only think you know. You’re once again blaming everything on vegetation growth and ignoring the oceans. It can’t be the oceans no matter what and the only argument you have to back that up is yet more of your specious waffle.
And you’re doubling down on the Byrd ice core data being contaminated. The data was not contaminated. It was only contaminated in your confirmation biased mind. All other ice core data was contaminated.
More from [Poyet, P., 2021. The Rational Climate e-Book: Cooler is Riskier. The Sorry State of Climate Science and Policies. Final First Edition, April 19th, 125 Figures, 185 Equations, 473 pp., e-ISBN 978-99957-1-929-6, DOI: 10.13140/RG.2.2.28648.80640, (Ch. 5 Glaciers, Ice-Cores, Arctic and Antarctic, Page 182 on Page 189; Also page 110.)]
“If I understand well: Oeschger has been unable to answer one single question asked by Jaworowski, but he states that he cannot be wrong because he’s been involved for so long that he cannot be mistaken, and finally the cherry on the cake, the argument of morality, Jaworowski is irresponsible because he dares ask questions. [Page 247]
3. Now, third stage, while drilling and extracting the core, when lifting up the column will let the gas reform from the clathrate and escape the sample throughout the cracks (this is somewhat following similar hysical processes to what happens when oil and gas are extracted by fracking). Furthermore various pollutions, contamination and corruption of the T preservation are unavoidable during the drilling, conditioning and transportation processes. While lifting up the ice core the same mechanisms that led to fractionation when the ice accumulated over time are also at play but in a reverse manner as the gases will transit from their hydrate form to gas again at different P/T (according to the phase diagram) and therefore at different moment and depths thwarting the records in the bubbles. Drilling decompresses cores excavated from deep ice, and contaminates them with the drilling fluid filling the bore-hole. Decompression leads to dense horizontal cracking of cores, by a well known sheeting process. After decompression of the ice cores, the solid clathrates decompose into a gas form, exploding in the process as if they were microscopic grenades. In the bubble-free ice the explosions form a new gas cavities and new cracks as reported by Shoji and Langway (1983) for a 2,037m long ice-core “Deep-ice cores drilled from the Greenland and Antarctic ice sheets undergo volume relaxation due to the expansion of air bubbles with time after core recovery”. These authors also report, and it gives an idea of the stress of the recovered sample, “decreasing rate of hydrostatic pressure of about 5.4bar.min-1 for each core length recovered of approx 1.9m”. Through these cracks, and cracks formed by sheeting, a part of gas escapes first into the drilling liquid which fills the bore-hole, and then at the surface to the atmospheric air. Particular gases, CO2, O2 and N2 trapped in the deep cold ice start to form clathrates, and leave the air bubbles, at different pressures and depth. [Page 249]
As a summary, all these problems arise simply because the ice cores do not fulfill the essential closed system criteria.” [Page 250]
Poyet states on page 251:
“On the other hand, the ice core data from the Taylor Dome, Antarctica, which are used to reconstruct the IPCC’s official historical record, feature a much more flattish time trend and range, i.e. 285 to 245 ppmv (Indermühle, et al. 1999). This difference strongly imply that ice cores are not a proper matrix for reconstruction of the chemical composition of the ancient atmosphere. Furthermore, Jaworowski (1997) claims that many discrepancies affect the ice cores and that (Oeschger et al., 1985) made an ad hoc attempt to explain some of these anomalies without success and further adds a very specific claim “In about ~6,000-year-old ice from Camp Century, Greenland, the CO2 concentration in air bubbles was 420 ppmv, but it was 270 ppmv in similarly old ice from Byrd, Antarctica”. Though, he does not provide the source of this, it is not difficult to find Fig.1 in (Neftel, 1982) to display exactly that sort of anomaly, though the age is more ~7,000-year-old corresponding to 1010 meters at Camp Century, Greenland and 900 meters at Byrd, Antarctica, see for yourself next Figure 108. [Page 252]
So we are left with inaccurate and dubious ice core results as the three fundamental premises are violated because the closed system criteria cannot be met, and which lead the entire CAGW edifice to crumble. Pre-industrial CO2 air concentration of at least 335 ppmv (Slocum, 1955) and pre-Boreal Holocene concentrations of up to 348 ppmv totally invalidate the low and arbitrary cherry picking of Callendar (1938) of 292 ppmv319 which appears more as pathological science (Langmuir, 1989) than anything else. “Callendar was prejudice in selecting from all his data roughly 30%, which showed concentration around 290 ppm, leaving the remaining 70% which showed concentrations over 300 ppm” (Foscolos, 2010) and he made a disservice to science. This practice of arbitrary selection of data sets matching prerequisites is also prejudicial to science and denounced by Jaworowski (1997) for Neftel at al.; Pearman et al.; Leuenberger and Siegenthaler; Etheridge et al.; Zardini et al.; among others.”
From his 2004 paper, Jaworowski, at page 252 in Poyet 2022, states that the IPCC concluded that all CO2 emissions post the industrial revolution were caused by humans burning fossil fuels and that this is based solely on the assumption that CO2 did not rise above 300ppm until after the industrial revolution. Jaworowski says that this assumption, which is based on ice core studies, is false and that IPCC projections should not be used for national and global economic planning.
Additionally Jaworowski says: “. . . they did not measure CO2 in the air bubbles and secondary gas cavities from such larger samples, but only from 1g samples.. . small [sample] size meant that [they were] probably uncontaminated.
Jaworowski (1992a)” Pages 242-243.
You ignore all inconvenient truths and facts. You’ve totally ignored the fact that Etheridge was comparing ice core samples from 2,000 years apart. The 3,000 YBP samples were wrong because they weren’t the same as his 1,000 YBP samples. Biased pseudoscience.
You have a confirmation bias and all arguments must be equal to your confirmation bias. You construct specious waffle arguments to try and make everything equal to your confirmation bias. Your comment on July 9, 2025 at 12:47 pm was nothing more then another bunch of excuses. You’ve said nothing that negates anything that I have said.
Jim Siverly on July 9, 2025 at 3:33 pm and July 9, 2025 at 4:02 pm
Part 1.
Dear Jim,
I will try to show where it goes wrong with the use of Te, compared to Tau, specifically for the biosphere, as the problems are very clear for that part…
To start with: Te and Tau are different things, but may be the same in specific circumstances.
The formula for Te is:
Te = mass / output
The formula for Tau is:
Tau = disturbance / effect
The first is about how long a molecule CO2 resides in the atmosphere, that is the residence time or turnover time.
The second is how long it takes to remove an extra injection of CO2 mass in the atmosphere back to 1/e (~37%) of the original injection. In the case of a linear ratio between disturbance and effect, the time period makes no difference for Tau.
The first is about molecular transfer, the second is about mass transfer. Both for natural and FF CO2 alike.
In the case of a one-way world (container/lake/bath tube model), Tau is always <= Te.
In the case of a bidirectional world (fountain model), Tau is completely independent of Te.
Then the "model":
We can separate the in/outflows in two main parts: atmosphere – biosphere and atmosphere – oceans.
Both show large bidirectional (mainly seasonal) flows.
1. The atmosphere – biosphere flows.
In 1750, according to the IPCC, there was a more or less stable dynamic equilibrium between the atmosphere and the biosphere, with an alternating bidirectional flow of 108 PgC/half year.
That gives for Te:
Te(a-g): 628 / 108 = 5.8 years
Te(g-a): 2500 / 108 = 23.1 years
For Tau:
As there is no disturbance, the effect is zero and Tau can't be calculated.
Remark: Te(g-a) is in fact mostly the effect of the much smaller reservoir of about 550 PgC in living vegetation. That gives a much faster Te(g-a) of 550 / 108 = 5.1 years. For our model, that plays no role at all.
Then we suddenly add 50% extra CO2 in the atmosphere, about the current increase, so that we can compare the results.
The observed increases in fluxes and decrease in the vegetation reservoir (according to the IPCC) gives:
Te(a-g) = 883 / 123 = 7.4 years
Te(g-a) = 2470 / 118.7 = 20.1 years.
Tau = (883 – 589) / (123 – 118.7) = 68.4 years
Remarks:
The increase of CO2 in the atmosphere is far more rapid than the increase in outflow into vegetation, because the biological growth of vegetation needs far more time to follow the extra pCO2 pressure. Even in ideal circumstances, the ultimate growth rate is about 50% of the extra CO2 level. Not 100%.
The back flow of CO2 from vegetation into the atmosphere follows the inflow in vegetation, mostly within the same year in other seasons, minus what is added to more permanent vegetation and soils. As the total level in vegetation + soils hardly changes, Te(g-a) decreases.
That also means that Te is not constant and the reverse formula (2): Outflow = L /Te is not applicable.
That all demonstrates that Tau and Te have very little in common and the results not only differ an order of magnitude, but also are nearly independent of each other. Add to that the Tau for the oceans of a similar order (and more accurate calculations) and then you will find the ~50 years real, observed, adjustment time…
About understanding the different models, please look at my presentation for the Clintel wrokshop in Athens, last September, with a direct confrontation with Harde, Koutsoyiannis, Stallinga and others. If that is not sufficient, we can discuss that here in detail.
https://www.ferdinand-engelbeen.be/klimaat/klim_img/on_the_co2_residence_time.ppsx
And, while Berry started with the same one-way "container/lake" model with only one Te out, he evolved to a two-way model in recent years, which is already more like what happens in the real world. Be it with the decay rates which are not relevant at all. Koutsoyiannis, Harde, Stallinga and others still stick to their one-way models.
"That is not an appropriate model in that continually accumulating human emissions, rather than a one-time 'dose,'"
Sorry, but for any process in dynamic equilibrium, only the distance between the "disturbed" pCO2 and the equilibrium pCO2 counts, no matter if that is a one-time injection or a continuous (increasing) supply. That can be seen in the quite constant Tau, while yearly human emissions increased a five fold 1960-2020 and CO2 in the atmosphere increased with some 30% over the same time period:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
Where A shows the sum of all human emissions since 1750, the observed increase in the atmosphere, the influence of the SST increase since 1850, calculated with the formula of Takahashi and the resulting ΔpCO2 between atmosphere and ocean surface.
B shows the observed net sink rate with a polynomial through the data.
C shows the calculated Tau.
That Tau is observed and not even based on a model is clearly demonstrated by David Burton…
Stephen P Anderson, July 9, 2025 at 5:25 pm
Stephen,
We didn’t separate human and natural CO2 at all in all our works. That is what Dr. Ed did.
In all our calculations, the human input is only handled as a separate, one-way supply into the atmosphere. That is all. In the atmosphere, it is mixed with all what is already there plus what is added by the natural cycles. In all following reactions it is handled as part of the mass changes, not separated at all.
The outputs are directly proportional to the partial CO2 pressure (pCO2) difference (not the absolute CO2 pressure!) with the ocean pCO2 and similar for water in plant leaves. For plants, the bulk of the CO2 uptake is completely independent from the pCO2 in the atmosphere and only depends of temperature and sunlight. Only a small percentage per year is directly proportional to the extra CO2 in the atmosphere. The same for the ocean surface temperatures over the seasons and the resulting in- and outflows.
That are the main differences in “model” that Dr. Ed and we have.
More to see in the sheets that I have made for a workshop in Athens:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/on_the_co2_residence_time.ppsx
Dave Burton, from JULY 9, 4:35 PM
Artifact: Something observed in a scientific investigation or experiment that is not naturally present but occurs as a result of the preparative or investigative procedure.
Your Tau model is an artifact of a self-fulfilling prophecy. The plot you made in your comment on Stallinga, P. (2023), “net natural CO2 removal rate vs. Mauna Loa CO2 level,” follows from Koutsoyiannis’ equation (A3), which is NS*(t) = K* [ S(t) – Se* ] or my equation (2) from July 8, 2025 at 12:32 pm. Your data fits the model, but unfortunately correlation does not equal causation. You even label the graph “fossil only” seemingly unaware of the fact that it violates the equivalence principle.
In short, your logic is flawed. You assume no annual increases in natural emissions and no change in equilibrium conditions. Then you apply an equation that assumes the sink rate is proportional to the disturbance and claim the calculated result is a “measured” adjustment time. That fails the smell test.
Thanks for the reference to the Moore and Braswell reference introducing me to some unfamiliar terms, donor-dependent flux and unit pulse (Dirac Delta) functions. I will investigate them for potential application to this discussion.
Brendan Godwin, July 9, 2025 at 7:38 pm
Brendan,
You have no idea of the differences between ice cores.
Two of the Law Dome ice cores have an enormous snow precipitation per year: 1.2 meter per year ice equivalent.
That makes that at 72 meters depth or ~40 years of snow/ice layers, the gas bubbles are already fully closed in the ice. Until that depth, there is 40 years of gas exchange with the atmosphere, which makes that the average age of the air, at the depth where the gas bubbles fully close, is only 10 years older than in the atmosphere:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/law_dome_firn.jpg
That means that the difference between the age of the ice and the enclosed gas is about 30 years. That is all.
There are differences between the closure time for different bubbles, which makes that the gas content of all bubbles at the same depth has a spread of about 8 years.
As there is a steady increase in CO2 over the past 100 years, the changes in CO2 level is easy to follow and also shows that there is no “leaking” of CO2 or diffusion within the ice core, surely not over such a short period.
That also shows that the compilation of the late Ernst Beck makes no sense: there was no “peak” of 80 ppmv around 1940, or that would have been measured in the Law Dome ice cores as a near equal peak, but with shorter duration.
I never said that CO2 is well mixed everywhere. It is well mixed in 95% of the atmosphere. It is not well mixed in the first few hundred meters over land, where huge CO2 sources and sinks are at work. Thus all CO2 measurements there, historical or not, don’t give you any clue of the real “background” CO2 level.
And Giessen hysteria? It looks more that you are getting hysteric if one shows you that the historical data were not so reliable. Have a look at the monthly averages for the modern station at Linden/Giessen:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_mlo_monthly.jpg
Compared that to what is measured on the top of a volcano…
The standard deviation for the historical CO2 data was 68 ppmv (1 sigma, not a sign of reliability!), of the modern station about half of it and at Mauna Loa a few ppmv (seasonal changes excluded) and at the South Pole less than 1 ppmv…
“Bud Bromley is a world renown expert on Henry’s Law. He worked with Henry’s Law his entire working career. It is his profession.”
Maybe he is, and I am not an “expert” in these matters, but I look at the evidence of what many “experts” tell me and accept their expertise, if what they say is reasonable.
So, what says Bud Bromley: that the recent CO2 increase is caused by Henry’s law because of the warming oceans. In the past 800,000 years, the CO2/T ratio never was above 20 ppmv/°C. Currently not more than 3-4 ppmv/°C for short term temperature changes (Pinatubo, El Niño) and -5 ppmv/°C for seasonal changes.
The change over the past 175 years the increase of CO2 in the atmosphere is over 100 ppmv/°C. That rings some alarm bells: impossible that Henry’s law got berserk.
Thus looking at what other “experts” say, I did see the work of Takahashi on near one million seawater samples and he concluded that the increase in pCO2 (the CO2 level in equilibrium with the atmosphere) with temperature is a simple formula, independent of the start conditions or composition of the seawater:
(pCO2)seawater @ Tnew = (pCO2)seawater @ Told x EXP[0.0423 x (Tnew – Told)]
Or calculated for the SST increase since the LIA (worst case): some 13 ppmv extra.
Since 1850: less than 10 ppmv extra.
Bud Bromley’s expertise indeed is quite strange…
And the ice core from the Siple core (not the Byrd core) indeed was contaminated with drilling fluid:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/siple_01.jpg
“Additionally Jaworowski says: “. . . they did not measure CO2 in the air bubbles and secondary gas cavities from such larger samples, but only from 1g samples.. . small [sample] size meant that [they were] probably uncontaminated. Jaworowski (1992a)” Pages 242-243.”
Which thus is clear nonsense: there is a huge range of 280-500 ppmv at the same depth from multiple samples where drilling fluid was found.
And then the following:
“Particular gases, CO2, O2 and N2 trapped in the deep cold ice start to form clathrates, and leave the air bubbles, at different pressures and depth.”
That indeed is true. But the reverse, does not lead to problems, as ice cores are at least stored for over a year at -20°C to expand. Then most clathrates decompose, as “grenades” that explode, causing cracks in the ice.
As N2 and O2 clathrates “explode” at much lower temperatures than CO2 clathrates, they should escape first, thus leaving higher CO2 levels behind. As the opposite is found, even within current much higher CO2 levels in the ambient atmosphere, that seems no problem at all.
The newest sublimation technique even sublimates everything of a sample under vacuum, leaving no ice at all, freezes water out and cryogenically freezes every gas to measure them later over a mass spectrometer, including the isotopic ratio’s…
The objections of the late Jaworowski are exactly the points that Etheridge et al. have investigated: drilling with three different methods, dry (hot coil) and wet, sampling CO2 top down in air, firn and ice and especially at closing depth both in firn and ice where the bubble closing starts and ends.
Jaworowski was a specialist in the radioactive outfall of Tsjernobyl, including in ice cores, but he never performed any CO2 measurement in ice, only had a lot of comments that were rejected only 4 years later. Still he insisted that he was right in 2002, 4 years after Etheridge’s work. That is your source…
“You’ve totally ignored the fact that Etheridge was comparing ice core samples from 2,000 years apart.”
Not that I know: the Siple ice core is much longer than the three Law Dome ice cores, but all ice cores show the same CO2 levels over the past 10,000 years in overlapping periods with a maximum difference between each other of +/- 5 ppmv:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/antarctic_cores_001kyr.jpg
and
https://www.ferdinand-engelbeen.be/klimaat/klim_img/antarctic_cores_010kyr.jpg
Despite extreme differences between the ice cores in accumulation rate: from 1.2 meter per year for Law Dome to a few mm/year for the inland cores like Vostok and Dome C and between -20°C and -40°C average temperature.
It is up to you who you want to believe… I look at all the evidence, no matter who says it and no matter if I like the data or not…
Jim Siverly wrote on July 10, 2025 at 10:10 am, “Your Tau model is…”
I have no “Tau model.”
There are four commonly mentioned time constants associated with atmospheric CO2, as I discussed in my Comment on Stallinga. The one which matters for climate is the “adjustment time” (roughly fifty years, determined from measurements). I sometimes describe it as the “effective lifetime.” The associated half-life is about 35 years.
The one which Demetris Koutsoyiannis, Ed Berry, Peter Stallinga, and a few others erroneously fixate on is the “turnover time” (estimated from models at at three to five years). It is also sometimes called the “residence time.”
Jim wrote, “The plot you made… follows from my equation (2) from July 8, 2025 at 12:32 pm” (‘(2) NS(t) = k* [ C(t) – C* ]’).
The plot does not follow from any model or the equations derived from any model. It is just data: measured CO2 data, and calculated emissions (from economic statistics). The observed linearity is simply what the actual data show.
That linearity is unsurprising because we know that the main (geophysical & biological) processes which accelerate the removal of CO2 as the CO2 level rises are roughly linear.
Jim wrote, “You even label the graph “fossil only” seemingly unaware of the fact that it violates the equivalence principle.”
Apparently I was unclear. “Fossil only” simply means that the data in the graph includes only fossil CO2 emissions, and does not include estimates of “land use change emissions.”
It is commonly estimated that current CO2 emissions due to land use changes are only about 1/10 the magnitude of fossil CO2 emissions, but the fraction was higher in the past.
Land use changes (clearing forests and draining swamps) cause the release of (non fossil) CO2, but the magnitude can only be estimated from very uncertain models. So there are two ways of accounting for it:
Option #1. We can include very rough estimates of land use change emissions in the estimates of anthropogenic CO2 emissions. This is more “fair,” but at the cost of widened error bars on our estimates of anthropogenic emissions.
Option #2. Alternately, we can count only fossil CO2 as anthropogenic emissions, and consider the land use change emissions as a diminishment of natural CO2 sinks. That has the advantage of resulting in much more precise “anthropogenic emission” numbers, because we aren’t adding the rather large uncertainty of those land use change emissions. But the cost is that our calculated CO2 removal rates are somewhat understated.
Since I have very low confidence in the models used to estimate land use change emissions, in my plot I chose Option #2. That is what “fossil only” means.
I explained that in the paper:
Here’s that plot annotated to identify a few key events associated with “outlier” data points:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot4.png
I also mentioned in the paper what the result is when Option #1 is used:
Jim wrote, “You assume no annual increases in natural emissions and no change in equilibrium conditions.”
Where did you get THAT idea? I said no such thing.
In fact, I can name several natural CO2 sources which I’m confident have increased. So what? There’s nothing remarkable about that. Natural CO2 sinks have increased faster.
It would be unreasonable to think that equilibrium levels cannot change. For one thing, we know from ice core data that CO2 levels at glacial maxima averaged around 190 ppmv, and during interglacial optimums they peaked around 280 ppmv, representing a roughly 90 ppmv shift in equilibrium CO2 level in the air (associated with very drastic environmental changes).
What’s more, the equilibrium between multiple carbon reservoirs depends on the total amount of carbon in the system. So if the total amount of carbon increases (due to burning coal), the equilibrium levels must also increase.
However, the atmosphere contains less than 3% of the carbon in the major carbon reservoirs (ocean, terrestrial biosphere/soil, and air), and our CO2 emissions have increased the total by less than 2%. So the change to the equilibrium levels due to that increase should be small.
Jim wrote, “you apply an equation that assumes the sink rate is proportional to the disturbance and claim the calculated result is a ‘measured’ adjustment time.”
I did no such thing. I just plotted the data. The linearity is obvious.
When you see an obviously linear plot, linear regression yields the equation which characterizes it. The equation follows from the data.
Perhaps I assume too much. Do you understand how to recognize linearity vs. acceleration vs. deceleration in a graph?
Ferdinand, from your comment July 10, 2025 at 4:07 am
The Tau model gets increasingly hard to understand. In your calculations for present day, you have
Tau = disturbance / [a difference in bidirectional flows]
Where is the derivation of this formulation?
In my objection to conflating a constant infusion with a one-time dose you wrote, “Sorry, but for any process in dynamic equilibrium, only the distance between the ‘disturbed’ pCO2 and the equilibrium pCO2 counts, no matter if that is a one-time injection or a continuous (increasing) supply.”
Where is that assumption validated? That could only be known if there was experimental data to confirm. There has been and likely never will be a cessation of burning fossil fuels.
Your graph C in the link you gave was calculated and, therefore, not observed. What is observed is that your calculation is based on a flawed model as Dr. Ed, Koutsoyiannis, Harde, Stallinga and others have been trying to explain to you.
I was unable to load the power point presentation. Can you check to see if the link is correct?
Dave Burton July 9, 2025 at 10:42 am
Dear Dave,
Did you ever learn to read?
Your comment shows you did not even read the legend to my Figure 3, which clearly says that it shows the exact data from IPCC Fig. 6.1.
My Figure 3 exactly represents the key carbon cycle data in IPCC’s Fig. 6.1. Maybe you are so incompetent that you cannot understand IPCC’s Figure. 6.1, and simply follow the numbers that show IPCC’s levels and flows for its Land-Air-Surface-Deep simulated carbon cycle.
The purpose of my Figure 3 is to make it easy to understand what is in IPCC’s Fig. 6.1.
You don’t understand either figure. You call these figures “unphysical.”
If you think you have better data on the fast carbon cycle than the IPCC spent about $500 billion to produce, then where is YOUR competitive carbon cycle diagram and your argument that somehow YOUR data is so much better?
You say my Figure 3 lower row for the “human carbon cycle” “has no basis in reality.”
But you did not even read my text that says the same thing about IPCC’s human carbon cycle. You did not read any of my papers that calculate IPCC’s true human carbon cycle using IPCC’s own natural carbon cycle data, to prove IPCC’s human carbon cycle is wrong as shown in IPCC’s Figure 6.1 and in my Figure 3.
The late Richard Courtney wrote that my work – that uses IPCC’s own data to prove wrong IPCC’s claim that H(1) is true – is the only breakthrough in climate science since 1980. You may disagree with Courtney, but you are not a qualified reviewer like he was.
In any case, I would think that anyone as involved as you are in climate science would have read what I wrote carefully. But you reject my papers that show this, when you have not shown there is any error in my argument.
You simply say, “I’m uninterested in analyzing that model, or the equations based on it. I prefer to focus on the real world.”
The “real world” you say. You are living in a pseudoscience dream world.
Then you change the subject to talk about Ah.
You say, “I showed you that your “Ah,” i.e., the anthropogenic processes which deplete the CO2 from the air, are negligible.”
No, you did not. You did junk science to make your claim.
My argument is simple. I simply assume human carbon follows the same rules as natural carbon follows to flow through the atmosphere, e.g., the climate equivalence principle.
Turns out this approach proves your claim is wrong. Further, there is no valid scientific basis to your claim.
You argue you can “ignore human emission in your mass balance arithmetic.”
You are wrong because when we include it, we get a different answer. We get the correct answer.
My paper above explains why your mass balance arithmetic is wrong, and you have not defended your error.
You don’t understand IPCC data that relates to this discussion.
You don’t understand my paper or its proof that H(1) is false.
You can’t do a correct carbon mass balance because you throw out the most important part of the balance.
Jim Siverly, July 10, 2025 at 12:31 pm
Jim, I think that David Burton has replied to most of your questions…
More details about what Tau means and different calculations can be found at Wiki:
https://en.wikipedia.org/wiki/Exponential_decay
In a former page of Wiki it was shown that for a linear response of a system in equilibrium, the formula:
Tau = disturbance / effect is independent of the time frame over which the ratio is measured. For non-linear decay rates, one need to do the calculation for each time frame again.
Both the uptake by the oceans and by vegetation are quite linear.
Effect in the case of CO2 is the net increase in output when the CO2 level above the equilibrium increases, the net increase in output is the difference between inputs and outputs, for each bidirectional exchange between reservoirs apart as good as for all exchanges together.
And in my opinion, a simple calculation, based on observations, is as valid as a direct observation.
Our idea of the real word is based on real world data, the “one-way” model is rejected by the same data:
If one has only 1.5-5% FF in the input, the one-way model of Koutsoyiannis, Harde, Stallinga,… never can show higher levels of FF in the atmosphere than 5%. In reality, the atmosphere already contains over 10% FF and the ocean surface over 6%.
If you click on the reference, the sheets are automatically downloaded, thus maybe found in your download map.
If that doesn’t work, I will make pictures of the relevant sheets…
Ferdinand,
Wiki is not a scientific reference. It has no scientific credibility. It has site moderators who push agendas. Your Fountain Model, where outflow is proportional to [pCO2(atm)-pCO2(ocean)] has no scientific basis-that is, there is nothing that it is derived from. There is no partial pressure of CO2(ocean). Henry’s Law states that the amount of gas that dissolves in a liquid is directly proportional to the partial pressure of the gas above the liquid. Dr. Ed’s hypothesis that outflow is proportional to level is derivable from Henry’s Law and the Ideal Gas Law. Your model has no natural basis. Also, you continue to violate the Equivalence Principle, although you continue to claim that you don’t, but Dr. Ed does. You don’t make any sense.
Ferdinand,
The partial pressure of CO2 is equal to the mole fraction of CO2 times the total pressure of the atmosphere. It has nothing to do with some imaginative pCO2(ocean).
Dave Burton, in answer to July 10, 2025 at 11:46 am, and Ferdinand Engelbeen July 10, 2025 at 1:41 pm
No, Ferdinand, Dave Burton replied unsatisfactorily to my questions. He claims the “CO2 removal rate vs. CO2 level” plot does not follow from any model. The plot in question has the form NS(t) = k* [ C(t) – C* ] with CO2 removal rate being net sink, NS(t), and CO2 level as C(t). When NS(t) = 0, C(t) = C* or as Dave’s preprint says, the “x-intercept gives an estimate of the equilibrium level, which is 285 ppmv. Like it or not, that is a model equation.
Ironically the explanation of “fossil only” misses the fact that sink rate is calculated from Eh(t) – dC(t)/dt which is another way of saying “fossil carbon not removed” in violation of the equivalence principle.
Furthermore, Dave admits that, “the equilibrium levels must also increase.” Yet his simple math model portrayed by the “CO2 removal rate vs. CO2 level” plot leaves no room for that possibility.
Ed wrote on July 10, 2025 at 1:35 pm, “My Figure 3 exactly represents the key carbon cycle data in IPCC’s Fig. 6.1.”
No, Ed, it represents your misunderstanding of AR5’s Fig. 6.1. They show in red the natural increases in natural CO2 sinks which result from elevated CO2 levels, and you misinterpreted the red as meaning those were “human” CO2 sinks.
Perhaps the AR5 authors should have used a different color, rather than using the same red that they used for human CO2 emissions. It was clear to me what they meant, but obviously it was unclear to you. (The AR6 authors used a quite different diagram for their figure 5.12, which I found less clear, but you might prefer it,)
For instance, the AR5 authors used a red arrow for 20 PgC/year (of the 80 PgC/year) of CO2 absorbed by the ocean from the atmosphere, and likewise a red arrow for 17.7 PgC/year of the CO2 emitted from the ocean into the atmosphere, because those increased fluxes are due to the elevated levels of atmospheric and ocean surface CO2. You interpreted those as “human.” But those are both natural CO2 fluxes.
The reason the AR5 authors drew them in red is because they represent the portion of the natural CO2 fluxes which are due to the rise in atmospheric CO2 level (and the rise in surface water DIC), which they understand (but you deny) is due to human CO2 emissions.
The physical mechanism for those increased fluxes is pretty obvious, too: a 50% elevation in CO2 partial pressure in the atmosphere results in a 50% increase in CO2 air molecules striking and being absorbed by the ocean surface.
Likewise, since the DIC in surface water tracks pCO2 in the air pretty closely, the AR5 authors estimated that that rise increases CO2 fluxes the other direction by 17.7 PgC/year.
Now, can we please discuss the actual, physical anthropogenic CO2 sinks?
You claimed that the human processes removing carbon from the atmosphere (your “An”) are not negligible. So I discussed those processes, one by one, here:
https://edberry.com/co2coalition/#comment-112419
When I say that “Ah,” i.e., the anthropogenic processes which remove CO2 from the air, are negligible, I mean that they are much smaller than the error bars on anthropogenic emissions, so they can be ignored in “mass balance” arithmetic.
1. Approximately 59 kt of CO2 per year are removed from the atmosphere by Direct Air Capture projects, worldwide. That’s about 0.00015% of anthropogenic emissions.
2. Approximately 50 Mt of CO2 per year is captured and stored by operational CCS facilities, but 99.9% of that is captured at the sources, so it’s really avoided emissions, not removals. But if you count it, that’s a little over 0.13% of anthropogenic emissions. Are you counting CCS as part of your “An”?
3. According to GCB (2024), cement carbonation is estimated to remove about 214 MtC from the atmosphere per year, globally, which is about 0.784 Gt of CO2. That’s conventionally considered a natural removal process, but IMO you could call it anthropogenic. But it’s only about 2% of anthropogenic CO2 emissions, so even that is still much smaller than the error bars on anthropogenic emissions. Are you counting cement carbonation as part of your “An”?
Can you identify any other anthropogenic sinks?
● If so, then what are they?
● If not, then please acknowledge that your “An” is negligible, so that we can move on.
“When my information changes, I alter my conclusions. What do you do, sir?”
– John Maynard Keynes (attributed)
Ferdinand Engelbeen, July 10, 2025 at 1:41 pm
The Wiki discourse on exponential decay is boilerplate. It explains the math applicable to a system at rest disturbed by “a quantity is subject to exponential decay if it decreases at a rate proportional to its current value.” Since CO2 increases annually, in part due to the fraction of industrial carbon contributing to it, I contend simple exponential decay does not apply.
Where is the former page of Wiki showing that, for a linear response of a system in equilibrium, the formula [ Tau = disturbance / effect ] is independent of the time frame over which the ratio is measured?
This sentence I do not understand: “Effect in the case of CO2 is the net increase in output when the CO2 level above the equilibrium increases, the net increase in output is the difference between inputs and outputs, for each bidirectional exchange between reservoirs apart as good as for all exchanges together.”
Also, if by “And in my opinion, a simple calculation, based on observations, is as valid as a direct observation,” you mean simple math, I’m not buying it.
Thank you for your patience with my attempts to understand your position. I did get the download of the power point presentation and will have a look now.
(Sorry about the botched </a> in that comment.)
Stephen wrote on July 10, 2025 at 2:55 pm, Wiki is not a scientific reference. It has no scientific credibility. It has site moderators who push agendas.”
I like to say that Wikipedia is untrustworthy for anything controversial. Inevitably, partisans for one side of the argument take over the articles, and turn them into propaganda. Gender issues and climate change are particularly notorious examples, but you really cannot trust Wikipedia for information about anything controversial. Here’s an eye-opening article:
Harvard Students Edit Wikipedia To “Dismantle The Patriarchy”
Since Jimbo Wales is a leftist, his thumb on the scale ensures that that side of the argument generally “wins” on Wikipedia.
But Wikipedia is not completely useless. For topics which nobody argues over it is usually fine.
For instance, it is good for looking up data cable pinouts:
https://en.wikipedia.org/wiki/IEEE_1284
The article on exponential decay is fine, too:
https://en.wikipedia.org/wiki/Exponential_decay
Ed,
I can’t sit quietly by and ignore the ignorance you show every time you mention C14. A year ago, I presented an oral paper at the annual meeting of the NW chapter of the American Physical Society in Bothell, WA, which I called “Challenging the Abuse of Atmospheric Radiocarbon Data “. You were featured, but you had company. A few corrections to your narrative:
• DeltaC14 is a measure of the C14/C12 ratio in a sample, and there is indeed a “balance” involved in determining the reference ratio, the C14/C12 ratio that gives Delta C14 = 0. The amount of C14 in fast cycle carbon is determined by the competition between the mostly constant production rate of C14 in the upper atmosphere, and the decay rate dictated by C14’s 5730 yr half-life. At the “balance level”, as much C14 is leaving the fast-cycle system by decay as is being added by upper atmosphere production. This balance level has nothing to do with flow rates into or out of the atmosphere as you assert.
• If an object containing carbon, say a piece of wood, is sequestered from the atmosphere for a long time because it is no longer growing, some of its C14 decays (to N14), and the C14/C12 ratio in the sample decreases. The magnitude of the decrease indicates the age of the sample. For example if C14/C12 is measured to be half of the reference value, the sample is about 5730 years old. You cannot extract a date from the C14 concentration alone, because without knowing how much carbon was in the sample to begin with, that concentration is meaningless. That is why the isotope ratio is used in dating, not concentration. It is not because Delta14C has a balance level and C14 concentration does not, as you claim.
• Let’s talk about atmospheric C14 concentration, measured say as the molar fraction of the atmosphere. This is the quantity that you and Harde and Salby and a couple of others thought was the same thing as DeltaC14. I believe that is what you mean by “14C” in your Figure 10 plot. You don’t say what the units are but add it to DeltaC14. Real physicists don’t add apples and oranges.
• You do not understand what is meant by “Suess effect dilution”. If you did, you might have called your paper “A calculation of Suess effect dilution.” Seuss effect dilution is what causes the amount of industrial carbon in the present atmosphere to be much less than what would be naively calculated by ignoring disequilibrium isofluxes. Climate scientists are not naïve on this point. You are. To be a credible challenger of the consensus you must understand the consensus first. You do not.
A thought experiment to help you, and others who are uneasy with disequilibrium isofluxes, to understand:
Imagine a short (few decades) stable period in a pre-industrial world, where the atmospheric CO2 level is, say 280 ppm. Solar variability is nil, Milankovitch cycles don’t change much on a decadal time scale, the ocean CO2 content has reached equilibrium with the atmosphere as dictated by Henry’s Law, the Revelle factor, etc., and the biomass is stable. In this idealized world the carbon levels in the major reservoirs are stable except for seasonal variations, but there are still balanced two-way exchanges much like today. Oceans outgas CO2 in one place and absorb it in another. Plants grow by taking in CO2 from the atmosphere and return it when they die and decay. Human emissions are 0. Atmospheric CO2 growth is 0. Net global uptake is 0. Natural emissions are exactly balanced by natural absorption. Now aliens land and use this idealized world to test thermonuclear weapons in the atmosphere. The tests double the atmospheric C14/C12 ratio to 2 parts per trillion, twice the one part per trillion that existed before.
Questions:
1. What happens to the atmospheric CO2? Answer: nothing, unless you want to worry about the effects of a part per trillion increase.
2. How does the C14 /C12 ratio change over time? Answer: it returns to one part per trillion in about a decade, just as it did after 1965 in the real world.
I think this thought experiment is useful because it shows how isotope changes need not be linked to level changes. The real world is more complicated than the idealized world described, but real-world processes like the decay of the bomb pulse can be understood by simple insights.
Dave Burton July 10, 2025 at 4:37 pm
You wrote:
Dear Dave,
Did you read the Figure 6.1 Legend?
IPCC’s Fig 6.1legend reads:
So, it looks like you can’t read, as I assumed in my last comment.
Next you wrote:
Not valid, Dave. Your reasoning is circular.
You assume human carbon outflow is negligible because you already assumed human carbon caused all the CO2 increase. The IPCC assumes the same thing in its red numbers in its Fig 6.1.
The proper physics solution is to treat the human carbon cycle and natural carbon cycle independently but using the same rules. This is a lot easier and far more accurate than the way you are doing it.
The one thing I did, that no one else did, was to recalculate IPCC’s red numbers using the same rules that IPCC used for its black numbers. That’s my breakthrough. It proves H(1) is false.
Einstein said the most difficult part of a physics problem is usually its formulation. I did the correct formulation of the problem. Anyone can repeat my calculations.
Your formulation of the problem is invalid and wrong. That’s why your solution is wrong.
Of course. Human carbon flows into the same “sinks” as natural carbon flows. Total human carbon has added one percent to the carbon in the natural carbon cycle.
Do you honestly think there is a precise fixed limit on these sinks?
You have seen the photo of the four trees that grew up in different CO2 levels. Every tree on the planet will soak up more CO2 if there is more CO2.
Your focus on sinks rather than sources, inflows rather than outflows is unnatural. That’ not how things work.
Your way is like riding a bicycle backward, downhill. You go out of balance and crash.
In summary, you are wrong about the red numbers in IPCC’s Fig 6.1.
You are wrong about using sinks that have, at best, 10% accuracy, to arbitrarily make decisions about human carbon that is only 1% of the total carbon in the carbon cycle.
David Andrews July 10, 2025 at 6:41 pm
Dear David,
Thank you for your comment because you support a lot of what I am teaching.
You agree with my balance levels but do not understand that I consider the natural production of 14C as an “inflow of 14C.”
I claim the reason carbon dating works is because Delta14C has a balance level, which means 14C does not. 14C changes with 12C in a manner that keeps Delta14C at its balance level. Why do you think we disagree?
I, Harde, and Salby may have mis-labeled a chart way back in 2019. We corrected this in our following publications. Are you perfect? You have made a lot of physics errors in your publications.
David. You know I understand the Suess effect dilution. Even my draft paper above explains it. I think you are upset because the Suess effect has turned out to be minimal, proving H(1) is false.
You wrote, “In this idealized world the carbon levels in the major reservoirs are stable except for seasonal variations, but there are still balanced two-way exchanges much like today.” Thank you. That is exactly what my carbon cycle model explains. Please explain that to the CO2C authors.
You say, in your mental experiment, the C14 /C12 ratio returns to its original level in about a decade. That is incorrect. It would return at the same rate Delta14C has returned since 1970, which is with an e-time of 16.5 years. It cannot return to its original value in ten years.
Jim,
I have several times had trouble understanding your thought processes, but what on earth does this mean?
“Ironically the explanation of “fossil only” misses the fact that sink rate is calculated from Eh(t) – dC(t)/dt which is another way of saying “fossil carbon not removed” in violation of the equivalence principle.”
While once you helpfully explained to Ed his error in interpreting the “simple math” associated with carbon conservation, now you seem to suggest that carbon conservation violates the principle that industrial and natural should behave the same??!!?? One way to insure that these two types are treated the same is to just analyze total carbon as all mainstream scientists do. Did you know that Richard Courtney, whose praise Ed repeats over and over, for separating their analysis, had a career in the coal industry? That by itself does not disqualify his opinion, but certainly raises some flags.
You are on record as saying that “you are on Ed’s side.” Perhaps that should explain to me why your logic is so hard to understand.
Ed,
Do you really not understand that the Seuss effect is minimal only because it has been diluted by disequilibrium isofluxes? And that no reputable scientist disagrees with that? And that therefore the small amount of industrial carbon in the present atmosphere says nothing about the cause for the rise? To understand the cause of the rise you have to stop pretending that you don’t understand the mass-balance (carbon conservation) argument.
From Ferdinand Engelbeen, July 10, 2025 at 1:41 pm and Jim Siverly, July 10, 2025 at 4:41 pm
This may be a bit premature, but if I don’t write it now, it may be gone forever.
From Ferdinand’s power point presentation at a Clintel wrokshop in Athens, last September (see his comment on July 10, 2025 at 3:43 am), I saw Tau defined as the usual disturbance / effect. However, there was a slide with the example:
Tau = (415 uatm – 295 uatm) / 2.35 uatm/year = 51 years
I interpret the denominator as the difference between the current CO2 level and what it was in preindustrial times. The numerator is the current CO2 sink rate. While I am still waiting for a formal presentation of the derivation of that equation, I was curious what would happen to my spreadsheet model if I ran it from 2018 (the last year of my available industrial emission data) until equilibrium assuming no further industrial emissions and a freeze of the natural emissions at the 2018 level. My model uses a 4-year residence time (turnover, e-time, etc.) and allows for an exponentially increasing biomass. In other words, the land and ocean reservoirs average more emissions gradually each year from 65 ppmv to 93 ppmv. The increase was necessary to correlate with the Mauna Loa data.
The model simulation resulted in an equilibrium value of 398 ppmv in 2045, down from 410 ppmv in 2018. The 1/e value of about 402 ppmv occurred in 2022 or about four years.
My hypothesis is this: no matter what the equilibrium CO2 level would be, if the world suddenly went net zero, the new CO2 would be at that new level in less than 30 years with a 63% reduction in only four years.
Re: Uncle Bert’s comment July 10, 2025 at 10:13 am
Dear Uncle Bert.
More excuses and specious waffle and totally lacking in any science. The deeper you dig yourself into the quagmire the more difficult it is to make any sense out of anything that you say. Everything you write is specious. Unvalidated assumptions and pseudoscientific rhetoric. I find myself agreeing with Jim Silverly. Your ideas are an artifact of your self-fulfilling prophecy. “the compilation of the late Ernst Beck makes no sense”. Any measurement that doesn’t fulfill your self-fulfilling prophecy makes no sense to you.
200,000 measurements from 901 locations from dozens of highly qualified and notable scientists produce data that doesn’t conform to the confirmation bias of the catastrophic anthropogenic global warming CAGW proponents so they invented a new term. “Background layer”. CO2 is well mixed everywhere unless it’s near one of the accurate scientific instruments from the 1812 to 1961 instrumental record. So the CAGW proponents invented a fictitious “background layer” just to cloud the argument.
“The standard deviation for the historical CO2 data was 68 ppmv (1 sigma, not a sign of reliability!), of the modern station about half of it”
You’re comparing monotonic ice core proxy data to Mauna Loa measurements. All that does is demonstrate you’re not a scientist and have no scientific argument.
“And the ice core from the Siple core (not the Byrd core) indeed was contaminated with drilling fluid”
Jaworowski produced measurements that doesn’t conform to your confirmation bias so you have to invent something wrong with it and attack the man. You fail to admit that all ice cores have drilling fluid contamination. Jaworowski’s had less than ALL the others and probably none at all.
Then the 1812 to 1961 instrumental measurements were not what you wanted so you’ve concocted a specious argument that they were contaminated from all the fly and insect farts. They only thing that’s contaminated is your brain.
“a simple calculation, based on observations, is as valid as a direct observation”
Calculations that give you the confirmation biased results that you are looking for are not measurements. You take real measurements, put them through a calculation and produce fake results.
Uncle Bert. You need to retire to your IPCC cubicle and retire from bring a political agitator. Do something meaningful with your life. Get a life.
I don’t know about the rest of you but I have lost my patience trying to wade through all of Uncle Bert’s specious waffle. It’s endless. It’s like how the Indians say they are drunk. Translated – “my head is eating circles”. As fast as the specious waffle comes around, you chew it up and spit it out but it just keeps coming around and around. They say when you die and go to Heaven, that’s if we all make it there, that life is eternal. I think there’s something after that for Uncle Bert’s specious waffle.
David Andrews
July 10, 2025 at 8:13 pm
David,
The “fossil only” issue arose in my comment (July 10, 2025 at 10:10 am) following Dave Burton’s at July 9, 2025 at 4:35 pm. I said, “You even label the graph “fossil only” seemingly unaware of the fact that it violates the equivalence principle.” Dave explained that “fossil only” meant omitting the land use fraction of industrial carbon. Got that so far?
OK, then I went back to look at the plot equation which is based on Eh(t) – dC(t)/dt = Sn(t) – En(t). The left-hand side basically means “fossil carbon not removed” in year t. It violates the equivalence principle, because the full Eh(t) that year is mixed in with the rest of the atmosphere and much more than half of Eh(t) gets removed.
Am I missing what you mean by carbon conservation? If you mean simple math as in the equation above, then we have a problem. And I think it’s because we don’t share the same understanding of the equivalence principle.
Jim Siverly July 10, 2025 at 9:58 pm
“My model uses a 4-year residence time (turnover, e-time, etc.) and allows for an exponentially increasing biomass. In other words, the land and ocean reservoirs average more emissions gradually each year from 65 ppmv to 93 ppmv. The increase was necessary to correlate with the Mauna Loa data.”
The basic problem is that one can match the Mauna Loa data with any combination of (net) sinks and temperature…
Thus one need to look at the physics behind the math.
The 4 years residence time of today includes all inflows and outflows, whatever their direction. Including two main cycles: from the warming oceans through the atmosphere to increasing vegetation in spring/summer and back in fall/winter. These cycles are near completely independent of the actual CO2 pressure in the atmosphere.
Indeed they did increase over (many) years, as you assume, but from the past to today that is only true in ratio for the ocean surface (according to the IPCC, but they didn’t give any explanation how and why that happens) and less than complete for the biological cycle: some 40% increase in the cycle for the CO2 increase in the atmosphere, despite 175 years time to get the same percentage.
Your thesis implies that the current equilibrium increased at about the same rate as the increase in the atmosphere, matching the 4 years residence time to allow for the difference.
A new equilibrium will be approached with a Te of 4 years at about 398 ppmv in 2045.
So far so good. Only one problem: the 398 ppmv is way above the equilibrium pCO2 of the oceans surface, which would be around 295 μatm (~ppmv, ppmv is in dry atmosphere, μatm in the atmosphere includes water vapor).
If we simply ignore the ice core results and start in 1958, the level in the atmosphere was 315 ppmv.
Assuming an equilibrium pCO2 of the oceans, that also starts at about 315 μatm in 1958.
With the increase in temperature, the pCO2 of the ocean surface increases with the formula of Takahashi:
(pCO2)seawater @ Tnew = (pCO2)seawater @ Told x EXP[0.0423 x (Tnew – Told)]
or with an increase of 0.6°C (HadSST3 global) that increases the overall pCO2 of the sea surface waters to:
pCO2(new) = 315*EXP(0.0423*0.6) = 323 μatm.
Less than 10 μatm increase in equilibrium pCO2 by the ocean surface over the period 1958-2025.
Vegetation hardly plays a role in the equilibrium: they watch and wane with the overall pCO2 in the atmosphere, which is determined by the ocean surface waters over the millennia and the availability of land in between ice ages.
That can be seen in the very small changes in δ13C over the past 800,000 years, despite huge changes of 90 ppmv in CO2 level, until humans started to emit FF CO2:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_d13C_lgm_cur.png
Even with an enormous increase in size between glacial and interglacial periods: that is completely dwarfed by the equilibrium set by the ocean surface temperature and the changes in size were slow enough to get equalized by the deep oceans cycle.
Moreover, if you calculate the equilibrium pCO2 down to where inflows and outflows are equal (thus zero net flow), over the period 1958-current, that shows a level of 285 ppmv. Here from David Burton:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
That is only calculated from the observed net sink rates, thus independent of any idea of the real level of Te or Tau.
Again the “old” equilibrium that didn’t change much over time.
For the underlying equations of the long Tau of around 50 years: already obtained in 1997 by Dipl.-Ing. Peter Dietze in a debate with the inventor of the Bern model, Fortunat Joos:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/Dietze_1997.png
More on that page at the website of the late John Daly:
https://www.john-daly.com/carbon.htm
And the discussion with Joos and others:
http://www.john-daly.com/dietze/cmodcalc.htm
https://www.john-daly.com/dietze/cmodcalD.htm
Jim Siverly, July 10, 2025 at 10:39 pm
Eh(t) – dC(t)/dt = Sn(t) – En(t)
Eh(t) is the human input, for 100% injected into the atmosphere as mass.
That increases the total mass of CO2 in the atmosphere.
– dC(t)/dt removes a certain amount of mass of CO2 out of the atmosphere, no matter the composition, thus original human and natural CO2 molecules alike, and that equals natural sinks minus natural sources, because of a lack of human sinks (again as mass, not in original FF molecules)…
Everybody of the “man-made” CO2 increase is talking about carbon mass transfers, only the “natural-made” CO2 increase people make a differentiation…
Jim Siverly July 10, 2025 at 4:41 pm
Unfortunately, the Wiki page had their simple formula of the decay rate for a linear ratio process on the same page as today for the exponential decay rate, but someone deleted it.
Anyway Peter Dietze in 1997 and many others after him (Lindzen, Spencer) used the same formula to calculate the effective adjustment (or life) time.
If there is a linear ratio between cause and effect, it doesn’t matter over what time frame Tau is calculated. In the case of the recent record since 1958, one can calculate Tau over 1 year (as I have done, be it on the smoothed sink rate) or over a period of 10 years or over the full period, you will obtain the same result. Of course, by using the polynomial, the results are already smoothed…
The sentence:
“Effect in the case of CO2 is the net increase in output when the CO2 level above the equilibrium increases, the net increase in output is the difference between inputs and outputs, for each bidirectional exchange between reservoirs apart as good as for all exchanges together.”
means that one can calculate the different Tau’s for each exchange between the atmosphere and the different reservoirs, if one knows the net outflux (that is difference between inputs and outputs) for each of them.
In that case total Tau(c) can be expressed as function of n exchanges:
1/Tau(c) = 1/Tau(1) + 1/Tau(2) +… …+ 1/Tau(n)
Dr. Ed, July 10, 2025 at 7:19 pm
Dear Dr. Ed,
Only one remark:
“Total human carbon has added one percent to the carbon in the natural carbon cycle”
I think that we all agree that human emissions get into the atmosphere for the full 100%, thus adding some 10 PgC/year to a total of CO2 that circulates through the atmosphere with 200 PgC/year as input and 205 PgC/year as output for the current CO2 cycles.
For the mass balance, the human input is the first cause for the increase of 5 PgC in the atmosphere, or you violate the mass balance. That is about mass transfer.
For the molecular balance, if the FF CO2 is only 1% of all CO2 in the atmosphere and nothing comes back with the return flows, the removal of FF molecules is 2.05 PgC/year, still near 8 PgC/year of FF molecules are added to the atmosphere each year.
Further, as the 2 PgC/year FF molecules are distributed into ocean surface and vegetation via the fast cycles, some of these FF molecules will return from the other reservoirs, increasing the FF molecular level in the atmosphere.
On the other hand, the increase in FF molecules also increases its ratio in the outputs…
The current, measured, increase of FF molecules in the atmosphere is already over 10% and in the ocean surface over 6%. In vegetation and deep oceans also increasing, but difficult to quantify. The former does only return waters with CO2 from ~1000 years ago, that does influence the current 13C/12C and Δ14C levels.
In short: The full input of FF CO2 gets into the atmosphere and gives its full increase in the atmosphere as mass and an enormous drop in 13C/12C ratio. About half that input as mass (whatever the origin) is removed and about 2/3 of that input as original FF molecules is replaced by CO2 molecules from other reservoirs…
Brendan Godwin, July 10, 2025 at 10:22 pm
A last comment to your “science”, as I see that it is just a waste of my time to discuss things with someone who doesn’t want to accept any data which he doesn’t like.
– “200,000 measurements from 901 places”
Of which 198.000 contaminated with local sources and sinks. Completely worthless to know the past global CO2 levels.
Those measurements that were over sea and coastal with wind from the seaside are on or below the ice core measurements. On or below. No peak at all in all the measurements over the oceans. Strange isn’t it?
https://www.ferdinand-engelbeen.be/klimaat/klim_img/beck_1930_1950.jpg
The minima are, not by coincidence, mostly from measurements over the oceans or coastal
That is already 70% of the global surface.
Then we have recent flight measurements, here over the Rocky Mountains:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/inversion_co2.jpg
Once over 700 meters, the CO2 levels are within a few ppmv of the Mauna Loa level for the same days.
In total: 95% of the air mass shows “background” CO2 levels within 10 ppmv from near the North Pole (Barrow) to the South Pole.
But according to Brendan, we should believe the historical (and current?) CO2 measurements in 5% of the atmosphere from highly contaminated areas over land.
– “You’re comparing monotonic ice core proxy data to Mauna Loa measurements. All that does is demonstrate you’re not a scientist and have no scientific argument.”
The ice core data are direct measurements of CO2 in the atmosphere, not “proxies”. Including an overlap of 20 years with the direct measurements at the South Pole. If you have any real “scientific” arguments, why we shouldn’t use these data for historical CO2 levels, then give them…
And I was comparing the historical CO2 data from Giessen:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/kreutz_08.jpg
Which show a range of 240-680 ppmv (wow, what a “background” range – CO2 at that time was expressed as tenths of a percent) and a standard deviation (“streuung”) of 66 ppmv with the
stdev of the modern station at Linden/Giessen of around 30 ppmv
and with the Mauna Loa stdev of some 2 ppmv and
the South Pole data stdev of less than 1 ppmv
and the ice cores with a stdev of 1.2 ppmv
If you have any scientific arguments why we should use the historical data from Giessen as the “real” background CO2 level of that time, be my guest.
– Jaworowski produced measurements that doesn’t conform to your confirmation bias
Jaworowski never, ever did any CO2 measurement in ice cores. He did measurements in ice fields of Scandinavia for the radioactive fallout of the Tsjernobyl disaster.
These icefields are at much higher temperatures than the Greenland or Antarctic ice cores and therefore have a lot of water veins where metal ions can migrate. That is near impossible for CO2 in ice cores at -20°C to -40°C.
Thus his critiques were based on quite different materials and circumstances.
One has calculated the theoretical migration of CO2 in the Siple Dome ice core by looking at the increase of CO2 near a melt layer. The conclusion: at middle depth the resolution increases with some 10% or from about 20 years to 22 years and near the bottom rock it doubles from 20 to 40 years. And near melt layers, on can find higher than average CO2 levels. Melt layers are typical for the Siple Dome ice core and absent in Law Dome and, as far as I know, any other Antarctic ice core.
Simply not important at all for migration and not measurable in any ice core that is colder:
https://catalogue.nla.gov.au/catalog/3773250
Bye bye…
Stephen P. Anderson, July 10, 2025 at 3:12 pm
“The partial pressure of CO2 is equal to the mole fraction of CO2 times the total pressure of the atmosphere. It has nothing to do with some imaginative pCO2(ocean).”
Of course the pCO2 is what you describe, but you are wrong about the pCO2 of the oceans: That is the base for Henry’s law and describes the partial pressure of the oceans in equilibrium with a small volume of air above it. That pCO2 is measured in the small air volume and is used as pCO2 of the ocean water.
When the pCO2 of the oceans and the atmosphere above it are equal, there is no net CO2 transfer between the two (still a lot of CO2 molecules are traveling in each direction, but flows are equal up and down).
The pCO2 of the oceans was measured with meanwhile several millions of samples, even on commercial sea ships with automatic equipment on board…
See further the compilation of Feely et al. for the reference year 1995:
https://www.pmel.noaa.gov/pubs/outstand/feel2331/maps.shtml
for the overall formula to calculate the net CO2 flux between atmosphere and oceans, based on the difference in pCO2 between atmosphere and ocean surface waters.
The whole interesting story starts about at:
http://www.pmel.noaa.gov/pubs/outstand/feel2331/exchange.shtml
Jim (and Ed too),
Ferdinand has responded to Jim’s equivalence principle concern, but I will too. Let’s go back to the beginning.
(change rate of atmospheric carbon) = (carbon addition rate by all processes) – (carbon removal rate by all processes).
Divide the PROCESSES into human and natural and indicate which by subscripts. MAKE NO DISTINCTIONS ABOUT CARBON TYPES OR YOU MAY GET CONFUSED.
Processes which add are E(missions). Processes which remove are A(bsorptions)
dC/dt = En + Eh – An – Ah
En = ocean outgassing, vegetation decay, etc
Eh = human burning of fossil fuels
An = dissolution of carbon into the oceans, photosynthesis, etc
Ah = removal by direct carbon capture technology, sequestration, etc. Unless you can name a human PROCESS which removes carbon of any type on the scale of Petagrams, we will ignore this term.
Then Eh-dC/dt = An – En
It is usually easiest to integrate this over time, and talk about stock changes in a fixed period.
The left-hand side is definitively measured to be positive in the industrial era. Therefore, the right-hand side is too. Natural processes are definitively removing more carbon from the atmosphere than they are adding.
Good luck making a model which says the human influence is small.
David Andrews July 11, 2025 at 9:48 am
Dear David,
Let’s use your equation:
dC/dt = En + Eh – An – Ah ………………(1)
Argument #1
Equation (1) works for natural and human processes individually:
dCn/dt = En – An…………………….(2)
dCh/dt = Eh – Ah…………………….(3)
Assume (2) is at equilibrium, so it is zero. Then we can easily find the six Te from IPCC’s data for its natural carbon cycle at equilibrium.
Then we can integrate (3) from 1750 to 2020 using data for annual human CO2 emissions.
By using the same Te in (3) as found in (2), we can calculate how fast human CO2 flows out of the atmosphere annually.
This is the key.
Human CO2 will flow out of the atmosphere and into the other carbon reservoirs, in proportion to its level, exactly as fast as natural CO2 is already flowing out of the atmosphere.
Human CO2 is a minor part of the total CO2 flows, so it can’t change the rules, or Te.
The sum of (3) from 1750 to 2020 is much less than the measured total CO2 increase.
This means your argument is wrong because you ignored the annual outflow of human CO2.
Therefore, nature did not stay at equilibrium from 1750 to 2020. Nature played a dominant part in the CO2 increase.
Argument #2
Rewrite (1) as follows:
dC/dt = (En– An) + (Eh – Ah) ………………………………. (4)
Integrate (4) from 1750 to 2020 to get:
Total CO2 increase = (Natural CO2 increase) + (Human CO2 increase)………………….(5)
This shows your argument depends on what you assume for Natural CO2 increase.
If you assume the natural increase is zero then you automatically conclude all the increase was Human CO2 increase.
When you drop Ah, you are assuming all the increase was Human CO2 increase. Therefore, your reasoning is circular, and wrong.
Ferdinand Engelbeen July 11, 2025 at 7:59 am
Dear Ferdinand,
Neither of your referenced articles negate my formulation that uses (1) and (2).
The proper use of such information is to fine tune my formulation.
But the proper way to fine tune my formulation might be to begin by expanding the number of land reservoirs and ocean reservoirs. That would allow simulation of different types of land and allow consideration of ocean flow.
The key to doing this is my formulation because it easily allows such expansion to multiple reservoirs and addition of flows between the new reservoirs.
As everyone knows, no model can perfectly describe nature. But my model comes closer than any other model because it is based on only two equations.
Ferdinand Engelbeen July 11, 2025 at 4:36 am AND July 11, 2025 at 7:59 am
Dear Ferdinand,
Please see my reply to David Andrews July 11, 2025 at 9:48 am
All arguments about the carbon cycle or “carbon mass balance” must use equations and numbers. Your use of numbers is not a valid argument because you are not showing where your numbers enter equations.
That’s why we must first agree on the formulation of the problem. Until then, numbers such as you and Dave Burton throw out have no relevance to our discussion.
I have provided the only complete formulation of the problem, and I have provided the way to numerically integrate levels and flows over time.
Until someone does a competing formulation, my formulation is the only game in town.
Ed,
You persist in being willfully ignorant by, once again, conflating human/natural processes with your “human/natural carbon”, despite my BOLD CAPS WARNING that doing so would confuse you. I made the “mass-balance” argument as clear as I could, but evidently it was not clear enough for “Winterberg’s best student”. I hope it was clear enough for Jim, but I am not optimistic. His logic has been kind of shakey recently.
Congratulations, once again. You have confirmed Hans Seuss’s 1955 comments about what are now called disequilibrium isofluxes. Indeed, your “human carbon” is but a small part of the present atmosphere as he predicted. But that is irrelevant to determining the cause of the CO2 increase. The mass-balance argument tells us about that. You have not refuted it. Obviously I have nowhere assumed anything about the constancy of natural processes. Data show clearly that natural sinks are increasing in response to the higher carbon levels in the atmosphere.
Ed, David, and Ferdinand,
Not that you are waiting with bated breath, but I am anxious to respond, busy until later today, and will respond sometime, hopefully.
Dr. Ed,
David Andrews has said it very correct.
But let’s go in more detail again. The whole discussion is about what caused the increase in CO2 mass in the atmosphere. Not where the human FF molecules reside or are transferred to. Even if they are all captured by the next available tree within seconds, that excludes the capturing of a natural CO2 molecule in the same season, except for a small increase in biomass over a year.
dC/dt = En + Eh – An – Ah
Where dC/dt and Eh are quite exactly known and Ah as human induced sink of CO2 mass (not sinks of human FF molecules!) is negligible.
Thus even if we don’t know En and An exactly, and thus the margins of the residence time Te are rather wide, we do know the difference between En and An quite accurately.
For the past years we can make the rough sums (as mass) in PgC/year:
dC/dt = 200 (En) + 10 (Eh) – 205 (An) – 0 (Ah)
Both En and An do already contain a certain percentage of FF molecules, but that is about transfer of molecules, and only of academical interest, as that doesn’t have any influence on the measured transfer of CO2/carbon mass, whatever its composition.
What is sure, is that all FF emissions as mass and as isotopic composition are for 100% injected into the atmosphere.
With 909 PgC in the atmosphere (2025) we have, with Te(c), the overall residence time of CO2 in the atmosphere:
Te(c) = 909 / 205 = 4.43 years
With a difference of CO2 in the atmosphere between 2025 and 1750 we have:
Tau = (909 – 589) / (210 – 205) = 64 years
A little overblown as the zero net outflow equilibrium slightly increased from 1750 to 2025 due to warming oceans from 589 PgC to 628 PgC which gives:
Tau = (909 – 628) / 210 – 205) = 56 years
So, which one is of interest?
Te is based on the sum of all outputs out of the atmosphere, no matter their direction or back flows from the receiving reservoir. Even if the back flows from oceans and vegetation were equal to the outflows from the atmosphere into the oceans and vegetation, Te will not change. But the net CO2 transfer from the atmosphere to the two main other reservoirs would be zero.
As the exact flows between the different reservoirs are only known with large margins of error and the flows between ocean surface and deep oceans not measured at all (that is based on the Bern model!), any calculation of the net outflow based on the residence times is very problematic.
The only time of interest is Tau, which shows how much net CO2 really get transferred from the atmosphere into the other reservoirs. The only point of discussion in that case is the shift of the equilibrium over time since 1750, but that is easily solved by using the formula of Takahashi for the increase of pCO2 of the ocean surface with temperature, confirmed by the back calculation of the measured net CO2 output to zero net output by David Burton and many others in the past:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
DAVID ANDREWS JULY 11, 2025 AT 8:57 PM
Dear David,
My simple demonstration using your own equation proves your interpretation of your equation is wrong.
You responded, as you always do when trapped, by attacking me personally, which is a giveaway that you are wrong.
You wrote:
Irrelevant?
Then show it in math, David. Show it in math.
Your capitalized statement is scientific insanity:
Wow! In theoretical physics, David, we always explore the next level of detail to get as much information as we can. And in this debate, that obvious next level is to consider human and natural carbon independently.
After all, the objective of this debate is to determine the effects of human CO2 emissions, as distinct from natural CO2 emissions. We can’t do that unless we look at each process separately.
We lose no information is this logical separation but we gain more insight. And that separate insight proves you are wrong.
That’s how we do theoretical physics, David. But you never learn.
You refuse to look at each process separately because you realize you lose the debate when we do.
(Yes, I was Winterberg’s best student, by far, as he wrote several times. Care to compare your PhD thesis with mine? My bet is you cannot follow the math and logic in my thesis, which was a breakthrough in climate physics, described in textbooks, exclaimed by Russian physicists, and still gets several citations every year. And, yes, I did score a perfect 800 on my SAT and finished in half the allotted time because the test should have been twice as long.)
Dr. Ed, July 11, 2025 at 12:18 pm
“When you drop Ah, you are assuming all the increase was Human CO2 increase. Therefore, your reasoning is circular, and wrong.”
We didn’t “drop” Ah for circular reasoning, Ah just is minuscule and less than 1% of Eh…
Your calculations should show:
F(a-g) – F(g-a) + F(a-s) – F(s-a) + F(s-d) – F(d-s) = dC/dt – Eh
As you use the overall Te of around 4 years in your calculation, the result is far too small and doesn’t reflect the real increase in the atmosphere.
Again, somewhere lost in the discussion:
With your Te of 4 years, most human emissions are redistributed into vegetation and oceans.
Despite that, there is a measured increase of CO2 in the atmosphere.
What is then the source of that extra CO2, as both oceans and vegetation increased in carbon content?
Ed,
“That’s why we must first agree on the formulation of the problem.”
Yes, we must agree on the formulation of the problem. I think we agree that the problem is to determine: “what has caused the atmospheric CO2 increase over the last century?”
Your formulation is to calculate the “human carbon” in the present atmosphere. Your central conceptual error is to not recognize, or at least not acknowledge, that this is an unimportant statistic determined by the mixing, on a short residence time scale, of atmospheric carbon with that in other reservoirs. Balanced mixing does not change levels, as illustrated by my little thought experiment. I know you care deeply about this unimportant statistic because it is your signature contribution, praised by coal man Richard Courtney. But your separate tracking of human and natural carbon has gotten you nowhere useful. It is the total carbon that matters, and that is tracked by the mass-balance analysis.
Between 1960 and 2010
350 +- 29 PgC of human emissions
158 +- 2 PgC of atmospheric accumulation
Therefore 192 +- 29PgC of net global uptake, because the carbon we added has to be accounted for.
The argument is remarkably simple and makes no assumptions about the constancy of natural processes. If you can discipline yourself not to go off on unnecessary tangents about different carbon types, you will see it too.
Ferdinand Engelbeen July 12, 2025 at 7:10 am
Dear Ferdinand,
Thank you again for your participation in this debate.
As you say, “The whole discussion is about what caused the increase in CO2.”
For this discussion, I have the option to rewrite our (1) as my (4)
dC/dt = (En– An) + (Eh – Ah) ………………………………. (4)
which when integrated over a period of years becomes:
Total CO2 increase = Total (En– An) + Total (Eh – Ah)………….(6)
Which is the same as my (5).
Now, we can insert your “rough sums” to get (6):
Total CO2 increase = Total Natural (200 – 205) + Total Human (10 – 0)………….(6a)
Hmm. It looks like your rough sums say the following:
Total CO2 increase = Total Natural (-5) + Total Human (+10)………….….(6b)
Your rough numbers say nature subtracted 5 and human added 10.
Do you really believe that? I don’t. But those are your numbers.
Further, I don’t agree at all with your definitions and calculations of Te and Tau. We can discuss these disagreements after you fix your numbers to make (6b) believable.
David Andrews July 12, 2025 at 11:15 am
Dear David,
Your physics is clutzy. Please put your numbers into equation (6) that I just wrote in my comment to Ferdinand:
Total CO2 increase = Total (En– An) + Total (Eh – Ah)………….(6)
Using Ferdinand’s numbers, this became:
Total CO2 increase = Total Natural (200 – 205) + Total Human (10 – 0)………….(6a)
Total CO2 increase = Total Natural (-5) + Total Human (+10)………….….(6b)
Ferdinand Engelbeen July 12, 2025 at 10:53 am
Dear Ferdinand,
Your following equation does not properly represent my calculations:
F(a-g) – F(g-a) + F(a-s) – F(s-a) + F(s-d) – F(d-s) = dC/dt – Eh
However, we have a bigger problem.
You claim Ah is less than 1% of Eh.
Your conclusion is based on your other errors. We must begin with IPCC’s natural carbon cycle data, shown in my Figure 3.
Then you have some problems to solve:
1. Your Tau of 50 years does not fit IPCC’s natural carbon cycle data.
2. Your Tau of 50 years does not fit the bomb test data that show Te = 16.5 years with a balance level of zero.
3. Your Tau is the time for a level to move 63% of the way to its balance level. Well, that is exactly Te. So, you have no basis to claim a Tau of 50 years, which is the same as saying Te is 50 years.
4. You assume human CO2 moves out of the atmosphere with a Tau of 50 years and then you conclude from this assumption that “Ah is less than 1% of Eh.”
5. You have not made a valid argument to justify your conclusion. Even IF you think Ah is small that does not justify dropping it from your equation.
6. Salby and Harde found that CO2 flows out of the atmosphere with Te much less than 3.5 years. You can see this in the monthly CO2 data. If your Tau of 50 years were in control, there would be no monthly sawtooth pattern in the CO2 data.
7. Your claim that H(1) is true conflicts with Munshi’s statistical analysis that shows the annual correlation of human CO2 emissions with annual CO2 increase is zero, which proves H(1) is false.
Dr. Ed, July 12, 2025 at 11:27 am
“Total CO2 increase = Total Natural (200 – 205) + Total Human (10 – 0)………….(6a)
Hmm. It looks like your rough sums say the following:
Total CO2 increase = Total Natural (-5) + Total Human (+10)………….….(6b)
Your rough numbers say nature subtracted 5 and human added 10.”
Indeed that is exactly what David and David and I are saying…
There simply is no appreciable human sink in this entire world… The only sinks are natural sinks, which absorb any mix of natural and human CO2 alike.
Even if you integrate all human emissions in the period 1958-2020, that is about 170 ppmv, while the measured increase is only 100 ppmv. Nature removed 70 ppmv CO2 out of the atmosphere into oceans and vegetation…
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_mlo_t_1960-cur.png
Ferdinand Engelbeen July 12, 2025 at 12:41 pm
Dear Ferdinand,
You say,
“Indeed, that is exactly what David and David and I are saying…
There simply is no appreciable human sink in this entire world… The only sinks are natural sinks, which absorb any mix of natural and human CO2 alike.”
That statement sinks your ship.
Even as you admit there are natural sinks, you are saying that there are no human sinks.
Does that begin with the first human CO2 molecule? Or the first ten?
You are saying that the jillions of trees on the planet will not accept the CO2 added by human emissions. This contradicts even the famous picture of four trees grown in different CO2 levels.
So, you are saying that the Te for human CO2 is much greater than the Te for natural CO2. Your argument violates the climate equivalence principle.
With this, I am outa here. Got better things to do today.
Ed,
I hadn’t seen your 10:38 post when I wrote my 11:15 post. Now I see your 11:47 post and later ones too.
A few points:
1. For a semi-quantitative analysis of why your calculation of “human carbon” in the present atmosphere is irrelevant, see my rebuttal to Skrable. https://pubmed.ncbi.nlm.nih.gov/36719939/ The mixing means that only about the last decade’s worth of C14 devoid “human carbon” should be expected to still remain in the atmosphere. That agrees well with the current measured atmospheric radiocarbon specific activity. This is the diluted Seuss effect which you have shown you are uncertain about even though you effectively calculated it. No one ever expected to measure the (undiluted) “Natural + 33% Human” curve in your Figure 9, because the composition of the present atmosphere only gives information about the last decade; earlier information is effectively erased by the mixing. I could make the case that my argument on the Skable analysis shows that, in the last decade at least, the rise is anthropogenic. Similarly the pre-1950 data shows a (diluted) Seuss effect. But a conservative conclusion is just to say that the present atmospheric composition is an unreliable indicator by itself of the atmosphere’s history because of mixing. Interpreting the composition as showing that the CO2 increase is mostly natural as you do, as if mixing doesn’t occur, is naïve and just plain wrong.
2. You make a case for analyzing details in physics, such as studying the human and natural cycle separately. Yes, that is often the case. I think the reason you are the only one doing it here is to be found in the paragraph above. And I am sure you know of many, many physics problems where the smart approach is to apply a conservation law rather than to grind through an unnecessarily detailed analysis. Carbon conservation is a quite useful constraint.
3. On your request that I insert numbers into your (6) to attribute the atmospheric growth to natural or human origins: I will use the Ballantyne numbers again, for the period 1960-2010, omitting error bars this time. The units are PgC
Total Increase = 158
Human input = 350
Natural input = -192
Yes, things would be a lot worse if natural sinks weren’t bailing us out. The ~45% “airborne fraction” has held up pretty well.
4. I see you are still haggling with Ferdinand about “Ah”. He is correct. Did you bother to read how I defined it?
Dr. Ed, July 12, 2025 at 12:37 pm
Dear Ed,
“Your following equation does not properly represent my calculations:
F(a-g) – F(g-a) + F(a-s) – F(s-a) + F(s-d) – F(d-s) = dC/dt – Eh”
Indeed, it shows what your calculations should show, but don’t show…
dC/dt and Eh both are quite exactly known. dC/dt – Eh is the overall removal of CO2 wherever in nature that may be, for human and natural CO2 together, whatever the mix in the atmosphere.
All bidirectional fluxes between the atmosphere and vegetation or oceans together should equal the net sink rate of what is removed out of the atmosphere as mass.
Then the other items:
“You claim Ah is less than 1% of Eh.”
Again… Ah is what humans exactly produce as CO2 mass sinks. That are things like reforestation in some countries, still dwarfed by clear cutting of forests in other countries, CCS (pretty good object for government subsidies, but the largest project did fail), etc. That is not about how much original FF molecules are removed with the increasing outflows into oceans and vegetation.
“1. Your Tau of 50 years does not fit IPCC’s natural carbon cycle data.”
The Tau of 50 years is calculated from the difference between the current CO2 level in the atmosphere with the “old” equilibrium (plus T influence) and the observed net outflow. Tau has nothing to do with CO2 cycles.
“2. Your Tau of 50 years does not fit the bomb test data that show Te = 16.5 years with a balance level of zero.”
The Te of 4 years also doesn’t fit, but you forget the “thinning” of the δ13C and Δ14C signals by the deep ocean returns of ~1000 years ago with 13C/12C and Δ14C of long before the bomb tests and fossil fuel use.
And you forget the 14C-free supply of FF…
That makes that the decay rate for Δ14C is much faster than for 12/13CO2 as mass and that the drop of δ13C is only 1/3 of what it should be if all FF remained in the atmosphere…
“3. Your Tau is the time for a level to move 63% of the way to its balance level. Well, that is exactly Te. So, you have no basis to claim a Tau of 50 years, which is the same as saying Te is 50 years. ”
You did calculate a Te of 4 years by adding all outputs out of the atmosphere together, but didn’t take into account the CO2 cycles that do move a lot of CO2, but don’t remove the same quantity out of the atmosphere than they move.
Some 200 PgC is moving through the atmosphere in half a year and just is cycling back in another half year, hardly affecting the CO2 level. Only some 5 PgC/year is removed by the extra CO2 pressure in the atmosphere or 16 PgC/year by the absolute CO2 pressure in the atmosphere.
“5. You have not made a valid argument to justify your conclusion. Even IF you think Ah is small that does not justify dropping it from your equation.”
Be my guest to find any human sink that can influence the results of our calculations…
“6. Salby and Harde found that CO2 flows out of the atmosphere with Te much less than 3.5 years. You can see this in the monthly CO2 data. If your Tau of 50 years were in control, there would be no monthly sawtooth pattern in the CO2 data.”
This is a good one: the seasonal sawtooth is caused by the influence of temperature on (deciduous forests) vegetation and is negative for temperature: -5 ppmv/°C
The year by year variability is caused by the influence of temperature on (tropical forests) vegetation and is positive for temperature: +3 to +4/°C.
On decades and longer (up to 800,000 years), the oceans surface temperature is dominant and there is the 50 years Tau based on.
“7. Your claim that H(1) is true conflicts with Munshi’s statistical analysis that shows the annual correlation of human CO2 emissions with annual CO2 increase is zero, which proves H(1) is false.”
This is a complete joke: Munshi first de-trended all the data and only looked at the variability of the data. As all the small variability (+/- 1.5 ppmv for the extremes) is caused by temperature and human emissions have hardly any variability, of course you only find a correlation between temperature and none with human emissions.
But if you look at the over 100 ppmv trend since 1958, the human emissions trend is 170 ppmv directly into the atmosphere and temperature has hardly a trend, here for the yearly changes:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em9b.png
Dr. Ed, July 12, 2025 at 12:58 pm
Dr. Ed, David Burton, Dave Andrews and I made it very clear that there are no appreciable human sinks. That is human made CO2 capturing mass sinks, no matter if that “mass” is 100% natural or 100% FF or anything in between. Sinks as mass, not sinks as (specific) molecules.
Again, once human FF CO2 is mixed in the atmosphere, it adds its full mass and 14C-free and low-13C fully to the atmosphere. Nature only removes about half that mass and replaces 2/3 of the FF 13C, thus nature is a sink for CO2, not a source.
Dear Ferdinand Engelbeen, and others using the simple math model to claim H1 is true.
Re: July 11, 2025 at 2:27 am
I think we have reached an impasse. I cannot continue countering what I consider flawed science and logic. In your last comment, you wrote,
“These cycles are near completely independent of the actual CO2 pressure in the atmosphere.”
That is patently false. Ocean outgassing and removal of CO2 are near completely proportional to the concentration gradient at the air-ocean interface. Even some of your colleagues here agree with that (I would hope).
Next regarding the problem you have with “398 ppmv is way above the equilibrium pCO2 of the ocean surface, which would be around 295 μatm.” You made the correct point that temperature does not account for the full difference between the new and old equilibrium pCO2’s. However, one must also take into account the increased CO2 levels in the reservoirs. Consider the first order reversible reaction between A B and its equilibrium K = [B] / [A]. If more reactant is added after the initial equilibrium is reached, a new equilibrium is reached with K = ([B] + x) / ([A] + (1-x)]. Assuming no change in temperature or pressure, K will remain the same. But both reactant and product end up at larger concentrations.
It’s self-fulfilling prophecy to use the “CO2 removal rate vs. CO2 level” plot of Dave Burton to argue no change in equilibrium pCO2. That’s because it’s based on the equation Eh(t) – dC(t)/dt = k * (C(t) – Co) which assumes negligible Ah, because (for some reason) sequestration is considered to be the only way a fossil fuel carbon gets removed. Below, I will derive a simple math model that will explain the correct way to interpret the mass balance logic you are using.
In the following derivation, I will use abbreviated terminology for time constraint reasons. I can explain any misconceptions later. I will shorten the mass balance equation to D = Eh + En – S. This is meant to be the equivalent of dC(t)/dt = Eh(t) + En(t) – Sn(t). I leave off the (t), but all calculations are intended to be valid for any year. For example, D(t) = C(t) – C(t-1).
I make two assumptions. First, that a fairly constant fraction of CO2 is removed and replaced by approximately the same amount each year. Second, that the sink, Sn(t) = S, contains a fraction of the human and natural carbon in proportion to the amounts that were emitted annually. Therefore, I am introducing a factor, f, such that f * S = Eh + En.
I need to show also that S = k * C, but it will have to be assumed for now because the demonstration requires t+1, t, t-1, etc. and there’s no time for that today (tonight now).
(1) D = Eh + En – k * C
(2) S = k * C
(3) f * S = ( Eh + En )
(4) ( Eh + En ) = D + S
(5) f * S = D + S
(6) D = ( f – 1 ) * S
(7) S = D / ( f – 1 ) and from (2) and (7),
(8) D / ( f – 1 ) = k * C
(9) D = ( f – 1 ) * k * C
First, I plotted D versus C to see if the correlation was decent. The intercept provides an estimate of ( f – 1 ) * k.
D = 0.0176 * C – 4.664. That makes the x-intercept 265 ppmv. Let’s put it this way. That correlation is about as good as the one Dave Burton and others use here:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Next, I calculated ( f – 1 ) * k for each of the individual average pairs of D(t) + D(t+1) and C(t) and C(t+1). The average was 0.00435. Next, I calculated f, using k = 0.25, finding an average of 1.017.
Finally, I calculated En(t) from (2) and (3),
(10) En = f * k * C – Eh
En gradually increases from 79 ppmv in 1959 to 99 ppmv in 2017. This is consistent with a pCO2 of 316 ppm that would be expected in 1959, but 396 ppm is a bit less than the 407 ppm I use for the Mauna Loa value in 2017. The use of a four-year turn around value of k = 0.25 suggests that is approximately correct and could conceivably have drifted somewhat. However, no one here seems to claim anything outrageously different than four years.
In summary, this analysis shows the shortsightedness of using the simple math model without consideration of the assumption I made on the basis of the equivalence principle. In every year, the amount of carbon sinked contains a share of both human and natural emissions in proportion to the amounts of each that were emitted. The human amounts have data to back them up. No one knows exactly how much of the natural emissions may have risen. This analysis shows that it is reasonable to expect an equilibrium level of carbon transferring between the various reservoirs to have risen substantially since pre-industrial times.
This is part 1. Part 2 is intended to show how Tau is not substantially different than Te. I know David Andrews will be holding me to it, but don’t hold your breath.
Note: I have not read any comments today, so I will have to catch up on this very interesting debate tomorrow.
Jim,
A few quick comments:
1. Like D (or S) Eh is a measured quantity. I assume you are inputting measured values.
2. Your (1) and your (4) are the same equation, rearranged. A third version is to me the most informative:
Eh – D = S – En The left-hand side is well known and definitively positive in the industrial era. It is “net global uptake”. The individual terms on the right are not well known, but by this equation their difference is. Do you agree it tells us that in the industrial era, more carbon has moved from the atmosphere into natural sinks than has gone the other way?
3. I think making the sink rate proportional to the carbon level would make more sense than making it proportional to emission rates.
4. You write “…(for some reason) sequestration is considered to be the only way a fossil fuel carbon gets removed”. That shows a misunderstanding of the mainstream view which I laid out on July 11 at 9:48 AM (Rocky Mountain time.) The natural sinks take in all carbon without discrimination. There is no equivalence principle problem. Mainstream science generally does not track “human” and “natural” carbon separately.
5. Your model is not far from the mainstream one (except for the time constants.) Therefore I don’t understand your comment about “the shortsightedness of using the simple math model without consideration of the assumption I made on the basis of the equivalence principle”. I think if you look back at my 7/11 post and read how An and Ah are defined, you will understand there is no equivalence principle problem or shortsightedness. Whether you know yet it or not, I think you will find your analysis confirms “H1”.
Jim Siverly, July 12, 2025 at 7:41 pm
“’These cycles are near completely independent of the actual CO2 pressure in the atmosphere.’
That is patently false. Ocean outgassing and removal of CO2 are near completely proportional to the concentration gradient at the air-ocean interface.”
There is an enormous difference between “the actual CO2 pressure”, thus the absolute pCO2 of the atmosphere and the “concentration gradient”. That is the exact point in discussion here.
The current absolute pCO2 in the atmosphere is about 415 μatm.
The (1995) concentration gradient between atmosphere and ocean surface was average only 7 μatm, according to Feely et al., based on near one million sea surface measurements.
The latter, together with chemical restrictions in the sea surface, makes that the sea surface only follows 10% of the change in the atmosphere and that the pCO2 of the ocean surface follows the pCO2 of the atmosphere with an exchange time of less than a year. That also implies that the pCO2 of the ocean surface closely follows the atmospheric pCO2 and thus the difference between ocean surface and atmosphere increases only very slowly.
Even for the deep oceans and vegetation, the uptake is directly proportional to the pCO2 difference with the “old” equilibrium, plus temperature influence, that would be 295 μatm nowadays.
The actual CO2 cycles between all reservoirs are around 200 PgC/year, while the calculated absolute sink rate, caused by the (current!) absolute pCO2 in the atmosphere is only some 16 PgC/year…
The of pCO2 in the receiving reservoirs only plays a role for the ocean surface, that closely follows the atmospheric pCO2, It plays zero role at the sink and upwelling places of the deep oceans and no measurable role in the uptake and release by plants, which simply remain in ratio with the “old” equilibrium.
Then the formula’s:
“(1) D = Eh + En – k * C”
That is for the absolute concentration (or absolute pCO2) in the atmosphere and should be
(1) D = Eh + En – k * ΔpCO2(atm-others)
Based on Feely et al. for the oceans: F = k•s•ΔCO2 between atmosphere and ocean surface.
and similar (but not easy to direct measure) between atmosphere and vegetation. The latter remains proportional to the pCO2 difference with the “old” equilibrium…
That means that your k*C is way to high and your decay rate much too fast…
“(3) f * S = ( Eh + En )”
As David already said: S is not a function of the inputs of one year, S is a function of the increase of actual pCO2 above an equilibrium, wherever that may be. S is completely independent of Eh + En for almost all what is sucked out of the atmosphere by plants in spring/summer (it even reduces pCO2 of the atmosphere) and only for a very small part depends on the extra pressure above equilibrium.
The main difference left is your residence time of 4 years, which is based only on all outputs of the atmosphere, without taking into account that most of these outputs are part of cycles that net removes zero CO2 out of the atmosphere. Only the difference between al inflows together and all outflows together, is the real decay rate of any CO2 mass (whatever its composition) out of the atmosphere and that is the calculated 50 years Tau…
David Andrews, July 12, 2025 at 11:35 pm
Thank you for taking time to critique my model.
1. Yes, I used the Bolen et al. data in Roy Spencer’s spreadsheet.
2. (1) and (4) simply mean S = k * C. Your third version is the slight of hand I’m trying to expose. As long as you believe Sn contains no fraction of Eh you will never understand Dr. Ed’s model.
Do I agree that more carbon has moved from the atmosphere into natural sinks than has gone the other way? Of course. But most of the annual amount remaining in the atmosphere originated from the natural sinks, because nearly all the human emissions are removed annually. That’s what my simple math shows.
3. The sink rate is proportional to the carbon level, S = k * C. But the relative amounts removed are in proportion to the amounts added. S = Eh/f + En/f
4. Not tracking “human” and “natural” carbon separately is what violates the equivalence principle using simple math. I modified the simple math to explicitly account for the equivalence principle.
5. No, my analysis confirms that industrial/human carbon is only a small fraction of the increase in atmospheric CO2 and there has been a large increase in biomass which contributes the majority of the increase in atmospheric CO2.
P.S., from your July 11, 2025 at 9:48 am comment: I laughed out loud at “[Jim’s] logic has been kind of shakey recently.” Give me a break. I have peripheral neuropathy, but so far it hasn’t affected my brain. I hope.
Jim,
You write “As long as you believe Sn contains no fraction of Eh you will never understand Dr. Ed’s model.”
What I called An, which is the same as your Sn, includes the absorption of ALL types of carbon. I made that clear when I wrote in my 7/11 9:48AM analysis “Divide the PROCESSES into human and natural and indicate which by subscripts. MAKE NO DISTINCTIONS ABOUT CARBON TYPES OR YOU MAY GET CONFUSED.”
I thought you understood , but rereading your earler 6/27 8:48pm comment, probably you did not. You wrote
“To be clear, I consider “Ah” as that fraction of atmospheric carbon removed naturally that was originally a fossil fuel. So if At is the total amount removed in a given time interval, At = An + Ah, where An is the non-fossil fuel carbon removed by natural processes.” I responded on 6/27 at 11:38pm “What you call “At” has always been “An” to me” but perhaps you missed that. My 7/11 analysis would make no sense if I used your definition of An. Now you have introduced Sn which is the same as your earlier At and my An.
In summary, we agree that natural absorption processes do not discriminate based on the source of the carbon. The mass-balance argument has NEVER claimed they did; only misinterpretations of the mass-balance argument have caused confusion. I am glad to see that you can say “Do I agree that more carbon has moved from the atmosphere into natural sinks than has gone the other way? Of course.”
But we are not on the same page on everything. You go on to say “my analysis confirms that industrial/human carbon is only a small fraction of the increase in atmospheric CO2”, as if that were important. I agree the present atmosphere has little carbon in it that once resided in a fossil fuel, but human emissions are still the cause of the rise, because natural processes have removed more than they added. I urged you to understand the disequilibriuim isofluxes which can change the atmosphere’s composition without changing levels and offered a little thought experiment. I laid this out again for Ed in my 7/12 1:41PM comment. I do understand his model, and why it is wrong.
Jim Siverly, July 13, 2025 at 7:21 am
In addition to what David said…
“2. But most of the annual amount remaining in the atmosphere originated from the natural sinks, because nearly all the human emissions are removed annually.”
As mass: only half the CO2 mass that humans ad per year are removed (as mix) in the same year.
As original FF molecules: you forget that the two fast cycles: ocean surface and vegetation not only remove FF molecules, but also bring them back in the next season. For vegetation: near fully within a year, for the ocean surface within a few years. Only what goes into more permanent vegetation and the deep oceans is gone for a long period.
“3. The sink rate is proportional to the carbon level, S = k * C. But the relative amounts removed are in proportion to the amounts added. S = Eh/f + En/f”
That is refuted by the observations: between 1958 and 2020, the human input increased from 1% to 5%. The observed ratio is over 10% FF in the current atmosphere and over 6% in the sea surface:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.jpg
and:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/d13C_brw_mlo_spo.jpg
Your simple math is based on the one-way “lake / bath tube” model, which is completely at odds with the real world…
“5. “… there has been a large increase in biomass which contributes the majority of the increase in atmospheric CO2.
The biosphere never can supply more CO2 than it removed first out of the atmosphere… Except for short periods like El Niño’s or when cooling to a new glacial period.
The oxygen balance shows that the biosphere is a net absorber of CO2 and so does satellites which monitor chlorophyll:
https://www.nasa.gov/feature/goddard/2016/carbon-dioxide-fertilization-greening-earth
and
https://tildesites.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
“We find the average CO2 uptake by the ocean and the land biosphere was 1.7 ± 0.5 and 1.0 ± 0.6 GtC/yr respectively;”
That was for the period 1992-2001. Meanwhile the net uptake of CO2 by the biosphere only increased…
Ferdinand,
It seems you and Dr. Ed. are defining Ah differently. Ah is human flow out of the atmosphere. It seems you and David are defining it as carbon capture, sequestration, etc. Ah isn’t trivial. It is essentially Eh.
Also, your answer, “That pCO2 is measured in the small air volume and is used as pCO2 of the ocean water,” is made-up science. That pCO2 is pCO2(atm), not pCO2(ocean). There is no small vapor of atmosphere just above the water that is pCO2(ocean).
Ferdinand,
Also, dC/dt=2ppm annually, based on flows, approximately 5% of that is human and 95% of that is natural. So humans contributed to about 0.1ppm annually of the increase.
David Andrews July 13, 2025 at 10:30 am states:
“I agree the present atmosphere has little carbon in it that once resided in a fossil fuel, but human emissions are still the cause of the rise, because natural processes have removed more than they added.”
How do we know the natural processes removed more than they added? Natural sinks removed less than all the emissions so the atmospheric content grew. There seems to be agreement FF emissions and natural emissions are removed by processes that cannot differentiate between them. It seems possible that if natural emissions are growing faster than the sinks atmospheric content will increase without FF additions. I do not think we have a good handle on the quantity of natural emissions. I think these points lead me to conclude the percent of natural emissions remaining in the atmosphere must closely match the percent of FF emissions remaining.
DMA,
“How do we know the natural processes removed more than they added?”
– Because consistenly over decades, the growth in atmospheric carbon has been only about 45% of human emissions. We can therefore conclude that natural processes absorbing atmospheric carbon into land/sea sinks are larger than emissions from those sinks. If it were the other way around, atmospheric carbon would be growing faster than human emissions. Data say it is not.
“I do not think we have a good handle on the quantity of natural emissions”
-You are correct that we do not, but we do have a good handle on the difference between natural absorption and natural emission rates. That difference, appropriately called “net global uptake”, is the amount of carbon that has “gone missing” from the atmosphere. It is the ~55% of human emissions not accounted for by measurements of atmospheric carbon growth.
“I think these points lead me to conclude the percent of natural emissions remaining in the atmosphere must closely match the percent of FF emissions remaining.”
-This has been one of Ed’s hangups too. There is indeed much more natural carbon around than carbon that was once contained in fossil fuel. And large natural exchanges between air, land, and sea thoroughly mix things up. Ed’s conclusion that the present atmosphere has little “human carbon” in it is correct. But his inference that therefore natural emissions have dominated the increase is wrong. Human emissions caused the growth (see my first paragraph here), but balanced exchanges which did not change levels hid the evidence. The atmosphere had extra “human carbon” after we put it there, but it mixed with the more abundant natural carbon in other reservoirs. These are the “disquilibrium isofluxes” I have discussed elsewhere. This is the “dilution of the Seuss effect”. You cannot understand what is going on without understanding these processes.
Stephen P Anderson, July 13, 2025 at 1:20 pm
You are right, there is some misunderstanding at work. The whole scientific world uses uses An as the fraction of CO2 that is sequestered by humans out of the atmosphere. Be it by planting new forests or carbon capturing ans sequestering (CCS). That are peanuts and the largest CCS project failed:
https://reneweconomy.com.au/chevron-concedes-ccs-failures-at-gorgon-seeks-deal-with-wa-regulators/
Our approach is that Eh, once injected into the atmosphere are part of the total atmosphere as mass and not anymore of interest for what happens with the total CO2 mass, as that is what “may” cause climate change. Only Qt is of interest. No matter how the original FF molecules are redistributed over the different reservoirs. Because Ah is minuscule, the sum of all natural sinks, An, are the only parameter that removes CO2 out of the atmosphere, human and natural molecules alike.
I think that you are mistaken about the pCO2(aq). For Henry’s law there is a (temperature dependent) fixed ratio between the CO2 level (pressure) in the atmosphere and the CO2 level in solution of seawater.
If the pCO2 of the atmosphere doubles, the CO2 level in seawater doubles.
Per Henry’s law, there is no net exchange of CO2 if the dissolved CO2 in seawater has the same apparent pressure as the CO2 in the atmosphere. Of course still there is a lot of exchange of molecules in each direction, but the number of molecules in each direction is equal.
One can theoretically calculate the CO2 content with its apparent pCO2 of the solution, based on alkalinity, salt content, DIC (dissolved CO2 + (bi)carbonates) or much easier by looking at the resulting pCO2 in the atmosphere, when atmosphere and water are in equilibrium.
That is done either by spraying seawater in a small volume of air or the opposite and measuring the pCO2 of the small volume of air.
Thus while strictly speaking, there is no measured pCO2(aq), the pCO2(atm) in equilibrium with seawater is as good as factor to be used in all flow calculations of CO2 transfer between the atmosphere and the ocean surface in either direction.
Stephen P Anderson, July 13, 2025 at 1:24 pm
“Also, dC/dt=2ppm annually, based on flows, approximately 5% of that is human and 95% of that is natural. So humans contributed to about 0.1ppm annually of the increase.”
The 5% is extra CO2 mass and adds its mass directly into the atmosphere. The 95% natural inputs increase to 97.5% (FF + natural) outputs, thus humans are fully responsible for the 2.5% increase of CO2 mass in the atmosphere.
No matter if all FF molecules remain in the atmosphere or every FF molecule is removed out of the atmosphere with the outputs.
For the inputs, the current ratio FF to natural is 5/95. But you forget that the other reservoirs also increased in FF content, the 95% return from oceans and vegetation is not FF free…
That makes that with only 1% to 5% FF input between 1958 and today, the FF content in the atmosphere is already over 10% and in the ocean surface over 6%.
Ferdinand,
Dr. Ed is also saying you can write two independent linear differential equations for natural flow and human flow. Of course you can. Do you know why? Because of the Equivalence Principle.
Ferdinand,
I’m not mistaken about Henry’s law. The partial pressure of the gases in the atmosphere determines the concentration of the gases in the ocean. That’s Henry’s Law. There is no pressure differential from some layer just above the surface to the atmosphere. The only pressure differential in the atmosphere is the hydrostatic pressure differential that causes the lapse rate. There is no radiative forcing that causes the lapse rate. That is also derived from the gas laws.
Ferdinand,
“The 5% is extra CO2 mass and adds its mass directly into the atmosphere. The 95% natural inputs increase to 97.5% (FF + natural) outputs, thus humans are fully responsible for the 2.5% increase of CO2 mass in the atmosphere. No matter if all FF molecules remain in the atmosphere or every FF molecule is removed out of the atmosphere with the outputs.”
It isn’t STATIC. (Caps for emphasis.) Most of the inputs from Natural and Human carbon are flowing out of the atmosphere without going into the math. Dr. Ed has already done a great job of showing you that. (You need to reread all three of his papers.) So, human carbon can’t be more than about 5% of the increase. Most of the increase has to be due to natural carbon. Dr. Ed was very conservative in his second paper and attributed 25% of the increase to humans, but it really isn’t. Humans are only responsible for about 10ppm. Almost nothing.
Stephen,
Ed is not wrong when he concludes from his calculations that “human carbon” makes up only a small part of the carbon in the present atmosphere. He is wrong when he thinks that implies that natural emissions are the dominant cause of the CO2 increase.
In the 1950’s, Hans Suess correctly noted that atmospheric radiocarbon levels were decreasing because of the addition on “cold” (C14 free) carbon from fossil fuel burning. A naive interpretation of the “Suess effect” would predict that if the ~33% carbon increase in the industrial era was from fossil fuel burning, then 33% of the new carbon would be cold. It is clearly not, and Suess in the 1950’s knew why. You are well aware that natural emissions are an order of magnitude larger than human ones. That means that there are large two-way exchanges between the atmosphere and land/sea reservoirs that mix the inventories and “dilute” the Seuss effect. There is a slight imbalance in these exchanges which accounts for atmospheric accumulation being only ~45% of human emissions (natural absorsption is greater than natural emissions) but most of the two way flow is balanced and does not change the atmospheric carbon levels. The balanced flow most certainly still does lower the “human carbon” content of the atmosphere. Ed has unknowingly been calculating the dilution of the Seuss effect rather than finding the cause of the CO2 increase.
I should have said “A naive interpretation of the “Suess effect” would predict that if the ~33% carbon increase in the industrial era was from fossil fuel burning, then the present atmosphere would be a mixuture of 33% cold carbon and 67% carbon with the usual C14/C12 ratio. “
David,
No Dr. Ed isn’t wrong. Dr. Ed’s logic and methods and derivations conform to every upper-level Chemistry, Physics and Math I ever have been taught. It is right out of the Physical Chemistry and Differential Equations textbooks. Now, your logic, doesn’t. I would respond to your Suess effect argument but what is the point? You are so twisted in your ideology that you can’t see science and mathematical truth when it hits you in the face. You continue to regurgitate Big Climate talking points (propaganda) with no science to back it up. Your “net global uptake” is poop. You need to read or reread Dr. Ed’s three papers and also Brendan Godwin’s book and pray to God for some understanding.
Stephen P Anderson, July 14, 2025 at 7:46 am
The CO2 pressure differential is between the ocean surface and the air layer just above it…
“the partial pressure of the gases in the atmosphere determines the concentration of the gases in the ocean.”
In this case it is just reverse: the CO2 concentration in the oceans determines the concentration of CO2 in the atmosphere…
Henry’s law does apply in both directions. The “equilibrium” pCO2 of the ocean waters changes with the sea surface temperature and if it gets higher than in the atmosphere, CO2 is degassing and increases the CO2 pressure in the atmosphere until bot are equal.
That happened over the past glacial-interglacial cycles: (ocean) temperature goes up and CO2 follows…
Stephen P Anderson, July 14, 2025 at 8:01 am
” Most of the inputs from Natural and Human carbon are flowing out of the atmosphere without going into the math.”
If you add 5% human input one-way and the increase in the atmosphere is only 2.5%, how then can the natural inflows have caused the increase?
Both the outputs to vegetation and oceans are larger than their inputs back to the atmosphere. A negative balance which should give an positive result in the atmosphere?
I have read Dr. Ed’s papers and indeed you can split the CO2 flows in “natural” and “human”. But I don’t see any particular reason to do that, as that only makes everything more difficult to follow and more prone for misinterpretations.
Human emissions are going for the full 100% directly into the atmosphere as mass, as low-13C and 14C-free.
All what the natural flows do is removing (not adding!) half of the increase in mass, replacing 2/3 of the FF molecules with CO2 molecules from other reservoirs and diluting the 14C “fingerprint” of FF in the same way.
The main problem for Dr. Ed’s calculations still is that he uses the much too short residence time of 4 years, that is the time that a single molecule CO2 resides in the atmosphere, before being switched with a CO2 molecule from another reservoir. That has nothing to do with the real decay rate of around 50 years for an injection of extra CO2 as mass (whatever its origin), back to the dynamic equilibrium of the pre-industrial times…
Dr Ed’s 4 years residence time violates the carbon mass balance: human FF emissions are very fast redistributed into atmosphere, oceans and biosphere, but there is a large gap between what remains in the atmosphere as calculated and what is observed. That extra CO2 can’t come from the oceans or vegetation, as these increased in carbon content, not decreased… Thus from where is that extra CO2?
Ferdinand Engelbeen, July 13, 2025 at 3:29 am
You wrote, “There is an enormous difference between … the absolute pCO2 of the atmosphere and the ‘concentration gradient,’” but that misses the exact point. We will never come to any understanding while you continue to drag out the same old talking points about what Feely considers an average concentration gradient in 1995. Simply put, if you average out the concentration gradients arriving at a small difference, you are in effect discounting most of the mass transfer that occurred during all the times that difference in concentration were maximal.
We have been over and over this. You are using K * ( pCO2now – pCO2old ) in your math resulting in very small K = 1/Tau. The planet doesn’t remember what pCO2 was in 1750. It only deals with the diurnal and seasonal differences applicable to the current time. We supplement the large amount of natural emissions which together are largely removed annually amounting to about ¼ of the CO2 in the atmosphere. Barring an apocalypse eliminating human life, the expanding biosphere may never end; not in 50 years, 500 years, or 50 million years. That makes Tau irrelevant. The only thing that need be said about a hypothetical net zero is that it will only take a few years for “pseudo” equilibrium to arrive. Te rules.
Having said that, a mea culpa is in order. There is a mistake in my assumption of f * S = Eh + En. Until I rework that assumption, I won’t be responding to comments about model differences with the exception of which physical processes apply.
In that vein, I will respond to your last paragraph,
“The main difference left is your residence time of 4 years, which is based only on all outputs of the atmosphere, without taking into account that most of these outputs are part of cycles that net removes zero CO2 out of the atmosphere.”
You have zero proof of that, only anecdotal evidence. Whether or not any removal process takes place in any specific e-time, the net e-time for the atmosphere is about 4 years as all agree. No process will remove all the annual emissions as long as emissions increase annually whether that be from industrial or biomass expansion.
“Only the difference between all inflows together and all outflows together, is the real decay rate of any CO2 mass (whatever its composition) out of the atmosphere and that is the calculated 50 years Tau…”
Again, there will never be proof of that due to our expected ever-increasing population or an end of the world. “Calculated 50 years Tau” is the operative phrase, because it’s based on the false idea that removal rate is proportional to the pCO2 difference with the “old” equilibrium.
DMA
July 13, 2025 at 1:45 pm
“It seems possible that if natural emissions are growing faster than the sinks atmospheric content will increase without FF additions. I do not think we have a good handle on the quantity of natural emissions.”
Yes and Yes. That summarizes the problem with the simple math. It doesn’t work if natural emissions increase and assumes all excess emissions are industrial emissions. David Andrews and Ferdinand Engelbeen are blind to that reality.
Jim and DMA,
You are completely wrong, and Jim you seem to be backsliding. First of all you should lose your habit of thinking about emissions only and ignoring natural absorption processes (which of course are not particular about whose carbon they absorb.) The method for computing net global updake doesn’t limit what natural emissions are doing. The DATA does allow you to say (for the last century but not always) that natural aborption exceeds natural emissions. If they both increase, net global uptake will still be positive as long as absorptions exceed emissions. You already agreed that more carbon has moved from the atmosphere into natural sinks than has gone the other way. But if natural emissions were to exceed natural absorption then there would be a net transfer of carbon from land/sea reservoirs INTO the atmosphere, and atmospheric accumulation would exceed human emissions. The DATA say that has not happened any time recently.
Stephen P Anderson
July 14, 2025 at 9:00 am
Here is how the Tau crowd rationalize the atmosphere containing a small percentage of fossil fuel carbon (FF) remaining in the atmosphere while causing all the excess carbon accumulating (making H1 true). The fast 4-year turnaround launders FF, but is unable to remove all excess carbon which is no longer identifiable as coming from any source, leaving a deficit of about half of the carbon equivalent to that sourced annually as FF.
Conveniently natural emissions don’t need to be accounted for and all absorptions are considered natural regardless whence they came. They assume an equilibrium remains as it has been since 1750 and use a bastardization of Henry’s Law to explain it. I’m coining the whole analysis Magic Math.
Jim Siverly, July 14, 2025 at 1:52 pm
“The planet doesn’t remember what pCO2 was in 1750. It only deals with the diurnal and seasonal differences applicable to the current time.”
It doesn’t need to. It does see the differences between 425 μatm in the atmosphere and 150 μatm near the poles where the waters with a lot of CO2 sink into the deep oceans, to return some 1,000 years later from the deep and heat up at the equator and increase its pCO2 to 750 μatm. The 150 μatm and 750 μatm of the ocean surface didn’t change much over time, as long as there is ice near the poles and the same maximum temperature near the equator.
Both the level in the atmosphere and the output increased in ratio over time
Te(a-d) = 900 PgC / 40 PgC/year = 22.5 years
Tau(a-d) = (900 – 628) PgC / 2 PgC/year = 136 years
The 2 PgC/year is not directly measured, it is the remaining gap in the net sink rate.
The seasonal differences between ocean surface and atmosphere remained about the same, as the average pCO2 of the ocean surface closely followed the increase of pCO2 in the atmosphere. The huge exchanges between ocean surface and atmosphere are caused by the seasonal temperature amplitude. As far as I know, that didn’t increase over time.
Te(a-s) = 900 PgC / 60 PgC/year = 15 years
Tau(a-s) = (900 – 628) PgC / 0.5 PgC/year = 544 years
The 0.5 PgC/year is directly measured as increase of DIC in the ocean surface
Then the biosphere. The exchange rate expanded from 100 to 120 PgC/year and the net removal rate from zero to 2.5 PgC/year (observed via the O2 balance).
Te(a-g) = 900 PgC / 120 PgC/year = 7.5 years
Tau(a-g) = (900 – 628) PgC / 2.5 PgC/year = 106 years
Overall Te and Tau:
Te(c) = 900 PgC / 220 PgC/year = 4.1 years
Tau(c) = (900 – 628) PgC / 5 PgC/year = 54.4 years.
“Barring an apocalypse eliminating human life, the expanding biosphere may never end”
Based on what happened over glacial and interglacial periods, the total biosphere expanded and did shrink in ratio to the CO2 level in the atmosphere. But that was at a “speed” of 0.02 ppmv/year. There is no reason at all that with a sudden drop in CO2 from 900 PgC back to 628 PgC the whole biosphere will shrink with 25% per year. It will slowly shrink back to the level of around 1750 with a Tau of some 50 years.
“No process will remove all the annual emissions as long as emissions increase annually whether that be from industrial or biomass expansion.”
That is not said or implied by anybody. What is said by the two Dave’s and me is that the both the biomass as the oceans are removing more CO2 than they add to the atmosphere. That is observed both in the biosphere (by the O2 balance) as in the ocean surface (by measuring DIC) and estimated for the deep oceans as difference for the total sinks and confirmed by tracers.
Even if all these cycles doubled, thus halving Te, that doesn’t affect Tau at all…
“It will slowly shrink back to the level of around 1750 with a Tau of some 50 years.”
That is for the overall Tau. The real Tau for the biosphere is:
“It will slowly shrink back to the level of around 1750 with a Tau of some 106 years.”
As that is the real speed of expanding/shrinking of the biosphere…
David,
It also disgusts me to see you insult (postmortem) an intellectual giant like Murry Salby. That’s when I knew you were nothing but a leftist hack. Here is Dr. Salby’s response to Macquarie University:
https://mlsxmq.wixsite.com/salby-macquarie/page-1f
Salby’s only crime was to tell the truth, just like Dr. Ed. They’ve gone against conventional wisdom. Conventional wisdom is usually wrong. How many classrooms still use Murry Salby’s text? Modern climate science is anti-science, anti-truth. It is an instrument of the left.
David Andrews
July 14, 2025 at 3:02 pm
“The method for computing net global updake doesn’t limit what natural emissions are doing.”
No, but it’s convenient to ignore them with Magic Math. If natural aborption and natural emissions both increase, net global uptake will only be positive if emissions exceed absorptions. That is a tautology. The question is how much of the increase is due to either FF or some increase in natural. You assume, or at least your Magic Math assumes, all the increase is FF.
Jim,
It is. It is a mathematical construct built to obtain a desired outcome without a semblance of reasoning or basis.
DMA and Jim,
“It seems possible that if natural emissions are growing faster than the sinks atmospheric content will increase without FF additions. I do not think we have a good handle on the quantity of natural emissions.”
Come on, as David already said: in the past 67 years the natural emissions never, ever were larger than the natural sinks. Never. Even if we don’t have a good handle on natural sources and sinks (and thus not on Te!) we have a quite accurate handle on En – A(n+h) and that was always negative, with a few borderline El Niño years…
Ferdinand,
It does not apply in both directions. One medium is air, and the other medium is liquid. Never has Henry’s Law been stated that the amount of gas in the air is proportional to the partial pressure of the gas in the liquid. NEVER EVER.
Ferdinand,
“The main problem for Dr. Ed’s calculations still is that he uses the much too short residence time of 4 years, that is the time that a single molecule CO2 resides in the atmosphere, before being switched with a CO2 molecule from another reservoir. That has nothing to do with the real decay rate of around 50 years for an injection of extra CO2 as mass (whatever its origin), back to the dynamic equilibrium of the pre-industrial times…”
You continue to violate the Equivalence Principle and you don’t care or don’t see it as a problem. “Be damned with science your agenda is more important.”
Jim,
“Here is how the Tau crowd rationalize the atmosphere containing a small percentage of fossil fuel carbon (FF) remaining in the atmosphere while causing all the excess carbon accumulating (making H1 true). The fast 4-year turnaround launders FF, but is unable to remove all excess carbon which is no longer identifiable as coming from any source, leaving a deficit of about half of the carbon equivalent to that sourced annually as FF.
Conveniently natural emissions don’t need to be accounted for and all absorptions are considered natural regardless whence they came. They assume an equilibrium remains as it has been since 1750 and use a bastardization of Henry’s Law to explain it. I’m coining the whole analysis Magic Math.”
That is a violation of the Law of Conservation of Mass. They violate so many scientific laws with their crazy constructs that they can’t see straight.
Jim,
“The fast 4-year turnaround launders FF, but is unable to remove all excess carbon which is no longer identifiable as coming from any source”
The processes that make the 4 year turnaround are in part not the same processes that permanently remove any excess CO2 out of the atmosphere. For the oceans the difference is clear: the ocean surface is largely responsible for the fast Te, but doesn’t remove much CO2 permanently.
The deep oceans add less than half of the oceanic Te, but are responsible for 4 times more CO2 removal than the ocean surface.
And the biosphere moves an enormous lot of CO2 back and forth between atmosphere and biosphere, but only a small part remains in more permanent vegetation.
And the increase of the basic pCO2 of the oceans, due to the increase of SST since 1750 is exactly known, thanks to the measurements on meanwhile over three million seawater samples…
Stephen,
“That is a violation of the Law of Conservation of Mass. They violate so many scientific laws with their crazy constructs that they can’t see straight.”
According to Jim and you,
5 PgC/year increase in the atmosphere is not caused by the 10 PgC/year human emissions, but by the increase of the natural inputs.
Observed: 5 PgC/year = 10 PgC/year + natural inputs – natural outputs
Or natural outputs are 5 PgC/year larger than the natural inputs.
Even if the natural outputs include half the human input of 5 PgC/year human supplied FF molecules, then still the full increase of 5 PgC/year in the atmosphere is caused by the human emissions.
According to your ideas, natural outputs are smaller than natural inputs.
Who is violating the carbon mass balance ánd the equivalency principle here?
Stephen,
You were ill-advised to bring up and attemp to defend Murry Salby. From his Wikipedia page:
“The National Science Foundation investigation report issued on 20 February 2009 found that Salby had overcharged his grants and violated financial conflict of interest policies, displaying “a pattern of deception, a lack of integrity, and a persistent and intentional disregard of NSF and University rules and policies” and a “consistent willingness to violate rules and regulations, whether federal or local, for his personal benefit.” It debarred Salby from receiving federal assistance and benefits until 13 August 2012.[9]” There is more.
I never met him, but have my personal reasons to question both his integrity and his science. After I noticed his C14 error (confusing “DeltaC14” which measures C14/C12 with C14’s abundance or molar fraction of the atmosphere) and published a note on it, he and coauthor Hermann Harde made a “correction” which can only be described as fraudulent. They engineered an unjustifiable background to make the C14 curve look like the DeltaC14 curve they had built their ridiculous model on. No real scientist would be fooled by that maneuver. It was aimed at his gullible followers. Apparently you are one of them.
One of the questions about climate skeptics that puzzles me is that while they proudly reject authority, they attach themselves to perceived “experts” and make little attempt to think for themselves. If you, Jim, and others want to unquestionably accept the Salby’s and the Berry’s views on things like mass-balance as the Truth because you don’t have the tools to do the thinking yourself, I can’t stop you. But you might ask yourself what it was that made Jim say to Ed a few days ago “I’m on your side”, rather than “I’m trying to work this out for myself.”
Ferdinand Engelbeen
July 14, 2025 at 3:53 pm
You are stuck on anecdotal data. Don’t you see that the 1,000-year-old CO2 returns from the deep experiencing a warmer world than in 1750 and somewhat greater biomass?
“Both the level in the atmosphere and the output increased in ratio over time.”
Did you mean the ratio of the level in the atmosphere versus the output increased over time? Regardless, I have no idea what your equations mean, because you have never shared a rigorous analysis of how Tau is derived.
“The seasonal differences between ocean surface and atmosphere remained about the same, as the average pCO2 of the ocean surface closely followed the increase of pCO2 in the atmosphere.”
That’s tantamount to saying there has been an increase in natural emissions. If there has been an increase in natural emissions, then FF cannot be responsible for all the excess CO2. H1 fails.
“As far as I know, [the huge exchanges between ocean surface and atmosphere caused by the seasonal temperature amplitude] didn’t increase over time.”
How could you know that unless assumed based on Magic Math? Even if temperature amplitude didn’t increase over time (although your Takahashi references contradict that), the biosphere has.
I’m still looking for where this Tau logic stems from. And while I think of it, why haven’t you responded to my analogy of A B reaction reaching the same equilibrium ratio while both concentrations increase after additional reactant is added to the system?
I think the speed of CO2 receding during interglacials was much less than 0.02 ppm/year. Largely because the temperature drop controlled the CO2 drop as it does the CO2 increase. So the equilibrium condition is controlled by temperature and changes according to Henry’s Law, etc. Tau has nothing to do with it.
“Even if all these cycles doubled, thus halving Te, that doesn’t affect Tau at all…”
I’m inclined to agree with the antecedent, but argue the precedent is irrelevant because Tau is ambiguously defined.
Ferdinand Engelbeen
July 14, 2025 at 4:07 pm
“natural emissions never, ever were larger than the natural sinks” is not the same as “natural emissions are growing faster than the sinks.” Sinks are larger, but only keeping pace with the increasing emissions.
Ferdinand Engelbeen
July 14, 2025 at 4:22 pm
“The processes that make the 4 year turnaround are in part not the same processes that permanently remove any excess CO2 out of the atmosphere.”
“…the ocean surface is largely responsible for the fast Te, but doesn’t remove much CO2 permanently.
The deep oceans add less than half of the oceanic Te, but are responsible for 4 times more CO2 removal than the ocean surface.”
Do you realize that is a hand-waving argument? You are basically saying that, the atmosphere and surface ocean participate mostly in fast turnover, and the ocean’s small part in Te removes most excess carbon. Actually, I agree with my paraphrase of your scenario. However, I am not sure what statement(s) I made you are objecting to or how it proves H1 true.
Furthermore, what do the other statements at July 14, 2025 at 4:22 pm have to do with my definition of Magic Math?
Jim Siverly, July 14, 2025 at 8:04 pm
It seems quite difficult for some here to understand the difference between Te and Tau.
Per definition:
Te = mass / output (residence time or turnover time)
Tau = change in mass (or pressure) / change in net mass (adjustment time or life time)
The difference is in the words “change” and “net”
For a one-direction process where all inputs flow via a container to outputs and nothing returns from these outputs back to the inputs, Tau <= Te (Stallinga, 2023). Only in that case. In all other cases, where some part of the outputs return to the inputs, Te and Tau are largely to completely independent of each other. That is where Berry, Harde, Stallinga, Salby, Koutsoyannis, you and too many other skeptics get wrong. They all still think that Te = Tau.
Both Te and Tau can be calculated, as far as the CO2 mass flows are known.
For e.g. the biosphere the current uptake is calculated at about 120 PgC/year, of which most is taken in in spring-summer.
That is based on the O2 balance and 13C/12C balance over the seasons.
Half of that, some 60 PgC/year already returns the same day as absorbed during the day at night, as plant and soil (bacterial) respiration. The other half comes back in fall-winter. The diurnal changes are rough estimates, based on direct δ13C measurements within forests.
The overall change is slightly better known, still with a large margin of error (+/- 60%), based on the oxygen changes:
https://tildesites.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
That shows a net uptake of about 2.5 PgC/year extrapolated for current years.
Thus for the current atmosphere – vegetation exchanges:
Te(a-g) = 900 PgC / 120 PgC/year = 7.5 years
For Tau, the net change in mass is the observed net sink rate, the change in plant growth for 93% of all plants on earth (C3-type plants) is directly proportional to the absolute CO2 pressure in the atmosphere, up to over 1,000 ppmv, thus
Tau(a-g) = (900 – 628) PgC / 2.5 PgC/year = 106 years
Te and Tau for vegetation differ more than an order of magnitude of each other…
The same calculations are valid for the deep oceans, where the pCO2 at the sink and source places hardly changed between 1958 and today, thus still with enormous differences for the increase of CO2 in the atmosphere.
The only exception is the ocean surface, where the pCO2 of the surface increased with the pCO2 of the atmosphere from zero in the past at equilibrium to 7 μatm today.
That means that my calculation for Tau(a-s) was way too high. It should be:
Tau(a-s) = 15 PgC / 0.5 PgC/year = 30 years
Still twice Te…
That is not Magic Math, that is calculating Te and Tau on known data. Which shows that using Te for the net removal of any extra CO2 (of whatever source) out of the atmosphere is way too fast…
David Andrews
You were ill-advised to ridicule and abuse Murry Salby based on Wikipedia. They are a socialist propaganda outfit. Whatever they said the truth would be 180 degrees the opposite. That’s an appalling attack by you.
David Andrews
Your abusive comment directed at Murry Salby based on Wikipedia is totally false and all lies.
Murry Salby responds to the attacks on his record
JoNova | August 11, 2022
https://climatecite.com/murry-salby-responds-to-the-attacks-on-his-record/
Murry Salby’s detailed response
https://joannenova.com.au/s3/jonova.s3.amazonaws.com/guest/salby-murry/re_nsf_r.pdf
As Jo Nova says and I concur: “any scientist who responds to a question about Murry Salby’s work with a reference to his employment is no scientist.
https://joannenova.com.au/2011/08/blockbuster-planetary-temperature-controls-co2-levels-not-humans/“
Jim Siverly, July 14, 2025 at 7:14 pm
“Don’t you see that the 1,000-year-old CO2 returns from the deep experiencing a warmer world than in 1750 and somewhat greater biomass?”
Not very relevant for the total CO2 in the atmosphere, which was ~290 ppmv then, somewhat 13 ppmv higher than 400 years later during the LIA. Thus returning waters only slightly higher in CO2 than in 1750.
Very relevant for their isotopic levels, as these were from CO2 sinks into the deep, long before the low-13C and 14C-free FF emissions and the 14C increase from the atomic bomb tests.
“Did you mean the ratio of the level in the atmosphere versus the output increased over time?”
Yes, for the atmosphere its CO2 level increased with about 50%, the outputs to the ocean surface increased with 33%. For vegetation only with 13%… Thus in both cases Te increases, be it less for the oceans than for vegetation.
“That’s tantamount to saying there has been an increase in natural emissions.”
You are still stuck at the idea that the inputs define the CO2 level in the atmosphere. That is only the case for the one-directional “lake” model, not for the real world where huge seasonal cycles are at work.
In NH spring-summer, the CO2 level in the atmosphere even drop some 10 PgC (~5 ppmv) on global level, despite the huge input from the ocean surface… Thanks to warming (and sunny) vegetation that sucks more CO2 out of the atmosphere than the warming ocean surface supplies.
“Even if temperature amplitude didn’t increase over time (although your Takahashi references contradict that), the biosphere has.”
The calculation was only for the ocean surface. The formula of Takahashi shows the same pCO2 difference for the same temperature change. If the temperature change over the seasons didn’t change, the seasonal uptake and release didn’t change either.|
The change in CO2 cycle height (both inputs and outputs) is both for vegetation (+12%) and for the deep oceans (+33%) not for the ocean surface.
“I think the speed of CO2 receding during interglacials was much less than 0.02 ppm/year. Largely because the temperature drop controlled the CO2 drop as it does the CO2 increase.”
The 0.02 ppmv/year was for the “fast” T increase of 5,000 years between a glacial and interglacial period. The opposite change is even much slower.
CO2 changes follow the increase with 800 +/- 600 years delay during warming and several thousands of years in opposite direction. A Tau of 50 years then is peanuts compared to the extremely slow changes in pCO2.
There is even no influence of the change in vegetation visible over the full 800,000 years, until the human use of FF… That is reflected in small changes in 13C/12C ratio at -6.5 +/- 0.4 per mil. The drop since 1850 is around -8.2 per mil in the atmosphere…
That of the A – B reactions I need to look that up…
Jim Siverly, July 14, 2025 at 7:27 pm
“’natural emissions never, ever were larger than the natural sinks’ is not the same as ‘natural emissions are growing faster than the sinks.’ Sinks are larger, but only keeping pace with the increasing emissions.”
Not only contradictory: if the natural emissions are growing faster, but don’t exceed total sinks, then they don’t contribute to the increase in the atmosphere. If they grow higher than total sinks, then the increase in the atmosphere would be larger than of human emissions alone.
And again: you have the order for vegetation in the wrong direction: sinks in vegetation are the first step, caused by temperature and sunlight. The releases of CO2 from vegetation follows later and except for a few El Niño years, are smaller than the uptake… For the oceans it is reverse, but again, the release is smaller than the uptake…
Dr. Ed,
The link to the Roth article comes up as the Robbins article: https://scienceofclimatechange.org/wp-content/uploads/SCC-Roth-Origin-of-CO2-V5-1.pdf. Interestingly, a google “I’m feeling lucky” search comes up the same thing. It must be an SCC Publishing issue. The full search gave me this option: https://scienceofclimatechange.org/roth-about-the-origin-of-co2-in-the-atmosphere/. Furthermore, the google AI comment on the full search has it bass ackwards: “The CO2 Coalition, in their study, argues that the increase in atmospheric CO2 is not primarily caused by human emissions, but the study is flawed and ignores the overwhelming scientific consensus.”
David Andrews June 30, 2025 at 8:50 pm
David,
I deleted your remarks that attack Salby from your above refrenced comment. I will otherwise leave the comment.
My reasons are (a) personal attacks are not part of a science debate, (b) Salby is not here to defend himself, (c) your attacks have no references, (d) your attacks make no contribution to this discussion, and (e) if I leave your attack on Salby, it will set a bad precedant to the discussions on my website.
We are here to discuss and debate climate science. Whatever a person has done in the past, or even accused to have done, is not relevant to the discussion of what the person has published or otherwise presented to the public.
Ferdinand Engelbeen
July 15, 2025 at 2:52 am
“Both Te and Tau can be calculated, as far as the CO2 mass flows are known.”
The calculation of Te is straight forward from first-order principles. Everybody knows how it’s done and understands it clearly. Your Tau is derived from the misconception that a disturbance will be restored to its original equilibrium state. The assumed FF disturbance is conflated by an additional disturbance due to natural emissions. Therefore, your Tau is ambiguous, corrupted, and impossible to document unless you survive human extinction and return in a century to report the situation.
You repeat the same mantra comprising anecdotal data to which I continue to reply, where is the justification of Tau that is based on your premise that preindustrial equilibrium returns with net zero FF?
Ferdinand Engelbeen
July 15, 2025 at 5:57 am
If you check the simple math data, you should find that the rate CO2 is rising is more often less than the output rate.
“You are still stuck at the idea that the inputs define the CO2 level in the atmosphere.”
Do you deny that [ inputs – outputs ] define the CO2 level? Please, no more anecdotal evidence that proves nothing. These are arguments by assertion, not scientific.
“The 0.02 ppmv/year was for the “fast” T increase of 5,000 years between a glacial and interglacial period. The opposite change is even much slower.”
More assertions without presenting data proving it. What 5,000 year periods? The data shows wide variations in rates of CO2 removal which, to my eye balling, all seem much less than 0.02 ppmv/year.
“A Tau of 50 years then is peanuts compared to the extremely slow changes in pCO2.”
Yes, because Tau has nothing to do with gradual CO2 equilibrium totally dependent on temperature. Tau is a fabrication gaslighting those of us bothering to check your math and unnecessarily alarming others about climate change.
Jim Siverly, July 15, 2025 at 7:07 am
Indeed that is an issue at their website. I have the article by Roth downloaded in the past with exact the same reference…
I have uploaded the real article and it can be downloaded at:
https://www.ferdinand-engelbeen.be/klimaat/klim_pdf/SCC-Roth-Origin-of-CO2.pdf
We have asked SCC to retract that article, because it contains so many errors and mispresentations of what we did write, that one can’t name it “science” at all. But they refused, because the author refused to do it…
To give a few examples:
In the abstract he writes:
“In such a system the concentration cannot rise more than the inflow. Therefore, since the concentration has risen by
50 %, the inflow must have risen by at least 50 %. ”
That is based on his idea that the atmosphere is a “lake / bath tube” model.
But the increase of inflows from the oceans increased only with 33% and from the biosphere with 11%. Thus his model of the real world is wrong, not ours…
“Another weakness of the study is its assumption that natural fluxes in and out of the atmosphere have remained unchanged for 250 years.”
Our study nowhere said or implied that the natural fluxes remained unchanged…
Only one point of the many points that show the “quality” of his remarks.
In chapter 13, the oxygen balance, he writes:
“Oxygen is consumed when fossil fuels are burned, and it is produced when plants grow (greening of the Earth). The oxygen mass balance merely reflects the accuracy of our estimates of these two processes; it says nothing about the source of the elevated CO2 concentration.”
In the same chapter the oxygen balance is shown as graph and clearly indicates how much oxygen is used burning FF and how much O2 is produced by the global biosphere, thus how much CO2 the global biosphere has absorbed, the remainder was absorbed by the oceans:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/bolingraph.gif
Which shows very clear that FF burning is the cause of the full increase, only reduced by the CO2 uptake from both the biosphere and the oceans.
If he doesn’t understand the oxygen balance, what does he understand at all?
Then the “new” study of Bernard Robbins.
He makes the same mistake as many before him, by comparing T variability with CO2 rate of change variability and “forgets” to plot the twice as steep slope of human emissions. These simply disappear in space, I suppose. Or they separately sink into oceans and biosphere without leaving one gram of CO2 in the atmosphere…
Here how that works:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/demetris_1b.png
The dark blue line is the human emissions/year, including the 2020 Covid drop.
The red line is the observed increase in the atmosphere, which may be 100% human or 100% natural or anything in between.
The green line is the net sink rate if the increase in the atmosphere is 100% human.
The light blue line is the net sink rate if the increase in the atmosphere is 100% natural.
In the latter case, every gram of what humans emitted is absorbed somewhere in nature. Very remarkable. And nature sinks about twice the amount that it supplied to the atmosphere…
Very, very remarkable…
Jim Siverly, July 15, 2025 at 8:47 am
“where is the justification of Tau that is based on your premise that preindustrial equilibrium returns with net zero FF?”
Except for a slight increase of the equilibrium since pre-industrial times, due to increased sea surface temperatures, the equilibrium can be back calculated from the ratio’s between net sinks and absolute CO2 pressure in the atmosphere. The intercept of zero sink is the equilibrium level in the atmosphere. Calculated by Peter Dietze (1997), Lindzen, Spencer, myself and recent by David Burton:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
That is a straightforward calculation that shows the equilibrium for any disturbance of any kind of dynamic equilibrium…
Ferdinand Engelbeen July 15, 2025 at 10:29 am
Dear Ferdinand,
Thank you very much for your comments and scientific challenges. You are certainly welcome to continue to make your challenges. Your challenges have been admirable.
However, you have proved wrong your special document published by the CO2 Coalition. When you use Dietze, Lindzen, Spencer, and Burton to attempt to enforce your arguements, you merely prove that Dietze, Lindzen, Spencer, and Burton are equally wrong about your claims that H(1) is true.
All these authors are deficient in their understanding of how to do systems models and such expertise is very relevant to this subject. Scientists can be very proficient in their own area of expertise, but few scientists also have the necessary expertise in systems engineering, systems models, probability, Markov chains to properly argue that H(1) is true in the face of my and other scientists proof that H(1) is false.
In addition, the null hypothesis is this debate is that H(1) is false. The burden of proof is on your side and your side has not met that burden of proof.
One other startling error that you made a few days ago, was to claim that it is incorrect to detrend time series data in order to calculate a correlation. On that subject, your claim is overturned by extensive literature in statistics.
Munshi is correct that his statistics prove there is no correlation between human CO2 emissions and the increase in atmospheric CO2. Munshi’s primary calculation was for annual data. He also tried 2-year, 3-year, 4-year, and 5-year data to find a correlation. All these tests failed to find a correlation.
The conclusion, supported by all good science, is when there is no correlation between two time series, there is no cause-effect relationship between these time series variables.
This fact alone proves you CO2 Coalition paper is pseudo science. If I were you or anyone in the CO2 Coalition, I would immediately reject this paper.
Best wishes,
Ed
Ferdinand Engelbeen
July 15, 2025 at 6:06 am
I don’t understand how “Not only contradictory:” applies to my statement that sinks are larger, but only keeping pace with the increasing emissions.
“if the natural emissions are growing faster, but don’t exceed total sinks, then they don’t contribute to the increase in the atmosphere.”
That is not necessarily true and you cannot use Magic Math to prove it so. Increasing natural emissions supplement the FF emissions which contributes to the CO2 rise. This is what the Berry, Harde, Stallinga, Salby, and Koutsoyannis papers are explaining.
“If they grow higher than total sinks, then the increase in the atmosphere would be larger than of human emissions alone.”
That’s Magic Math. Natural emissions and FF emissions are increasing at about the same rate as the sinks are. You should be seeing that for yourself, if you’re working on step-wise integration.
I don’t know where I claimed any order for vegetation being in the wrong direction. I can’t deal with anecdotal data, because I cannot evaluate it out of the context of a full carbon cycle. Something like Dr. Ed and others have demonstrated.
Jim Siverly, July 15, 2025 at 9:14 am
“If you check the simple math data, you should find that the rate CO2 is rising is more often less than the output rate.”
What does that prove? That there is a huge variability in sink rate, not in source rate, because the known source is twice as high as the increase in the atmosphere and the difference also is half the human emissions.
“You are still stuck at the idea that the inputs define the CO2 level in the atmosphere.’
Do you deny that [ inputs – outputs ] define the CO2 level?”
Inputs – outputs = NET output, thus Tau,
Te = mass / output = mass / input when output = input and for a “one way” process, the input dictates the level in the atmosphere and therefore the output…
I did forget to show the Eemian for the equilibrium changes with temperature:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/eemian.gif|
Some 100 ppmv increase for 10°C increase for Antarctic temperatures or between 15-20 ppmv/°C for global temperatures.
According to Takahashi for modern times: about -13 ppmv between MWP and LIA and back +13 ppmv today since the LIA. +3.5 ppmv/°C for 1-3 year events (Pinatubo, El Niño) and -5 ppmv/°C for seasonal changes.
The current increase is over 100 ppmv/°C if temperature was the origin of the increase, which it is not.
Thus the oceans are not the cause of the increase in the atmosphere, neither is vegetation…
Dr. Ed, July 15, 2025 at 11:01 am
One can’t prove that a hypothesis is right, one can only prove that a hypothesis is wrong, if it violates even the smallest, minuscule fact. I haven’t seen any proof that our work violates any observation of any kind. Thus still is getting strong.
The main argument is simply in the carbon mass balance, all the other observations just support the human cause of the increase, but are not even necessary.
The mass balance shows that human emissions are larger than the observed increase in the atmosphere, thus nature is a net sink for CO2 (whatever the combination of natural and FF CO2 in the atmosphere), not a net source.
Any attempt to show that natural emissions are even a part of the increase violate the carbon mass balance.
Then:
“One other startling error that you made a few days ago, was to claim that it is incorrect to detrend time series data in order to calculate a correlation.”
This is really a mathematical joke.
Let us start with two independent variables that cause changes in a third, dependent, variable.
One has no trend and a lot of variability, the other has zero variability, but a huge trend. The net result of both together is a huge trend with huge variability:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_t_em.png
With an error in it: human emissions are labeled as d(em)/dt, while that are just the emissions/year.
Both temperature dT/dt and dCO2/dt are moving 12-month averages with a lot of variability.
dT/dt has zero trend and all variability. Human emissions are all trend and near zero variability.
Now, when analyzing these data, all the CO2 variability of the increase indeed is caused by temperature variability in the derivatives, but as dT/dt has no trend, it is not responsible for the trend in dCO2/dt, while the emissions/year show twice the trend of dCO2/dt…
That means that looking at the variability on the de-trended data shows what is responsible for the variability but effectively removed the cause of the trend of CO2 in the atmosphere!
Simply said, every type of program that looks at the variability for the cause of the increase in the atmosphere is doomed to fail, including the RRR approach of Koutsoyiannis…
At last, here the influence of a few extremes in temperature around the 100 ppmv trend in the past 67 years of accurate measurements:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/wft_trends_rss_1985-2000.png
Ferdinand Engelbeen
July 15, 2025 at 11:10 am
“Inputs – outputs = NET output, thus Tau…”
Yes, Tau. A construct of Magic Math. We will go round and round getting nowhere, I’m afraid.
I suppose, too, you won’t be agreeing that Tau has nothing to do with the interglacial shifts in equilibria. I already acknowledged temperature is only fractionally responsible for the excess natural emissions. Biosphere expansion and FF account for the rest, thus oceans, vegetation, temperature, and FF all contribute to increasing CO2 in the atmosphere.
One of the first papers I saw on this subject was ( http://www.co2web.info/ESEF3VO2.pdf ) by Tom Segalstad in 1998. He addressed much of the mass balance ideas brought out by Ferdinand Engelbeen and others here but concluded the quantification of the processes discussed led to a conclusion that closely matches Dr. Ed’s numbers. He was very critical of the IPCC treatment of ocean chemistry and modeling of CO2 /temperature dependence. He was also critical of the ice core data based on his interaction with Jaworoski who apparently worked on them extensively.
DMA, July 15, 2025 at 1:42 pm
I had similar discussions with Segalstad and others in the early 2000’s with the same arguments. Nothing since then has changed… The main difference: the main use of the residence time to “prove” that humans are only part of the increase. Still violating the carbon mass balance…
Take this one:
“Both radioactive and stable carbon isotopes show that the real atmospheric CO2 residence time (lifetime) is only about 5 years, and that the amount of fossil-fuel CO in the atmosphere is maximum 4%”
The supply of FF was 1% to 5% of the total inputs between 1958 and current, but meanwhile the observed increase in the atmosphere is already over 10% FF and in the ocean surface over 6% FF.
The “life time” of the bomb 14C is between 12 and 20 years, still 3 to 5 times slower than the 4 years residence time…
And about Jaworowski: he never performed a CO2 measurement in ice cores. He was a specialist in radioactive fallout from Chernobyl and looked at the presence (and migration) of these metal ions in relative warm ice fields of Scandinavia (with a lot of water veins. He translated his experience to objections against ice core CO2 measurements, which can’t be compared at all, at least as for the much lower temperatures and the lack of water veins, large enough to pass CO2 molecules…
All his objections from 1992 were rebutted by the work of Etheridge et al. from 1996 on three high accumulation and high resolution ice cores at Law Dome. Despite that he repeated his objections in the early 2000’s…
See: https://www.ferdinand-engelbeen.be/klimaat/jaworowski.html
Jim Siverly, July 15, 2025 at 1:01 pm
Jim, Te is about mass / outflow, not [input – output], which is NET outflow.
Ferdinand,
“The main argument is simply in the carbon mass balance, all the other observations just support the human cause of the increase, but are not even necessary.
The mass balance shows that human emissions are larger than the observed increase in the atmosphere, thus nature is a net sink for CO2 (whatever the combination of natural and FF CO2 in the atmosphere), not a net source.
Any attempt to show that natural emissions are even a part of the increase violates the carbon mass balance.”
If the most that human emissions have ever been is 4-5% of the total emissions every year since 1750, then how can the total amount of human CO2 in the atmosphere be more than 5%? By the way, this is a carbon mass-balance question.
Stephen and Jim,
You both seem to half accept the mass balance argument when you agree that nature is a net sink, and that “of course natural processes are removing more carbon from the atmosphere than they are adding.” But you seem to be hung up on a different point, the same one that has confused Ed for several years. Remember, Ed’s calculations, Jim’s spreadsheet, AND MAINSTREAM SCIENCE all agree that there is little of what Ed calls “human carbon” in the present atmosphere. You seem to think, as Ed did, that cinches the case that the rise is dominated by natural processes (the very same ones that are removing net carbon from the atmosphere!) That is where you and Ed are in disagreement with mainstream science, Ferdinand, and me.
My July 14 posts at 8:10 and 8:16 AM explained why the “human carbon” content of the present atmosphere would be what it is even with 100% of the atmospheric rise coming from human emissions. The only counter-argument against that post so far is Stephen’s “net global uptake is poop”. If that is the best you can do, case closed. But there is also work to be done getting you to understand adjustment times, that I am leaving to Ferdinand.
David,
What are you talking about? I never agreed that nature is a net sink. I believe nature is a net emitter. It has to be. That is the only thing that makes sense mathematically.
David,
Ed Berry has already made the argument with his model derived from physics. He’s already showed net global uptake is poop. dC/dt= Input – Output. Output is proportional to CO2 level. Falsify his hypothesis. If dC/dt=0, input=output, then what is Tau?
If human emissions have never been more than 5% since 1750 then how can human CO2 be more than 5% of the total atmospheric composition?
Stephen,
Data says unambiguously that atmospheric accumulation is only 45% of human emissions. See Ballantyne cited multiple times above. Where does the rest of the “human carbon” go if not into natural land/sea sinks?
None of the stuff being talked about here is new. See:
https://scienceofclimatechange.org/wp-content/uploads/Andrews-2023-Clear-Thinking-about-Atmospheric-CO2.pdf
David,
You don’t answer questions. You just refer to dogma.
Stephen P Anderson, July 15, 2025 at 10:00 pm
“dC/dt= Input – Output. Output is proportional to CO2 level”
1. Output of the atmosphere is NOT proportional to the absolute CO2 pressure, but proportional to what Henry’s law dictates for the ocean surface. Not that it makes much difference, as input – output is a meager 5 PgC/year (~2.5 ppmv/year) at a level of 900 PgC in the atmosphere. For the absolute output that makes some 16 PgC/year. That is all. All the rest of the 200 PgC/year is what other processes absorb and bring back and these processes are largely independent of the CO2 pressure in the atmosphere. Like the uptake by vegetation in spring/summer: 120 PgC/half year only from the sun and temperature. The net effect of the full biological cycle is only 2.5 PgC/year more out than in.
2. Add the human FF emissions / sinks to that formula:
dC/dt = Input – Output + FF – human induced sinks
dC/dt = -5 PgC + 10 PgC – 0 PgC
dC/dt = +5 PgC fully caused by human FF emissions.
That is the mass balance.
That says nothing about what happens with the individual FF CO2 molecules, which may (in part) reside in the atmosphere or may all replaced (NOT removed as mass!) by CO2 molecules from other reservoirs.
3. For input = output:
If input = output, the formula for Tau:
Tau = extra CO2 / extra output
can’t be calculated, because there is no extra output.
At the moment that there is extra CO2 in the atmosphere above the equilibrium with the ocean surface, per Henry’s law, Tau can be calculated and both for oceans and vegetation, that is a linear function: the extra output is directly proportional to the extra CO2 in the atmosphere.
For the current atmosphere that gives:
Tau = (900 – 589) / 5 = 62 years.
The 900 PgC in the atmosphere and the 5 PgC/year inputs-outputs are observed. the 589 PgC in 1750 was based on ice core measurements, but may have shifted over time (as is the case for the average ocean surface).
Thus what is the current equilibrium where inputs = outputs?
That can be back-calculated. As both the (deep) oceans and the biosphere react in ratio to the extra CO2 in the atmosphere, the point of zero difference between inputs and outputs is easy to obtain:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Or about 282 ppmv or 607 PgC, slightly higher than in 1750, due to an increased sea surface temperature.
That makes that the current Tau gets:
Tau = (900 – 607) / 5 = 59 years.
Several others like Dietze (1997), Lindzen, Spencer and others have calculated the current “equilibrium” CO2 level in the atmosphere between 280 and 300 ppmv
What has that to do with Te? Simply nothing. The output may be 20 or 200 or 2000 PgC/year with a calculated Te of 50 or 5 or 0.5 years, that has zero influence on Tau, which can be calculated independently of Te as long as inputs – outputs 0.
Tau is the real removal rate (adjustment time or lifetime) of any extra CO2 in the atmosphere as mass, whatever the origin of the extra mass.
Te is the average time any individual CO2 molecule (whatever the origin) remains in the atmosphere, before being transferred to another reservoir. Either by mass removal or by replacement.
4. How can there be more FF CO2 in the atmosphere than 5% with only 1% to 5% (1958-current) in the inputs?
Quite simple: the 1-5% in the inputs is “fresh” FF CO2. Part of the total FF emissions in the past were distributed into vegetation and ocean surface and now are recycled back to the atmosphere as “old” FF CO2. Thus FF accumulates over time in all three reservoirs…
Only what gets into more permanent vegetation and soils doesn’t return and what goes into the deep oceans returns only after many centuries…
I hope this made it clear what the difference between Tau and Te means…
The sentence
“as long as inputs – outputs 0”
had the smaller than / larger than signs, but these disappeared…
So the text should be:
“as long as inputs – outputs do not equal zero”
David Andrews
July 15, 2025 at 9:01 pm
If you want to get me to understand adjustment times, maybe you should help Ferdinand answer my question about an A to B reversible reaction reaching the same equilibrium ratio while both concentrations increase after additional reactant is added to the system. What is Tau for the time to establish the new equilibrium and why should it be any longer than the original relaxation time?
Ferdinand Engelbeen
July 16, 2025 at 2:51 am
“1. Output of the atmosphere is NOT proportional to the absolute CO2 pressure, but proportional to what Henry’s law dictates for the ocean surface.”
You’ve asserted this countless times here. It disagrees with mainstream scientists who are not fooled by Magic Math. It’s time for you to show a proof of 1. And not with anecdotal data, which is not proof.
I know that you are going to say it is the NET output that is proportional to the difference, as in F = k•s•ΔCO2. Where is Feely’s use of that formula derived from first principles?
Jim Siverly, July 16, 2025 at 6:29 am
“I know that you are going to say it is the NET output that is proportional to the difference, as in F = k•s•ΔCO2. Where is Feely’s use of that formula derived from first principles?”
Jim, I am really surprised that you even question that formula…
From the atmosphere into the oceans, the gas transfer is:
F- = k*s*pCO2(atm)
Where (s) is the solubility in seawater and (k) the kinetic forcing function, the gas transfer velocity.
the opposite transfer is:
F+ = k*s*pCO2(aq)
In both cases a lot of CO2 molecules are going from one medium to the other medium.
The overall transfer then is:
F = k*s*ΔpCO2(atm-aq)
Compared to the [Te(s-g) – Te(g-s)] of Dr. Ed, the influence of the CO2 mass in the atmosphere is about the same, as for any gas mass equals partial pressure. A doubling of CO2 mass in the atmosphere will give a doubling of CO2 transfer from atmosphere to ocean surface.
For the oceans, that is not the case, because of all carbon present in the surface (~900 PgC) only about 1% is pure, dissolved, CO2 which causes the equilibrium pCO2 of the ocean surface. The carbonates, bicarbonates, pH and temperature all influence the pure [CO2] and thus the pCO2 of the surface, but not in direct ratio to their mass.
Thus Te(s-g) is not applicable as surrogate for the CO2 transfer between ocean surface and atmosphere.
In the first formula:
F- = k*s*pCO2(atm)
(s) plays no role, and must be dropped.
Ferdinand Engelbeen July 16, 2025 at 2:51 am
Dear Ferdinand,
Jim, Stephen, and others are correct.
The outflow of carbon from the atmosphere depends only on the level (or pressure) of carbon in the atmosphere divided by an e-time. Since the earth is not sealed with plastic, the carbon cycle easily flows between the carbon reservoirs.
This simple equation is more than physics. This result of the whole field of systems engineering that no one in the CO2 Coalition will even study. I usually reference the book by Jay Forester (MIT): Principles of Systems. Get a copy and read it. If you can’t understand it, as I predict, this means you and everyone else in the CO2 Coalition does not know WTF you are talking about when you attempt to define a carbon cycle.
This is more than physics. This is systems engineering. We have people like you, Burton, Happer, Lindzen, Spencer, and all the rest of the CO2 Coalition clan, who think they know systems engineering but they don’t. So, they screw it up. You and they are way out of your field of expertise when you attempt to deal with a subject like the carbon cycle, which is a system.
To say the ocean determines how much carbon flows out of the atmosphere, is analagous to saying that a charity determiines how much money I send it, when it is obvious that I determine how much money I send to a charity. That is a system. That is how nature works. The reservoir that holds the carbon sets the outflow of its carbon. A sink doesn not determine the outflow of another reservoir. Your focus on sinks misses the whole method to solve the problem.
This is the opposite of govenment taxes that determine how much money I send them. But government is not free flowing system. Government is a forced structure that steals our money.
A key part of a simple system is that Outflow = Level / Te
All pharmcology models use this equation, for example, and it works.
The fact that I could reduce my system equations of for the carbon cycle to an electric circuit proves that my model is physicially correct. It reduces to Ohm’s Law. My carbon cycle model functions like an electric circuit. Your’s does not.
Your and the CO2 Coalition’s handwaving arguments do not even have a mathematical structure. You don’t even know how to define a carbon cycle model. Your so-called mass conservation is a piece of junk from the viewpoint of physics, systems, and simple bookeeping. You have nothing that you can reduce to Ohm’s Law to demonstrate that your hypotheses are truly simulating nature.
You cannot follow the very simple process of separating your mass balance equation into two separate models, one for natural carbon and the other for human carbon. Such separation is fundamental to this problem and the proper way to solve this problem, e.g., calculation the effect of human CO2 on the level of atmospheric CO2.
If I were the teacher and a student could not understand that we need to make this separation in order to solve this problem, I would flunk the student and suggest he pursue another subject, like maybe being a rock star.
When you, and others like Andrews, talk about a natural carbon atom “taking the place of a human carbon atom”, you are so far out in limbo land that you should take up another profession entirely.
The CO2 Coalition should get out of this subject because they claim expertise that they do not posess. As a result, they are destroying the progress of atmospheric physics.
Jim,
I do want to help you understand adjustment time. Here is a little exercise which I hope will convince you that one time constant does not describe the carbon cycle. Unlike Ferdinand’s analysis, mine is mostly qualitative but I hope gives insight.
Start by imagining a two-box system called “atmosphere” and “surface ocean”. (Temperatures are stable throughout.) The CO2 content in one box has reached a Henry’s Law equilibrium with the CO2 content in the other box. Now introduce a steady trickle of CO2 to “atmosphere”. The CO2 concentration there grows, it no longer is in equilibrium with “surface ocean”, and net CO2 is transferred to “surface ocean”. The dynamics could be analyzed with Henry’s Law and a time constant which measures how much “surface ocean” lags “atmosphere”. Let’s guess that time constant is 4 years. After a while, turn off the CO2 trickle into “atmosphere” [net zero!], and in four-ish years the system settles into a new and stable equilibrium with higher CO2 levels than it originally had. In this model, it will stay there indefinitely.
“But wait”, you say, “that model is too simple!” I agree, so we will add a third box called “deep ocean” which exchanges carbon with “surface ocean”. The mechanisms for doing that include the sinking of organic matter, and circulation patterns with vertical components. Since extra carbon has been introduced to “surface ocean”, we can expect the net result is to transfer carbon from “surface” to “deep”. This will reduce the “back pressure” of carbon in “surface ocean” and allow a decrease in atmospheric carbon. Do you care to argue that the time constant for that adjustment is also 4 years? Of course it is not. The physical processes are entirely different. A credible analysis estimates one century. Some older and much longer estimates are, in my view, doubtful. I am not sure if the consideration of biological dynamics in parallel with surface-to -deep transfers reconciles one century with Ferdinand’s 50 years.
You have a few times noted that you had to postulate “exponentially” growing natural emissions to keep up with the Mauna Lua curve. That is because of your too-short time constant.
Ed,
1.You have not been able to tell me how natural processes that remove more carbon from the atmosphere than they add, are nevertheless are responsible for CO2 growth.
2. We agree that there is little of your “human carbon” in the present atmosphere. I have told you why: the dilution of the Seuss Effect, known about since the 1950’s. You have not responded.
I have several times judged high school debates. When one debater ducks question from the other, that debater loses. You lose, Ed.
David Andrews July 16, 2025 at 9:33 am
Dear David,
That is one of the most complicated pseudo explanations of a simple concept I may have read.
First, you have no formula for adjustment time, so it is meaningless in the context of this discussion. It has no bearing on how to calculate or explain the evolution of the carbon cycle. It is a diversion from physics.
Second, the only meaningful time constant is e-time because it has a real formula that predicts things and applies universally to our discusion.
Third, for a simple explanation of how carbon flows in IPCC’s carbon cycle model, see my Figure 7. The top row illustrates IPCC’s natural carbon cycle at equilibrium. Change the numbers if you wish but every set of suggested numbers will have an equilibium distribution. This is the condition where the carbon flows between the boxes are equal.
The second row in Figure 7 illustrates human carbon at equilibrium if all human emissions ended. The human carbon cycle will have the same percentages in each box as the natural conbon cycle because of the climate equivalent principle.
Figure 7 shows human carbon left in the atmosphere at equilibrium is about 4 ppm when human carbon has added about one percent to the carbon in the natural carbon cycle.
Such equilibrium represents a maximum entropy for the carbon cycle.
Figure 7 shows what happens to human carbon that we introduce into the atmosphere. The addition of human carbon to the atmosphere begins in a low entropy condition. Human carbon will flow to the other boxes in a manner that increases the entropy as fast as possible.
Human carbon cannot increase the CO2 level in a manner that would lower the entropy of either the human carbon cycle or the natural carbon cycle.
The CO2 Coalition’s argument that human carbon causes all the CO2 increase, or somehow causes the natural carbon cycle to cause the CO2 increase fail because they lower the entropy of the total carbon cycle, which is an impossible.
David Andrews July 16, 2025 at 9:55 am
“1.You have not been able to tell me how natural processes that remove more carbon from the atmosphere than they add, are nevertheless are responsible for CO2 growth.”
Your question itself shows you do not understand the physics of the carbon cycle. Even in my last comment, I explained the basics of how human carbon affects the carbon cycle.
“2. We agree that there is little of your “human carbon” in the present atmosphere. I have told you why: the dilution of the Seuss Effect, known about since the 1950’s. You have not responded.”
Read my draft paper above.
First, we disagree WHY human carbon is a small part of the present atmosphere. You claim it is because natural carbon atoms “replaced” human carbon atoms in the atmosphere. Your explanation defies physics and would decrease the entropy if it happened.
Second, the Seuss effect is a calculated effect, not a cause. It does not even deserve a special name but you make a big deal of it because you incorrectly believe it somehow strengthens your argument. It does not.
The D14C data show human carbon has lowered the D14C level by less than 8%. That proves human carbon is less than 8% of the atmosphere.
This D14C “dilution” is a result of the continuing inflows of human carbon and natural carbon into the atmosphere. These inflows set balance levels. The dilution is a measure of the human carbon balance level compared to the natural carbon balance level. Period.
At the risk of sounding silly (I’m an old land surveyor who’s expertise is in knowing what to measure and mostly at sea on the technicalities in this discussion) I will ask if the mass of the atmosphere is constant? It seems that the mass balance approach assumes that it is but Dr. Ed’s approach does not. I know that lots of atmospheric gasses are added and removed by natural and anthropogenic processes.
DMA,
A better name for the argument often called “mass balance” is simply “carbon conservation.” If human emissions put 100 units/yr of carbon into the atmosphere, but the measured carbon growth rate is only 45 units/yr, then by carbon conservation, natural processes must be removing 55 units/yr and putting it in somewhere else. The carbon can’t just evaporate. These are good average numbers. Ed is trying to convince you that these same natural processes are somehow adding carbon to the atmosphere, but he never directly tells us how. That is because they are not.
Ferdinand,
“Output of the atmosphere is NOT proportional to the absolute CO2 pressure, but proportional to what Henry’s law dictates for the ocean surface. Not that it makes much difference, as input – output is a meager 5 PgC/year (~2.5 ppmv/year) at a level of 900 PgC in the atmosphere. For the absolute output that makes some 16 PgC/year. That is all. All the rest of the 200 PgC/year is what other processes absorb and bring back and these processes are largely independent of the CO2 pressure in the atmosphere. Like the uptake by vegetation in spring/summer: 120 PgC/half year only from the sun and temperature. The net effect of the full biological cycle is only 2.5 PgC/year more out than in.”
You and David keep repeating stuff that has no scientific basis. That is not Henry’s Law. You know it is not Henry’s Law. I’ve shown you that it is not Henry’s Law, but you continue to insist it is Henry’s Law. Read any Chemistry 101 textbook and it will recite Henry’s Law exactly like I have stated. Dr. Ed showed in his first paper that C14 bomb data supports his hypothesis, L/Te = outflow. How is it possible to debate people who refuse to accept natural law? You don’t accept the Equivalence Principle. You don’t accept the gas laws. You don’t accept scientific method. You refuse to answer my questions. You and David are so chained to your beliefs that you can’t accept that they are wrong.
David Andrews
Aren’t the units computed as a percentage of the atmosphere? If that mass is changing the units aren’t the same. Human emissions are tons of CO2 but total CO2 is in tons computed by multiplying a measured percentage times a figure that maybe not constant.
Ferdinand,
So, for input=output, Tau has no meaning then what is Te?
David Andrews July 16, 2025 at 11:27 am
David,
There you go again:
“… then by carbon conservation, natural processes must be removing 55 units/yr and putting it in somewhere else.”
You have physics backwards. “Natural processes” don’t “remove” human carbon from the atmosphere, like a dump truck removes garbage.
Human carbon flows out of the atmosphere toward its equilibrium distribution in the carbon cycle, thereby increasing its entropy.
Simple calculations based upon human emissions and reasonable Te for the six flow nodes, show human CO2 cannot cause all, or even most, of the CO2 increase because human carbon added to the atmosphere flows to the other boxes too fast to allow human CO2 to cause all the CO2 increase.
You are trying to tell people that human emissions cause all the increase in the face of carbon cycle data, including D14C data, that prove your claim is impossible.
I don’t need to prove how nature would cause the CO2 increase. You need to prove that human CO2 caused the increase.
Science requires we use the null hypothesis which says all changes are natural until proven otherwise. The burden of proof is on you to prove otherwise.
You have not and cannot do that.
Stephen Paul Anderson, July 16, 2025 at 11:40 am
Stephen. if the ocean surface in average, per Henry’s law, is in equilibrium with the atmosphere, that is when in average there is a fixed ratio between CO2 in the atmosphere and the ocean surface waters, then still a lot of CO2 can be exchanged, because some parts (near the equator) are warmer, thus release CO2 and some parts are colder, thus absorb CO2. That is called a dynamic equilibrium. CO2 is removed near the poles and that sinks with the cold waters into the deep oceans, to return some 1,000 years later near the equator, releasing its CO2 again.
At that moment there still is a
Te(a-d) = 589 PgC / 25 PgC/year = 23 years.
For the reverse flow:
Te(d-a) = 37,100 PgC / 25 PgC/year = 1,484 years.
Tau is not calculable as (input = output) and division by zero is not possible.
There is no usable information in Te(a-d) or Te(d-a), as the only point of interest is if the input and output flows are equal and neither of these two gives us that information.
In the current atmosphere the CO2 mass is already 900 PgC which makes that the outflows (and also inflows) into the deep oceans increased (let us assume in ratio, thus + 50%):
Te(a-d) = 900 PgC / 40 PgC/year = 22.5 years
Te(d-a) = 37,100 PgC / 40 PgC/year = 928 years
The output from the atmosphere to the deep oceans increased in ratio, thus Te(a-d) remained about the same, but as the carbon content of the deep oceans hardly changed, Te(d-a) did change a lot.
Again, that doesn’t give the slightest information of the actual change of CO2 in the atmosphere or deep oceans.
What happened to Tau? Yet it is calculable: the estimated net sink rate from the atmosphere into the deep oceans (input – output) is 2.0 PgC/year. That gives for Tau:
Tau(a-d) = (900 – 589) PgC / 2 PgC/year = 155 years
If Tau doesn’t change over time, which is the case for a linear decay, then we can calculate the carbon increase or decrease in the atmosphere, ocean surface, deep oceans and vegetation for the past and the future – if human emissions and temperature are known…
Tau gives us usable information, Te doesn’t.
Dr. Ed, July 16, 2025 at 11:58 am
“Simple calculations based upon human emissions and reasonable Te for the six flow nodes, show human CO2 cannot cause all, or even most, of the CO2 increase because human carbon added to the atmosphere flows to the other boxes too fast to allow human CO2 to cause all the CO2 increase.”
Simple calculation indeed shows that human FF is readily distributed over all reservoirs, which all increase in carbon content. But as human emissions (according to your Te’s) are fast getting out of the atmosphere, where is the rest of the observed increase in the atmosphere coming from?
Something doesn’t add up in your carbon mass balance…
Ferdinand Engelbeen
July 16, 2025 at 7:13 am
I know your mind is made up, but humor me while I try to understand your interpretation of F = k•s•ΔCO2.
Do you agree that output from the atmosphere is equivalent to – dCO2/dt, where CO2 is the concentration of CO2 in the atmosphere (the minus sign indicates output is reducing CO2)?
Second, by splitting Feely’s equation, do you agree that F- = k*p(CO2) = – dCO2/dt?
Also, that F+ = k * s * pCO2(aq) = + dCO2/dt?
Finally, at equilibrium, although there is no net transfer, do those forward and reverse rate equations still apply?
Ferdinand Engelbeen July 16, 2025 at 1:04 pm
Since human CO2 can’t cause all the CO2 increase, the only other possibility is natural CO2 increased.
However, I don’t need to show or prove how nature is doing that.
(This is somewhat like an astromoner finding something is causing a planet to deviate from its expected orbit. The astronomer does not have to find WHAT is causing the deviation in order to prove his calculations are correct. Typically, someone else finds the cause.)
Science requires we use the null hypothesis which says all changes are natural until proven otherwise. The burden of proof is on you to prove that my calculations are wrong or the numbers I use are wrong.
Ferdinand,
So, Te = L/outflow=589PgC/25PgC/yr=23.6 years. Where did you get your outflow from?
Ferdinand,
Also, what Te(c) vs. Te(a-d)?
DMA
July 16, 2025 at 11:05 am
July 16, 2025 at 11:45 am
Although there are gasses entering and exiting the atmosphere, their concentrations remain relatively constant except CO2 which has been gradually increasing. Fortunately, we have the Mauna Loa and other places monitoring it. It’s more difficult to measure CO2 in other reservoirs. The mass balance has to do with where the fossil fuel carbon went. I have no idea why David Andrews doesn’t see the obvious that whatever is no longer in the atmosphere is somewhere distributed between the other reservoirs. The hard part is what Dr. Ed did, to use estimates of reservoir content and mass transfer rates to figure out what went where when. David Andrews’ simple math is insufficient to explain all the data correctly using the correct physical principles involved.
“Aren’t the units computed as a percentage of the atmosphere?”
That’s a good question. The volume of the atmosphere is constant and the mass is easily determined by C * V. Ocean concentrations are measured, but the volumes vary widely and it’s impossible to know concentrations and volumes of the land.
That’s why Dr Ed’s methods are so useful. It allows a way to evaluate the estimates and synchronize them with the known values which are mainly just the changing concentration of CO2 in the atmosphere. If there’s any missing carbon, you can be sure to find it somewhere in a tree or on the ocean floor.
David Andrews
July 16, 2025 at 9:33 am
I will just add two things to Dr. Ed’s answer at July 16, 2025 at 10:16 am. First, the long 50-year Tau is an artifact of using the preindustrial value of CO2 as the equilibrium concentration if net zero ever happened. Because of bioexpansion, the new equilibrium will be at a much larger CO2 value.
Second, yes, I postulated “exponentially” growing natural emissions to keep up with the Mauna Loa curve using an e-time of about four years. I also tried no change in natural emissions and postulated slowly increasing e-time to maintain the agreement with Mauna Loa data. But that required deviating greatly from the universally accepted constant e-time of about 4 years. I couldn’t make it correlate with both constant natural emissions and constant e-time. Can you demonstrate a scenario matching Mauna Loa data using a 4-year e-time without increasing natural emissions?
Ed,
Must I go back to your old papers and identify plots which show human emissions greater than atmospheric accumulation? The world understands: those plots mean net global uptake has consistently been positive. The world understands: that proves natural processes are removing net carbon from the atmosphere. The world understands: that proves human emissions cause the CO2 rise. A dump truck analogy works. Nine dump truck loads move carbon from land/sea reservoirs to the atmosphere. Ten dump truck loads move carbon from the atmosphere to land/sea reservoirs. As a result, natural processes mitigate the increase in atmospheric carbon that humans cause. You know the consistently positive net global uptake falsifies your false theory and that makes you panic.
Please don’t repeat that your calculation shows only a small “human carbon” component in the present atmosphere. That is a correct conclusion in line with mainstream science, anticipated 70 years ago, and not particularly important.
Entropy??? Careful Mr. Ed, I taught thermodynamics. Go ahead, pursue this line. Make my day.
Ed,
Must I go back to your old papers and identify plots which show human emissions greater than atmospheric accumulation? The world understands: those plots mean net global uptake has consistently been positive. The world understands: that proves natural processes are removing net carbon from the atmosphere. The world understands: that proves human emissions cause the CO2 rise. A dump truck analogy works. Nine dump truck loads move carbon from land/sea reservoirs to the atmosphere. Ten dump truck loads move carbon from the atmosphere to land/sea reservoirs. As a result, natural processes mitigate the increase in atmospheric carbon that humans cause. You know the consistently positive net global uptake falsifies your false theory and that makes you panic.
Please don’t repeat that your calculation shows only a small “human carbon” component in the present atmosphere. That is a correct conclusion in line with mainstream science, anticipated 70 years ago, and not particularly important.
Entropy??? Careful Mr. Ed, I taught thermodynamics. Go ahead, pursue this line. Make my day.
Jim,
“universally accepted constant e-time of about 4 years. ” (?!)
…universally accepted by novices that don’t understand the difference between adjustment time and residence time perhaps. So you really think the time constant for surface ocean/ deep ocean mixing is four years? Or do you think that particular mixing time is irrelevant? Can you tell me where I referenced the 1750 equilibrium in my little exercise? You are not making much sense. Explain yourself.
Jim,
I just noticed your comments about the growth in carbon in the ocean (“acidification”) and in the biosphere (the greening that the CO2 coalition talks about.) Of course that results from natural processes moving carbon out of the atmosphere and into those reservoirs. It is where the net global uptake went. What I don’t understand is why you apparently think that supports the wrong notion that natural processes cause the atospheric increase.
Ferdinand,
“Observed: 5 PgC/year = 10 PgC/year + natural inputs – natural outputs
Or natural outputs are 5 PgC/year larger than the natural inputs.
Even if the natural outputs include half the human input of 5 PgC/year human supplied FF molecules, then still the full increase of 5 PgC/year in the atmosphere is caused by the human emissions.
According to your ideas, natural outputs are smaller than natural inputs.
Who is violating the carbon mass balance ánd the equivalency principle here?”
You. You are violating the carbon mass balance and the equivalence principle. You flunk Physics 101. Let me help you.
dCO2/dt = Inflow – Outflow
Inflow=Lb/Te (Lb=Balance Level)
Outflow= L/Te
L=430ppm
If we use dC/dt=2ppm/yr (4.24PgC/yr) and a Te of 4 years from Dr. Ed’s paper.
Outflow=430ppm/4yr=107.5 ppm/yr
Inflow= 107.5ppm/yr+ 2ppm/yr =109.5ppm/yr
Balance Level = 109.5ppm/yr(4yr)=438ppm
Te (eTime) is the time it takes for Level to reach 0.693 the distance from the level to the balance level. So, in 4 years from now, the level should be 435.54ppm.
If inflow is 5ppm human and 104.5ppm natural, then in 4 years when the level is 435.5ppm, human CO2 can be no more than 20ppm of the total. Outflow, which is 107.5ppm/yr, is 4.945ppm/yr human and 102.555ppm/yr natural. So, of the 2ppm/yr increase, 0.055ppm is human and 1.945ppm is natural. Natural emissions are greater than natural sinks. This is conservation of mass and in compliance with the equivalence principle.
David,
Dr. Ed has talked about adjustment time. Te is the time it takes for level to go 0.693 the distance to the balance level. So, in 4 years it will be at 435.5ppm. In 8 years it will be at 437.2 ppm. In 12 years it will be at 438ppm. So, some of the CO2 molecules have very short residence times and some have long residence times. It takes 3 or 4 Te’s to reach the balance level. (Actually, it never does. That is the nature of Euler’s number.) Residence time has nothing to do with the mathematics of the conservation of mass of carbon in the atmosphere.
Ferdinand,
P.S.-This is the solution to the first order linear differential equation. There is no other solution.
Stephen P Anderson, July 16, 2025 at 11:56 pm
“dCO2/dt = Inflow – Outflow
Outflow= L/Te
L=430ppm”
So far so good. Then:
“Inflow=Lb/Te (Lb=Balance Level)”
Say what? Are you saying that soil bacteria which remove plant rests and humans, which exhale 40,000 ppmv CO2 do that in ratio with CO2 in the atmosphere?
“If we use dC/dt=2ppm/yr (4.24PgC/yr) and a Te of 4 years from Dr. Ed’s paper.
Outflow=430ppm/4yr=107.5 ppm/yr
Inflow= 107.5ppm/yr+ 2ppm/yr =109.5ppm/yr
Balance Level = 109.5ppm/yr(4yr)=438ppm”
There it goes completely wrong.
Te has nothing to do with the decay rate of any extra injection of CO2, from whatever source.
Te = mass / output.
Between 1750 and current, both mass and output may have increased with 50% (which is not the case, outputs did increase more slowly), leaving a rather constant (or increasing) Te.
Between 1958 and 2025 dCO2/dt increased a five fold from 0.5 ppmv/year to 2.5 ppmv/year.
Simply said: Te and dC/dt have nothing in common and the 4 years residence time and the real decay rate or adjustment time (Tau) are completely different items.
Why is that? Because most of the outflows are (near) completely independent of the absolute CO2 pressure in the atmosphere. These are temperature, sunlight, bacterial and other biological processes, independent of how much CO2 resides in the atmosphere.
The height of the inflows and outflows has zero impact on the decay rate of CO2 in the atmosphere, only the difference counts: dCO2/dt = inflows – outflows.
dCO2/dt is quite exactly known, outflows only roughly, thus Te is even far from certain.
Then the balance level: that can be back calculated from the level in the atmosphere and the resulting dCO2/dt. Where dCO2/dt = 0, that is the balance level:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Between 280 and 300 ppmv.
“Te (eTime) is the time it takes for Level to reach 0.693 the distance from the level to the balance level. So, in 4 years from now, the level should be 435.54ppm.”
Te is level / output, that “can” be like Tau, the time to reach 1/e of the balance level, if and only if all inflows, container and outflows are unidirectional. That is the “lake / container / bath tube” model. Then Tau is smaller than to equals Te.
If there are back flows, which is the case for 95% of all CO2 flows the real world, then Te and Tau are decoupled and completely independent of each other. That is the “fountain” model, where lots of CO2 are pumped in and out, without any influence on the quantity that is really removed.
The calculated Tau, based on the current 420 ppmv and the calculated balance level of around 290 ppmv and the observed dCO2/dt of 2.5 ppmv/year gets:
Tau = (420 – 290) / 2.5 = 52 years
“So, of the 2ppm/yr increase, 0.055ppm is human and 1.945ppm is natural. Natural emissions are greater than natural sinks. This is conservation of mass and in compliance with the equivalence principle.”
One little problem: the CO2 level, both in the oceans and the biosphere increased with in total about 1 ppmv/yr as mass. Both oceans and biosphere together supplied near 2 ppmv/yr to the atmosphere.
Total increase in all containers together: 3 ppmv/year, with an external (human) supply of 2 ppmv/year. Something doesn’t add up here…
Moreover, with 1% to 5% in the input (1958-current) the observed FF level in the atmosphere is already over 10% and in the ocean surface over 6%… With your calculation that would be less than 1%.
Stephen P Anderson, July 17, 2025 at 12:13 am
“Te is the time it takes for level to go 0.693 the distance to the balance level.”
That is the essence of the discussion here:
Te is NOT the time it takes to decay to the balance level. That is Tau.
Te in this real world has nothing to do with reaching a balance level, it only shows how long an individual CO2 molecule “resides” in the atmosphere, before being removed (with a change in mass) or replaced (without a change in mass) out of the atmosphere. Only 2.5% of CO2 mass is removed per year, while 25% per year is replaced.
Or a difference between 50 years for Tau and 4 years for Te.
David Andrews
July 16, 2025 at 9:38 pm
I can’t immediately tell you what the time constant for surface to deep ocean is, but I’m sure I can get it from Dr. Ed’s paper. It will be different because of the concentration and volume differences. The important point to note is that not all the atmosphere carbon going to the surface is removed to the deep. There is a gradual increase in CO2 there as well, which contributes to the excess CO2 increasing in the atmosphere.
Truck load analogies are not compatible with physical processes. Stick to Magic Math.
July 16, 2025 at 9:50 pm
Better yet, graduate to step-wise integration and compartment modelling. Then you will see for yourself how natural emissions and FF both contribute to atmospheric increase.
Ferdinand,
“Why is that? Because most of the outflows are (near) completely independent of the absolute CO2 pressure in the atmosphere. These are temperature, sunlight, bacterial and other biological processes, independent of how much CO2 resides in the atmosphere.”
Dr. Ed’s hypothesis is based on Henry’s Law, the Ideal Gas Law, and correlates well with C14 bomb data. Te is e folding time which comes from the solution of the differential equation. Your Tau is a mathematical construct. It does not come from the solution of the conservation of mass equation, and it has no basis in math or physics. Its basis is a desired outcome. Dr. Ed’s model is beautifully simplistic and violates no natural laws. Your’s isn’t. Dr. Ed’s solution comes straight from the textbooks that I studied. Your’s does not. Your Tau violates the Equivalence Principle and treats human CO2 and natural CO2 differently. As long as you insist that non-science and non-logic are your basis, we are at an impasse.
Sorry but I have to stop here…
I need to make a presentation for a direct confrontation with Hermann Harde about the same subject for the Scandinavian Skeptics conference and need to transfer all my data to a new computer (thanks to Microsoft, which made Windows 11 not compatible with my only 7 years “old” model), my 3D-printer got broken and I just sold my brand new solar panels that I didn’t use, because of the perfidious change in tariffs they will imply when installed.
Still will finish the A-B item and the Berry challenge within a few days I hope, as promised.
David,
Jim,
“universally accepted constant e-time of about 4 years. ” (?!)
“…universally accepted by novices that don’t understand the difference between adjustment time and residence time perhaps. So you really think the time constant for surface ocean/ deep ocean mixing is four years? Or do you think that particular mixing time is irrelevant? Can you tell me where I referenced the 1750 equilibrium in my little exercise? You are not making much sense. Explain yourself.”
4 years is the universally accepted eTime for outflow from the atmosphere. If you would read Dr. Ed’s paper he says that the eTime for surface ocean to deep ocean is different. I thought we were all talking about atmospheric carbon? The eTime for atmosphere to land will be different than atmosphere to surface ocean, but total eTime is faster than the fastest individual eTime. That’s why the Bern Model is wrong. Thus, we get an overall eTime of 3.5 to 4 years.
Ferdinand,
“One little problem: the CO2 level, both in the oceans and the biosphere increased with in total about 1 ppmv/yr as mass. Both oceans and biosphere together supplied near 2 ppmv/yr to the atmosphere.
Total increase in all containers together: 3 ppmv/year, with an external (human) supply of 2 ppmv/year. Something doesn’t add up here…
Moreover, with 1% to 5% in the input (1958-current) the observed FF level in the atmosphere is already over 10% and in the ocean surface over 6%… With your calculation that would be less than 1%.”
Show your evidence.
David Andrews July 16, 2025 at 9:34 pm
Gee, David, I’m really scared. You may have taught thermodynics but that does not mean you KNOW thermodynamics.
So, challenge me on my comments above about entropy.
Jim,
You have not given us much information about your spreadsheet but assert various conclusions. Some of your comments make me wonder whether it is constrained by carbon conservation. For example “There is a gradual increase in CO2 [in the surface ocean] as well, which contributes to the excess CO2 increasing in the atmosphere.” I imagine your spreadsheet has a row for each year, and columns showing carbon stocks in different places. If you sum all the stocks in a row (year), how does that sum vary year to year?
My other main question about your analysis is one asked before but neither you nor Ed nor anyone else has responded. When you say “Then you will see for yourself how natural emissions and FF both contribute to atmospheric increase” are you simply saying that the present atmosphere contains only a small quantity of “human carbon”? You should know what I think of that argument.
Stephen,
A last comment:
Dr. Ed’s hypothesis is based on Henry’s Law, the Ideal Gas Law, and correlates well with C14 bomb data.
Dr. Ed’s hypothesis should be based on Henry’s Law, which implies a current equilibrium between atmosphere and average ocean surface of 295 ppmv for the current average sea surface temperature. Not 438 ppmv, according to your calculation, which is based on a Te of 4 years only, not the real, calculated from observations, decay rate of 50 years:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
Where A are the FF emissions, observed increase in the atmosphere, the influence of temperature on the equilibrium pCO2 of the ocean surface since 1850, calculated with the formula of Takahashi and the resulting ΔpCO2 between atmosphere and ocean surface.
B is the observed net dCO2/dt with a polynomial to avoid the year by year variability, caused by T variability.
C is the resulting Tau, which is what shows the time to reach 1/e of the ΔpCO2.
The latter is based on every calculation of e-fold decay rates for any process in dynamic equilibrium where one of the components is changed.
https://en.wikipedia.org/wiki/Exponential_decay
Again Te is NOT the decay rate of CO2 to a new equilibrium. That is Tau. Te only shows how long a single CO2 molecule resides in the atmosphere, thus how much CO2 mass is moved through the atmosphere, not how much CO2 mass is REmoved…
And where do we make any differentiation between FF and other CO2? Once in the atmosphere, FF CO2 increases the total mass of the atmosphere with 5 ppmv/year and half that amount as total mass (not the FF CO2 alone) is removed out of the atmosphere. No matter its composition.
Berry’s solution violates the carbon mass balance, because of his use of the much too short residence time, which does not reflect the observed decay rate of about 50 years.
Stephen P Anderson, July 17, 2025 at 7:06 am
Net uptake by the biosphere, based on the oxygen balance and oceans as remaining difference:
https://tildesites.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
“We find the average CO2 uptake by the ocean and the land biosphere was 1.7 ± 0.5 and 1.0 ± 0.6 GtC/yr
respectively”
Increase in the ocean surface, about 10% of the increase in the atmosphere:
https://tos.org/oceanography/assets/docs/27-1_bates.pdf
Figure 3 and Table 2.
Increase in the deep oceans: the remainder of the net sinks for dCO2/dt minus FF emissions.
Increase of FF in atmosphere and oceans:
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2001GC000264
Figure 4.
Based on the drop in 13C/12C ratio: over 10% FF in the atmosphere and over 6% in the ocean surface, calculated for a δ13C level of FF of -25 per mil and an atmosphere at average -6.4 per mil δ13C. Vegetation grows, thus with more CO2 uptake than release, which enriches the atmosphere in 13C at +24 per mil δ13C. Thus is not the cause of the enormous δ13C drop, not seen in the past 800,000 years, when δ13C levels were average -6,5 +/- 0.4 per mil, despite huge changes of 90 ppmv over glacial / interglacial transitions.
Ferdinand Engelbeen July 17, 2025 at 7:38 am
Dear Ferdinand,
You wrote, “Berry’s solution violates the carbon mass balance, because of his use of the much too short residence time, which does not reflect the observed decay rate of about 50 years.”
That is not true because my model begins with the Continuity Equation (1), which ensures my model conserves carbon mass. This conservation is entirely independent of Te.
This negates everything you claimed in your comment because you have based your claims on your fiction about my model.
Your model does not conserve carbon because (a) you have no continuity equation that forces conservation of carbon mass and (b) my Section 3.1, equations (10) and (11) show the critical error in your carbon mass balance equation.
Ferdinand.
“Dr. Ed’s hypothesis should be based on Henry’s Law, which implies a current equilibrium between atmosphere and average ocean surface of 295 ppmv for the current average sea surface temperature. Not 438 ppmv, according to your calculation, which is based on a Te of 4 years only, not the real, calculated from observations, decay rate of 50 years:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
Where A are the FF emissions, observed increase in the atmosphere, the influence of temperature on the equilibrium pCO2 of the ocean surface since 1850, calculated with the formula of Takahashi and the resulting ΔpCO2 between atmosphere and ocean surface.”
It is based on Henry’s Law and the Ideal Gas Law. Henry’s Law doesn’t imply what you say it implies. Your’s and Takahashi’s ΔpCO2 is not part of Henry’s Law. If you keep repeating it is, I’ll keep repeating it isn’t.
Ferdinand,
Is the Scandinavian Skeptic’s Conference in English and is it going to be recorded?
Dr. Ed, July 17, 2025 at 8:18 am
dL / dt = Inflow – Outflow (1)
Agreed
Outflow = L / Te (2)
Upside down…
Te = L / outflow but you may only reverse that formula if, and ONLY if, all flows are unidirectional from input via the container to the output.
How do you calculate the 60 ppmv/year in spring/summer into vegetation with that formula, when the outflow goes from near zero to maximum in a few months, even lowering the L in the atmosphere?
Lb = Inflow * Te (4)
Completely wrong: Lb is not set by the inflows, it is set by the equilibrium between ocean surface and atmosphere per Henry’s law at current SST, that is about 295 ppmv.
Again your formula is true if, and ONLY if, all flows are unidirectional, or the “lake/container/bath tube” model. Not applicable at all for the real world, where 95% of all CO2 flows are just cycling in and out the atmosphere.
Further, one can threat the human and natural flows apart, but that makes no sense at all, as once the human FF is added to the atmosphere, its mass is there for 100% and only can be removed as mass, not apart as “human” and “natural” CO2, even if it is possible to do that.
Sorry I have to go now, I did make some example of how FF accumulates in the atmosphere, but that is somewhere at the beginning of this discussion…
Stephen P. Anderson, July 17, 2025 at 8:36 am
Takahashi’s formula IS the change in ratio of CO2 between atmosphere and ocean waters per Henry’s Law. That is the change in solubility of CO2 in seawater with temperature of about 4%/°C. That is all. Not over 100 ppmv/°C as your calculation shows.
The conference is partly in English, partly in Scandinavian languages, I hope that there is simultaneous translation, although I can understand some Norwegian.
I suppose that there will be video’s of the debates with English translations…
“Completely wrong: Lb is not set by the inflows, it is set by the equilibrium between ocean surface and atmosphere per Henry’s law at current SST, that is about 295 ppmv.”
Staggers the imagination. Maybe Harde can get through to him. He seems like an honest guy but his mind is twisted by years of propaganda.
Stephen Paul Anderson July 17, 2025 at 10:06 am
Thank you, Stephen. Your comments are correct.
Ferdinand has so many incorrect comments that I do not have time to correct them all. And he repeats his incorrect comments over and over.
Perhaps the biggest revelation in all these comments is that the CO2 Coalition, including Lindzen and Happer, support what Ferdinand says.
Where have all the true scientists gone?
Harold Lewis, Emeritus Professor of Physics, University of California, wrote in his resignation letter to the American Physical Society, on October 8, 2010, that IPCC’s climate theory “is the greatest and most successful pseudoscientific fraud I have seen in my long life as a physicist.”
Stephen P Anderson
July 16, 2025 at 11:56 pm
You nailed it. I was struggling with how to use Magic Math to show how natural emissions have added to the excess CO2.
(1) D = Eh + En – k * C
(2) Let En = g * Eh
(3) D = Eh * ( 1 + g ) – k * C
(4) Eh = ( D + k * C ) / ( 1 + g )
Using “g” being approximately 20, according to IPCC estimates, and your numbers:
Outflow = 430ppm/4yr = 107.5 ppm/yr and Inflow = 107.5ppm/yr + 2ppm/yr = 109.5ppm/yr,
Eh equals a quite reasonable estimate of the current annual influx of industrial carbon of about 5.2 ppm.
I don’t want to comment too much on Ferdinand’s views until he is back to respond. However, I agree with Dr. Ed that he asserts the same dogma repeatedly, most which are arguably incorrect. What is most central to his argument is his assertion that “[balance level] is set by the equilibrium between ocean surface and atmosphere per Henry’s law at current SST, that is about 295 ppmv.” This is something we should explore in greater detail. What say you?
Thanks Dr. Ed and Jim.
Jim, I don’t think it really matters if Ferdinand returns. I can cut and paste his replies as if he were here because they don’t change. He seems to revere Takahashi. This idea that 95% of CO2 flows are just cycling in and out of the atmosphere is such a crazy assertion. Anyone who puports to understand the Equivalence Principle would not say that. Dr. Ed’s model aligns with everything I learned in physics, chemistry, math. Dr. Lewis is right. This is a surreal world we live in.
Ferdinand Engelbeen July 17, 2025 at 8:56 am
You wrote:
My model meets those conditions because all its flows are outflows.
You wrote:
It depends upon the time step that I use. If I use annual time steps, then I use annual averages for the data. If I use monthy time steps, I use monthly averages for the data. Etc. No problemo.
You wrote:
Lb is defined by (4). It is not related to any conditions or equilibriums. It is a logical deduction from (1) and (2).
It is clear that you have not even read my description of my model.
Lb is relevant to all flows because Levels always move toward their balance levels. Te is the time a level takes to move (1 – 1/e) of the way to its balance level.
Lb is a critical definition to determining Te or even your Tau. If you don’t define the balance level, you cannot properly calculate Te or even Tau. Since you do not use balance levels to evauate your time constants, all your calculations are wrong and meaningless. Throw them all out. Your math is invalid.
You wrote:
Your claim does not apply to my formula (2).
Please forget about all your lake etc models. My model is none of those. If you can’t understand my model and its uniqueness, then you are not qualified to judge it.
Your remarks make it clear that you have not even read my explanations of my (1) through (8).
Further, there is NO “cycling”. There are only flows. My model, which is only equation (2) and its deriviatives, fully accounts for ALL flows between reservoirs. There is no cycling. That crazy idea is proposed only by those who do not understand the meaning and power of (2).
You wrote:
It not only makes sense to track human and natural flows separately, anyone who does not track these flows separately simply does not know how to use the power of theoretical physics.
Sorry, Ferdinand, you are way out of your field of expertise in this subject. Too bad that Lindzen and Happer agree with you because this means they also are way out of their fields of expertise when they address this subject.
David Andrews
July 17, 2025 at 7:26 am
I don’t have the other reservoirs in my spreadsheet. I downloaded Dr. Roy Spencer’s model and added the exponentially increasing natural emissions to provide a good fit to the Mauna Loa data. So many others have done this analysis, I don’t need to reinvent the wheel. I do find my model useful to test results and conclusions claimed by others. Expanding to more than one compartment involved complications I found too difficult to resolve at the time. For example, one can add a middle layer between the surface ocean and the deep. There is also a model that uses two land reservoirs. Again, others have already done the multi-compartment modelling and I’m satisfied to trust those results.
I don’t know what question neither Ed nor I have answered. The present atmosphere contains approximately the quantity of “human carbon” that results from our model calculations based on the known data and estimates of other data not well-known. For example, it is not well-known exactly what the annual natural emissions are, but it is about twenty times the human input. That amount corresponds to approximately a fourth of the atmosphere sinked every year. The more human carbon that remains in one year, the more that gets removed the next year. The numbers are never exactly known, but the models can track estimates within realistic variability limits.
The only assumptions I use are the 4-year e-time which means sinking ¼ of the carbon per year and that natural emissions are about twenty times the human input. These are IPCC estimates.
Regarding carbon conservation, I just updated my spreadsheet to make sure the total human emissions equaled the current atmosphere content plus the cumulative amounts of human emissions removed annually. That required a formula for the amount of human-sourced carbon sinked annually. In case you wanted to start your own spreadsheet, here it is. Let H = Eh and Ht is the human emissions introduced in year t.
Total H removed = K * ( Ht + (1-K) * Ht-1 + (1-K)^2 * Ht-2 + (1-K)^3 * Ht-3 …., etc.
The (1-K) represents that for each K * Hn removed every year, (1-K) remains in the atmosphere. My spreadsheet shows that in 2018, 20 ppm of human emissions remains, about 5%. This is a lower bound, because it doesn’t include any account of the human emissions that returned from the sinks. That is why I never proceeded to expand my spreadsheet.
Jim,
“What is most central to his argument is his assertion that “[balance level] is set by the equilibrium between ocean surface and atmosphere per Henry’s law at current SST, that is about 295 ppmv.” This is something we should explore in greater detail. What say you?”
It is difficult to decipher what that even means. I believe the 295ppm is the preindustrial level he is using. He is calling that the balance level. All of this since 1750 has raised the level to 430ppm due to FF, which is 135ppm above the balance level of natural inflows and outflows. He calculates Tau as 430-295/2.5ppm/yr= 54 years. The 2.5 is dCO2/dt. So he’s saying the 2.5ppm/yr comes from taking 5ppm/yr (human emission) in half. So, inflow minus outflow would be a negative 2.5ppm/yr. So, it would take 54 years to decay back to the balance level. If it wasn’t for the dastardly human emissions we would be at 295ppm.
However, I will give him some credit because he is saying that more CO2 is good. It is just that his understanding of why is all messed up.
If they could show something that has been derived from the continuity equation or laws of nature that supports the idea that half the CO2 stays in nature, but they can’t even do that. Their model is built to achieve a desired outcome. The Equivalence Principle is a law of nature, but somehow, their natural carbon that cycles in and out of the atmosphere and human carbon don’t violate this Principle. What screwed up pseudoscience. I’m with Dr. Lewis.
Stephen P Anderson
July 17, 2025 at 6:13 pm
I think 295 is the “new” equilibrium value that he expects CO2 to return to in Tau years, the old being 280. He often links to that graph showing a small increase in CO2 due to temperature based on Takahashi’s equation.
The 430-295/2.5 ppm/yr = 54 years is what I don’t get. In words it means Tau = disturbance / (result or effect) implying that we will go to 295 ppm losing 2.5 ppm/year. I don’t think Tau assumes any more human emissions, because that would make Tau infinity. Tau is for net zero and the time to return to yesteryear. That’s what makes this Tau discussion futile. We will never get back there to prove one way or the other.
Yes, there is this magic sink that only acts on human carbon, and when human carbon is gone, it stops.
Ferdinand Engelbeen, July 17, 2025 at 7:58 am
Should have included the “Bolin” graph, which shows the calculated drop in oxygen and related FF CO2 emissions and the calculated increase of oxygen and related uptake of CO2 by the biosphere, the observed O2/CO2 levels and the CO2 uptake by the oceans, filling the gap in the period 1990-2000.
https://www.ferdinand-engelbeen.be/klimaat/klim_img/bolingraph.gif
I have seen a more recent update, but haven’t located it yet.
Jim and Stephen,
“If we use dC/dt=2ppm/yr (4.24PgC/yr) and a Te of 4 years from Dr. Ed’s paper.
Outflow=430ppm/4yr=107.5 ppm/yr
Inflow= 107.5ppm/yr+ 2ppm/yr =109.5ppm/yr
Balance Level = 109.5ppm/yr(4yr)=438ppm”
107.5 ppmv/yr was the original balance level for 0 PgC/yr human input, inflow = outflow and 4 years Te at 277 ppmv. Per year that gives:
Inflow = 107.5 ppmv + 5 ppmv = 112.5 ppmv
Inflow – outflow = 3 ppmv
Outflow = 107.5 ppmv + 2 ppmv = 109.5 ppmv
Increase in the atmosphere fully caused by FF emissions
New equilibrium for a constant supply of 5 ppmv FF CO2:
For a Tau = Te of 4 years and L(o) = 430 ppmv (assuming that L(o) increased to the previous years L)
L(t) = 430 + 2 * 4 = 438 ppmv
For Tau = 50 years and L(o) = 295 ppmv (for the current SST):
L(t) = 295 + 5 * 50 = 445 ppmv
In both cases the new equilibrium is above the current CO2 level in the atmosphere, thus the FF inputs still are above the outputs, until outputs catch up with the extra input.
The main difference is that in the case of a 4 years Tau, the non-extra equilibrium moves up together with the atmospheric level, which is the case for the sea surface, and for both the deep oceans and vegetation, still the “old” equilibrium is working, as the linear response of the net output shows.
Bye for now.
Ferdinand Engelbeen July 18, 2025 at 3:04 am
Dear Ferdinand,
Although your numbers begin similar to my numbers, your description does not make it clear why you got your numbers. Nature is not as complicated as you make it out to be.
Try to describe everthing you just wrote in simple equations that show cause and effect.
My equation (2) (added to my (1) for mass conservation) solves the complexity problem with simple, valid physics.
Equations (1) and (2) are all we need to describe the flows in the carbon cycle. It makes cause and effect clear and it allows intellingent time-step calcuations for both levels and flows.
Ferdinand,
Yes, we concur, human inflow is greater than human outflow, but natural inflow is greater than natural outflow. Also, in Dr. Ed’s model the balance level is set by inflow. We can’t figure out what sets your balance level. The only thing that would make sense is natural inflow sets your balance level, but it is only the natural inflow from 1750. How nature does that you will need to explain. If that is the case, then natural inflow was about 70ppm/year. Now, natural inflow is about 105ppm/yr. Natural inflow has increased by about 35ppm/yr. How do you reconcile that with your model?
Ferdinand Engelbeen
July 18, 2025 at 3:04 am
At the risk of piling on, I have the same question as Stephen. How do you reconcile 107.5 ppmv/yr, “the original balance level for 0 PgC/yr human input…and 4 years Te at 277 ppmv?” 277/4 is less than 70 ppmv/year. We fail to see how the “old” equilibrium is working.
Dr. Ed,
Did you ever reveal the error in your Figure 11? The caption already explains, “Bit (should be But) the plot assumes H(1) is true and it plots the O2 effect as if human caused all the CO2 increase shown on the horizontal axis.”
The only other objectionable thing I could see is with the arrows indicating that about a 15 ppm atmospheric increase was balanced by the same amount of land and ocean uptake. Whereas the uptake was only about half of the “extra” emissions. If that isn’t the error, I look forward to your explanation.
Stephen and Jim,
Sorry, indeed I did mix ppmv and PgC where it should be either PgC or ppmv.
Doesn’t matter for the basic reasoning but matters for the calculations…
From
“If we use dC/dt=2ppm/yr (4.24PgC/yr) and a Te of 4 years from Dr. Ed’s paper.
Outflow=430ppm/4yr=107.5 ppm/yr
Inflow= 107.5ppm/yr+ 2ppm/yr =109.5ppm/yr
Balance Level = 109.5ppm/yr(4yr)=438ppm”
The IPCC’s natural carbon cycle between atmosphere and land was 108 PgC/yr, that was my confusion.
Good, then again:
If we use dC/dt = 2ppm/yr (4.24PgC/yr) and a Te of 4 years from Dr. Ed’s paper and assume that the total increase of the basic inflows and outflows increased from 79 ppmv/year to 94 ppmv/year then
Inflow = 94 ppmv/yr + 5 ppmv/yr FF CO2 = 99 ppmv/yr
Outflow = inflow – dC/dt = 97 ppmv/yr = 94 ppmv/yr + 3 ppmv/yr
dC/dt = 2 ppmv/yr is fully caused by the inflow of FF CO2
The inflow increases first by the human input, the increase in output follows later. Not reverse.
That is the essence of the story, the rest can be calculated in the same way as in my previous comment.
Total outflows are, of course larger than total inflows, no matter if one splits the inputs and outputs in “natural”, which hardly changed over the years with 79 ppmv/yr and the rest all human caused (as mass, not as remaining FF CO2 molecules).
For the underlying differences in model as used by Dr. Ed and me, see next comment…
Jim Siverly, July 18, 2025 at 10:52 am
“The “outgassing” data from 1990 to 2000 are OK. But the plot assumes H(1) is true and it plots the O2 effect as if human caused all the CO2 increase shown on the horizontal axis.”
I still am waiting for the explanation of Dr. Ed why that figure doesn’t show that half of human emissions (as mass) gets about fifty/fifty in oceans and vegetation…
Nowhere the plot assumes H(1) is true.
The plot is quite simple:
At the right side are the calculations of O2 use and CO2 release from FF burning if all these changes remained in the atmosphere.
At the left side are the observed CO2 increases and O2 decreases in the atmosphere for each year.
At the bottom is the calculated uptake in the biosphere, based on the O2 release and the difference is what the oceans absorbed. Of that difference, the part that was absorbed in the ocean surface also is measured at about 10% of the increase in the atmosphere, but not separated in the plot.
Further, the “outgassing” is the change in O2 caused by the warming of the oceans and is only for the difference between the two arrows, not the observed CO2/O2 changes.
Ferdinand,
Your numbers and percentages don’t add up.
Inflow = 94 ppmv/yr + 5 ppmv/yr FF CO2 = 99 ppmv/yr
Outflow = inflow – dC/dt = 97 ppmv/yr = 94 ppmv/yr + 3 ppmv/yr
dC/dt = 2 ppmv/yr is fully caused by the inflow of FF CO2
If human CO2 is 5ppm/99ppm then it can’t be less than 5% of the outflow because it mixes in the atmosphere. This puts human CO2 outflow at 4.89ppm, not 3ppm. That means that of the 2ppm increase in dC/dt, only 0.11ppm is human CO2 and 1.89ppm is natural CO2.
Ferdinand Engelbeen
July 18, 2025 at 10:54 am
“The inflow increases first by the human input, the increase in output follows later.”
That is Magic Math slight of hand. Never mind the equivalence principle. It reminds me of alarmists explaining why CO2 lags interglacial warming. First CO2 causes a little warming which is followed by more CO2-caused warming. The tail wags the dog, making the dog wag more.
“Total outflows are, of course larger than total inflows…which hardly changed over the years with 79 ppmv/yr and the rest all human caused (as mass, not as remaining FF CO2 molecules).”
Let me try and repeat that back: Beginning with 79 ppmv/year, natural inflows have hardly changed, but total inflows rose to 97 ppmv/year, the increase all human caused. (Each mass of 4 FF carbons emitted got replaced with a mass of 5 natural carbons regardless of the source of the molecules).
Feel free to expound on that.
Jim,
I have looked back on the discussion of the last few weeks to see if there is anything I could have said better. I concede that my description of exchanges between the surface and deep oceans did not get to the heart of the difference between residence time and adjustment time. Further, Ferdinand has not been able to convince you there is any difference, and your conversation with him seems to have gotten bogged down in minutia missing the big picture.
Let’s go back to your July 1 10:38pm comment:
“….Apparently, we both agree that the industrial carbon is not largely left in the atmosphere. Your terrestrial biomass growth is one sink. The oceans are an obvious second. The deep ocean is basically an infinite sink. We also agree on where the extra carbon is coming from. The only disagreement is on how much of the observed increase in atmospheric CO2 is caused by industrial carbon or an additional natural component.”
I agree with your breakdown of where we agree and where we disagree. We agree that the “extra carbon” from fossil fuel burning is spread all over the place, acidifying oceans and stimulating biomass growth. But you say that since the present atmosphere contains little “human carbon”, fossil fuel burning is not responsible for much of the atmospheric growth. Tell me if I am missing something, but I believe that is your (and Ed’s) ONLY argument.
I have said repeatedly that mainstream science, while attributing all of the atmospheric carbon level change to human emissions, still predicts low levels of atmospheric “human carbon” in the present atmosphere. This is because of those balanced exchanges, also known as disequilibrium isotope fluxes, also known as Seuss effect dilution, that I urged you to understand. The issue neither you nor Ed ever address is why you think that, despite all the mixing going on (which is changing only the carbon makeup of the reservoirs, not their levels), the present composition of the atmosphere should naively be taken as measuring the human and natural contributions to CO2 growth. It does not.
Jim,
I have looked back on the discussion of the last few weeks to see if there is anything I could have said better. I concede that my description of exchanges between the surface and deep oceans did not get to the heart of the difference between residence time and adjustment time. Further, Ferdinand has not been able to convince you there is any difference, and your conversation with him seems to have gotten bogged down in minutia missing the big picture.
Let’s go back to your July 1 10:38pm comment:
“….Apparently, we both agree that the industrial carbon is not largely left in the atmosphere. Your terrestrial biomass growth is one sink. The oceans are an obvious second. The deep ocean is basically an infinite sink. We also agree on where the extra carbon is coming from. The only disagreement is on how much of the observed increase in atmospheric CO2 is caused by industrial carbon or an additional natural component.”
I agree with your breakdown of where we agree and where we disagree. We agree that the “extra carbon” from fossil fuel burning is spread all over the place, acidifying oceans and stimulating biomass growth. But you say that since the present atmosphere contains little “human carbon”, fossil fuel burning is not responsible for much of the atmospheric growth. Tell me if I am missing something, but I believe that is your (and Ed’s) ONLY argument.
I have said repeatedly that mainstream science, while attributing all of the atmospheric carbon level change to human emissions, still predicts low levels of atmospheric “human carbon” in the present atmosphere. This is because of those balanced exchanges, also known as disequilibrium isotope fluxes, also known as Seuss effect dilution, that I urged you to understand. The issue neither you nor Ed ever address is why you think that, despite all the mixing going on (which is changing only the carbon makeup of the reservoirs, not their levels), the present composition of the atmosphere should naively be taken as measuring the human and natural contributions to CO2 growth. It does not.
David,
No, we don’t agree that extra carbon from FF is acidifying the ocean. What we have said that according to Henry’s Law, the amount of a gas in the liquid is proportional to the partial pressure of the gas above the liquid. Since fossil fuel only accounts for 5% of the partial pressure increase, it only accounts for 5% of the acidification, if there is any.
David,
Also, Suess effect dilution is bad science. Dr. Berry’s model falsifies Suess Effect dilution.
David Andrews
July 19, 2025 at 11:28 am
“…I believe that is your (and Ed’s) ONLY argument.”
Of course, I can’t speak for Dr. Ed, but I think he would agree that one argument is the relatively minor amount FF emissions contribute to atmospheric growth compared to natural emissions. The other issue I have is the adjustment time. It’s ambiguous, unmeasurable, and most likely based on incorrect physical science.
The issue you think hasn’t been addressed has been addressed over and over. The “mixing” is accompanied by increasing levels. It follows from what the models yield. The model I use is a one compartment model, a slim version of the multi-compartment model that Dr. Ed explains in the article we are discussing. My model allows me to examine the known data and justify how it could happen in light of standard physical processes and mathematics, like first-order diffusion and differential equations. The data doesn’t compute without including a substantial gradually increasing contribution from natural emissions.
If it helps for you to attribute all the excess carbon to humans, I can understand that to a certain extent. However, I make a distinction between the FF carbon which can be accounted for, an additional human-caused natural contribution that cannot be accounted for, plus an additional contribution that is wholly natural, also unaccounted for. Examples of some non-FF human-caused natural emissions are land use change and cement manufacture, but those are still considered industrial carbon and accounted for. The 8 billion population increase probably accounts for more of the non-FF human-caused natural emissions than has been accounted for. Other sources of increasing natural emissions could be the warming oceans, volcanoes, forest fires, etc.
The bottom line is that it is not naive to decipher the human and natural contributions to CO2 growth and the present composition of the atmosphere. It’s being diligent and scientific. There are two groups of modelers, the linear ones and the non-linear ones. The latter use a combination of Te and Tau. The former use only Te. The references to Ed’s articles make that clear. I’m with the linear modelers, because they make the best arguments.
Jim,
You have given me the goal of trying to make a clearer exposition of adjustment time.
What makes you think that the FF emissions make a “relatively minor” contribution to CO2 growth compared to natural emissions? Is it the present composition of the atmosphere, or is it the ~20x larger gross number, or is it something else? Where are natural absorptions in your model, and is their magnitude constrained by the measured positive net global uptake?
David Andrews
July 19, 2025 at 11:28 am
“The deep ocean is basically an infinite sink”
Atmospheric CO2 sinks with the surface ocean. It doesn’t bypass the surface and go directly into the deep ocean.
“We agree that the “extra carbon” from fossil fuel burning is spread all over the place, acidifying oceans”
The oceans are not acidifying. They are not acid and never will be. Saying the oceans are acidifying is alarmist propaganda. designed to create hysteria. The only people who say that are socialist political activists. There is no science in any of this, it is anti-science.
It is impossible for humans to control atmospheric CO2 concentrations. Atmospheric CO2 concentrations are controlled by Henry’s Law and Henry’s equilibrium ratio which in turn is controlled by sea surface temperatures. If humans add CO2 to the air, that is mixed with the CO2 already in the air and the oceans will absorb more to keep the ratio in balance. If humans remove CO2 from the air the oceans will put it back.
“adding more CO2 to air does not change the Henry’s Law coefficient for combination CO2 gas and ocean water. . . . evidenced by experimentation in thousands of published studies since the mid 1800’s. This is well known established science, and it is the fundamental underlying science of the multi-billion dollar per year instrumentation industry of gas chromatography. . . . Henry’s Law coefficient (a ratio) is dependent on the temperature of the ocean surface, which is the interface between CO2 gas in the air and CO2 gas in ocean surface.”
Bromley, Bud 2023 EPA Submission Document; Comment submitted by Clare Livingston “Bud” Bromley III; Posted by the Environmental Protection Agency on Aug 10, 2023; https://www.regulations.gov/comment/EPA-HQ-OAR-2023-0072-0504; Attachment 3 Comment by Bud Bromley on the proposed rule by the Environmental Protection Agency; New Source Performance Standards for Greenhouse Gas Emissions from New, Modified, and Reconstructed Fossil Fuel-Fired Electric Generating Units: Emission Guidelines for Greenhouse Gas Emissions from Existing Fossil Fuel-Fired Electric Generating Units; and Repeal of the Affordable Clean Energy Rule
https://www.regulations.gov/document/EPA-HQ-OAR-2023-0072-0001
Sorry for the delay in my replies for now…
“There are two groups of modelers, the linear ones and the non-linear ones. The latter use a combination of Te and Tau. The former use only Te.”
That indeed is the heart of the matter, as that is quite different, depending of the model one has in mind.
For the “one-way container / lake / bath tube” model, as used in many engineering programs for chemical reactions, the inputs dictate the level in the atmosphere and the level in the atmosphere dictates the outputs.
The residence time Te and the adjustment time Tau are equal and one may reverse the formula for Te without problems:
Te = mass/ sum(outputs)
Tau = extra mass / sum(extra outputs)
Here such a “classic” model of the atmosphere:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/mass_fluxes_classic.jpg
In that case, and only in that case, Tau = Te and one may revert Te to get the output:
Output = mass / Te
In that case, and only in that case, one may assume that Te also represents Tau.
In the case where part of the outputs are recycled back to the inputs, independent of the mass in the atmosphere, the situation is completely different and Te and Tau are largely to completely independent of each other. That is the “fountain” model, where large amounts of CO2 are cycling in and out, independent of and without affecting the CO2 level in the atmosphere.
Then still:
Te = mass / sum(outputs)
Where outputs = outputs to the cycles + non-cycling outputs and outputs to the cycles are inputs back to the container(s).
Tau = extra mass / sum(extra outputs), where extra outputs are only the non-cycling outputs.
The latter is what changes the mass in the container, not what cycles in and out…
Here the real world flows (based on 2020 IPCC estimates for the different exchanges):
https://www.ferdinand-engelbeen.be/klimaat/klim_img/mass_fluxes_real.jpg
Which model and which Tau is the real world one?
In the case of the “classic” model, any “marker” in the inputs never can exceed its ratio in the inputs in any further part of the flows: neither in the container, nor in the outputs.
In the case of the “fountain” model, any extra inflow of a “marker” in the inputs can asymptotically go up to 100% of the mass in the container, because part of the “marker” is recycled back to the container.
With 1% to 5% FF CO2 of the inputs (1958 – 2020), the atmosphere already contains over 10% FF CO2 in the atmosphere and 6% FF CO2 in the ocean surface and a similar (hard to measure exactly) increase in the biosphere and a small “traced” increase in the deep oceans:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
That means that the “classic” model is at odds with the real world and one may not use Te as Tau.
“The other issue I have is the adjustment time. It’s ambiguous, unmeasurable, and most likely based on incorrect physical science.”
The formula for Tau is the exponential decay rate, or the time for any dynamic process in disequilibrium to go back to equilibrium where the remaining disequilibrium gets 1/e (~37%) of the initial disequilibrium.
If (and only if) the net removal rate is in exact ratio to the height of the difference, then the period over which Tau is calculated plays no role.
Tau can be calculated from the distance to the equilibrium and the resulting net removal rate. If the equilibrium is not exactly known, one can back calculate the equilibrium where the net removal rate is zero.
David Andrews
July 19, 2025 at 8:39 pm
Again, my model gives a lower bound to the industrial carbon contribution which is twice the natural “new” carbon added annually. Yet it’s only 5% of the total carbon which is equivalent to 14% of the rise, assuming a rise of 140 ppm. That means half the annual increase from natural carbon contributes 86% of the rise. I’m still trying get my head around that. It must be related to the 20x larger annual.
Natural absorptions are the usual uptake by plants and ocean. Their magnitude is determined by the average annual sink of about 25% of the carbon in the air.
I look forward to your version of adjustment time. Notice I am vehemently opposed to the notion that the “normal” equilibration point is still 280 or 290 something. Those days are gone.
Ferdinand Engelbeen
July 20, 2025 at 4:28 am
“That is the “fountain” model, where large amounts of CO2 are cycling in and out, independent of and without affecting the CO2 level in the atmosphere.”
What causes CO2 to cycle in and out of the atmosphere? Why would Henry’s law not be active in this process?
DMA, July 20, 2025 at 8:23 am
“What causes CO2 to cycle in and out of the atmosphere? Why would Henry’s law not be active in this process?”
Temperature is the main cause of the huge, mostly seasonal inflows and outflows:
In spring/summer: increasing temperatures and more sunlight increases photosynthesis far beyond any influence of the CO2 pressure in the atmosphere: some 120 PgC nowadays is sucked out of the atmosphere.
The influence of the pCO2 of the water in the plant’s leaves plays a minor role: while the pCO2 in the atmosphere increased with some 50%, the seasonal uptake by plants since about 1750 increased only with 13%.
About half of it is already recycled back into the atmosphere at night, by soil (bacterial) and plant respiration. The other half is recycled back in fall/winter and these processes are completely independent of the CO2 pressure in the atmosphere: fungi, bacteria and animals produce a lot of CO2 out of plant parts, no matter how much CO2 is in the atmosphere.
That is not completely in balance: some 2.5 PgC/year nowadays is removed into more permanent vegetation and soils. That is what is the real influence of the CO2 increase in the atmosphere and that gives the real e-time…
Here a graph of the influence of vegetation on the CO2 level in the atmosphere: that goes from minimum to maximum in a few months time, as can be seen in the opposite δ13C and CO2 changes in the atmosphere:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/seasonal_CO2_d13C_MLO_BRW.jpg
Exact CO2 changes, due to the uptake/release by vegetation can be calculated from the O2 changes, after taking into account the O2 drop by burning fossil fuels:
https://tildesites.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
Figure 7, last page…
For the oceans: also temperature, in reverse order as for the biosphere:
Increased SST in spring/summer increases the pCO2 of the ocean surface, releasing some 50 PgC/year in spring/summer and a similar cooling induces a similar uptake in fall/winter.
See Figure 2 in:
https://tos.org/oceanography/assets/docs/27-1_bates.pdf
The pCO2 (ocean) figures for BATS (Bermuda station) are monthly figures and give the clearest view of the changes over a year.
The overall difference over a year also is about 2.5 PgC/year and that is the real influence of the 50% increase of pCO2 in the atmosphere on the ocean’s total uptake per Henry’s law…
Jim,
So you are modeling absorptions separately from emissions, rather than using the empirically positive net global uptake as a constraint. What does your model yield for net global uptake?
Brendan,
I agree that a better description of the ocean situation is that the added carbon there is making them “less basic” rather than “acidifying”. My point is simply that oceans are clearly one of the net sinks contributing to the positive net global uptake. Your comments suggest you agree. Those who argue that the atmospheric carbon increase is coming from warming oceans have a problem explaining why the oceans are getting less basic, i.e. contain more carbon. Those who argue that the atmospheric carbon increase is coming from decaying vegetation have a problem explaining how plants manufacture carbon. They don’t. They temporarily borrow it from the atmosphere.
I looked at the EPA testimony you linked. It was unsubstantiated opionion. It gave me nothing to argue with.
Ferdinand Engelbeen
July 20, 2025 at 4:28 am
Are you familiar with the adage, “You are entitled to your own opinion, but not your own facts?” I think in an original version it was no right to be wrong in your facts. I am referring to your description of the classic model as “the case where part of the outputs are recycled back to the inputs, independent of the mass in the atmosphere.” That is your opinion of how the atmosphere works and it has been demonstrated wrong by a host of authors noted in Dr. Ed’s references. Your Tau, as being different from Te, is a creation of what you opine as atmospheric reality.
To show that your view of reality is correct, you will need to demonstrate how the linear modelers are wrong, with better data than anecdotes, Magic Math, and a fountain model which allows no increase in “what cycles in and out…”
Is there a paper or textbook somewhere that explains this sentence? “In the case of the “fountain” model, any extra inflow of a “marker” in the inputs can asymptotically go up to 100% of the mass in the container, because part of the “marker” is recycled back to the container.”
“The formula for Tau is the exponential decay rate….”
Back on July 12, 2025 at 7:41 pm, I explained that if you add more reactant to an A to B reaction, the decay rate, i.e. relaxation time, does not change. The concentrations of each moiety will increase, but the new equilibrium will be established in the same time frame. Your model suggests that the decay rate depends on the difference between the reactant concentration and the concentration of the product at the time additional reactant was added. In fact, the reaction rate always depends on the absolute concentration. The reaction continues even at equilibrium where an equal amount of product reacts reversibly in proportion to its concentration and corresponding rate constant.
Statements such as, “If the equilibrium is not exactly known, one can back calculate the equilibrium where the net removal rate is zero,” are best illustrated by experimental data, not observational anecdotes.
David Andrews
July 20, 2025 at 10:37 am
For net global uptake in the last year of my model’s data (2018), I have -2.58 ppm. That is total sink – total sources. Maybe that should be 2.58 ppm, total sources – sink.
Jim Siverly, July 20, 2025 at 11:53 am
“That is your opinion of how the atmosphere works and it has been demonstrated wrong by a host of authors noted in Dr. Ed’s references.”
My response to DMA is still in moderation, and explains in detail why the residence time Te is NOT the real decay rate of an extra CO2 input into the atmosphere.
But here a summary of my latest email to others than here in this discussion:
The formula that shows Ed’s “e-time” is:
Te = level / outflow.
Where Te in general is called “residence time” or “turnover time” by about any engineer in this world. Even the IPCC uses that definition.
Te shows how long an individual CO2 molecule “resides” in the atmosphere before being removed out of the atmosphere, either with an equal change in CO2 mass or without a change in mass, by simply replacing it with a CO2 molecule from another reservoir.
The latter difference is an important one, as that is the exact difference between the model of Berry and the model used in our work for the CO2 Coalition.
e-time or as most is used: Tau is the time that is needed to reduce an extra input of some reactant in a dynamic process back to 1/e (~37%) of the original extra input. That is expressed as:
Tau = extra level / extra outflow.
Where “extra” even may be positive or negative, compared to the equilibrium level where inputs = outputs.
Te and Tau are very clear, different, definitions for different times, even when these times may be equal in specific circumstances.
If (and only if!) all inflows, container and outflows are unidirectional from inputs to outputs, without any direct or indirect recycling from outputs back to inputs, then (and only then!) Te = Tau.
Then Berry reverses that formula:
Balance level = inflow * Te
Again, one may do that if (and only if!) all flows are unidirectional and there are no returns from the outputs back to the inputs.
That was the original approach of Berry, until a few years ago.
His newest approach is to use all Te’s back and forth between the atmosphere and the other reservoirs.
If the three outflows out of the atmosphere would have remained in ratio to the increase in the atmosphere, then the Te’s didn’t change over time. That is not the case:
The increase in CO2 level in the atmosphere was about 50% since 1750.
The increase in CO2 outflow from atmosphere to ocean surface was only 33%
The increase in CO2 outflow from atmosphere to land was only 13%
Thus any calculations based on fixed Te’s (used as Tau’s) over time don’t reflect reality.
To the contrary, one can calculate the real Tau, based on the increase of CO2 in the atmosphere, compared to the “historical” equilibrium of ~280 ppmv, increased to ~295 ppmv for current times for the increase in sea surface temperature. That gives around 50 years e-time (Tau) over the period 1958-current:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
Where A is the total FF emissions since 1750, the measured increase in the atmosphere, the calculated increase of pCO2 of the ocean surface with the formula of Takahashi and the resulting pCO2 difference between atmosphere and ocean surface. That is the driving force for any extra CO2 uptake by the ocean surface,
If there is no difference, then inputs and outputs are equal and there is no net exchange (but still a lot of exchanges).
B is the observed net sink rate and
C is the calculated Tau, based on the polynomial though the net sink rate.
One can back calculated the zero-net-exchange to obtain the recent equilibrium, here by colleague David Burton:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Several others have done that: Peter Dietze (already in 1997!), Lindzen, Spencer, myself,… All obtained an equilibrium between 280-300 ppmv and a Tau of around 50 years.
Here from Peter Dietze:
https://www.john-daly.com/carbon.htm
Thus not only Te doesn’t reflect reality, it largely changes over time, thus never may be used to calculate what the equilibrium level should be. No matter how many references Dr Ed refers to with the same opinion.
Then your:
“K = [B] / [A]. If more reactant is added after the initial equilibrium is reached, a new equilibrium is reached with K = ([B] + x) / ([A] + (1-x)]. Assuming no change in temperature or pressure, K will remain the same. But both reactant and product end up at larger concentrations.”
Of course that is true, but only as long as you add an extra amount of reactant. If you stop adding that extra, the reaction will go back to the old equilibrium.
In the case of CO2 in the atmosphere, humans add more reactant each year, but the sinks don’t follow as fast, thus any new equilibrium will be above the current disequilibrium.
For a constant input of 5 ppmv FF CO2/year:
With a Tau of 4 years:
Old equilibrium: 425 – 2.5 * 4 = 415 ppmv
New equilibrium: 425 + 2.5 * 4 = 435 ppmv
With a Tau of 50 years:
Old equilibrium: 425 – 2.5 * 50 = 300 ppmv
New equilibrium: 425 + 2.5 * 50 = 550 ppmv
In both cases, with halving the human input, there will not be any further increase of CO2 in the atmosphere and with zero FF input, the CO2 levels will sink back to the old equilibrium, wherever that may be.
So your model says natural sources exceed natural sinks. Your model is falsified by data. You know, that “Magic Math.”
David Andrews
July 20, 2025 at 1:05 pm
No, my model is not falsified. You did not include human emissions that are part of the total emission sources that exceed the combination of both in the sinks. It was 4.74 FF + 91.9 natural – 94.1 sunk. There is no purely natural sink like a FF emission or a sequestration. It’s your Magic Math that fails.
Jim,
OK, I missed the “total” before sources. The Magic Math did not fail. It told us net global uptake in your model is positive, as measured. Great!
Now to another earlier question:
“What makes you think that the FF emissions make a “relatively minor” contribution to CO2 growth compared to natural emissions? Is it the present composition of the atmosphere, or is it the ~20x larger gross number, or is it something else?”
Ferdinand Engelbeen
July 20, 2025 at 1:04 pm
You are repeating the same mantra without validating your assertions. Not one example of data showing Tau is longer than Te. You make predictions about equilibrium conditions without evidence of what they will be. That is not scientific.
Your Tau being different from Te is a concoction of your perception that things will return to an old equilibrium. There are scenarios that can be imagined, like net zero FF while continually increasing natural emissions. Or halving FF. Or another ice age. But all static scenarios subject to a constant Te will result in a new equilibrium in less than 30 years as reservoirs adjust to their balance levels. If inputs continue to change, their will never be a new balance level because the level keeps changing to adjust to the new inputs.
I just entered zero FF and a return to 65 ppm/year input in my spreadsheet. It goes to 280 ppm in 25 years. Of course, my model could be wrong. But it is based on the universally accepted 4-year Te, IPCC estimates of reservoir content, and correlation with Mauna Loa data. Do you have a model that meets all that criteria?
Regarding the A/B reaction you wrote, “Of course that is true, but only as long as you add an extra amount of reactant. If you stop adding that extra, the reaction will go back to the old equilibrium.”
There is no “but only.” There is an initial reaction starting with a known amount of reactant. It goes to equilibrium with a Te = Tau. Adding extra reactant creates a disturbance which returns to equilibrium with the same Te = Tau and both reactant and product at larger concentrations. The equilibrium ratio is the same, the Te is the same, but the old concentrations are not. My point being, there are new CO2 concentrations in the atmosphere and the reservoirs and using 280 ppm as a reference is no longer valid. All Tau = 50-year projections are based on that, as far as I can tell.
“In the case of CO2 in the atmosphere, humans add more reactant each year, but the sinks don’t follow as fast,…”
The data seems to indicate sinks have been keeping up for decades now.
“…thus any new equilibrium will be above the current disequilibrium.”
Isn’t that my point?
David Andrews
July 20, 2025 at 5:38 pm
“What makes you think…?”
I honestly don’t have a good answer for that. My estimated incremental increase in natural emissions is less than the annual FF carbon input. The “minor” claim refers to the relative amounts remaining in the atmosphere, like only 14% of the rise. The cliché trying to get my head around it applies. I’ll need to sleep on it.
Jim Siverly, July 20, 2025 at 9:35 pm
“But it is based on the universally accepted 4-year Te, IPCC estimates of reservoir content, and correlation with Mauna Loa data.”
The 4-year Te is universally accepted as the residence time and has zero connection with Tau, the universally accepted adjustment time of around 50 years. Universally accepted, except by you and a group around the Science of Climate Change…
“Not one example of data showing Tau is longer than Te. You make predictions about equilibrium conditions without evidence of what they will be. That is not scientific.”
Sorry, but have you not even looked at the observations and back-calculation towards the real world equilibrium?
Here from Peter Dietze, already from 1997:
http://www.john-daly.com/carbon.htm
Here from David Burton from last year:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Lindzen, Spencer and many others come to a Tau of around 50 years and a basic equilibrium of around 280-300 ppmv, based on observations, but you say that they do that without any evidence?
The IPCC uses much longer Tau’s, but they include a saturation of the different reservoirs for CO2, which is only the case for the ocean surface, not until over 1,000 ppmv for the biosphere and not in sight ever for the deep oceans.
That is the reason that the ocean surface follows the atmosphere with a Te of less than a year and its pCO2 follows the atmosphere with only 7 μatm difference, thus its “new” equilibrium pCO2 remains near the atmospheric pCO2.
Te is the residence time and may be used as Tau if (and only if!) the resulting change in output and new equilibrium is caused by the extra input of one of the reactants. If there are processes involved that are largely to completely independent of the height of the inputs, then Tau and Te have no connection with each other at all.
That is the case for the output into vegetation and the return of CO2 from all life on earth. That is already half the universally accepted Te of 4 years… And half the universally accepted Tau of 50 years, which is the only figure of interest, as that shows how much NET CO2 is removed each year out of the atmosphere in direct ratio to the extra CO2 in the atmosphere…
And one can calculate the increase in the atmosphere with any Tau one likes. The difference is, that with a Tau of 50 years, the basic equilibrium didn’t change (except for the influence of temperature) and with a Tau of 4 years, the basic equilibrium increases with the CO2 level in the atmosphere…
“The data seems to indicate sinks have been keeping up for decades now.”
Not at all: CO2 increased with 50% in the atmosphere, while the sinks in the oceans increased with only 33% and in the biosphere with only 13%. Thus Te was not constant and may not be used as fixed ratio at all.
The NET change (inputs – outputs) remained in ratio to the NET change in the atmosphere, thus Tau remained constant…
I have sent my “model” already to Ed, but here again the references:
https://www.ferdinand-engelbeen.be/klimaat/klim_doc/Ed%20Berry_challenge.docx
and the accompanying Excel sheet with the calculations is here:
https://www.ferdinand-engelbeen.be/klimaat/klim_xls/Berry_fluxes.xlsx
The spreadsheet was made for periods of 10 years, as Berry asked for, but I (still) am working on a general spreadsheet over the full period from 1850 on…
David Andrews
July 20, 2025 at 10:53 am
“Those who argue that the atmospheric carbon increase is coming from warming oceans have a problem explaining why the oceans are getting less basic”
That is an extremely weak argument. It is alarmist’s propaganda based on one measurement off Hawaii with volcanoes spewing CO2 into the water. Measurements from other sites around the world show the opposite. Ocean Ph over coral reefs goes up and down like a yo yo on a daily basis. There is no global measurement. Liu et al 2009 shows South China Sea Ph higher than it was 6,000 years ago and has been rising for the past 50 years. And there is no experimental data anywhere showing CO2 being absorbed from the atmosphere is the cause of the oceans being less basic.
“I looked at the EPA testimony you linked. It was unsubstantiated opionion. It gave me nothing to argue with.”
You’re doing nothing more than avoiding inconvenient truths. Did you read Attachment 3 in full?
Bud Bromley is a world renown expert on Henry’s Law. It was his profession. He used it every day for his entire career. He was speaking from his knowledge gained from a lifetime of experiments and conducting experiments. He was also speaking from many hundreds of references that he did not quote in his submission. You can read them all from his web site. https://budbromley.blog/2022/05/20/correcting-misinformation-on-atmospheric-carbon-dioxide/
He is well published.
Brendan,
David Burton and I have had a lot of discussions with Bud Bromley in the recent past and he has quite remarkable ideas about Henry’s law…
Take from your reference:
“Ocean surface demonstrates the capacity to rapidly absorb orders of magnitude more CO2 than humans produce, and then recover to trend.”
Wow. The observed (yes, observed!) uptake in the ocean surface is only 10% of the increase in the atmosphere. Not orders of magnitude. Observed at seven monitoring stations, which measure a lot of sea surface constants over the years.
See: https://tos.org/oceanography/assets/docs/27-1_bates.pdf
Figure 3 and Table 2.
The drop in pH over the years is small, but again is measured in all seven stations. See Figure 7 in the reference.
Then he produces pages and pages and pages of text, without much meat until about the Pinatubo eruption:
“Nature rapidly absorbed the added CO2 and then more rapidly accelerated again to reset its CO2 concentration to trend. ”
Which is not what happened: human emissions were NOT fully absorbed, still increased, but at a lower speed during the Pinatubo eruption. Here for the increase in the atmosphere over the 1991 Pinatubo and 1998 El Niño episodes:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/wft_trends_rss_1985-2000.png
Only a few ppmv less increase around a 100 ppmv trend since 1958 caused by 170 ppmv fossil fuel emissions over the same period.
Then: “By elimination, there is no other known, logical or physically possible sink for such a large amount of CO2 to be absorbed so rapidly other than ocean surface.”
He never heard of the biosphere? The influence of the Pinatubo was far more pronounced by the extra uptake of CO2 by the green earth, as a lot of leaves, normally part of the day in the shadow of other leaves now received scattered sunlight from the fine aerosols that the Pinatubo emitted.
How do we know the difference? Because the 13C/12C ratio changes in opposite direction for vegetation uptake or release of the biosphere and in parallel for the oceans.
See: https://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_dco2_d13C_mlo.jpg
And his whole CO2 calculation was completely at error, as he used ppm as “mass” ratio, while ppm, as used by NOAA and the whole scientific world, uses ppm as volume ratio…
Better look for more reliable sources…
Ferdinand,
“Where Te in general is called “residence time” or “turnover time” by about any engineer in this world. Even the IPCC uses that definition.
Te shows how long an individual CO2 molecule “resides” in the atmosphere before being removed out of the atmosphere, either with an equal change in CO2 mass or without a change in mass, by simply replacing it with a CO2 molecule from another reservoir.”
Te is “e folding time.” It isn’t residence time or adjustment time or Tau. It arises from the solution to the continuity equation. Tau does not arise anywhere. We’ve shown you from the solution to the Continuity Equation that the 2ppm yearly rise is mostly natural. That’s all there is to it. This is when you need to reach across the table, shake hands and resign. You are just digging a hole.
Ferdinand,
Also, it seems you are trying to apply Chemical Equilibrium concepts to Atmospheric CO2. What is your A and what is your B?
Ferdinand,
So typically, if A is in equilibrium with B, the equilibrium constant k=[B]/[A]. What is the equilibrium constant and what are A and B?
Stephen P. Anderson, July 21, 2025 at 8:57 am
“Te is “e folding time.” It isn’t residence time or adjustment time or Tau. ”
According to Dr. Ed:
“Outflow = L / Te (2)
where Te is the “e-time,” so defined because it is an exponential time. Berry’s e-time Te is the same as IPCC’s turnover time, T (IPCC, 2007, p. 948).”
But the IPCC’s “turnover time” or “residence time” (RT) is simply:
RT = L / outflow. That is not the e-folding time of an extra input of CO2 (whatever the source). Only if all flows are unidirectional, then Te = RT
Dr. Ed uses Te = RT throughout all his calculations, while the IPCC uses an overall RT of about 4 years and increasing slower Tau’s (Te’s) for each exchange between compartments apart, and includes saturation levels for each compartment.
“We’ve shown you from the solution to the Continuity Equation that the 2ppm yearly rise is mostly natural.”
We have shown that the 2 ppmv/yr rise can be only caused by the 5 ppmv/yr supply of FF. The 5 ppmv FF is supplied directly into the atmosphere for 100% as mass and nowhere else.
Other compartments only can remove 3 ppmv/yr CO2 as mass out of the atmosphere, no matter what the outgoing mix of natural and FF CO2 is. Dr. Ed’s and your carbon mass balances don’t fit at all: if the increase is partly natural, and part of the FF increases the total carbon mass in other compartments, where does that extra CO2 in the atmosphere comes from?
Have a look at this graph:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/demetris_1b.png
The dark blue line are FF emissions (without land use changes).
The red line the observed increase in the atmosphere, which may be 100% human caused or 100% natural or any mix in between.
The green line are the sinks in the case that the increase in the atmosphere is 100% human.
The light blue line are the sinks in the case that the increase in the atmosphere is 100% natural.
The light blue sinks in nature are twice as deep as the increase in the atmosphere for a 100% natural increase…
So where does the natural CO2 that causes any increase in the atmosphere comes from?
A is CO2 in the atmosphere, B is CO2 in the oceans.
A is in equilibrium with B when the concentrations in atmosphere and ocean surface have an equal pCO2 per Henry’s law.
That is at a concentration ratio constant of about 0.85 in water, compared to air at 25°C, if I remember well.
When A gets increased with a one-shot 50%, 90% of the ocean surface reacts very fast with a Tau of less than a year, but get saturated at 5% of its own carbon level, which is near equal to the carbon level in the atmosphere (~900 PgC).
pCO2 levels at the ocean “edges” (polar and equatorial) hardly change and remove/release CO2 with a difference, caused by the 50% extra CO2 in the atmosphere with a Tau of about 125 years…
If anyone want to wade through the specious waffle from Uncle Bert at July 21, 2025 at 6:26 am you are welcome.
He starts with a paper that is a pal reviewed CAGW biased paper. It assumes that the oceans only absorb human CO2. Ocean acidification in the title. Ocean acidification is a pseudoscientific lie. Cherry picks a short times series for ocean pH from selected sites that calculates, not measures, pH in the DIC, not the oceans. The DIC is a piece of chemistry invented by the CAGW alarmists because it produces confirmation bias results.
A meaningless undescribed chart. And all wrapped up in yet more specious meaningless waffle.
It is Uncle Bert’s desperate attempt to falsify the Pinatubo experiment conducted by Bromley and Tamarkin.
Bromley & Tamarkin 2022; Correcting Misinformation on Atmospheric Carbon Dioxide; https://budbromley.blog/2022/05/20/correcting-misinformation-on-atmospheric-carbon-dioxide/
They examined data following the explosive volcanic eruption of Pinatubo on the island of Luzon in the Philippines in June 1991. This eruption emitted large amounts of aerosols into the atmosphere blocking sunlight and reducing SSTs and surface temperatures. This altered the Henry’s Law ratio causing a reduction in oceanic emissions lowering the atmospheric concentrations. There was a large natural movement down in atmospheric concentrations of CO2 post the eruption, followed after that by an even larger natural movement back up.
The large movement down in CO2 concentrations post the eruption occurred despite the fact that during this same period, human emissions of CO2 continued unabated. Natural emissions also continued from, e.g. biosphere decay & ocean emissions. During 1991-1992 there was an El Nino event which caused increased emissions from a warmer Pacific Ocean. On top of that, the volcano itself added large amounts of CO2 gas to the atmosphere. In spite of all these emissions, overall SSTs dropped post the eruption causing a large drop in atmospheric CO2 concentrations.
“despite the CO2 additions by humans, natural sources, a volcano and an El Nino. Nature rapidly absorbed the added CO2 and then more rapidly accelerated again to reset its CO2 concentration to trend.”
“The environment, mostly ocean surface (since ocean about 71% of Earth’s surface,) demonstrated rapid CO2 absorbance capacity which is 239 times larger than maximum possible net human emissions. We conclude that net human emissions are trivially minor, negligible, and absorbed and re-emitted along with the 239 times larger change in natural CO2.”
“In the 2 years following the June 15, 1991 eruption of the Pinatubo volcano, the natural environment removed more CO2 than the entire increase in CO2 concentration due to all sources, human and natural, during the entire measured daily record of the Global Monitoring Laboratory of NOAA/Scripps Oceanographic Institute (MLO) May 17, 1974 to June 15, 1991. Then, in the 2 years after that, that CO2 was replaced plus an additional increment of CO2.”
Uncle Bert has tried to take on the world’s foremost expert on Henry’s Law and failed miserably.
Uncle Bert. Dr Ed has said you are out of your depth on the subject matter you are discussing with him, you are way out of your depth on Henry’s Law as well.
Ferdinand,
I can’t believe you’re debating me about this. Why don’t you read Dr. Ed’s first paper? His model is mathematically derived. Te is “e folding time.” It is the time it takes Lb to move 1-1/e the distance to L. I’ve followed Dr. Ed the whole way (for years) and taken the time to read and re-read all his works. It appears to be the same as IPCC’s turnover time. Not sure what residence time is. Dr. Ed has talked about adjustment time before, but it is not derived from the solution to the continuity equation-it is essentially several “e times.”
Also, I’ve shown you mathematically that the dC/dt=2ppm can’t be all FF. It isn’t even 10%. Your Fountain Model doesn’t allow any mixing in the atmosphere and somehow keeps carbon segregated. You’ll need to specifically explain how nature does this “cycling.” Also, you need to explain what is A? What is B? And, therefore what is k? I would think the Climate Coalition would be searching for the truth.
Ferdinand Engelbeen July 21, 2025 at 2:49 pm
Dear Ferdinand,
Even though we disagree on climate physics, I appreciate your effort to clarify your position.
Indeed, I use IPCC’s turnover time and use the same reference you supplied (IPCC, 2007, p. 948). I began with equation (2) because that is how systems models work. That’s why my flow formulas derived from (2) reduce to electric circuit theory. I found later that IPCC had already defined (2) as turnover time.
Also, Stephen is correct that turnover time is also known as e-folding time.
Eq (2) is fully reversible in the way I use it. Again, this is standard systems theory that is proven to work. Dalton’s Law of Partial Pressures follows (2).
There are examples where outflow does not follow (2). Flow of water over a dam, and flow of water out of a hole in the bottom of a container, do not follow (2).
While I have not read every word the IPCC has published, I am not aware that the IPCC uses any formula for outflow for its carbon cycle than (2).
I replicated IPCC’s Fig. 6.1 data for IPCC’s natural carbon cycle. This is a necessary calibration point for any carbon cycle model.
I do not see that you have replicated IPCC’s natural carbon cycle with your formulas. Why not?
IPCC does not define residence time the same as turnover time. IPCC specifically uses a different definition for residence time, as my 2019 paper explains.
I do not see that IPCC “uses” 4 years for any calculations. The only reference that I found where IPCC refers to “4 years” is in its definition of turnover time it say it is about 4 years.
My replication of IPCC’s natural carbon cycle shows that IPCC’s data from its Fig 6.1 produces an e-time of 3.5 years. This is what IPCC is referring to when it says about 4 years.
In my opinion, you have no physical basis for your Tau. You are using data that happen to be close to their balance level, and you think the progress to their balance level has slowed down. You think that carbon just swished around without changing the levels. No proof. Just a bad idea. My simple model explains all the data that you claim need a Tau.
You even confirm this when you say later that Tau is the time for the level to move 63% of the way to its balance level. That proves your Tau is the same as my Te.
So, if you begin with Te and you end with Te, then everything in between is also Te.
Your model is imaginary and not connected to reality. Your model does not represent reality. You have tried to develop your model as a curve fit to the data that you have.
You have no model structure that does what my equations (1) and (2) do.
We must always begin with a mathematical structure for our hypotheses. Then we can check to see how our hypotheses fit the data. Without such a structure, we can’t predict anything, which means we not have a valid hypothesis.
You say, “We have shown that the 2 ppmv/yr rise can be only caused by the 5 ppmv/yr supply of FF. The 5 ppmv FF is supplied directly into the atmosphere for 100% as mass and nowhere else.”
That is nonsense. First, the data you use do not prove in any way that your interpretation of the data is correct. That claim violates the scientific method.
Second, my model explains the data.
You claim, “Dr. Ed’s and your carbon mass balances don’t fit at all: if the increase is partly natural, and part of the FF increases the total carbon mass in other compartments, where does that extra CO2 in the atmosphere comes from?”
First, please show me where you think my formulation does not fit the data.
Second, I have no obligation as a scientist to explain where the extra CO2 is coming from.
My formulation and calculations, using valid data, prove the extra CO2 is NOT coming from human CO2.
The null hypothesis that we must follow in our research is that all changes are natural until proven to be human. The burden of proof is on you to prove the CO2 increase is human caused.
I looked at your graph:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/demetris_1b.png
It does not prove the CO2 increase is human caused. The first failure is it uses sinks. Sinks are not valid data. Sinks are not part of a systems model. To model using sinks is like saying a capacitor is an electron sink without know the size of the capacitor. The so-called net natural contribution has no meaning at all because it is based on fiction.
Real models are based on outflow, not inflows.
The real comparison of annual human emissions with annual change in the CO2 level has been done my Munshi. He showed there is no correlation. Therefore, there can be no cause effect relationship of human CO2 with the CO2 increase. You objected that Munshi’s calculations are detrended, but there you are wrong. All correlations of time- series data must be detrended.
Munshi’s proof that human CO2 cannot have caused the CO2 increase is not rebuttable.
So, really, the only conclusion we can draw from your graph is that human CO2 did NOT cause the CO2 increase.
Brendan Godwin, July 21, 2025 at 5:32 pm
Brendan, if you can’t make a distinction between data as they are observed and the interpretation of these data, then we can’t have a real discussion about the data.
The pH, and other data from seawater can be calculated from any pair of measured data, even from the far past.
pH measurements in the past were based on glass pH meters and had an accuracy of +/- 0.1 pH unit. By far not accurate enough to measure a change in seawater of 0.1 pH unit in 170 years time.
Modern pH measurements are based on colorimetric measurements and are far more accurate.
In several stations one has plotted the colorometric pH measurements and the calculated measurements together. That is the case for e.g. ALOHA (Hawaii) station:
https://www.pnas.org/doi/pdf/10.1073/pnas.0906044106
Figure 1 shows the pCO2 level in the atmosphere, as measured at Mauna Loa , thus not far away and the calculated pCO2 of the ocean surface and included water vapor pressure near the surface, which in average was about 15 μatm lower than in the atmosphere. That means that in average CO2 is entering the oceans from the atmosphere, even if in some summers the oceans were net emitters.
CO2 dissolving in the oceans lowers its pH, no matter if you call it “acidification” to scare people or lowering the alkalinity.
That is reflected in the pH drop over different depths of the surface (not the deep oceans) over a period of 15 years.
They plotted the calculated pH, based on DIC and TA (total alkalinity) together with colorometric direct measurements. These in general match each other within a fraction of a tenth of a pH unit…
If all seven stations show a similar pH drop over time, then that pH drop, no matter how small, is real.
“The DIC is a piece of chemistry invented by the CAGW alarmists because it produces confirmation bias results.”
If you don’t even know that DIC is simply the sum of dissolved CO2 + bicarbonates + carbonates, what are you then discussing at all? And it is impossible to measure a pH from salts. One can only measure the pH of solutions, in this case thus seawater.
“In spite of all these emissions, overall SSTs dropped post the eruption causing a large drop in atmospheric CO2 concentrations” and
“the natural environment removed more CO2 than the entire increase in CO2 concentration due to all sources, human and natural”
As you believe what Bromley says, then give me the data where the CO2 levels in the atmosphere dropped, besides the “normal” drop in the NH spring/summer, thanks to vegetation growing new leaves…
And besides the “normal” spring/summer uptake, the extra uptake by vegetation after Pinatubo, thanks to scattered sunlight, was much stronger than by the oceans. Even both together did NOT remove more CO2 than emitted by human FF fuels use, as the increase in the atmosphere slowed, but did NOT drop.
Have a look at their Figure 11 of your reference of their work: in the years after the Pinatubo, the increase in the atmosphere was a lot smaller than in previous and following years, but still an increase, not a drop.
Your source of what Henry’s law means is not very reliable, to say the least…
Stephen P Anderson, July 21, 2025 at 5:41 pm
“Te is “e folding time.” It is the time it takes Lb to move 1-1/e the distance to L”
I do completely agree with that, I only disagree with Dr. Ed using the residence time of the IPCC as Te. Te is NOT the 4 years residence time of the IPCC. Te (or better Tau, as used by the whole scientific community) is 50 years, as can be calculated from the increase in atmospheric data and increase in NET sink rate. And L also can be calculated from atmospheric data over the past 67 years and is between 280 and 300 ppmv. Not 315 ppmv for the current 325 ppmv in the atmosphere… That is the main difference between Dr. Ed’s opinion and our opinion…
“I’ve shown you mathematically that the dC/dt=2ppm can’t be all FF. It isn’t even 10%. Your Fountain Model doesn’t allow any mixing in the atmosphere and somehow keeps carbon segregated. You’ll need to specifically explain how nature does this “cycling.””
If humans add 5 ppmv/year to the atmosphere, for the full 100% as mass, completely independent of any other inflow or outflow, and there are practically no human CO2 sinks as mass, then the human 5 ppmv/year do fully increase the total mass in the atmosphere with 5 ppmv/year.
The observed increase in the atmosphere is only 2 ppmv/year. Thus the total of other transfers of CO2 mass in and out the atmosphere must remove 3 ppmv CO2/year as CO2 mass to fulfill the carbon mass balance. No matter how much % FF CO2 is already in the atmosphere or in the outputs or inputs. The full increase of CO2, as mass, thus is caused by the one-way addition of 5 ppmv/year FF CO2 and nothing else.
As already several times explained: both the oceans as the biosphere are net sinks for CO2, whatever the isotopic composition in any of the compartments. It is about carbon mass transfer, not where the FF molecules go. Even if the isotopic changes give a good indication of where to the human FF is transferred and resides. Once in the atmosphere, all FF is mixed with the rest of the CO2 and what goes out (and comes back) is a mix of natural and FF CO2. As good as the “fountain” model will rapidly mix the small extra input with all what is already in the basin.
In the period 1958-2025, the total mass of CO2 in all compartments increased from the supply of some 170 ppmv FF emissions. In the atmosphere with 100 ppmv, in vegetation with about 35 “ppmv” (PgC is of course a better metric), in the ocean surface with some 7 “ppmv” and about 28 “ppmv” disappears for a long time into the deep oceans.
If one assumes that any of the 100 ppmv rise in the atmosphere comes from the other reservoirs, then show me the detailed mass balance, where that CO2 originates…
Ed,
Can you confirm that the ONLY result of your calculations which suggest that the atmospheric CO2 increase over the last century has natural causes is the modest percentage of “human carbon” in the present atmosphere?
Dr. Ed, July 21, 2025 at 7:58 pm
Dear Dr. Ed,
“Also, Stephen is correct that turnover time is also known as e-folding time.”
That is where we already disagree. The turnover time is the average time that a CO2 molecule “remains” or “resides” in the atmosphere. That also cán be the e-folding time if (and only if!) all flows are one-way in to out. Not when 95% of all CO2 flows return to the inputs in the same year, but in another part of the day or in another season.
The IPCC agrees that in 1750 some 168.4 PgC of CO2 cycles in and out the atmosphere which contains 589 PgC, or a residence time of 3.5 years, with equal inflows and outflows thus at its dynamic equilibrium.
In about the year 2000, including 240 PgC extra in the atmosphere (at 829 PgC), the outflows increased to 200.4 PgC/year. That gives a residence time of 4.1 years. Which, according to your theory is impossible: Te must remain the same as the fixed factor between the driving force and the output.
Then we have the difference between inflows and outflows, which is the only metric of interest that shows that the process is above its equilibrium: only 4 PgC/year more output than input for 240 PgC extra in the atmosphere.
The exponential decay towards its dynamic equilibrium, for this process gets:
Te = 240 / 4 = 60 years.
An order of magnitude slower than the residence time…
“IPCC does not define residence time the same as turnover time. IPCC specifically uses a different definition for residence time, as my 2019 paper explains.”
Sorry, the IPCC has very clear definitions of turnover time vs. residence time vs. adjustment time:
https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_AnnexVII.pdf page 2237 for “lifetime”:
“Response time or adjustment time (Ta) is the time scale characterizing the decay of an instantaneous pulse input into the reservoir.”
“In simple cases, where the global removal of the compound is directly proportional to the total mass of the reservoir, the adjustment time equals the turnover time: T = Ta.”
“Carbon dioxide (CO2) is an extreme example. Its turnover time is only about 4 years because of the rapid exchange between the atmosphere and the ocean and terrestrial biota. However, a large part of that CO2 is returned to the atmosphere within a few years. The adjustment time of CO2 in the atmosphere is determined from the rates of removal of carbon by a range of processes with time scales from months to hundreds of thousands of years.”
“Turnover time (T) (also called global atmospheric lifetime) is the ratio of the mass M of a reservoir (e.g., a gaseous compound in the atmosphere) and the total rate of removal S from the reservoir: T = M/S. For each removal process, separate turnover times can be defined. In soil carbon biology, this is referred to as mean residence time.”
While we don’t agree at all with the time scales of hundreds to thousands of year of the IPCC, they make it clear that one can’t use the 4 years turnover/residence time of CO2 in the atmosphere as the e-time to remove an extra mass of CO2 out of the atmosphere…
That is part 1…
Dr. Ed,
Part 2.
“You have no model structure that does what my equations (1) and (2) do.”
Nobody disagrees with (1). We only disagree with (2), as the real world Te is around 50 years, not 4 years.
Here -again- what our real world model shows:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/mass_fluxes_real.jpg
The only important difference with the IPCC flows is that we don’t isolate the deep oceans from the atmosphere, but split the flows in 50 PgC/season back and forth between atmosphere and ocean surface and 40 PgC/year back and forth directly between the atmosphere and the deep oceans. That is what bypasses the extreme long e-times of the IPCC.
The turnover/residence time still is exactly the same as your turnover/residence time at 3.8 years, but the adjustment time is the real one: about 50 years. Which fits the past 67 years within one ppmv. I have send you the Excel sheet calculations for the years 2010-2020 and the graph:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/berry_2010.png
“First, the data you use do not prove in any way that your interpretation of the data is correct. That claim violates the scientific method.”
Sorry Dr. Ed, but I don’t think that any bookkeeper in this world will agree with you. If one adds 5 PgC/year directly into the atmosphere and the measured increase in the same atmosphere is only 2 PgC/year, then the 5 PgC supply is the one and only cause of the increase in the atmosphere. No matter how much CO2 cycles between the reservoirs. That is called a mass balance. A simple matter of bookkeeping…
“First, please show me where you think my formulation does not fit the data.”
With a Te of 4 years, the increase in the atmosphere caused by human FF is only a few % of the measured increase. That gap should be filled with “natural” CO2 from other reservoirs, but the other reservoirs also increased in carbon, thus can’t be the source of the extra CO2 in the atmosphere…
“Second, I have no obligation as a scientist to explain where the extra CO2 is coming from. ”
If your carbon balance doesn’t fit the observations, as a scientist you have the obligation to show why that is…
“It does not prove the CO2 increase is human caused. The first failure is it uses sinks. Sinks are not valid data. Sinks are not part of a systems model.”
Any movement of CO2 in/out the atmosphere must obey the carbon mass balance at any second of the day to eternity (except radioactive 14C). As good as the total energy in an electric system must be conserved, no matter where it flows or resides.
That implies that the quantities per year in that graph above and below zero must be exactly the same for each year. We know two quantities with quite good accuracy: human emissions (based on sales/taxes) and increase in the atmosphere. We know the difference between these two with quite good accuracy, thus then remains the question, what is the net sink rate for 100% human increase and for 100% natural increase. In the latter case, the sinks must absorb every gram of human emissions and the net sink rate is twice the increase in the atmosphere. Very remarkable…
“The real comparison of annual human emissions with annual change in the CO2 level has been done my Munshi. He showed there is no correlation.”
I think that Munshi is a she…
Of course there is no correlation in the variability, if one variable has hardly any variability. The cause and effect is exactly in the trends, not in the variability…
How do you prove that the increase of CO2 in the atmosphere is not caused by the twice as steep slope of FF emissions but by temperature without a slope?
By detrending, thus effectively removing the cause of the slope of the increase in the atmosphere…
Some 20 years ago I did made the proof of the pudding for a similar discussion: I mixed two variables: one with a steep trend and no variability at all and one double sinus with only variability and no trend at all. The dependent variable was 0.5 x the first variable + all the variability of the second one with a small lag, to make it as “real” as can.
Then I asked some “attribution” program (don’t remember which one, Anova?) to show me the relative contributions of the two inputs to the result. That failed completely, because the program attributed near all contribution to the double sinus… Can be repeated for any attribution program…
Ferdinand,
[Ferdinand]:
“I do completely agree with that, I only disagree with Dr. Ed using the residence time of the IPCC as Te. Te is NOT the 4 years residence time of the IPCC. Te (or better Tau, as used by the whole scientific community) is 50 years, as can be calculated from the increase in atmospheric data and increase in NET sink rate. And L also can be calculated from atmospheric data over the past 67 years and is between 280 and 300 ppmv. Not 315 ppmv for the current 325 ppmv in the atmosphere… That is the main difference between Dr. Ed’s opinion and our opinion…
“I’ve shown you mathematically that the dC/dt=2ppm can’t be all FF. It isn’t even 10%. Your Fountain Model doesn’t allow any mixing in the atmosphere and somehow keeps carbon segregated. You’ll need to specifically explain how nature does this “cycling.””
If humans add 5 ppmv/year to the atmosphere, for the full 100% as mass, completely independent of any other inflow or outflow, and there are practically no human CO2 sinks as mass, then the human 5 ppmv/year do fully increase the total mass in the atmosphere with 5 ppmv/year.
The observed increase in the atmosphere is only 2 ppmv/year. Thus the total of other transfers of CO2 mass in and out the atmosphere must remove 3 ppmv CO2/year as CO2 mass to fulfill the carbon mass balance. No matter how much % FF CO2 is already in the atmosphere or in the outputs or inputs. The full increase of CO2, as mass, thus is caused by the one-way addition of 5 ppmv/year FF CO2 and nothing else.”
1) Dr. Ed doesn’t use Te as residence time. He explained IPCC describes Te as turnover time.
2) If the whole scientific community uses Tau=50years, then our whole scientific community is in serious need of psychotherapy. Tau doesn’t exist.
3) Currently L is 430ppm.
4) Human CO2 and natural CO2 mix in the atmosphere. Sinks can’t differentiate them. Outflow is proportional to L for all CO2. I’ve shown you mathematically if dC/dt=2ppm = Inflow – Outflow, then most of the 2ppm is natural. Read Dr. Ed’s paper.
5) You flunk physics with your inaccurate mass balance assuming that human and natural CO2 don’t mix in the atmosphere and that nature can differentiate.
Ferdinand Engelbeen July 22, 2025 at 8:49 am
Dear Ferdinand,
Since you think you are a better statistician than Jamal Munshi, who is a professional statistician, I posted his paper above – just below your paper – for all to read.
Munshi concludes human CO2 emissions and increases in atmospheric CO2 are uncorrelated. Do you have a defense?
(This is only part 1. I will follow with another comment on your other claims.)
Just a note of another paper that is pertinent to this discussion. It is discussed and linked in this article https://mailchi.mp/climatedn/cdn_newsletter_250716?e=98e02c0608
It discusses the isotope arguments for FF being the whole cause of the increase being called into question with the better quantification of CO2 emissions from river systems as that CO2 has the same makeup of isotopes as fossil fuels.
DMA, July 22, 2025 at 1:42 pm
That paper is discussed out at WUWT:
https://wattsupwiththat.com/2025/06/25/under-reported-old-carbon-is-not-the-source-of-increases-in-atmospheric-co2/
Ferdinand Engelbeen July 22, 2025 at 2:25 pm
Dear Ferdinand,
Your WUWT paper does not discuss this article that DMA referenced:
https://climatediscussionnexus.com/2025/07/16/matthew-wielicki-on-co2-isotopes/
Also, your WUWT paper does not dicuss these:
https://scitechdaily.com/scientists-were-wrong-plants-absorb-31-more-co2-than-previously-thought/
https://www.nature.com/articles/s41586-025-09023-w
https://www.nature.com/articles/s41561-024-01476-4?fromPaywallRec=false
Dr. Ed, July 22, 2025 at 12:56 pm
According to Munshi:
“A key relationship in the theory of anthropogenic global warming (AGW) is that between annual fossil
fuel emissions and annual changes in atmospheric CO2. The proposed causation sequence is that
annual fossil fuel emissions cause annual changes in atmospheric CO2 which in turn intensifies the atmosphere’s heat trapping property.”
Most of my statistics knowledge is from 60 years ago, but someone who writes that annual (!) emissions must correlate with annual (!) changes in atmospheric CO2 must never have heard of noise around a trend.
This is really stupid. 98% of the correlation between the variability of maximum 2 ppmv around a trend of over 100 ppmv is caused by temperature variability, but temperature gives less than 10 ppmv increase in the atmosphere from warming ocean surfaces since 1958 and zero trend in the derivatives. Temperature is responsible for all the temporal (2-3 years) variability, but not responsible for the bulk of the CO2 increase in the atmosphere…
Here the response for the trends since 1960 with temperature:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_co2_1960_2012.jpg
Compare that with the response to summed FF emissions:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1960_cur.jpg
Or since 1900 from ice cores – firn – MLO and FF emissions:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1900_1911.png
But of course there is no correlation between FF emissions and increase of CO2 in the atmosphere, according to a professional statistician.
Case closed.
Dr. Ed, July 22, 2025 at 3:05 pm
The second paper in following:
https://climatediscussionnexus.com/2025/07/16/matthew-wielicki-on-co2-isotopes/
is what is discussed at WUWT
And the text contains a grave error:
“devoid of 14C and depleted in 13C”
The “devoid of 14C” is right, “depleted in 13C” is just the opposite:
Most is carbonate rock at near zero δ13C. After dissolution in river water and release in the atmosphere, it is at about -6.5 per mil δ13C and still higher in δ13C than the current atmosphere at -8.2 per mil δ13C…
One can see these two as a positive feedback for the human influence on the isotopic changes for 14C and a negative feedback for δ13C.
Then the second of your references only shows that the human emissions probably were larger than estimated too: if the sinks in pants are greater than expected and the net sinks remains the same, then the sources also are underestimated…
The third reference again is the article discussed at WUWT
The fourth reference is about old 14C depleted carbon, which figures were used in the third reference.
In general: all these new findings are from CO2 flows that are already going on for thousands to many millions of years. These are already in the “basic” CO2 (isotopic) fluxes and only substantially changed when the natural environment changed.
For the 14C level that changed only with solar activity in very small steps over the past 60,000 years.
The 13C/12C ratio changed only with -6.5 +/- 0.4 per mil δ13C over the past 800,000 years
The 14C level dropped together with fossil fuel use, so that correction tables were needed for radiocarbon dating from 1870 on.
The 13C/12C ratio dropped to below -8.2 per mil in the atmosphere and similar in the ocean surface since 1850 in complete ratio to FF emissions.
It would be very remarkable that something in nature would mimic FF emissions in exact ratio and time…
Ferdinand Engelbeen
July 22, 2025 at 3:08 pm
You won’t understand Munshi’s work if you stop your study of it at making fun of what you mistakenly expected it to say. Briefly his work shows there is no correlation between the rate of change of FF emissions and the rate of change of temps proving that the correlations you demonstrate are spurious and no more meaningful that the correlation of FF emissions and shark attacks on nurses.
Dear Uncle Bert.
“if you can’t make a distinction between data as they are observed and the interpretation of these data, then we can’t have a real discussion about the data”
It is impossible to have a real discussion with you about anything. The data is the data. If that disagrees with your world view then. IYO, that data must be interpreted in a way that agrees with your world view. You start with an answer then devise specious constructs that agree with your answer.
“In several stations one has plotted the colorometric pH measurements and the calculated measurements together. That is the case for e.g. ALOHA (Hawaii) station”
Your reference once again used pseudoscience in the title. Can’t you produce real references from real scientists?
Your Figure 1 is a cherry picked short timeline of 18 years to show your confirmation bias, There are large gaps in the real measurements which were all from the DIC. That’s not the same as the oceans.
pCO2 is not concentration and it is misleading to use it to try and show atmospheric CO2 is being absorbed in the ocean. The DIC is different from the ocean. The d13C isotopic ratio for the DIC is -.5 to +2.0 per mil. The oceans are -10 per mil.
“CO2 dissolving in the oceans lowers its pH”
Where is your experimental data?
Warming oceans lowers the pH.
“the extra uptake by vegetation after Pinatubo, thanks to scattered sunlight, was much stronger than by the oceans”
You really are full of it aren’t you. As far as you’re concerned vegetation is the only thing that absorbs CO2 and you avoid the oceans like the plague. The oceans are a real inconvenient truth aren’t they? The oceans are far and away the largest emitter and absorber of CO2.That’s an inconvenient truth for you.
“DIC is simply the sum of dissolved CO2 + bicarbonates + carbonates”
The DIC is dissolved inorganic carbon. That is different from dissolved organic carbon which is different again from the oceans.
“give me the data where the CO2 levels in the atmosphere dropped, besides the “normal” drop in the NH spring/summer”
Perhaps you should read Bromley and Tamarkin’s paper.
Their experiment demonstrated that nature’s measured impulse absorbed 239 times the human-produced CO2 impulse. To be specific, this is the specific impulse calculation of CO2 that was removed from the atmosphere in 2 years after Pinatubo. Their experiment demonstrated that nature is controlling CO2 concentrations, not humans.
This comment will generate yet another page of specious waffle which is endless. I don’t have time to wade through all your nonsense, I have a life to live. This dialog started with me responding to David Andrews. He has either asked you to reply because he lacked the knowledge himself, or you have just barged in. Socialist political activists are 24/7 devoted to their cause. Normal people have lives to live.
Ferdinand Engelbeen
July 21, 2025 at 2:49 pm
In response to Stephen, you asked, “…if the increase is partly natural [emissions], and part of the FF [emissions] increases the total carbon mass in other compartments, where does that extra CO2 in the atmosphere comes from?”
It’s a seminal question. If natural emissions have not remained roughly the same as in preindustrial times, then what changed to introduce the extra carbon, other than FF emissions? I previously suggested some increase was caused by the expanding population which continues to plow fields, cut down trees, and dig holes to build homes and bury garbage. The other likely increase comes from the deep ocean mixing with the warmer surface. In addition to being warmer than 300 years ago, the CO2 content may be greater than what is being sinked these days.
Your math, your model, and your mind set is committed to defending your position which depends on no biosphere expansion other than what results from sinking FF carbon. What does your math and model predict, if FF continues to add 10 Pg/year and the natural emissions continue with a constant 200 Pg/year? What will the subsequent CO2 concentration be in twenty years? And what will the increase from the previous year be?
Ferdinand,
Dr. Ed is not required to explain why natural CO2 is increasing to falsify the human-caused CO2 theory. He isn’t one to guess. That’s not how science works. Maybe if all the money that had been spent supporting this fraudulent science had been spent toward objective research, then maybe we would know the answer. One thing I will say is that nothing about this world is constant other than nature constantly varies. So the idea that Mother Nature was in perfect balance at 280ppm doesn’t make much sense.
To Everyone,
I added a new paper by IvanR. Kennedy, John Runcie, Angus N. Crossan, Raymond Ritchie, and Jennifer Marohasy.
It is now the third PDF file above.
Their paper offers a new unique alterative hypthesis to explain how nature may increase the CO2 level.
In an ongoing email conversation, Gregory R. Wrightstone, Executive Director, CO2 Coalition, wrote to Jennifer Marohasy about this paper:
“If we accept all that you have just provided, you must explain why and how this abiogenic CO2 source suddenly began increasing and continues to increase. This is contrary to how geologic processes work. Increases or decreases to any mantle-derived CO2 or CO2 from weathering would occur over much larger time scales.
And the increase just happens to mirror human emissions.”
Jim,
“What makes you think that the FF emissions make a “relatively minor” contribution to CO2 growth compared to natural emissions? Is it the present composition of the atmosphere, or is it the ~20x larger gross number, or is it something else?”
You were fooled by the present composition of the atmosphere, weren’t you. Just like Mr. Ed.
DMA, July 22, 2025 at 4:00 pm
Even in my rusted knowledge of statistics, I remember that one need to be aware of spurious correlations between variables that have a similar trend. That is the reason that in many cases the correlations are taken from de-trended data.
That goes good in many cases, but fails completely, if the bulk of the trend is caused by a variable with hardly any variability and a huge trend. As is the case for human emissions and the increase in the atmosphere.
In the case of the increase in the atmosphere, indeed the variability in rate of change is fully caused by the variability in rate of change of temperature. But we know from the formula of Takahashi for the influence of temperature on the ocean surface pCO2 per Henry’s law, that the pCO2(aq) increased with less than 10 μatm, while the observed increase is 100 μatm and the supply of FF by humans some 170 μatm over the same period.
So the question then is if the extreme good correlation between FF emissions and increase in the atmosphere is plausible or not and if another (known or unknown) cause may be involved.
As FF emissions are 1.7 times the observed increase in the atmosphere, there is a huge possibility that they are the cause of the increase, simply based on the carbon mass balance.
The two other main probable sources, oceans and biosphere, are proven net sinks for CO2, thus can’t be the cause of the increase and all other known sources are either too small or too slow.
Remains some unknown sources as recently the discovery of extra 14C-free CO2 releases from rivers.
The point is that such releases are already going on for millennia (like coal seam fires) to as long as the earth has liquid water and some solid land. These CO2 emissions, including their 14C and δ13C “fingerprints” are already included in the pre-industrial CO2 levels and isotopic compositions.
Only if they changed completely in parallel with human emissions, then they are of interest, which is partly the case for the river emissions, where they act as a feedback to the human caused increase in the atmosphere.
What I don’t accept of Munshi is that he only looked at yearly (!) variability, that is looking at the noise around de-trended data and then concluding that there is no correlation, implying that there is no correlation between the trends.
If he had looked at e.g. 5 year intervals (or 5 year moving averages), he would have seen that the effect just fades away and only leaves a very small trend for temperature.
Brendan Godwin, July 22, 2025 at 5:19 pm
Brendan, I am only interested in the data, no matter who did measure them or the titles they use to describe them.
“Your reference once again used pseudoscience in the title. Can’t you produce real references from real scientists?”
Thus if you don’t like the title, then the data are pseudoscience?
And again, they don’t measure the pH of DIC, they measure the pH of seawater, even as it passes continuously from the intake of (commercial) sea ships, fully automatically:
https://www.mdpi.com/1424-8220/18/8/2622
“pCO2 is not concentration and it is misleading to use it to try and show atmospheric CO2 is being absorbed in the ocean. The DIC is different from the ocean. The d13C isotopic ratio for the DIC is -.5 to +2.0 per mil. The oceans are -10 per mil.”
Brendan, this only shows that you have not the slightest knowledge of ocean chemistry…
The deep oceans are near zero per mil δ13C and ocean surface between +1 and +5 per mil δ13C and carbonate rocks (dropped by coccoliths out of DIC) also are near zero per mil.
It is at the ocean-atmosphere border that δ13C changes dramatically with -10 per mil δ13C from ocean water to air and -2 per mil from air into ocean waters. Net change -8 per mil δ13C if both flows are in equilibrium.
Or a near constant -6.5 +/- 0.4 per mil δ13C over the past 800,000 years in the atmosphere:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_d13C_lgm_cur.png
And a near constant +4.95 +/- 0.2 per mil δ13C over the past 600 years in coralline sponges (~DIC):
https://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
Until humans started their significant use FF from 1850 on.
“As far as you’re concerned vegetation is the only thing that absorbs CO2 and you avoid the oceans like the plague”
I only look at what the data say:
On short term vegetation is dominant:
Seasonally: -5 ppmv/°C (negative!)
Year-by-year: 3.5 ppmv/°C (positive)
Long term, the oceans are dominant: 4.2%/°C (both directions)
“Their experiment demonstrated that nature’s measured impulse absorbed 239 times the human-produced CO2 impulse.”
I have read their paper and did see Figure 11, which contradicts what they say in the same paper.
Ans 239 times the the human CO2 impulse during a few days has an immeasurable effect on the CO2 increase in the atmosphere…
Bye bye (as long as it lasts)
Dr. Ed, July 22, 2025 at 8:44 pm
Besides what Gregory Wrightstone writes, several items in that paper just don’t add up.
From the abstract:
“Our findings reveal that warming waters absorb atmospheric CO2 by promoting calcium carbonate formation, acidifying seawater and boosting CO₂ release to the atmosphere in late autumn and winter, when atmospheric CO₂ becomes highest”
As far as I know, seawater gets warmer in spring/summer, releasing some 50 PgC CO2 in a few months. Reverse in fall/winter. Kennedy’s findings just do the opposite…
Then we have the oxygen balance: this new find doesn’t involve any interaction with oxygen. Only biological processes do involve huge O2 changes and these show that the biosphere is the main cause of the decrease of CO2 in the atmosphere in spring/summer and increase in fall/winter.
Processes like found by Kennedy et al. only can have a very small influence.
https://www.ferdinand-engelbeen.be/klimaat/klim_img/bender_dO2.jpg
The measurements at Barrow give the clearest indication of the seasonal changes in CO2 and O2
And last, but not least, one can never deduce a long term trend from the variability within a year or a few years, until the trend is significantly larger than the noise…
Stephen P Anderson, July 22, 2025 at 8:42 pm
“Dr. Ed is not required to explain why natural CO2 is increasing to falsify the human-caused CO2 theory. He isn’t one to guess. That’s not how science works. ”
No, but he must explain as a scientist how an increase of CO2 of about half the FF emissions in the oceans and biosphere can have increased any CO2 in the atmosphere, as his model only allows for a (small) part of the increase due to human FF emissions. That is while the CO2 sinks in both oceans and biosphere exceed sources from the same reservoirs. His carbon mass balance doesn’t fit the observed increase in the atmosphere…
“Maybe if all the money that had been spent supporting this fraudulent science had been spent toward objective research, then maybe we would know the answer.”
Still most of all field research is of high quality, but the interpretation of the data is manipulated by a small group of “scientists” with an agenda…
“One thing I will say is that nothing about this world is constant other than nature constantly varies. So the idea that Mother Nature was in perfect balance at 280ppm doesn’t make much sense.”
Nobody says that Nature is constant: for the current SST, the CO2 in the atmosphere should be around 295 ppmv. Only that the change in CO2 ánd isotopic composition nowadays is much faster than in the far past, up to at least 800,000 years (ice cores) or several millions of years (foramins).
Jim Siverly, July 22, 2025 at 7:22 pm
“What does your math and model predict, if FF continues to add 10 Pg/year and the natural emissions continue with a constant 200 Pg/year? What will the subsequent CO2 concentration be in twenty years? And what will the increase from the previous year be?”
The Excel sheet with the calculations for all 20 years is here:
https://www.ferdinand-engelbeen.be/klimaat/klim_xls/Jim_fluxes.xlsx
Starting conditions:
905 PgC in the atmosphere, 200 PgC/year cycling in and out (only natural), 628 PgC equilibrium in the atmosphere for the current SST and 50 years Te for net removal.
Assumption: cycles increase in ratio with the increase in the atmosphere (as mix of natural + FF) . Natural remains 200 PgC, difference is FF “caused”, but does not indicate the ratio of FF/natural within the cycle.
Several starting conditions can be changed, including a small increment per year in the FF emissions.
The calculations are based on a fixed equilibrium and a fixed Te. I still am working on a “floating” equilibrium and the full database since 1850…
Results:
Year 0:
Atmosphere: 905 PgC
In: 200 PgC + 10 PgC = 210 PgC
Atmosphere: 915 PgC (temporarily)
Net out: (915 – 628) / 50 = 5.7 PgC
Out: 210.0 – 5.7 = 204.3 PgC
Atmosphere: 909.3 PgC
Increase in atmosphere: 4.3 PgC
Year 1:
Atmosphere: 909.3 PgC
In: 200.9 + 10 PgC = 210.9 PgC
Atmosphere: 919.3 PgC (temporarily)
Net out: (919.3 – 628) / 50 = 5.8 PgC
Out: 210.9 – 5.8 = 205.1 PgC
Atmosphere: 913.4 PgC
Increase in atmosphere: 4.2 PgC
Year 10:
Atmosphere: 944.0 PgC
In: 208.6 + 10 PgC = 218.6 PgC
Atmosphere: 954.0 PgC (temporarily)
Net out: (954.0 – 628) / 50 = 6.5 PgC
Out: 218.6 – 6.5 = 212.1 PgC
Atmosphere: 947.4 PgC
Increase in atmosphere: 3.5 PgC
Year 20:
Atmosphere: 975.8 PgC
In: 215.6 + 10 PgC = 225.6 PgC
Atmosphere: 985.8 PgC (temporarily)
Net out: (985.8 – 628) / 50 = 7.2 PgC
Out: 225.6 – 7.2 = 218.5 PgC
Atmosphere: 978.6 PgC
Increase in atmosphere: 2.8 PgC
As one can see, the net sink rate increases with the distance to the (old) equilibrium and a new equilibrium will be reached when extra output = extra input with extra CO2 in the atmosphere at extra input * Te
That is at Lnew = 628 + 10 * 50 = 1128 PgC
When the extra input stops, the extra output will exponentially go back to zero and the level in the atmosphere back to the “old” equilibrium of 628 PgC.
Why search for a reason that atmospherc CO2 is increasing? It is staring us in the face. Human emissions are two times larger that atmospheric accumulation.
David Andrews
July 22, 2025 at 9:23 pm
What does your math predict, if FF emissions continue to add 10 Pg/year and the natural emissions continue with a constant 200 Pg/year? What will the subsequent CO2 concentration be in twenty years? And what will the increase from the previous year be?
Ferdinand,
His model does explain that human CO2 is about 20-30 ppm of L which is 430ppm.
David,
Your assumptions are not evidence.
Jim,
The best prediction I can make, assuming constant human emissions of 10 Pg/yr for the next 20 years, would be to also assume that the “airborne fraction” remains around 45% as it has for 75 years. That is, each year the atmosphere would gain 4.5 Pg, so after 20 years it would be up by 90 Pg. Notice that the constant natural emission rate assumed (your 200) doesn’t matter since, by my assumption of a constant airborne fraction, I have guaranteed that net natural absorption is a constant 5.5 Pg/yr. (Note that once again you have focused on natural emissions, forgetting about natural absorption.)
One could certainly be concerned that, going forward, the natural processes that have until now been mitigating the atmospheric CO2 rise might saturate, causing the CO2 growth rate (and airborne fraction) to increase. That is a legitimate concern motivating some research. But for the PAST 75 years the data on the airborne fraction are in. They leave no room to argue that the natural processes are causing the increase.
I am glad you phrased the question in terms of steady rates. You have often referred to “exponentially increasing” rates with no justification except to make your model work. Indeed the human emission rates have been increasing, and that accounts for the positive second derivative of the Mauna Loa curve. But all it takes is steady human emissions to maintain steady growth in atmospheric CO2.
Jim,
I see that my response and Ferdinand’s are different. That is probably the outcome you wanted. His model effectively has the airborne fraction decreasing with time quite dramatically in 20 years, with constant human emissions. While I recognize that “airborne fraction” is only a convenient summary of data and represents nothing fundamental, I am skeptical that it could fall to 28% in 20 years.
Ferdinand Engelbeen
July 23, 2025 at 1:26 am
FE says “If he had looked at e.g. 5 year intervals (or 5 year moving averages), he would have seen that the effect just fades away and only leaves a very small trend for temperature.”
Munshi in fact followed his first work with another that did the same analysis for different time intervals and came to the same conclusion as he had on this referenced paper. I will look for that paper and get a link. I think it is likely already cited in Dr. Ed’s work.
I found Munshi’s work on other time intervals:
https://chaamjamal.wordpress.com/2018/12/19/co2responsiveness/
David Andrews
July 23, 2025 at 7:25 am
DA’s question “Why search for a reason that atmospherc CO2 is increasing? It is staring us in the face. Human emissions are two times larger that atmospheric accumulation.”
Because all the policies recommended to cure the “Climate Crisis” are based on the assumption that we can control atmospheric CO2 by ending our use of fossil fuels. I don’t think there is a “Climate Crisis” but am convinced there is a Climate Policy Crisis that costs dearly in coin and life.
If you and EF are correct will ending the use of fossil fuels end the rise in atmospheric CO2?
DMA,
Yes. Solid science says that ending the use of fossil fuels would end the rise in atmospheric CO2. There is some disagreement on the rate of fall after “net zero”. Ed’s opinions are very much outliers.
To Everyone:
Today, I took some time to review our progress in these debates. This comment is a result of this review. I will make this part of my rebuttal paper as well.
I will appreciate your suggestions on how I can improve this explanation.
A major source of confusion is between those who follow my calculation of the human and natural carbon independently, and those who do not. There is a precedent in physics my method. It is the Partition Principle.
The Partition Principle is used in Statistical Mechanics and Quantum Physics, but it also applies to classical physics. In many cases, including this one, it is the only way to calculate the corrrect answer.
The way I calculate the carbon cycle by separating human carbon atoms from natural carbon atoms follows the Partition Principle of physics.
This separation is necessary to correctly calculate the human carbon cycle and thus the effect of human carbon atoms on the CO2 level as distinct from the effect of natural carbon atoms on the CO2 level.
All calculations made without this separation are fundamentally wrong.
Therefore, In the manner that I defined the “Climate Equivalence Principle,” I now define the “Climate Partition Principle.”
The Climate Partition Principle is a special case of the Partition Principle … an extremely simple case.
There are only two parts to the partition. The variables are continuous. Human carbon atoms and natural carbon atoms are identical. They follow the same rules. There are no substitutions between the partitions. Human and natural carbon atoms do not interact or replace each other.
Neither carbon cycle interferes with the other. Their levels and flows are independent.
Human and natural carbon cycles have their own equilibriums, which represent the maximum entropy for the number of carbon atoms in each partition.
Each carbon cycle has continuing flows from each reservoir to adjacent reservoirs. At equilibrium, these counter flows are equal, but the flows continue.
IPCC defines its natural carbon cycle at equilibrium. This equilibrium results in certain percents of the total atoms residing in each of the four defined reservoirs: land, air, surface ocean, and deep ocean. This equilibrium also allows the calculation of the Te for each outflow node, using Te = Level / Outflow (at equilibrium).
Because human and natural carbon atoms follow the same flow rules and have the same Te’s, their equilibrium percentages are equal.
If either carbon cycle gets new carbon atoms, this adds to the total mass and lowers the entropy in this carbon cycle.
When a carbon cycle is not at its maximum entropy, the carbon cycle will change its flows in a manner that allows the carbon cycle to approach equilibrium as fast as possible.
This is the correct way to calculate the changes in each carbon cycle and to calculate the effect of human carbon on the CO2 level.
All calculations so far presented by the CO2 Coalition representatives are wrong because they have not properly formulated their carbon cycles.
In my opinion, most of the disagreement in these discussions is because the CO2 Coalition reps do not use correct physics. Until the CO2 Coalition reps wake up to proper physics, we will never agree.
Ferdinand Engelbeen
July 23, 2025 at 7:20 am
Thank you for your spreadsheet showing the twenty year future. It’s great. I think I deciphered your formula correctly, but I would like you to confirm it. Meanwhile, I will update my dropbox app so that I can show you the result of back calculating your formula to earlier years.
La_end = (La_begin + Ff_start) – F_netout
F_netout = [ (La_begin + Ff_start) – La_base ] / Te
F_in = Fn_start + Ff_start
F_out = F_in – Fnetout
DMA, July 23, 2025 at 10:25 am
Thanks for the link…
The first point that immediately did attract my attention, is his use of different scales for the different graphs.
For the emissions, the same scale for the 1 to 5 year trends.
For the increase in the atmosphere, smaller scales, so that it is not directly visible that the variability gets smaller.
The same for the “airborne fraction”, to a lesser extent.
And why not plotting emissions and increase in the atmosphere together?
The same visual trick was used for the de-trended data, with a difference in scale of a factor 3.
Nevertheless, as already said: there is absolutely no correlation between the variability of the FF emissions and the variability around the trend of CO2 in the atmosphere, for the simple reason that the FF emissions have hardly any variability. Thus looking at the (temperature caused) variability gives a completely spurious answer.
Just the opposite of the warning that one must be aware of spurious correlations between two similar up going variables…
I am pretty sure that Munshi’s approach would fail with my test of 20 years ago with two variables, one with a slope and no variability at all and another with a double sinus and no slope at all…
And again, in this case, it is entirely possible ánd plausible that the trend of FF emissions is the cause of the increase in the atmosphere, as these emissions are fully added directly into the atmosphere and only can be removed into other reservoirs.
His work does contain a link to another of his works, where he explains why one must use detrended data to avoid spurious correlations. That link doesn’t work, but I probably have found the paper:
https://download.ssrn.com/16/10/12/ssrn_id2851418_code2220942.pdf
That contains following sentences:
“In this kind of empirical evidence, the theoretical time scale at which the proposed causation works must match the time scale of the correlation (Box, 1994). Thus a correlation between emissions and changes in atmospheric and oceanic carbon dioxide must exist at an annual time scale and a correlation between emissions and warming must exist at a decadal time scale.”
Wow. I never have heard of such short time scales.
Because of the relative huge temperature induced noise, one need at least 5 years of data to have certainty about the CO2 trend and as far as I know, climate is at least over a period of 30 years…
With that kind of definitions, one never can obtain any sea level change observation, as there is absolutely no correlation per minute, day, year or even 20 years (only a statistical one) between the real sea level and the observations…
David Andrews
July 23, 2025 at 10:05 am
Thank you for your prediction, as I’m hoping it will get us on the same page. In other words, understanding why we insist on our positions, as I expect we will.
July 23, 2025 at 10:17 am
No worries about not having the same answer as Ferdinand. There are no certainties about the future, because no one has been there yet.
im Siverly, July 23, 2025 at 2:45 pm
Completely right…
Ff_incr eventually can be added each year to make it even more realistic…
and the increase in inflow each year is in ratio to the increase in the atmosphere, but plays no role in our calculations, which is based on the net outflow.
Dr. Ed
July 23, 2025 at 2:30 pm
Thanks for hosting this educational debate. So often do new concepts get introduced that I never realized would apply to this discussion.
I have trouble with this statement, “Because human and natural carbon atoms follow the same flow rules and have the same Te’s, their equilibrium percentages are equal.”
First, there will never be equilibrium as long as inflows and outflows continue to evolve.
Second, why is it necessary for percentages to be equal, even if some type of pseudo equilibrium could be defined? Take a simple reversible chemical reaction. At equilibrium, it would be some coincidence if the percentage of the product turned out the same as the reactant. I’m pretty sure you meant something different than what you wrote.
It’s clear to me that choice of models cause the main disagreement of the two camps participating in this discussion. Your model is linear. Maybe that’s implied by the Partition Principle. That’s a new concept for me to review.
Ferdinand and others use non-linear models. What makes them non-linear is assuming a constant atmosphere concentration in the past as what determines the rate of mass transfer. For example, one model says,
Outflow = (pCO2now – pCO2then) / Tau or ==> 2.8 ppm/year = (420 ppm – 280 ppm) / 50 years.
Linear models use mass transfer proportional to absolute concentration. Those model’s solutions require solving differential equations, not simple math.
Jim,
Let me build on the little model you suggested. (You understand that the numbers I use are nominal only.) That model was:
10 Pg/yr human emissions (measured)
4.5 Pg/yr atmospheric accumulation (measured)
5.5 Pg/yr net global uptake (deduced)
200 Pg/yr natural emission (guesstimated)
205.5 Pg/yr natural absorption of ALL carbon types (deduced from guesstimate)
Thus 200 Pg/yr of carbon is counter-flowing in both directions and COMPLETELY BALANCED. The only imbalance between natural inflow to the atmosphere from land/sea reservoirs and outflow from the atmosphere to land/sea reservoirs is the 5.5 Pg/yr “net global uptake” that mitigates the rise is atmospheric carbon and increases the land/sea reservoir levels. The 200 Pg/yr balanced flow does NOTHING to the levels in the atmosphere or land/sea reservoirs. But it is 20x bigger than human emissions and it does do something. It mixes the atmospheric carbon with the land/sea carbon. Anthropogenic emissions into the atmosphere mean “human carbon” concentrations are higher there than in the land/sea reservoirs. So the mixing moves “human carbon” from the atmosphere to the land/sea reservoirs. While these balanced mixing flows move exactly zero net carbon, they change the composition of the atmosphere by reducing the “human carbon” therein.
The positive net global uptake tells you where the atmospheric CO2 rise is coming from: us. The mixing (which you will recognize either as a “disequilibrium isotope flux”, or what I have been calling the mechanism that dilutes the Seuss effect) hides the evidence that we are responsible. Balanced exchanges just scramble the atmospheric carbon composition without changing the overall carbon levels. The net flow of “human carbon” out of the atmosphere does not correspond to a net flow of carbon. That is why hardly anyone besides Ed bothers to track “human carbon”. Its concentration in the present amosphere does not tell you what Ed thinks it tells you.
Ed,
Your proclamations, which appeal only to the authority of yourself, are just plain silly.
“All calculations made without this [human/natural] separation are fundamentally wrong.” This is nonsense. You are certainly free to do the calculation your way. The 99% of scientists who didn’t do it your way are still correct and gained insights that you missed. In particular you missed the “mass balance” (carbon conservation) argument. Physicists appreciate analyses that use conservation laws, whose elegant simplicity can sometimes appear “Magical”.
“Because human and natural carbon atoms follow the same flow rules and have the same Te’s, their equilibrium percentages are equal.” (?) I don’t think this is what you meant to say, but I have no idea what you did mean to say.
“All calculations so far presented by the CO2 Coalition representatives are wrong because they have not properly formulated their carbon cycles.” The total carbon cycle envisioned in invoking carbon conservation is well formulated. There is no need for a lot of detail. Inputs of carbon to the atmosphere come from human and natural emissions, with the human emissions adding long sequestered carbon to the fast cycle. Natural processes remove carbon from the atmosphere and put it in land/sea reservoirs without any bias on the source of that carbon. Human processes that remove carbon of any type from the atmosphere are negligible. You know the consequences of this simple formulation.
Jim Siverly July 23, 2025 at 4:20 pm
Dear Jim,
IPCC’s model has four main carbon reservoirs. Such a model will have an equilibrium if no new carbon is added to any reservoir. Equilibrium has constant levels and constant outflows. At equilibrium, the carbon will be distributed among the reservoirs with certain percentages.
Human carbon will try to move to these same percentages. If the inflow of human carbon stopped, the human carbon cycle will flow to these same percentages. Then the levels will be constant.
Imagine four ponds connected by tubes. Pour water into one pond and the water will flow to the other ponds until the system is at equilibrium.
IPCC defined its natural carbon cycle at equilibrium, with atmospheric CO2 at about 280 ppm. These flows and levels let us calculate the six Te for this model. Once we know these Te, we can calculate how human carbon flows through the carbon cycle. Human and natural carbon will have the same Te because their carbon atoms are identical.
This model may not apply to chemical reactions. However, I do know that pharmacological models follow the same model that I use
My equation (2) makes my model linear. Outflow is proportional to the first power of the level. Double the level and we double the outflow.
The Climate Partition Principle is an addition to the above description. It means that we must do our carbon cycle calculations by putting natural carbon in one partition and human carbon in another partition, and carbon does not flow between these partitions.
Just for completeness to all with an interest, excluding the argumentative one. Although this will be treated with the usual distain, denial ignorance wrapped up in another specious waffle argument.
Carbon Isotope Ratio Formula 17Jun25 https://www.researchgate.net/publication/392822758_Carbon_Isotope_Ratio_Formula_17Jun25
Further at Page 767-2, https://www.researchgate.net/post/The_physical_processes_of_global_warming_and_climate_change–How_can_alternative_viewpoints_be_resolved/767
Philip Mulholland explains how NOAA measured -10‰ δ¹³C CO2 in the oceans.
DMA, July 23, 2025 at 10:25 am
In addition to what I have already said about Munshi’s work:
Munshi only looked at the difference between the variability one independent variable (FF emissions) with the dependent variable (CO2 increase in the atmosphere).
In the real world, there are two independent variables which influence the CO2 increase in the atmosphere: FF emissions and temperature, the latter can be huge over long periods like ice ages.
As there is a huge (mostly) short-time correlation between temperature variability and CO2 rate of change variability in the atmosphere, all what Munshi did prove is that there is no correlation between FF emissions and temperature…
Brendan Godwin, July 23, 2025 at 9:24 pm
“These two groups are separated by δ13C values of -8.7 0/00 (Air) and -10 0/00 (Ocean) measured for atmospheric and oceanic mobile carbon dioxide gas respectively.”
Mulholland uses following link of NOAA for the -10 per mil for CO2 from the oceans:
https://gml.noaa.gov/outreach/isotopes/mixing.html
That doesn’t contain any direct measurements of CO2 in the ocean waters, but it is known from physics that at the water-air border (and reverse) the heavier isotopes escape slower from one medium to the other medium, which makes that there is a discrimination of about -10 per mil δ13C for CO2 going from the oceans to the atmosphere and about -2 per mil δ13C in opposite direction. Or in average -8 per mil if both flows are in equilibrium.
See: https://scope.dge.carnegiescience.edu/SCOPE_16/SCOPE_16_1.5.05_Siegenthaler_249-257.pdf
“Now the fractionation factors can be computed numerically from eqs. (2):
α(as) = 0.9984= 1 – 1.6‰
α(sa) = 0.9905= 1 – 9.5‰”
I can’t make much of the second link as that discussion is mainly about the influence of the sun on climate, not the topic here.
And I see that you are a Postma believer. Maybe of interest for you:
https://climateofsophistry.com/2023/01/31/ferdinand-engelbeen-another-zeta-5th-columnist/
And that second link does contain some very good advise:
“It is also surprising how emotional this subject has become for many people. Pejorative name-calling and labeling abound within many internet forums. Please — such things are not welcome here. Pejorative language is not conducive to successfully resolving alternative viewpoints.”
Maybe Brendan can learn something of that advise?
Dr. Ed, July 23, 2025 at 2:30 pm
“This separation is necessary to correctly calculate the human carbon cycle and thus the effect of human carbon atoms on the CO2 level as distinct from the effect of natural carbon atoms on the CO2 level.
All calculations made without this separation are fundamentally wrong.”
Sorry, but here we do completely disagree. There is no fundamental difference in any way between human induced and natural CO2 in any process where amounts, pressure or temperature are involved. Only a small (!) differentiation in isotopic composition for biological processes and at physical borders.
Once human FF emissions are supplied to the atmosphere, in all following processes of mass transfer they behave in exact the same way as natural emissions, thus there is not the slightest need to separate them in “natural” and exact the same “human” parts. That “separation” can be theoretically done, but is only of academic interest and makes everything more complicated without purpose.
“Human and natural carbon cycles have their own equilibriums, which represent the maximum entropy for the number of carbon atoms in each partition. ”
This sentence doesn’t make any sense.
The equilibrium level must be exactly the same, or you violate the equivalence principle. In the following texts, you do confirm that principle.
“All calculations so far presented by the CO2 Coalition representatives are wrong because they have not properly formulated their carbon cycles.”
We didn’t use any carbon cycle in our work, as that was not necessary for the overall calculations of the carbon mass balance, the O2 balance, the 13C/12C balance and the 14C balance: we only used the differences between ins and outs, as what goes in must remain in the atmosphere or go out. No matter the source or height of what goes in and or where it goes.
How much carbon cycles between the different compartments is not of the slightest interest for the changes in the atmosphere or any other reservoir: only the difference between ins and outs is what changes the carbon mass in a reservoir and that is quite exactly known for the atmosphere from atmospheric and FF emission data. That shows that more FF CO2 is coming in than as difference is going out as net sink and that difference is exactly known, but of no interest where that goes or how it is partitioned between oceans and vegetation.
Our approach matches the carbon mass balance and doesn’t violate any observation. Your calculations violate the carbon mass balance, as the calculated increase in the atmosphere is much smaller than observed and the main reservoirs that should supply the extra “natural” CO2 also increased in carbon, while they should have decreased…
Ferdinand Engelbeen July 24, 2025 at 2:42 am
Dear Ferdinand,
Thank you again for your comments. It is clear that we disagree on the fundantals of physics.
You have made your points clear. There is no more to discuss. I appreciate your participation in this debate.
I trust that you feel like you have had the opportunity to freely make your points.
Ed
David Andrews July 23, 2025 at 8:35 pm
It is surprising that you taught Thermodynamics and yet you have no appreciation of how and when to use the Partition Principle.
Ferdinand,
It isn’t about agreeing or disagreeing. The math isn’t on your side.
David Andrews,
I thought it was 97% of scientists. Is it now 99% of scientists? You chastise Dr. Ed for appealing to his authority, but then you invoke the authority of the 99%. The problem is that Dr. Ed is correct, and your 99% are wrong. You and your 99% haven’t made one salient point.
Jim,
Dr. Ed is stating that the human carbon cycle is independent of the natural carbon cycle. Human carbon cycle doesn’t affect the natural carbon cycle and vise versa. Nature treats them both the same. I think the Partition Principle is another way of looking at the Equivalence Principle. We would not be here if nature didn’t conform to those two Principles.
David,
Yes, humans are adding about 5PgC to the atmosphere every year, but that causes only about 20PgC of the total carbon in the atmosphere. We’ve shown you the solution to the continuity equation. I think you stopped being a scientist a long time ago and became a politician. I think many of your 99% fit that bill.
Brendan Godwin, July 23, 2025 at 9:24 pm
I have looked at the references in Philip Mulholland’s work: NOAA did only say in that reference that the CO2 out of the oceans (not IN the ocean waters!) is at -10‰ δ¹³C.
That indeed is the case: with an average near zero δ¹³C in the ocean waters, at the water – air border, the lighter (and faster) 12CO2 escapes faster than 13CO2, which gives a change of -10‰ δ¹³C between CO2 in the water and CO2 in the atmosphere. The same happens in opposite direction with a difference of -2‰ δ¹³C, thus leaving +2‰ δ¹³C behind in the atmosphere. Average -8‰ δ¹³C, if the flows are equal.
Calculated here:
https://scope.dge.carnegiescience.edu/SCOPE_16/SCOPE_16_1.5.05_Siegenthaler_249-257.pdf
From the abstract:
“Isotopic fractionation factors for the CO2 transfer between atmosphere and ocean are calculated, taking into account equilibrium and kinetic fractionation. Diffusion of CO2 into the water, which is rate limiting for mean oceanic conditions, fractionates the carbon isotopes only little. 13C/12C fractionations are found to be -1.8 to – 2.3‰ for atmosphere-to-ocean transfer, and -9.7 to -10.2‰ for ocean-to-atmosphere transfer.”
Stephen P Anderson, July 24, 2025 at 7:10 am
Stephen, even the nicest math and fancy formula’s fail on simple facts like adding 10 PgC/year to the atmosphere and looking at the result, which only shows a 5 PgC/year increase, that proves that the 10 PgC/year is the cause of the 5 PgC/year…
Dr. Ed, July 24, 2025 at 4:40 am
Indeed we are at the point to agree that we disagree on the fundamentals of this discussion like the carbon mass balance.
As I have a lot of other problems to solve for the moment and need to prepare for a (similar!) debate in Oslo, I stop here with my reactions, but still are working on the “split” CO2 flows…
Thank you indeed for your hospitality, which indeed is quite rare nowadays…
Ferdinand Engelbeen
July 23, 2025 at 1:26 am
FE says “If he had looked at e.g. 5 year intervals (or 5 year moving averages), he would have seen that the effect just fades away and only leaves a very small trend for temperature.”
The Munshi paper cited above says:
A rationale for the inability to relate changes in atmospheric CO2 to fossil fuel emissions is described by Geologist James Edward Kamis in terms of natural geological emissions due to plate tectonics [LINK] and by Viv Forbes in terms of the natural Henry’s Law equilibrium with much larger store of CO2 in the ocean [LINK] . The essential argument is that, in the context of much larger natural flows of carbon dioxide and other carbon based compounds, it requires circular reasoning to describe changes in atmospheric CO2 only in terms of fossil fuel emissions. It is shown in a related post, that in the context of large uncertainties in carbon cycle flows, it is not possible to detect the presence of fossil fuel emissions without the help of circular reasoning [LINK] .
Carbon cycle flows cannot be directly measured and they must therefore be inferred. These inferred carbon cycle flows contain large uncertainties. The essence of this argument is that the in climate science mass balance of the carbon cycle with and without fossil fuel emissions, the declared uncertainties in carbon cycle flows are ignored. In the related post cited above [LINK] it is shown that when the declared uncertainties are taken into account, the much smaller fossil fuel emissions cannot be detected net of uncertainties in the much larger carbon cycle flows because the carbon cycle balances with and without fossil fuel emissions within its uncertainty bounds.
I believe these quotes and others in Munshi paper address the criticism you mentioned. Do you have an answer to Munshi’s claim or a refutation of his work? I just can’t see how if FF emissions are the cause of ALL of the increase there is not a correlation id the detrended data.
FE
I apologize for this last post. I think you have addressed it above but none of todays comments came into my view until I posted it.
DMA, Brendan, Ed, Stephen, etc.
I don’t think I can do better than my explanation to Jim (on 7/23 at 8:16pm) on why the low level of “human carbon” in the present atmosphere does not tell us human emissions are unimportant. Indeed, the explanation is somewhat more subtle than the other one you are all unable to understand: that a positive net global uptake unambiguously means we, not nature, are the source of the CO2 rise.
So I will move on. Your inability to understand is your problem, not mine.
DMA, July 24, 2025 at 1:25 pm
No problem at all. I think there is some delay if one doesn’t use the refresh button (Ctrl+F5) and only sees the changes after a restart and there is a delay for (too long?) replies which need moderation…
As a final comment, the main point of disagreement:
There is no fundamental difference between our and Dr. Ed’s ideas of the fundamental physics involved.
The main difference is at the process side:
Dr. Ed assumes that all outputs of all reservoirs involved are directly proportional to the CO2 levels/pressures in the different reservoirs. Therefore one can use output = level / Te where Te = RT, the turnover/residence time.
In that case, the small extra input from fossil fuels use has little influence on the CO2 level in the atmosphere.
We assume that the largest parts of the outputs are not proportional to the CO2 levels/pressures in the different reservoirs, but depend mainly of temperature, sunlight and biological processes, both for the outputs as for the inputs, which makes that a large part of the outflows of the atmosphere into other reservoirs are simply recycled in reverse and have little influence on the CO2 level/pressure in the atmosphere.
In that case, the small extra input from fossil fuel use is the main driver for the increase of the CO2 level in the atmosphere.
The correlation coefficients between atmospheric CO2 and climate (and atmospheric CO2 change and climate change) demonstrate these factors are uncorrelated over the most recent 550 million years of evidence.
550 million year correlation coefficient (CO2 and climate): 0.29
550 million year correlation coefficient (CO2 change and climate change): 0.10
No correlation means causation is impossible!
Therefore, changing CO2 cannot be the cause of climate change.
Fact: Oceans are the greatest storehouse of carbon dioxide on the planet.
Science: A warming global climate will raise ocean temperatures which, as a consequence, will outgas relatively more CO2 to the atmosphere, thus climate change CAN cause increasing atmospheric CO2.
Q.E.D.
End of story.
Bob,
End of story? I don’t think so. If ocean outgassing was dominant, CO2 atmospheric accumulation rates would exceed human emission rates. They don’t. Measured carbon levels in the ocean are increasing; that is a probem if you think oceans are a net source rather than a sink. Higher atmospheric carbon levels push carbon INTO the oceans, especially in the cooler polar regions.
Ferdinand Engelbeen
July 25, 2025 at 12:27 am
“There is no fundamental difference between our and Dr. Ed’s ideas of the fundamental physics involved.” And “We assume that the largest parts of the outputs are not proportional to the CO2 levels/pressures in the different reservoirs.…”
Those statement are hugely contradictory. However, the disagreement between your camp and Dr. Ed’s will go on ad infinitum I’m afraid. That is sad, because it’s not an either-or situation. There is only one set of true physical principles at play. One cannot pick and choose what “processes” one wants to use to make the data fit to one’s idea of reality.
I’m on dropbox again and I finished working on back calculating your model, Dr. Roy Spencer’s, and my spreadsheet based on Spencer’s model. I added the natural emissions missing from the former two models. Spencer’s model back calculates perfectly. Your model seems to have a bug, because I expected it to back calculate ok, as well, but it didn’t. Maybe you can explain my error.
https://www.dropbox.com/scl/fi/hckovmziez0g1rpzvu97c/Jim_fluxes.xlsx?rlkey=jxl8bnq5tpwd9wt3r32rqy7d5&dl=0
My spreadsheet was modified from my original upgrade of Spencer’s. I used the Mauna Loa data to back calculate the 1959-2018 years using the formula NEn = Cn – Cn-1 * ( 1 – 1/Te ) – HEn where NE and HE are natural and human emissions, respectively. Astute observers will notice that as a form of Magic Math:
D = Eh + En – Sn.
From 1750 to 1958, I used my original estimate of exponentially increasing natural emissions. That was simply a process of extrapolating the fit to Mauna Loa data assuming there was a constant e-time (or residence, turnover, etc.). Because the Mauna Loa data is confined to a relatively narrow time interval, the extrapolation can be made to end at 280 +/- ? ppm without deviating much from a best fit. I also used a best fit to the Mauna Loa values to do the back calculation for the 1959 – 2018 years.
The takeaway from this exercise is to notice both the Spencer model and my model fit the data. Therefore, the question is, which model most likely represents a physical realistic process? It makes no sense to me that the net amount of carbon sinked annually is proportional to the difference between what the pCO2 is now versus what is was in 1750. That’s what the Spencer model says and does. My model says the amount sinked is proportional to the current atmosphere content. Period. That is standard physics and a fundamentally different concept than the one Spencer’s model is based on.
You can play around with different scenarios of net zero, net natural or various increasing amounts of both in future years. More data from 2018 on can be added as a check on how well my model performs.
David Andrews
July 23, 2025 at 8:16 pm
Your description of the human flow supplementing a constant inflow of natural carbon seems like a good first-glance explanation of what’s going on. Magic Math confirms it. Here’s the problem. Look at Ferdinand’s “Jim’s fluxes” spreadsheet that I amended and linked to below. In Spencer’s model, I tabulated the Te values for the whole period 1750 to 2018. Those values gradually increase from 3.14 years to about 4.3 years. What physical processes were changing during the past three centuries that would cause residence time to increase that much?
You wrote, “The net flow of ‘human carbon’ out of the atmosphere does not correspond to a net flow of carbon.” What does that mean and what difference does it make, even if you could support it with some model more explanatory than simple math?
I showed how increasing natural emissions supplement FF emissions and enable correlating the Mauna Loa data with a physically realistic constant e-time. I proposed various sources for where the extra carbon comes from. Now where is your evidence that there is no extra carbon and natural emissions have remained the same for centuries?
David Andrews
July 25, 2025 at 8:55 am
You never stop do you.
“Measured carbon levels in the ocean are increasing”
Why because you have cherry picked MLO data showing that. One location is not the world. MLO is surrounded by volcanoes that are constantly spewing CO2 into the oceans.
CO2 in the oceans at Grays Reef is falling.
https://www.pmel.noaa.gov/co2/story/Grays+Reef
Jim,
None of my arguments have been about time constants, and you give me no reason to start looking at them now. Getting them right is important, but they have no bearing on the question of where the atmospheric carbon rise is coming from. They are a distraction.
Carbon conservation plus data on human emissions and atmospheric accumulation tell us WITHOUT DOUBT that natural processes are removing carbon from, not adding it to, the atmosphere. You thought you saw a loophole in that argument but have failed to identify it. All you have been able to do is to reproduce Ed’s (and Hans Suess’s, Skrable’s, mainstream science’s, and my own) conclusion that what Ed calls “human carbon” is but a minor component of the carbon in the present atmosphere. That by no means implies that human emissions are but a minor contributor to atmospheric carbon rise. That is Ed’s biggest conceptual error, and you seem to be all-in with it.
I don’t think I need to again go through the arithmetic of my 7/23 post. My statement “The net flow of ‘human carbon’ out of the atmosphere does not correspond to a net flow of carbon” should be self-explanatory. In my analysis I separated the natural exchanges between atmosphere and land/sea reservoirs into the (unbalanced) net global uptake component removing carbon from the atmosphere, and the remaining EXACTLY BALANCED exchanges that homogenize the carbon composition of the various reservoirs but don’t affect AT ALL the total carbon levels in any of them. Why does that matter you ask? The simple “net global uptake” analysis shows that human emissions are responsible for the increase. The mixing represented by exactly balanced exchanges (aka “disequilibrium isotope flues, aka as “Seuss effect dilation mechanism”) changed the composition of the reservoirs without changing levels and fooled you, Ed, and Skarble into naively thinking that “human carbon fraction in the present atmosphere” equals “human contribution to the atmospheric CO2 rise.”
Nowhere in the above is there any need to invoke “extra carbon” or changes in natural emissions over the past few centuries. I don’t need to respond to whatever fudge-factors your undocumented model requires to agree with Mauna Loa data.
What do you find difficult about the consensus view? I could say that it wins by Occam’s razor, but the case is much stronger than that. But I know that the notion of “consensus” is red meat to those who have declared themselves to be on Ed’s side.
Jim Siverly, July 25, 2025 at 10:54 am
Jim, the essence in this case is in the model, in that sense that Ed (and you and many others) assume that all outflows are only CO2 level/quantity/pressure dependent in the different reservoirs.
That is a fundamental error, as at least half of the total yearly outflow, the one into vegetation, is near completely independent of the actual CO2 level/pressure in the atmosphere.
Only depends of temperature and sunlight. Even so much, that it goes from minimum to maximum within a few months, sucks so much CO2 out of the atmosphere, that the CO2 level in the atmosphere drops, despite the opposite extra supply of CO2 from the warming oceans.
Of the (1750, natural) 108 PgC and (2000, human caused extra) 14 PgC that all bio-life releases over a year, mainly in fall and winter, only 2 PgC is stored in more permanent vegetation and soils. The net difference, which is the result of the 240 PgC (human caused) increase in the atmosphere thus only caused a very meager 2 PgC extra uptake by the total biosphere…
That makes that your back-calculation, which is based on the absolute CO2 pressure in the atmosphere is completely at odds with the real world.
In both my and Spencer’s series, you use a fixed in/decrease of CO2 based on the original level of 628 PgC and the calculated 50 years adjustment time.
The real net removal rate of some extra CO2 above the 628 level is in ratio to the difference between the actual CO2 level and the original equilibrium, which makes that in back-calculation the removal rate reduces to zero when the 628 PgC is asymptotically reached again.
Brendan Godwin, July 25, 2025 at 6:27 pm
Congratulations Brendan. You were able to find a negative (?) trend of the pCO2 in seawater within corals which show a seasonal change in pCO2 of the oceans between 250 and 750 μatm.
Can you show me how large that trend is?
It’s time the waffleator packed his bags for Oslo and spread his propaganda to a different audience. He said:
July 24, 2025 at 9:02 am
As I have a lot of other problems to solve for the moment and need to prepare for a (similar!) debate in Oslo, I stop here with my reactions
And
July 25, 2025 at 12:27 am
As a final comment
Yet here is he still waffling on. He just can’t help himself.
Brendan Godwin, July 26, 2025 at 4:41 am
If I have five minutes time in between the preparations for Oslo, it always is a joy to tease Brendan to see how he reacts…
BTW, what is the trend in ocean pCO2 in these Greys Reef? I didn’t find any trend data, only a lot of extreme (seasonal) noise…
Ferdinand Engelbeen
July 26, 2025 at 2:03 am
You claim assuming “that all outflows are only CO2 level/quantity/pressure dependent in the different reservoirs…is a fundamental error, as at least half of the total yearly outflow, the one into vegetation, is near completely independent of the actual CO2 level/pressure in the atmosphere.”
This contradicts CO2 Coalition’s own anecdotal evidence of four trees growing faster as a function of CO2. I say anecdotal, because you will claim it is the difference in CO2 today than 280 ppm then. But you would only be an assertion without scientific experimental evidence.
AI says, “Photosynthesis rate is the speed at which plants convert light energy into chemical energy, typically measured by the rate of carbon dioxide uptake or oxygen release. Factors like light intensity, carbon dioxide concentration, and temperature significantly influence this rate.”
Notice that it doesn’t say, “factors like carbon dioxide concentration difference between now and preindustrial time.” Plants don’t know what CO2 was centuries ago. If you want to make a convincing argument, then do or show an experiment that shows vegetation growth more proportional to the concentration difference than to the absolute CO2 concentration.
“[My gobbledygook] makes your back-calculation, which is based on the absolute CO2 pressure in the atmosphere, completely at odds with the real world.”
That speaks for itself, no further comment needed.
Dr. Spencer’s model, while applying the same physically wrong science you use, back calculates perfectly in the same manner as his forward calculation does. He used what you mistakenly call the “real net removal rate.” You have never shown how the difference between the actual CO2 level and the original equilibrium is the true rate determining mechanism. Other than the climate community, no other scientific community agrees with you. Examples to the contrary are welcome.
I wish you all the best in Oslo.
David Andrews
July 25, 2025 at 7:58 pm
In an earlier note to Ferdinand I said “I’m working on a way to demonstrate how the simple math you and David Andrews rely on can give ambiguous results based on somewhat arbitrary choices of variables.”
You responded July 8, 2025 at 7:44 pm with, “You seem to have been distracted from that goal or maybe have given up. My goal here is to keep you focused on it.”
Well, I put up the spreadsheets comparing Ferdinand and Spencer’s simple math models with my model demonstrating that one can arrive at the same results using different variables, i.e., removal rate constants and emission inputs.
Now you are saying I gave you no reason to look at time constants, “they are a distraction.” I really should stop beating my head against the wall, eh? [a reference to an old Bazooka Joe Gum joke]
You claim, “The net flow of ‘human carbon’ out of the atmosphere does not correspond to a net flow of carbon” should be self-explanatory. I’m sorry, but that seems like a denial of the equivalence principle.
Moving on, I’ll try to follow your logic. You categorize (separate) natural exchanges between atmosphere and land/sea reservoirs into two situations, (1) the preindustrial case where EXACTLY BALANCED exchanges homogenize the carbon composition of the various reservoirs without affecting AT ALL the total carbon levels in any of them, and (2) the present case where human emissions cause unbalanced exchanges resulting in net global uptake removing carbon from the atmosphere. Then you conclude, “[this] simple ‘net global uptake’ analysis shows that human emissions are responsible for the increase.” Voila!
That model is Magic Math, because it assumes no change in carbon levels, despite evidence to the contrary, and applies non-standard physical principles. My model needs to invoke “extra carbon” and changes in natural emissions to explain the known data and remain consistent with standard physical principles. Fortunately, the potential for finding evidence of extra carbon exists. Where is your evidence that carbon levels haven’t increased and how would you explain any evidence they have?
Jim Siverly, July 26, 2025 at 9:03 am
One need to make a differentiation between the seasonal and longer term fluxes between the atmosphere and the biosphere.
If the CO2 level in the atmosphere instantly doubles, the output in the biosphere hardly increases and needs decades to catch up with the extra CO2 in the atmosphere and even then doesn’t double.
With 50% extra in the atmosphere over the past 175 years, the increase of the fast cycle (thus the amount of extra living vegetation) only increased with 13%, that is all and only 25% of the extra FF of each year emitted in the atmosphere is absorbed into more permanent vegetation and soils as extra mass for longer periods.
“Dr. Spencer’s model, while applying the same physically wrong science you use, back calculates perfectly in the same manner as his forward calculation does.”
My calculations match these of Spencer within 1 PgC when you shift the 20 years start to 2022. It is your faulty interpretation that gets wrong, both in the future as in the past…
“Plants don’t know what CO2 was centuries ago.”
Plants adapt to temperature and the amount of CO2 that is in the atmosphere: when temperature and the CO2 level increased from an ice age to an interglacial, from about 190 to 290 ppmv, plant and animal life did expand and reversed when a new ice age arrived. Thus vegetation did “remember” its original CO2 level…
If one would stop all FF emissions, then the world will stop “greening” and instead will start “browning”, as the CO2 levels drop to the original atmospheric CO2 levels of around 280-300 ppmv which is the equilibrium with the ocean surface today. As they did over ice ages and interglacials: there is zero impact of plant life on the δ13C level over 800,000 years, while the CO2 levels increased and decreased with 90 ppmv, completely dominated by the slow changes in ocean surface temperatures and related pCO2.
“Other than the climate community, no other scientific community agrees with you.”
Dietze, already in 1997 and heavily against the IPCC’s Bern model, Spencer, Lindzen, and many others all use the same “real removal rate”, based on the difference in pCO2 between the two main reservoirs: atmosphere and oceans. The latter dominates the CO2 level in the atmosphere, except when humans add more CO2 than oceans and biosphere can remove.
As far as I know, that are not members of the “climate community”.
David Andrews
At July 25, 2025 at 6:27 pm I replied to your comment at July 25, 2025 at 8:55 am re: “Measured carbon levels in the ocean are increasing”. You failed to reply. Instead you let the waffleator respond for you. You did the same the previous time as well. You obviously don’t have the intellectual capacity or knowledge to reply on your own.
David Andrews.
At JULY 25, 2025 AT 7:58 PM you yet again cited a reference to consensus. Anyone who cedes to consensus as a reference is not a scientist.
On JULY 14, 2025 AT 5:43 PM you attacked Murry Salby’s science by reference to his employment. Whoever does this is not a scientist.
You continually taint your comments with these anti-science political statements. All this does is prove that you are not a scientist but a political activist. This renders your comments worthless. To be taken with a grain of salt. You are not in this discussion to find a scientific pathway to the truth, you are here to push your political agenda.
Brendan Godwin July 26, 2025 at 7:59 pm
Dear Brendan,
Well put. I agree with you.
Ed
Ferdinand Engelbeen
July 26, 2025 at 12:45 pm
No, one doesn’t need to do any differentiation with my model. I will make two modifications to it with 1) 50% pulse and 2) net zero with a continuing gradual natural emission increase. You can freeze the natural emissions at any point. In all cases, CO2 will return to a new equilibrium level according to a four-year e-time.
1) https://www.dropbox.com/scl/fi/g6zj3et0vs3o9pfk0jzim/Jim_fluxes1.xlsx?rlkey=kz95m7zhp7ohflh209x84niuy&dl=0
2) https://www.dropbox.com/scl/fi/603gxxzkdk3l5mw43slxo/Jim_fluxes2.xlsx?rlkey=b23hjfhdhpakttqeemy5wjtbc&dl=0
“…from about 190 to 290 ppmv, plant and animal life did expand and reversed when a new ice age arrived. Thus vegetation did “remember” its original CO2 level…”
That is speculation based on anecdotal data completely devoid of proof, Ferdinand.
Roy Spencer is the climatologist who publishes the monthly UAH temperatures chart. Richard Lindzen has been called “an expert on climate change for four decades.” In no way can they be considered outside the climate science community.
The reference to Peter Dietz is quite interesting. I previously ignored it (to my great regret), because I considered it an appeal to authority from another one of the 50-year Tau, not 4-year Te, proponents. I reviewed about a third of the discussions with fellow IPCC contributors Dietz documented in his open review comments relating to his Carbon Model Calculations paper. I will finish reading those comments before providing a more detailed analysis. Suffice for now to say Dietz assumes removal is proportional to the difference between pCO2 now and 280 ppm, the preindustrial pCO2, without any confirming evidence that it is based on sound physics. The 50-year Tau, 55-year in Dietz’s case, is based on the pCO2 now – 280 ppm difference. [(408-280)/50 = 2.56 ppm/year, the approximate average removal rate in 2018] That makes it a circular reasoning argument. The same one you make.
You referenced Dietz over a dozen times here. Many of those times Dr. Ed noted the circular reasoning. I tried asking about A B reactions hoping you would see the relevance to the rates being proportional to actual concentrations, not differences between now and some original level. The Feely equation is proportional to delta pCO2, meaning d(pCO2)/dt – k * dCO2aq/dt now, not a preindustrial difference. If you continue to promote the 50-year Tau, you really should come up with some scientific evidence of the underlying physics.
Jim,
Thanks for your excel work. Excellent. I guess David and Ferdinand can keep arguing but math is hard to argue with.
Ferdinand Engelbeen July 25, 2025 at 12:27 am
Dear Ferdinand,
You wrote:
So, if I understand you correctly, you are saying that these extra processes increase, not decrease, the flows between the reservoirs compared to my (2) which says Outflow = Level / Te.
If so, then you are simply arguing that the real Te are smaller than the Te I derived from IPCC’s own data. And it in that case, we agree.
That is because Delta14C data show the IPCC Te are too large because they would have reduced the balance level of Delta14C to near -300. (Ignore David Andrews’ objection to this because he is irrational.)
Your argument that these extra processes increase the flow argues for smaller Te to explain the Delta14C data.
This blows your argument that your Tau is 50 years or more.
Jim Siverly July 26, 2025 at 12:45 pm and July 26, 2025 at 11:57 pm
Dear Jim,
Thank you for your excellent Excel calculations.
I have one question that maybe indicates I do not follow your use of “back calculations.”
That is because we cannot start with any distribution of carbon among the carbon reservoirs and from that determine what a prior distribution may have been.
This is because the carbon flows between the reservoirs always move the carbon distribution closer to their equilibrium percentages. Since all distributions flow toward their equilibrium distributions, it is impossible to determine a prior distribution.
Or perhaps I misunderstand what you mean by back calculations.
Jim,
I advised you to understand disequilibrium isotope fluxes a few weeks ago. You flunked that assignment. I see you also have borrowed one of Ed’s favorite tricks. When you don’t have an answer to an argument, misrepresent that argument and argue against the misrepresentation. The balanced exchanges I am talking about have nothing to do with pre-industrial times and you know that. I fear you are purposely wasting my time, but I will give it another shot.
Remember: Natural Absorption(NA) = Natural Emissions(NE) + Net Global Uptake (NGU) by simple math, and NGU has been positive over the last century by data and carbon conservation. From the nominal numbers we have been using, NGU is only 2-3% of NA. Of course NGU mitigates the atmospheric carbon rise from human emissions by removing carbon from the atmosphere and adding it to land/sea reservoirs. NGU changes carbon levels in reservoirs. But the remaining 97-98% of NA is, call it NAb, is exactly equal to NE. Three questions for you.
1. If NE = NAb, and NE is the quantity of carbon moving from land/sea reservoirs to the atmosphere, and NAb is the quantity of carbon moving from the atmosphere to land/sea reservoirs, how much do these exchanges together effect carbon levels? (You may study this question with a spreadsheet if you need to.)
2. If the atmosphere is rich in “human carbon” compared to the land/sea reservoirs because that is where smokestacks and exhaust pipes put it, do the same balanced two-way exchanges move net “human carbon” in one direction or another? Which way?
3. Does your answer to 2. “violate the equivalence principle”?
You can vary assumptions about natural emissions all you want. To match the data you must then also vary natural absorption to fit the measured NGU. Have fun beating your head against the wall with that “extra carbon”.
I don’t know why you think I assume “no change in carbon levels”. They are indeed changing because previously sequestered FF carbon is being put in the atmosphere and from there spreads to other fast-cycle reservoirs. The mass balance argument is corroborated by an observed expansion of the biosphere and carbon increases in the ocean. (Note that I avoided saying “ocean acidification”; I don’t want to wake up Brendan.)
Which of my physical principles is nonstandard in your opinion? Note that I still haven’t linked my argument to time constants, not that they are unimportant.
I have not seen your spreadsheet, but I think I know what your problem is. You think ”human carbon” leaving the atmosphere implies level changes, because you didn’t do your disequilibrium isotope flux homework. So you add extra natural emissions to match the Mauna Loa data, then you need extra natural absorption … Pretty soon you have “exponentially” increasing natural emissions and a headache
Jim Siverly, July 26, 2025 at 11:57 pm
There is an error in your calculation of my return to the equilibrium, which makes part of the problem in the back-calculation: you calculate the net outflow from the FF emissions from the previous year, while for Spencer’s calculation you use the FF emissions for the same year. Makes some difference, but still not what it should be, if you use the “real” decay rate.
In both cases, you don’t reflect what Spencer, me and others have done, as we calculated the 50 years Te/Tau from the CO2 level in the atmosphere and the net outflow as calculated from known human inputs and observed increase in the atmosphere. While you calculated the one-way outflow only for the atmosphere out, based on the (roughly observed) total outflows, not the back-flows from the other reservoirs. These are implied in your calculation as increasing together with the overall outflow, as that is the difference with the
The main difference still is that you assume a constant ratio between output flow and total amount of CO2 in the atmosphere, no matter the change in Te/Tau with the CO2 increase.
Moreover, you use some “self fulfilling” prophecy’s by calculating the “natural” inflows from I don’t know where before 1958 and calculate them from the CO2 level in the atmosphere after Mauna Loa measurements started.
How do you know these inputs? Dr. Ed uses the levels in the oceans and biosphere to calculate the inputs to the atmosphere, but you calculate them with the same turnover time…
I don’t think that many will disagree with the fact that the biosphere expanded and did shrink together with temperature and CO2 levels over the ice ages and interglacials. The point is that this had no measurable effect on the δ13C levels, until humans started to emit fossil fuel CO2:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_d13C_lgm_cur.png
That is a definitive proof that the oceans are the dominant cause of the CO2 changes in pre-industrial times.
And as you may know, the oceans at the “edges” (poles and equator) have near-constant temperatures and thus pCO2(aq), where the ocean waters sink in the deep or are upwelling and that is the dynamic “memory” for the pCO2 in the atmosphere…
“In no way can they be considered outside the climate science community.”
Come on Jim, you know as good as I know, that these are not supporting the mainstream science about the “catastrophic” GH effect. Neither do they support the hundreds or thousands years “life time” of our extra CO2 in the atmosphere from the Bern model. But they all recognize the about 50 years “adjustment” time and reject the 4 years residence time or Te as completely irrelevant for the decay rate of any extra CO2 in the atmosphere, of whatever source.
“The 50-year Tau, 55-year in Dietz’s case, is based on the pCO2 now – 280 ppm difference. [(408-280)/50 = 2.56 ppm/year, the approximate average removal rate in 2018] That makes it a circular reasoning argument. The same one you make.”
That is where you are completely mistaken. Peter Dietze indeed used the “historical” CO2 level in the atmosphere as equilibrium, but the current equilibrium was calculated from the net removal rate over different years by Spencer, myself and David Burton, because we now have the net removal rates at different CO2 levels in the atmosphere. That makes that it is easy to back-calculate the “real”, current, equilibrium level where the net removal rate is zero.
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Only the net removal rate is plotted against the CO2 level in the atmosphere, without any assumption of Te/Tau. That shows an equilibrium of between 280-300 ppmv and thus a Te/Tau of around 50 years as result. Not reverse.
Jim,
Half way you can see that my text doesn’t fit: that was when I saw that you used the output data to calculate the inputs to the atmosphere. Can you elaborate on that, where the input data to the atmosphere are based on?
David Andrews July 27, 2025 at 9:16 am
David, your so-called explanation is unnecessarily complicated, so much so that you can get pretty much any result you wish to promote.
The only way you can make a valid point is to use my equation (2) for human and natural carbon independently because they include all the flows we are talking about.
Then show how you get from these equations to your equations. We need that connection to evaluate your equations.
If you can’t do that, then you are wasting everyone’s time with pseudo-science.
Dr. Ed, July 27, 2025 at 8:26 am
“So, if I understand you correctly, you are saying that these extra processes increase, not decrease, the flows between the reservoirs compared to my (2) which says Outflow = Level / Te.”
Indeed the extra processes increase the flows between the different reservoirs in both directions: while the increase in the atmosphere is about 50% since 1750, the in/outflows with the oceans increased about 33% and with the biosphere about 13%. Thus not in ratio to the increase in the atmosphere.
Moreover, the absolute height of the flows is of zero interest for any changes in any reservoir, only the difference between inflows and outflows changes the CO2 mass in any reservoir.
That difference is directly proportional to the distance with the equilibrium, which for the current SST is between 280-300 ppmv, as can be back-calculated from the different CO2 levels over time and the observed net removal rate,
That makes that the calculated Te (or Tau) is around 50 years, not the 4 years of the turnover time.
The 14C and 13C/12C ratio’s are “thinned” by the return of deep ocean waters which contain relative more 13C and 14C than fossil fuel emissions. That makes the Tau of both 14C and the 13C/12C ratio are a lot shorter than for the extra 12C/13C removal out of the atmosphere.
Jim Siverly, July 26, 2025 at 11:57 pm
Some part where I didn’t react on:
“The Feely equation is proportional to delta pCO2, meaning d(pCO2)/dt – k * dCO2aq/dt now, not a preindustrial difference. If you continue to promote the 50-year Tau, you really should come up with some scientific evidence of the underlying physics.”
The Feely equation shows the different delta pCO2’s for different parts of the oceans. For 90% of the sea surface, that difference only leads to a very small uptake by the ocean surface layer of about 10% of the increase in the atmosphere. That is because of physical and chemical restrictions in uptake. That is known as the Revelle/buffer factor. And measured as increase of DIC in the ocean surface waters.
The IPCC uses the total ocean surface as limiting factor for the CO2 access to the deep oceans, with as result the long residual uptakes of part of the current increase of hundreds to thousands of years.
Far more important is where the ocean waters sink into the deep oceans.The temperature there is year-round around freezing near the floating ice, which makes that the pCO2 of the ocean waters can be as low as 150 μatm( ~ppmv). The same for the upwelling places near the equator, where year-round high SST is measured and as high as 750 μatm for pCO2(aq).
That makes that a lot of CO2 (and oxygen) is taken from the atmosphere and directly moved into the deep oceans, without the physical and chemical restrictions of the rest of the sea surface.
My own estimate, based on the “thinning” of the δ13C “fingerprint”, is around 40 PgC/year that goes directly into the deep oceans (mainly in the N.E. Atlantic) and comes back some 1,000 years later near the coast of Peru/Chile.
What does that make when CO2 increases in the atmosphere? The extra pressure will increase the output into the polar sink places and reduce the emissions at the upwelling sites. For the current pCO2 difference with the atmosphere, the estimated (to close the “gap” with atmosphere, ocean surface and vegetation) is about 20% of the human emissions as carbon mass. Again in complete ratio with the “old” equilibrium.
The carbon increase in vegetation also is calculated, based on the O2 balance since about 1990. That is about 25% of human emissions as carbon mass. Even with large year-by-year variability in uptake by vegetation, in average all three reservoirs do sink CO2 in ratio to the “old” equilibrium.
Dr. Ed
July 27, 2025 at 8:41 am
“My” idea of a back calculation is just reversing the forward calculation. Dr. Spencer’s model makes it easy because he has a simple formula Cn = Cn-1 + EHn – ( Cn-1 – C0 ) / 50 where EHn is the industrial emissions added in the current year. Notice the removal is NET removal of only 2%/year based on fitting the Cn results to the Mauna Loa data. So the 50-year figure is an artifact of the assumption that the removal process is proportional to difference between now and way back when. It never seemed right to me.
Now back to answering back-calculation question. One can solve Spencer’s simple formula for Cn-1 and get
Cn-1 = [ Cn – Ehn – C0/50 ] / ( 1 – 1/50 )
Since the Cn, EHn, and C0 are known, you just work back from there to C0 = 1750 or wherever you want to start. With my model, back calculating is only possible with the known CO2 values from 1959 on. I can estimate the natural emissions, ENn, from ENn = Cn – EHn – Cn-1 * ( 1 – 1/Te ). Before that I don’t know what Cn-1 is. That’s when I extrapolate back using exponentially-derived estimates of ENn from a fit to the Mauna Loa data. So both my model and the Spencer model fit data to a formula. But I argue my formula, dare I say your formula, makes more physical sense.
The bottom line is a back calculation is, at best, only as good as the forward one from which it is derived. While Spencer’s model is wrong, in my opinion, it is consistent. Ferdinand’s has a bug which may or may not be my error. His formula seems to be different than Spencer’s somehow.
The overall point I’m making and only one that really interests me is what the true science dictates. I’m OK being wrong, I just want to be wrong for the right reason.
“…we cannot start with any distribution of carbon among the carbon reservoirs and from that determine what a prior distribution may have been.”
I agree that we can’t know the exact past distribution. That’s why I always call my back calculation an estimate. The fact that it is based on a simple exponential function and nails the Mauna Loa data gives me confidence that the estimate is pretty darn close to accurate. I think I remember finding other ways to fit the data, but not both using constant Te and extrapolating back to around 280 in 1750.
David Andrews
July 27, 2025 at 9:16 am
“I fear you are purposely wasting my time…”
Sir, no one demands you comment here. If you feel compelled to respond, that’s on you.
Answer to 1. From year 2018, I estimate NE was 91.9 ppm and NAb was less than 89.5, therefore they were not the same. It was a typical year with natural contributing 2.5 ppm more than the year before.
2. In 2018, I estimate at least 4.5 ppm of human-sourced carbon was removed, almost as much as was emitted that year. I haven’t estimated how much human-sourced carbon returned to the atmosphere, but it’s a relatively small amount. That’s because human-sourced carbon in the ocean is diluted and the return is proportional to that diluted concentration.
3. My answer in 2 perfectly follows the equivalence principle. It’s what Dr. Ed’s article is all about.
I am pleased to find you are OK with a biosphere expansion. Your physical principles are based on Magic Math, not laws of nature. That may be why you avoid time-constants.
I think my problem is your problem accepting the consequences of biosphere expansion, because “Pretty soon you have “exponentially” increasing natural emissions.”
Ed,
Gosh, I thought the two points I have been making were pretty simple.
1. Since the atmosphere has been accumulating carbon at a rate slightly less than half the rate we have been adding it, natural proccesses must on balance have been removing carbon to the land/sea reservoirs, not adding it to the atmosphere.
2. The continual mixing between reservoirs homogenizes their content. That makes it incorrect to assume, as you do, that the small “human carbon” content of the present atmosphere implies only a small contribution to the rise from human emissions.
Which of these points do you find too complicated? You have had a few years to study them.
David Andrews July 27, 2025, at 2:34 pm
David, it is your duty show how your equations derive from my (2). Without that connection, all your claims and questions are without a foundation.
Is that too complicated for you to do?
Ferdinand Engelbeen July 27, 2025 at 11:38 am
Dear Ferdinand,
You wrote:
Your admission (1) is all that is needed. Thank you. Therefore, your model supports a shorter Te, which corresponds with the shorter Te revealed by the Delta14C data.
Your argument (2) is invalid because the Delta14C data show the Delta14C balance level was unaffected by the bomb tests, and the Delta14C balance level shows the proportion of the human carbon balance level to the natural carbon balance level.
For example, if human carbon caused all the CO2 increase, that would have lowered the Delta14C balance level to -333. Clearly, this has not happened.
The Delta14C balance level is between zero and -8. That means Te is much smaller than 4 years. This proves your Tau of 50 years is invalid.
Remember, the balance levels are determined by the present (not past) inflows of natural carbon and human carbon. There is no “replacement” argument that affects the balance level argument. Pure natural carbon has a Delta14C of zero.
Therefore, your arguments (1) and (2) converge to two simple conclusions: Te is smaller than 4 years and human carbon has a negligible effect on the level of atmospheric CO2.
Ed,
The topic is whether human emissions cause the CO2 increase, i.e, your H1. Carbon conservation and the measured positive net global uptake prove that they do.
Your C14 analysis is a joke.
David Andrews July 27, 2025 at 7:15 pm
David, you have just proved what I suspected.
You cannot connect your so-called argument with my equation (2).
Therefore, you have no argument. You are not even in the game.
You have been an imposter acting as if you knew something about this subject.
I asked you a very simple question related to the core of this discussion, which is equation (2).
This is simply physics, David.
Your unstated answer is that you don’t know how to connect your ramblings to equation (2).
Thanks for this revelation.
Ferdinand Engelbeen
July 27, 2025 at 9:25 am
Hopefully, something from my response to Ed at July 27, 2025 at 12:46 pm helps explain some of the confusion. It’s ironic that you cite self fulfilling prophecy while your whole model is based on self-fulfilling prophecy. At least I know why it is, as I’ve explained.
I’ll skip your real decay rate paragraph until I study the spreadsheet.
You claim, “you don’t reflect what Spencer, me and others have done….” I don’t understand how you can say that when I duplicated Spencer’s spreadsheet fully and exactly as he published it. I even downloaded an original version when he posted it on his website five years ago. His model is one-way outflows. If you have a problem with that, take it up with him. My model has both natural and human emission inflows, I just don’t assume a constant natural inflow as you do. I will add graphics for both our data and see which does a better job correlating Mauna Loa data.
My model doesn’t have a change in Te. Of course there’s a constant outflow/level. Nature is increasing its outflow as it strives to reach its new balance level, to put it in Dr. Ed’s vernacular.
“How do you know these inputs?” As explained to Ed, from fitting the Mauna Loa data assuming constant Te. It makes sense, because it goes to the likelihood that human activity, such as burning and growing stuff, increases CO2 output exponentially.
You may have “definitive proof that the oceans are the dominant cause of the CO2 changes in pre-industrial times,” but I don’t see how that rebuts anything I have proposed.
Not supporting not supporting the mainstream “catastrophic” science does not make one outside the climate community. Spencer complains about being boxed in on either side.
I’m not “completely mistaken.” Dietze calculated 55 years, because he didn’t have a quarter century more data that we have. But he got it the same way, a plot of CO2 versus deltaCO2 and assumed the same wrong formula you and the rest use. Again, I say wrong only happy to be shown otherwise. By the way, I have a scientific reason for assuming a constant Te: what physical processes have changed that warrant a variable Te?
Jim Siverly, July 27, 2025 at 8:19 pm
“His [Spencer’s] model is one-way outflows”
Spencer’s and many other’s and my model is about NET outflow, not one-way outflows…
“Cn = Cn-1 + EHn – ( Cn-1 – C0 ) / 50”
That is about the same formula that I used in my calculations:
La(n) = La(n-1) + Ff_start – (La(n-1) + Ff_start-La_base)/Te
I used the “In between” La(n-1) + Ff_start to calculate the net flow, Spencer used the “old” C(n-1).
Further, my calculations were asked to use a fixed 10 PgC/yr FF supply and not the real figures for Mauna Loa and the real supply.
Both Spencer’s and my approach doesn’t involve inflows or outflows at all, only net flows. Dr. Ed wanted to see what the in- and outflows do. That I did extra by looking at what the inflows and outflows could be.
So Spencer and I agree with each other. And you don’t agree:
“Notice the removal is NET removal of only 2%/year based on fitting the Cn results to the Mauna Loa data.”
Here we still agree.
“So the 50-year figure is an artifact of the assumption that the removal process is proportional to difference between now and way back when.”
Here again, we strongly disagree: The 2%/year figure is the observed (!) decay rate for every CO2 level increment in the atmosphere since Mauna Loa started its measurements. Thus not based on any past known or unknown “old” equilibrium.
“Observed” in that way that human emissions are quite accurately known from taxes on sales and burning efficiency and the increase in the atmosphere is very accurately known from measurements.
To the contrary, one can back-calculate the current equilibrium from the observed decay rates since 1958 as Spencer and many others and I and David Burton have done.
“As explained to Ed, from fitting the Mauna Loa data assuming constant Te. It makes sense, because it goes to the likelihood that human activity, such as burning and growing stuff, increases CO2 output exponentially.”
I didn’t talk about the outputs which are based on Te. I was talking about the inputs to the atmosphere, which have nothing to do with Te from the atmosphere, but with the Te from the oceans and the Te from the biosphere.
You used the Mauna Loa data to calculate the total input as a fit for the net removal of CO2 out of the atmosphere, while you don’t have any idea what the real inputs are. That is just curve fitting…
Moreover, for the mass balance: even in your calculations, the new inputs are less than the old outputs, thus nature NET removed CO2 mass out of the atmosphere, about half what humans as FF mass added in the previous year. Any bookkeeper will confirm you that the FF addition is the cause of the increase, no matter how much FF “labeled” CO2 returns to the atmosphere within the next season or next year(s).
Human activity increased the CO2 levels in the atmosphere with about 50%. The overall outputs into the oceans increased with 33% and in the biosphere with 13%. Not 50%. Thus Te, based on the 4 years La/F(out) was not constant and increased over time. The Te of 50 years, based on the NET outflow remained more or less constant.
Dr. Ed, July 27, 2025 at 7:03 pm
“Therefore, your model supports a shorter Te, which corresponds with the shorter Te revealed by the Delta14C data.”
I am not that familiar with the delta 14C data, but as far as I know the delta Te for 14C after the nuclear bomb tests is between 12 and 20 years, far beyond the 4 years Te that you use for the bulk CO2 output…
“Your argument (2) is invalid because the Delta14C data show the Delta14C balance level was unaffected by the bomb tests”
To the contrary, the 14C level before the bomb test was already affected by the zero-14C human FF supply, so that correction tables for radiocarbon dating were needed and after the bomb tests, the drop in 14C was way faster than calculated without FF emissions. In the coming decades, the 14C level will further drop to below the historical levels:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/graven_14C.png
I have done calculations on the “thinning” of the δ13C human “fingerprint” in the atmosphere and that shows that about 2/3 of the human FF CO2 input directly into the atmosphere is replaced by CO2 from other reservoirs, mainly by deep ocean exchanges. Replaced, not removed as CO2 mass. One can calculate how much deep ocean water is needed to do that replacement: about 40 PgC exchange with the 1,000 year old deep ocean waters is sufficient.
https://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg
0 PgC/year is the δ13C drop if all human FF emissions remained in the atmosphere…
And last but not least, as already explained to Jim, your Te of 4 years for the bulk CO2 in the atmosphere increased over time, because the total level of CO2 in the atmosphere increases with 50%, but the in/outflows with the oceans increased only 33% and with the biosphere only 13%…
Jim,
What you derisively call “Magic Math”, and Ed calls “too complicated”, I call “carbon conservation” and dead simple. Conservation principles are the bedrock of physics.
I looked for your spreadsheet on Ed’s site and didn’t find it, so I will continue to have to guess what you are up to. Your 7/27 9:16AM post, and talk of “extra carbon”, suggests that you are postulating a new category of carbon in addition to “human” and “natural”. (Demetris Koutsoyiannis tried the same thing. After I labeled his new category “super-natural carbon” he dropped it.) Perhaps you think some source like deep-sea volcanos is important and underestimated. Like FF, it would be an uncompensated transfer into the fast carbon cycle from a previously sequestered stock. But such a source is already included in the mass balance calculation. You might want to check your spreadsheet to see if human emissions are 2x atmospheric carbon growth as in the real world.
Your insistence that the equivalence principle does not allow balanced exchanges to move net “human carbon” from the atmosphere where it is dense to land/sea reservoirs where it is sparse is bonkers.
Ferdinand Engelbeen July 28, 2025 at 3:41 am
Dear Ferdinand,
I’m sorry but your explanation does not save your failed hypothesis.
You admit that you are not familiar with the Delta14C data. Therefore, you are not in a position to argue that it does not prove your hypothesis is wrong. You have not studied my papers and my rebuttal above to your CO2 Coalition paper.
When you understand the Delta14C level, you will see that we are not talking about the Te of Delta14C, which happens to be 16.5 years, and all your (and Dave Burton’s) calculations of this value are incorrect.
The key feature of the Delta14C data is that it proves its balance level has remained and still is less than about 8% below its historic balance level upon which all carbon dating is based.
You wrote:
“To the contrary, the 14C level before the bomb test was already affected by the zero-14C human FF supply, so that correction tables for radiocarbon dating were needed and after the bomb tests, the drop in 14C was way faster than calculated without FF emissions. In the coming decades, the 14C level will further drop to below the historical levels:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/graven_14C.png.”
Indeed, human CO2 has lowered the Delta14C balance level a small amount below its long-term balance level. No problem with that. But that supports my calculations that show human CO2 has had only as small effect on the CO2 increase above the reference level of 280 ppm.
The key is that the present Delta14C balance level DOES NOT support your claim that human CO2 is a significant cause of the CO2 increase. It shows that natural CO2 is the dominant cause of the CO2 increase. There is no way you can deny this.
You wrote:
“I have done calculations on the “thinning” of the δ13C human “fingerprint” in the atmosphere and that shows that about 2/3 of the human FF CO2 input directly into the atmosphere is replaced by CO2 from other reservoirs, mainly by deep ocean exchanges. Replaced, not removed as CO2 mass.”
Sorry, but the Delta14C proves your calculations are wrong. Your hypothesis predicts an incorrect result. Therefore, your hypothesis is wrong.
You wrote:
“And last but not least, as already explained to Jim, your Te of 4 years for the bulk CO2 in the atmosphere increased over time, because the total level of CO2 in the atmosphere increases with 50%, but the in/outflows with the oceans increased only 33% and with the biosphere only 13%…”
Sorry, but the Delta14C data prove your above conclusions are wrong.
David Andrews July 28, 2025 at 9:03 am
David,
I can’t believe you are back with more of your math-deficient, hand-waving declarations that have no connection to real physics or to the issue under discussion.
You wrote to Jim:
“What you derisively call “Magic Math”, and Ed calls “too complicated”, I call “carbon conservation” and dead simple. Conservation principles are the bedrock of physics.”
But you have not shown anywhere that you are following conservative principles.
I asked you to derive your physics and math from my equation (2), which I connect with (1) to assure carbon mass conservation. So, all my work is based on carbon mass conservation because all my equations are derived from (1).
You can make no such claim legitimately. So, you resort to hand-waving statements. Maybe you should go into politics and forget physics.
You wrote toJim:
“You further claim that the climate equivalence principle does not allow balanced exchanges to move net “human carbon” from the atmosphere where it is dense to land/sea reservoirs where it is sparse is bonkers.”
Your argument is invalid, David, because you have no physics equations to even follow how carbon flows between the carbon reservoirs.
Please, next time you come back, please show us how you derive your imaginary model in terms of equations that derive from my (1) and (2).
Ferdinand Engelbeen
July 27, 2025 at 9:31 am
I will try to catch up and not duplicate too much. I was working on dropbox and Windows issues.
“Can you elaborate on that, where the input data to the atmosphere are based on?”
I think I answered this already in response to Dr. Ed. I’ll repeat with a better explanation, hopefully. I could see from Spencer’s original spreadsheet that he had no contribution from natural emissions. By default, his model assumes them to be whatever they are. Whether he started with a Dietz/Burton/Engelbeen-derived Tau and then found the Mauna Loa fit or first tweeked the fit and then found the same Tau as you and others, I don’t know. It’s a question for Dr. Spencer that I was too ignorant to ask at the time. What is clear, is that he assumed the removal rate was proportional to the difference between the pCO2 now and whatever it was in 1750. Just as Deitz, you, and others do.
Sensing this was wrong, I added natural emissions of about twenty times the human emissions and assumed the removal rate was directly proportional to whatever the pCO2 was in the current year. Then I had to figure out what the natural emissions would have to be to get a fit to the Mauna Loa data. That took a while, but was enabled by assuming the formula was exponential. I didn’t put the equation in the “Jim fluxes” spreadsheets, because it was originally in terms of ppm and I didn’t take time to convert it to PgC. So I just copied and pasted the ppm values and then converted to PgC. Call me lazy, but actually I was pressed for time. Now with all your questions, I’m even more pressed for time because I want to finish reading the Dietz comments.
With the appearance of your 20-year spreadsheet, I was able to attempt a back calculation, but failed. However, back calculation on Spencer worked perfectly. Next, I used the same approach to back calculate my spreadsheet. Because I had the extra variable, natural emissions, I could only do 1959 to 2018 where I had both Cn and Cn-1. So prior to 1959, I just used natural emissions from my original data fit. The formula to back calculate the Mauna Loa era natural emissions is
ENn = Cn – Ehn – Cn-1 * ( 1 – 1/Te )
I amended my spreadsheet to show the exponential equation and a graph of the fit. I noticed the exponential estimate at 2019 (cell AA274) was off by about 1 PgC. That’s not bad, considering my fit was an eye-ball one. Also, there was an error at cell AA214, which was corrected by replacing the wrong back-calculation formula with the exponential formula.
https://www.dropbox.com/scl/fi/ojyikq5ds5wgl6g5b0jsp/Jim_fluxes3.xlsx?rlkey=9lzxmuc33j6qs1hcgngy5mxtd&dl=0
July 27, 2025 at 12:19 pm
“…Again in complete ratio with the “old” equilibrium… all three reservoirs do sink CO2 in ratio to the “old” equilibrium.”
You continue to apply anecdotal data to validate your preconceived notions. Unscientific and unsatisfactory. This may fly at climate conferences, but I suspect you will continue to get pushback from anyone outside the Tau camp.
To be continued…
Dr. Ed, July 28, 2025 at 9:24 am
“You admit that you are not familiar with the Delta14C data.”
I didn’t say that I don’t know anything about the Δ14C data, but I haven’t looked at it with the same depth as for the δ13C data… David Burton did a lot of work on it and I am pretty sure that he has done a good job in our common work.
But here a graph I made already 20 years ago to show how the Δ14C data from the bomb tests are “diluted” by the deep ocean waters, making the bomb tests peak decay rate a lot faster than for an extra input of bulk 12/13CO2:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/14co2_distri_1960.jpg
Of all CO2 as mass in 1960, about 97% returned back as mass from the deep oceans in the same year as absorbed. From the bomb tests, only 45% of 14C as “mass” returned in the same year, the rest did just begin their ~1000 year journey…
That makes that your calculation of the “fixed” 14C balance is completely at odds with reality, because you haven’t taken into account the ~1000 years delay between the extra 14C uptake and the current 14C “old” release.
Thus the decay rate of Δ14C from the bomb tests is much faster than the decay rate of about 50 years for an extra input of FF CO2 and moreover has absolutely nothing to do with the 4 years turnover time, which is the base for your Te…
The same happens with the 13C/12C ratio, which is “diluted” by 13C rich (compared to FF) deep ocean returns.
Thus looking only at 14C and 13C/12C ratio’s give you an underestimate of the real cause of the CO2 increase in the atmosphere, for the simple reason that an exchange in isotopes without a change in total mass has nothing to do with the decay rate of an extra CO2 mass (of whatever composition) in the atmosphere.
“Therefore, you are not in a position to argue that it does not prove your hypothesis is wrong. You have not studied my papers and my rebuttal above to your CO2 Coalition paper. ”
Wow. I have studied your papers in depth and that was a reason to react here. I still wonder why a clear explanation of the current scientific knowledge does stir so much controversy and hostile comments from some in the skeptic community… Maybe because one doesn’t like the result?
Take you stance against our graph nr 11 of the uptake/release of O2 as proof that nature is a net sink.
https://www.ferdinand-engelbeen.be/klimaat/klim_img/bolingraph.gif
You say:
“Figure 11 assumes H(1) is true. On that basis it plots O2 concentration as a function of CO2 concentration, assuming human CO2 causes all the CO2 increase”
Which is a complete false accusation. Nowhere is “assumed” that humans cause all the CO2 increase. All what was plotted is the calculated O2 use and CO2 increase from burning fossil fuels at the right side, based on sales (taxes) and burning efficiency, the observed decrease in O2 and increase in CO2 at the left side and the calculated O2 production of the biosphere to fill the gap between calculated and observed O2 use. When plants absorb CO2, they release O2 in equivalent amounts, thus plants also reduced the CO2 increase in the atmosphere. The oceans filled the remainder of the CO2 uptake.
Nowhere is there a NET natural release of CO2. None. All based on observations and direct calculations from observations.
Jim Siverly
July 28, 2025 at 11:47 am
“What is clear, is that he assumed the removal rate was proportional to the difference between the pCO2 now and whatever it was in 1750. Just as Deitz, you, and others do.”
Jim, again… Neither Spencer, or I or most other skeptics of the alarmist “catastrophic” global warming used the old equilibrium as base for the 50 years decay rate of extra CO2 in the atmosphere. Only Dietze did that, because the time period to calculate Te/Tau over a longer period was rather short.
As you have calculated yourself, the Te of the NET removal rate during the Mauna Loa time indeed is 2% of the increase, over any time period that you want (beyond the year-by-year noise). That points to a exponential decay rate, where the response is linear in ratio to the increase of CO2 in the atmosphere.
One then can calculate back to the zero net decay, where the true equilibrium is. Again: we didn’t use that in reverse.
Here the plot in real order:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
A is the sum of all emissions, the observed increase in the atmosphere and the influence of T on the pCO2 of the oceans. That is a small change in ΔpCO2. If you don’t like it, just drop it. If you want the absolute sinks, be my guest and do the same calculations with a full ΔpCO2 from the atmosphere to zero pCO2. Gives you either some 16 PgC/year pressure dependent CO2 output flow (with the 50 year Tau plus 195 PgC/year non-pressure dependent outflows) or a lot longer Te/Tau…
B is the calculated net sink rate per year from A: increase minus emissions. Independent of the absolute height of CO2 in the atmosphere, only dependent of the difference between increase in the atmosphere and increase in emissions.
C is the calculated Te/Tau from A and B.
The order of calculation is from A to C. Not reverse…
No need to know or calculate or estimate any (uncertain) out- or inflow from or to the atmosphere, as we have much more accurate net outflow calculations…
Ferdinand Engelbeen
July 28, 2025 at 2:55 am
“Both Spencer’s and my approach doesn’t involve inflows or outflows at all, only net flows.”
I consider that a confession. Let’s examine net flows. I claim the 50-year figure is an artifact of the assumption that the removal process is proportional to difference between now and way back when. That doesn’t sound like net flow to me. Yet the removal (decay) rate both you and Spencer use is ( Cn-1 – Co ) / 50.
How is that a net flow? That basically says net flow is the amount of annual FF emissions that nature couldn’t remove, because she only removes a fiftieth of the difference of what’s in the atmosphere now and what she remembers it was in 1750. Unbelievable.
“The 2%/year figure is the observed (!) decay rate…Thus not based on any past known or unknown “old” equilibrium… “Observed” in that way that human emissions are quite accurately known…and the increase in the atmosphere is very accurately known from measurements.”
Your “not based on any past known or unknown “old” equilibrium” is contradicted by your use of ( Cn-1 – Co ) / 50. Can’t you see that? It’s circular logic. You observe the 2% rate from the slope of the plot of delta C vs C. Then you all use the intercept as the 1750 Co value Spencer, for example, used to produce his Mauna Loa data fit. To do that you have to assume no change in natural emissions and ignore e-time for the “no change in natural emissions” scenario changing from 3.14 to 4.86 years.
“That is just curve fitting…” Of course. What do think Spencer was doing using 0.02/year and 294 ppm to fit the Mauna Loa data? One makes certain assumptions to formulate a model. One can use the wrong assumptions and formulas and still get a good fit. Which assumptions are more physically correct is the question to be answered.
Finally, for your two last paragraphs, Magic Math bookkeeping is not scientific and even if your 33% and 13% numbers were accurate to the PgC, 46% is darn close to 50%.
Ferdinand Engelbeen
July 28, 2025 at 12:42 pm
Do you deny that your spreadsheet uses “the old equilibrium as base for the 50 years decay rate of extra CO2 in the atmosphere” after you just acknowledged both you and Dr. Spencer use ( Cn-1 – C0 ) / 50 as your decay rate in your formulas?
Please don’t use e-time Te when you mean adjustment time Tau, as in, “the Te of the NET removal rate.” The jargon is confusing enough as it is. While we are on the subject, “decay” is not appropriate for the current situation with increasing FF emissions and quite possibly increasing natural emissions, as well. As I have shown, there is no need to use anything but Te of about 4 years. Furthermore, there is no data that definitively proves that the atmosphere will decay to preindustrial times with an e-time of 50 years. That is a purely speculative model-based assertion of the Tau camp.
You have shown the acc_decay.png diagram with plots A, B, and C maybe a dozen times and I never really understood how you calculated the e-folding times. Would it be possible to show the formulas? Otherwise I have no idea how you “calculate back to the zero net decay, where the true equilibrium is.”
Ferdinand Engelbeen July 28, 2025 at 11:59 am
Dear Ferdinand,
1. Dave Burton does not correctly explain the Delta14C data.
2. Your old graph does not show the information that my plot shows.
3. The return of the Detla14C to its original zero-balance level after the bomb tests proves the Delta14C balance level remained near zero even as the bomb tests increased Delta14C.
4. The bomb tests had no effect on the natural inflow of Delta14C or its balance level of zero.
5. Since 1950, increased human 12C emissions caused an inflow of carbon with a Delta14C of -1000. This sets a balance level that reflects this inflow and this human carbon balance level mixes with the natural carbon balance level of zero.
6. Your hypothesis that “about 97% returned back as mass from the deep oceans in the same year as absorbed” is neither relevant nor backed by data.
7. Your hypothesis that “From the bomb tests, only 45% of 14C as “mass” returned in the same year, the rest did just begin their ~1000-year journey…” is imaginative.
8. The natural Delta14C inflow before the bomb tests continued during and after the bomb tests. The is no basis in data to claim that this natural inflow changed.
9. Your comment that my “calculation of the “fixed” 14C balance is completely at odds with reality” is incorrect. First, I do not consider the 14C balance level. Second, I use the Delta14C balance level that exactly matches excellent data.
10. Your comment that I “haven’t taken into account the ~1000 years delay between the extra 14C uptake and the current 14C “old” release” is irrelevant and ridiculous. I use the natural and human inflows since 1950, which is all that matters.
11. You wrote, “the decay rate of Delta14C from the bomb tests is much faster than the decay rate of about 50 years for an extra input of FF CO2.”
Indeed, it is. We can measure its Te at 16.5 years with a balance level of zero, proving your 50 years is imaginary.
12. The rate return of Delta14C back to its original balance level is set by its Te. A longer Te would have slowed the outflow of carbon from the atmosphere and extended the time for Delta14C to return to its balance level.
The Te of the return (16.5 years) rules out your hypothesis that Te (or Tau) is 50 years.
13. You commented that Delta14C “and 13C/12C ratio’s underestimate of the real cause of the CO2 increase in the atmosphere, for the simple reason that an exchange in isotopes without a change in total mass has nothing to do with the decay rate of an extra CO2 mass (of whatever composition) in the atmosphere.”
Your comment is not true. The Delta14C balance level is the combined balance level set by the Delta14C inflow with a balance level of zero and the human carbon inflow with a balance level of -1000. Delta14C data show the contribution of human carbon is very small.
You bring up an additional point separate from the above discussion:
This regards your Figure 1.4.2:O2-CO2trends 1990–2000, figure from the IPCC TAR (2003), that is also my draft Figure 11.
You wrote, “Nowhere is it “assumed” that humans cause all the CO2 increase.”
Well, this figure has an arrow titled “fossil fuel burning” that goes from 352 ppm to 382 ppm, and an arrow titled “atmospheric increase” that goes from 352 ppm to 367 ppm.
These arrows assume human CO2 emitted between 1990 to 2000 caused the CO2 level to increase from 352 ppm to 367 ppm.
Without this assumption, the figure should have named the arrows to, say, “total human CO2 inflow” and “net human CO2 inflow.”
The figure does not allow that natural CO2 might have caused some of the CO2 increase.
Jim Siverly, July 28, 2025 at 2:19 pm
“I claim the 50-year figure is an artifact of the assumption that the removal process is proportional to difference between now and way back when. ”
Sorry, my fault. Indeed figure C of the graph I sent is the calculation relative to the “old” equilibrium plus a small increase in equilibrium, due to the increased SST since 1850.
1. Let us begin with clearing some confusion about the differences in definitions…
Te (Berry) and τ/Tau (general) and Ta (IPCC) meanings are exactly the same: all assume an exponential decay rate for any change in one of the reactants of a process in equilibrium. That is the time needed to reduce the change to 1/e of the original disturbance in all three definitions. Only the exact figures are quite different.
In the case of Te, Berry and several others and you use the 4 years turnover/residence time, where a one-shot extra CO2 in the atmosphere follows the same decay speed as the overall output rate, which only is allowed if (and only if!) all outflows are unidirectional and no back flows are involved ánd if (and only if!) all outflows are driven by the CO2 pressure in the atmosphere. In that case Te = C/Fout and thus Fout = C/Te (equation 2 of Berry).
For any single CO2 molecule in the atmosphere, the turnover/residence time is always applicable, but only in that case the CO2 mass transfer is the same as the CO2 molecule transfer and both Te and Tau are equal:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/mass_fluxes_classic.jpg
In the case of τ/Tau, that is the time needed to remove 1/e of the disturbance relative to the (“original”) equilibrium for a one-shot impulse.
If (and only if) the net (important: net!) output is in exact ratio to the change in disturbance, it doesn’t matter over what time frame Tau is calculated, even if the equilibrium is not known at all.
That is the case for both the oceans and vegetation (up to over 1,000) ppmv. Thus one doesn’t need the “original” equilibrium to know Tau.
Only in the case that all flows are unidirectional and all outflows are CO2 pressure related, then Tau = Te. In all other cases, Te and Tau are completely independent of each other:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/mass_fluxes_real.jpg
The Ta of the IPCC’s Bern model is model based and assumes saturation of all reservoirs for CO2, which is only the case for a large part of the ocean surface. Not to over 1,000 ppmv for vegetation and not for the next thousands of years for the deep oceans, even if we burn lots of coal, oil and gas…
In all cases, it doesn’t matter that the input is a one-shot amount of FF CO2 or a continuous, increasing, supply of FF CO2. The (net) removal rate is a function of the total amount of CO2 in the atmosphere (for Te) or the difference between the total amount of CO2 in the atmosphere and the (old) equilibrium, thus the total increase over time, not only the extra input of one year.
2. The calculation of Tau.
If (and only if!) the net (!) output is directly proportional to the extra level in the atmosphere, then the formula for Tau is quite simple:
Tau = disturbance / effect
Or in the case of the atmosphere and what I used in graph C for each year:
Tau = [pCO2(atm) – pCO2(eq)] / net output
Where net output = outputs – inputs = FF emissions – increase in the atmosphere (= graph B).
As we know the FF emissions and the increase in the atmosphere quite exactly, there is no need to know any inputs or outputs or the sum of these, to know the net output with high accuracy.
Indeed I used the “old” equilibrium, but because the net outputs in this case are in exact ratio to the height of the change, one can use the current changes to obtain the current Tau.
That makes that one can calculate Tau from the accurate data from 1958 on.
Here the “old” equilibrium based Tau’s compared to the 10-year moving “modern” Tau’s.
Calculated with Tau(n) = [C(n) – C(n-9)] / [Fnetout(n) – Fnetout(n-9)]:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/decay_10.png
The modern Tau seems to be somewhat higher (~55 years) in average than the “old” Tau, based on the old equilibrium. The old Tau was calculated on the polynomial through the net sink rates, that gets of course a lot less noise…
This calculation of Tau doesn’t involve any knowledge of CO2 in- or outfluxes or “old” equilibrium or natural/FF CO2 ratio…
Even if the atmospheric in- and outflows doubled over time (halving the turnover/residence time and thus your Te), that has zero influence on the net removal rate of CO2 out of the atmosphere, because only the difference between inflows and outflows is what changes the total mass of CO2 in the atmosphere, not how much comes in and goes out. The latter only determines the net outflow in the case that all outflows are CO2 pressure related, which for 95% is not the case in the real world…
As the 50-55 year Tau is clearly working over the full 170 years of human emissions, up to now, I don’t see any reason to assume that without human emissions the CO2 levels will not return back to the old equilibrium.
Except if you accept the hundreds to thousands years of the IPCC’s Bern model…
Dr. Ed, July 28, 2025 at 5:11 pm
1. “Dave Burton does not correctly explain the Delta14C data”.
There is some discussion with David Andrews, but David Andrews completely rejects your calculations. So, who is right? I am more confident in Andrews’ calculations than in yours, because of my past experiences…
2. “Your old graph does not show the information that my plot shows”.
It shows information that is not in your plot: that a large inflow of ~1,000 year old CO2 from the deep oceans returns today to the atmosphere. That CO2 is not contaminated by atomic bomb tests and fossil fuel emissions and thus is an important input that “dilutes” the δ13C and Δ14C input from the current FF input.
3.-5. “The return of the Detla14C to its original zero-balance level after the bomb tests proves the Delta14C balance level remained near zero even as the bomb tests increased Delta14C.”
The return is not yet ended and will go to below zero for Δ14C.
6.-7. “Your hypothesis that “about 97% returned back as mass from the deep oceans in the same year as absorbed” is neither relevant nor backed by data.”
The data for 1960 show a net uptake by oceans and vegetation, of which about 25% is absorbed by the biosphere, 5% by the ocean surface and 20% by the deep oceans.
The “dilution” of the δ13C data (and estimates from deep ocean sinks) shows a deep ocean-atmosphere flux of about 40 PgC/year. The level of Δ14C some 1,000 years ago was about 50% of the bomb tests and with a 10% radioactive decay that gives a 45% return of what did go into the deep oceans in 1960.
These were not exact worked-out figures, but give an indication of why the decay rates of δ13C and Δ14C are much faster than of the bulk mass removal of any extra CO2 injected in the atmosphere.
8.-10. Not relevant.
11.-12. “The rate return of Delta14C back to its original balance level is set by its Te. A longer Te would have slowed the outflow of carbon from the atmosphere and extended the time for Delta14C to return to its balance level.
The Te of the return (16.5 years) rules out your hypothesis that Te (or Tau) is 50 years.”
Again, you are mixing the decay of an isotopic ratio with the decay of the CO2 mass. The isotopic ratio is “thinned” by deep ocean returns, which you (and the IPCC) have not in your (or their) calculations. That makes that the Te for the isotopic ratio’s of δ13C and Δ14C are faster than for the total extra mass of CO2 in the atmosphere. The faster decay of the isotopic ratio’s in no way rules out the observed decay of 50-55 years of the extra CO2 mass in the atmosphere, but it rules out the 4 years Te, which has no bearing at all in the net (!) removal rate of any extra CO2 injected in the atmosphere.
13. “Your comment is not true. The Delta14C balance level is the combined balance level set by the Delta14C inflow with a balance level of zero and the human carbon inflow with a balance level of -1000”
And an input of ~1,000 year old pre-industrial CO2 with higher δ13C and lower Δ14C than in the current atmosphere…
Then we have figure 11 as example how your comments are at odds with what we did write:
“Well, this figure has an arrow titled “fossil fuel burning” that goes from 352 ppm to 382 ppm, and an arrow titled “atmospheric increase” that goes from 352 ppm to 367 ppm.
These arrows assume human CO2 emitted between 1990 to 2000 caused the CO2 level to increase from 352 ppm to 367 ppm.
Without this assumption, the figure should have named the arrows to, say, “total human CO2 inflow” and “net human CO2 inflow.”
The figure does not allow that natural CO2 might have caused some of the CO2 increase.”
“fossil fuel burning” and “total human CO2 inflow” are equivalent. So far so good.
“atmospheric increase” is what is measured at Mauna Loa and is “net human CO2 inflow.” as mass, as that is what remains as human “caused” CO2 mass in the atmosphere.
“The figure does not allow that natural CO2 might have caused some of the CO2 increase.”
That would be quite difficult: if FF CO2 is already larger than what is measured as increase in the atmosphere, then the natural flows only can net (!) remove CO2 out of the atmosphere.
What doesn’t imply that all human FF molecules still reside in the atmosphere. Even if all FF CO2 molecules were exchanged with “natural” CO2 molecules, that doesn’t change the fact that the increase in CO2 mass is fully caused by the FF emissions…
Thus we didn’t “assume” that FF emissions are the cause of the increase. The data show that the increase (as mass!) in the atmosphere is caused by the addition (as mass!) of more FF CO2 than is observed as increase in the atmosphere…
Ferdinand Engelbeen
July 29, 2025 at 4:23 am
I appreciate your interpretation of the e-time terminology. I would prefer and recommend we make a distinction between Te which is based on absolute concentrations, as I and Dr. Ed use, and Tau based on net flows proportional to century-long concentration differences. Can we agree on that for the purposes of these discussions?
My second request is that you explain where you find the rule that my 4-year e-time is only “allowed if (and only if!) all outflows are unidirectional and no back flows are involved?” A standard two-compartment model of a one-time pulse will always have bidirectional flows between the compartments. My model doesn’t show the second compartment, but that is where the “mostly” natural inflow to the atmosphere is coming from. If you like, I will link to a website demonstrating how the equations are derived.
Next, do you have an experimental evidence of “Classic view 2020” shown in your first link?
Can we agree that saturation of any reservoir is irrelevant because surface ocean CO2 goes to the deep and from there to the ocean floor? Nothing stops those processes continuing to infinity, if you apply realistic physical-chemical processes.
Also, can we agree that your hypothesis of net removal rate being a function of the difference between the total amount of CO2 in the atmosphere and the (old) equilibrium has never been experimentally verified?
Thank you for the calculation of Tau details. I will work on that and respond back soon.
Ferdinand Engelbeen
July 29, 2025 at 4:23 am
I previously and mistakenly assumed your smooth curve generating old Tau came from the linear fit you showed in graph B. Now you say it comes from a polynomial regression. Is that of Fnetout values? I was not able to duplicate your modern Tau data in your second link. What are the formulas for Fnetout(n) and Fnetout(n-9)?
I am trying to verify your claim, “This calculation of Tau doesn’t involve any knowledge of CO2 in- or outfluxes or “old” equilibrium or natural/FF CO2 ratio…” Until then, I prefer not to respond to the rest of your comment.
Ed,
Even the Trump Administration disagrees with you:
“The annual increase in concentration is only about half of the CO2 emitted because land and ocean processes currently absorb “excess” CO2 at a rate approximately 50 percent of the human emissions. Future concentrations, and hence future human influences on the climate, therefore depend upon two components: (1) future rates of global human CO2 emissions, and (2) how fast the land and ocean remove extra CO2 from the atmosphere. We discuss each of these in turn.”
Climate Working Group (2025) A Critical Review of Impacts of Greenhouse Gas Emissions on the U.S. Climate. Washington DC: Department of Energy, July 23, 2025
releasesd 7/29/25
Jim Siverly, July 29, 2025 at 10:42 am
Sorry, my fault: graph B indeed shows the linear fit, not the original polynomial that was used for the calculation. Doesn’t make much difference, except at the start and end of the calculations. Here the right one with the polynomial formula:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.jpg
just replace the .png of the previous one with the .jpg of this one. I didn’t think about it, because the former one had the A/B/C marks and this one not…
That was used for the calculations of the “old” Tau’s, relative to the original equilibrium + the pCO2(eq) increase caused by the increase in SST since 1850, per formula of Takahashi.
The new Tau’s are based on the change in pCO2 of the atmosphere at Mauna Loa over a period of 9 years (not 10, was too much in a hurry, I suppose):
Tau(n) = [C(n) – C(n-9)] / [Fnetout(n) – Fnetout(n-9)]
Where C(n) and C(n-9) are the CO2 levels at Mauna Loa of the current year and 9 years back, thus the increment of CO2 in the atmosphere.
Fnetout(n) and Fnetout(n-9) are the calculated (raw) differences between increase in the atmosphere and human emissions for the current year and 9 years back in time, thus the net increase in absorption of CO2 mass, somewhere in other reservoirs, caused by the increase in concentration of CO2 in the atmosphere.
If the net removal of CO2 is directly proportional to the increase of CO2 in the atmosphere, then it doesn’t matter over what period one calculates Tau, even without any knowledge of the “old” equilibrium or the exact in- and outflows. One need only the observed increase of the pCO2 in the atmosphere and the calculated net uptake…
Jim Siverly, July 29, 2025 at 9:48 am
1. Agreed to use Te and Tau as separate things, to keep the discussion clear.
2. About the “no back-flow” point. That was used for a one compartment model: Many (Koutsoyiannis, Harde, Stallinga,… use the “lake/bath tube/container” model with one-directional inflows, container and one-directional outflows:
`Koutsoyiannis does that very detailed in his RRR approach, which indeed is superb for… lakes, which is his specialization:
https://www.itia.ntua.gr/en/getfile/2474/1/documents/water-16-02402-v2.pdf
Which is way over my head for his formula use, but when the result seems to prove that 2 + 2 = 3, something in his reasoning doesn’t fit reality…
I used a simple “river/lake/river” as example of such a process:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/classic_view.png
Important points:
In that case Te = Tau = mass / output = RT (turnover/residence time)
In no way a “marker” in the inputs can exceed its input ratio in all following parts.
For a one compartment process, if you have back-flows, the situation is completely different:
I used the “fountain” model to make the difference as clear as possible:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/real_view.png
Important points:
In that case, RT and Tau are completely decoupled and Te hardly exists as function of the pumping around, despite an enormous outflow of the basin into the cycling pump.
RT is a function of a process that is not or hardly influenced by the level/pressure in the basin
Tau is only influenced by the extra level in the basin and not at all by how much circulates, thus completely independent of the total “outflow” out of the basin.
Any “marker” in the input can asymptotically increase to 100% of the basin.
That was for the discussion in Athens, September last year…
In the case of multiple reservoirs, that makes it more complicated, but then the second problem: processes that move CO2, independent of its pressure in a reservoir, again plays a major role, compared to the small effect of CO2 pressure changes…
If we may assume that “earth” is a second reservoir where all outflows of the atmosphere go in and come back as similar inputs then we have:
Your 4 years Te is based on the calculated total sum of outputs out of the atmosphere into “earth”.
Your inputs are back-calculated to show the observed difference between the previous year and the new year CO2 concentration, based on the 4 years Te of the outflows.
Dr. Ed calculates the total inflow from the different Te’s of the different reservoirs, but also assumes that the outflow into “earth” is 4 years, based on the total outflows.
We don’t use inflows and outflows at all, only the extra pressure difference in the atmosphere with the “old” equilibrium and the observed net sink rate, or for modern times the ratio between the increments of CO2 pressure in the atmosphere and the observed increase in net sink rate. That gives the Tau of 50-55 years.
So which approach is the right one?
Te could be the right one, if all processes were 100% CO2 level/pressure dependent.
Because 95% of all processes that move huge quantities of CO2 (mainly diurnal and seasonal) between the reservoirs are temperature and biological dependent, Tau is the right one, as that shows the real, small, effect of the increase in CO2 pressure in the atmosphere on the change in net uptake.
3. “Can we agree that saturation of any reservoir is irrelevant because surface ocean CO2 goes to the deep and from there to the ocean floor? Nothing stops those processes continuing to infinity, if you apply realistic physical-chemical processes.”
Be careful, the ocean surface indeed gets saturated for any change in the atmosphere within a year and the IPCC uses that for the “isolation” of the deep oceans from the atmosphere, which leads to Tau’s of hundreds to thousands of years.
You do that indirectly: with a Te of 4 years, the “equilibrium” between atmosphere and “earth” also goes up with the increase in the atmosphere and when human emissions should stop completely, there is only a small change to a lower level…
4. “Also, can we agree that your hypothesis of net removal rate being a function of the difference between the total amount of CO2 in the atmosphere and the (old) equilibrium has never been experimentally verified?”
As the ratio between increase in the atmosphere and increase in net uptake remained and remains relative constant, the real world proof is given…
David Andrews July 30, 2025 at 5:49 am
David,
Thank you very much for this information.
Indeed, President Trump may lose the Lighthiser v Trump climate lawsuit on this very issue, which could overturn all his executive orders on climate and energy.
The courts properly make their decisions based on the data presented in a trial, as the court did in Held v Montana.
So, you and the Democrats could win a smashing big victory in Lighthiser v Trump because, at the moment, your side and the CO2 Coalition have Trump convinced that you are correct.
Dr. Ed, July 28, 2025 at 5:11 pm
A small addition about the O2/CO2 plot:
“The figure does not allow that natural CO2 might have caused some of the CO2 increase.”
The figure only shows the calculated release of CO2 and use of O2 from burning fossil fuels, the uptake of CO2 and release of O2 by the biosphere and the results of observations, where the oceans fill the gap of the remaining uptake.
There is no restriction at all that blocks the results of any natural release of CO2: if that was additional to the release by FF use, then the observations would be at the right side of the FF release of CO2.
If e.g. the biosphere was a net emitter of CO2 and not a net sink, then the oxygen use would have been larger than of FF only…
Ferdinand Engelbeen
July 30, 2025 at 6:41 AM
I see the equation on graph B is a polynomial fit and that the line just looks linear. That’s my fault, but it has nothing to do with my confusion over your calculation of new Tau from n and n-9 data. I generated a new spreadsheet to show my calculations. What am I doing wrong?
https://www.dropbox.com/scl/fi/6e7f6y10gukegc7vqk28v/New-Tau.xlsx?rlkey=8e1qnz65yi5at2ztdb24ir1fj&dl=0
I also tried plotting net removal of CO2 [delta CO2 – FF emissions] versus the increase of CO2 in the atmosphere [delta CO2] and found a very low correlation, not even close to being directly proportional. Please define the variables more clearly in terms of Mauna Loa data and known FF emissions.
Jim Siverly, July 30, 2025 at 11:23 am
Indeed you are right: my calculation (again) was based on the 10-year increments, compared to the “old” equilibrium of 285 ppmv for each year, not on the difference over 10 years in itself…
The problem is that there is an enormous – temperature induced – noise on the net sink rate, which is small: +/- 2 ppmv for the 100 ppmv trend, but very huge for a 5 ppmv/year increase.
So forget the 10-year increments, these remain too noisy.
What is left is the total increase since 1958 with accurate measurements and reasonable accurate FF emissions.
That is an increase of near 100 ppmv (414.24 – 315.97) between 1959 and 2020, with a net sink rate increase over the same time frame of 1.86 ppmv/year (2.29 – 0.44), based on the polynomial to avoid the influence of the huge noise.
Interesting to note: the increase of CO2 in the atmosphere since 1958 is already 80% of the total increase increase since 1850. That also is the case for about 80% of human emissions ánd also the case for 80% of the net sink rate.
Which points to a very linear ratio as response of the sinks to the extra CO2 in the atmosphere.
A small point of difference: I wondered about the difference between the 50 and 55 years Tau between the “old” and “new” calculations. That difference is in what is taken as human emissions:
Spencer and others and I in the past used the total emissions, including land use changes. In our common work for the CO2 Coalition we used only FF emissions, without far more uncertain land use changes. That gives a difference of about 10% in human emissions and Tau…
Ferdinand Engelbeen
July 31, 2025 at 2:29 am
I have been reviewing the evolution of Carbon Cycle Modeling starting with the comments of Peter Dietz on the John Daly website. The dialogue is fascinating considering some of our discussion here.
Tom Wigley in response to Peter Dietz: “It is, of course, quite possible to produce highly simplified (or ‘reduced-form’) versions of these models; but the original ‘first principles’ model must always be better and more credible than the simpler model. The real strength of first principles models is that they do not have free parameters that can be arbitrarily tuned to match observations.”
Peter responds to Tom Wigley, “The clue of my model is that I only consider the *change* in uptake flux which is proportional to the CO2 partial pressure increment against the equilibrium, e.g. 280 ppm. This reflects the acting main physical and chemical laws and thus is valid for the bulk of the sink fluxes….”
“It is remarkable that both Peter Dietze and Jarl Ahlbeck find that the present equilibrium value is the same as the pre-industrial. Shouldn’t the increase have started already? Best regards, Lars Kamél”
Peter responds, “Lars, you should not misinterpret the perturbation state as a shift of equilibrium. We consider the (final) equilibrium towards which any concentration increment will “decay” to 1/e within 55 years, as constant, i.e. 280 ppm. The equilibrium is *not* expected to shift within the geological short time of fossil fuel use – consider the huge oceanic sink capacity including shells and corals.”
Jarl Ahlbeck, “If the diffusion is controlled by a first order Fick’s equation to a greater extent than by the second order, the absorption rate is almost directly proportional to C(surf.carbon)-C(deep layer carbon) or to C(atm)-280 ppm. The rate constant may be calculated statistically from available data. The problem is the intercorrelation between emissions and concentration making an idealized batch describing recent data almost as well (constant airborne fraction) as when taking significant mass transfer to deeper layer into account (variable airborne fraction). I have walked around the problem by calculating the airborne fraction from data although I do not like this parameter, it feels a little unscientific.”
I found this interesting reference by Enting et al., 1994: https://unfccc.int/resource/brazil/documents/enting_2001a.pdf with the following quote,
“These fluxes are net fluxes superimposed on large natural gross fluxes of carbon. In many cases the models will consider the gross fluxes, particularly when calculating isotopic effects. The distinction is well-understood within the field of carbon cycle modelling, but sometimes causes confusion when results are reported.”
That last phrase is an understatement considering the exchanges you are having with Dr. Ed and some of us here.
From the Enting et al. paper comes the equation 2.123 dC/dt = Qfoss (t) + Dn (t) – Socean (t) – Sfert (t) – Sresid (t)
Except for Qfoss, the fossil emission rate, all other terms are net fluxes. One of the co-authors of that paper was Tom Wigley. He wrote an earlier paper with a similar equation, 2.123 d(deltaC)/dt = I + Dn – X – F, where I = Qfoss, X = Sfert, and F = Socean. He defines deltaC as C – Co. Since dCo/dt is zero, his equation is a form of Enting et al. Technically, each of the net flux terms should be written as k * S(r-a) – k’ * S(a-r) to reflect the true mass transfer process between the atmosphere and the reservoirs.
Wigley defined X as a terrestrial feedback (transfer from the atmosphere to the terrestrial biosphere). While Dn – X accounts for the “full” net terrestrial transfer, there is no similar appreciation for the effect of ocean outgassing which would moderate the value of F, the ocean sink. Without a +Y to offset F, analogous to X offsetting Dn, an important variable becomes embedded in the net variable F. I believe this leads to the misconception that flows are proportional to net concentration differences. The most egregious misuse of that concept is in assuming a net flux is proportional to the difference between a concentration now compared to what it was in 1750. That is the basis of the models of Dietz, Spencer, et al.
My contention is that flows are proportional to absolute concentrations which takes into account the probabilities affecting the mass transfer from one reservoir to another. Net fluxes erase that fundamental aspect. Now I just need to find the experimental evidence that proves it.
Sorry, the Enting et al. equation comes from https://unfccc.int/resource/brazil/documents/enting_2001a.pdf
Wigley’s paper can be found at https://b.tellusjournals.se/articles/10.3402/tellusb.v45i5.15739
Jim Siverly, July 31, 2025 at 5:43 am
Thanks for remaining me of the discussion between Peter Dietze and the others from the “mainstream” side…
There still are two main differences with the mainstream “model” and our “model” since that time:
1. The saturation of all reservoirs at different levels, no matter the emissions in the Bern and similar models:
https://gmd.copernicus.org/articles/11/1887/2018/
See Figure 5 for a pulse of 100 PgC (we have emitted 170 PgC over the past 65 years…): after 100 years still 40% remains in the atmosphere, because of the isolation of the deep oceans by the ocean surface layer and its physical and chemical restrictions for exchanges with the atmosphere.
Also in the Enting paper: formula 9.2 shows:
GO (t) = 0.131 + 0.201*e^-t/362.9 + 0.321*e^-t/73.6 + 0.249*e^-t/17.3 + 0.098*e^-t/1.9
The last term is the restricted uptake into the oceans surface at about 10% of the change in the atmosphere (the “Revelle”/buffer factor) and that restricts the speed of uptake for the other levels. The worst ones are the 363 years (for calcification?) and 13% that never gets away.
That is reflected in their Figure 9.2…
For a linear model (Dietze, Spencer, we) there is no such restriction (at the ocean “edges”) and in 100 years the airborne fraction will drop to 25%, after 150 years to 12.5%, etc…
Because we now have far more data than in 1997, it looks like that the Bern model is more and more at odds with reality, but still not (too) bad, as the last three terms are faster or similar than the constant t/50 of Dietze and others.
With a linear model, all human releases since 1750 will increase the deep ocean C content with only 1%, leading to an ultimate remaining increase of 1% in the atmosphere or 3 ppmv…
2. The difference between pressure related processes and other processes.
Almost all huge (seasonal) CO2 exchanges between the reservoirs are caused by temperature related processes and related biological processes, largely independent of the CO2 level in the different reservoirs.
Your (and Dr. Ed’s) approach implies that the total output depends of the total CO2 level/pressure in the atmosphere, and the inflows depend of the CO2 levels in the other reservoirs. Which, at least for the biosphere is for 95% not true for the CO2 flow from atmosphere into vegetation and for 100% not the case for the reverse flow…
Then: “Net fluxes erase that fundamental aspect.”.
The problem in this case is that the gross fluxes are only known with large margins of error, while the net flux is quite accurately known, be it with a huge, temperature related, noise…