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.