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.
DMA and Jim,
“It seems possible that if natural emissions are growing faster than the sinks atmospheric content will increase without FF additions. I do not think we have a good handle on the quantity of natural emissions.”
Come on, as David already said: in the past 67 years the natural emissions never, ever were larger than the natural sinks. Never. Even if we don’t have a good handle on natural sources and sinks (and thus not on Te!) we have a quite accurate handle on En – A(n+h) and that was always negative, with a few borderline El Niño years…
Ferdinand,
It does not apply in both directions. One medium is air, and the other medium is liquid. Never has Henry’s Law been stated that the amount of gas in the air is proportional to the partial pressure of the gas in the liquid. NEVER EVER.
Ferdinand,
“The main problem for Dr. Ed’s calculations still is that he uses the much too short residence time of 4 years, that is the time that a single molecule CO2 resides in the atmosphere, before being switched with a CO2 molecule from another reservoir. That has nothing to do with the real decay rate of around 50 years for an injection of extra CO2 as mass (whatever its origin), back to the dynamic equilibrium of the pre-industrial times…”
You continue to violate the Equivalence Principle and you don’t care or don’t see it as a problem. “Be damned with science your agenda is more important.”
Jim,
“Here is how the Tau crowd rationalize the atmosphere containing a small percentage of fossil fuel carbon (FF) remaining in the atmosphere while causing all the excess carbon accumulating (making H1 true). The fast 4-year turnaround launders FF, but is unable to remove all excess carbon which is no longer identifiable as coming from any source, leaving a deficit of about half of the carbon equivalent to that sourced annually as FF.
Conveniently natural emissions don’t need to be accounted for and all absorptions are considered natural regardless whence they came. They assume an equilibrium remains as it has been since 1750 and use a bastardization of Henry’s Law to explain it. I’m coining the whole analysis Magic Math.”
That is a violation of the Law of Conservation of Mass. They violate so many scientific laws with their crazy constructs that they can’t see straight.
Jim,
“The fast 4-year turnaround launders FF, but is unable to remove all excess carbon which is no longer identifiable as coming from any source”
The processes that make the 4 year turnaround are in part not the same processes that permanently remove any excess CO2 out of the atmosphere. For the oceans the difference is clear: the ocean surface is largely responsible for the fast Te, but doesn’t remove much CO2 permanently.
The deep oceans add less than half of the oceanic Te, but are responsible for 4 times more CO2 removal than the ocean surface.
And the biosphere moves an enormous lot of CO2 back and forth between atmosphere and biosphere, but only a small part remains in more permanent vegetation.
And the increase of the basic pCO2 of the oceans, due to the increase of SST since 1750 is exactly known, thanks to the measurements on meanwhile over three million seawater samples…
Stephen,
“That is a violation of the Law of Conservation of Mass. They violate so many scientific laws with their crazy constructs that they can’t see straight.”
According to Jim and you,
5 PgC/year increase in the atmosphere is not caused by the 10 PgC/year human emissions, but by the increase of the natural inputs.
Observed: 5 PgC/year = 10 PgC/year + natural inputs – natural outputs
Or natural outputs are 5 PgC/year larger than the natural inputs.
Even if the natural outputs include half the human input of 5 PgC/year human supplied FF molecules, then still the full increase of 5 PgC/year in the atmosphere is caused by the human emissions.
According to your ideas, natural outputs are smaller than natural inputs.
Who is violating the carbon mass balance ánd the equivalency principle here?
Stephen,
You were ill-advised to bring up and attemp to defend Murry Salby. From his Wikipedia page:
“The National Science Foundation investigation report issued on 20 February 2009 found that Salby had overcharged his grants and violated financial conflict of interest policies, displaying “a pattern of deception, a lack of integrity, and a persistent and intentional disregard of NSF and University rules and policies” and a “consistent willingness to violate rules and regulations, whether federal or local, for his personal benefit.” It debarred Salby from receiving federal assistance and benefits until 13 August 2012.[9]” There is more.
I never met him, but have my personal reasons to question both his integrity and his science. After I noticed his C14 error (confusing “DeltaC14” which measures C14/C12 with C14’s abundance or molar fraction of the atmosphere) and published a note on it, he and coauthor Hermann Harde made a “correction” which can only be described as fraudulent. They engineered an unjustifiable background to make the C14 curve look like the DeltaC14 curve they had built their ridiculous model on. No real scientist would be fooled by that maneuver. It was aimed at his gullible followers. Apparently you are one of them.
One of the questions about climate skeptics that puzzles me is that while they proudly reject authority, they attach themselves to perceived “experts” and make little attempt to think for themselves. If you, Jim, and others want to unquestionably accept the Salby’s and the Berry’s views on things like mass-balance as the Truth because you don’t have the tools to do the thinking yourself, I can’t stop you. But you might ask yourself what it was that made Jim say to Ed a few days ago “I’m on your side”, rather than “I’m trying to work this out for myself.”
Ferdinand Engelbeen
July 14, 2025 at 3:53 pm
You are stuck on anecdotal data. Don’t you see that the 1,000-year-old CO2 returns from the deep experiencing a warmer world than in 1750 and somewhat greater biomass?
“Both the level in the atmosphere and the output increased in ratio over time.”
Did you mean the ratio of the level in the atmosphere versus the output increased over time? Regardless, I have no idea what your equations mean, because you have never shared a rigorous analysis of how Tau is derived.
“The seasonal differences between ocean surface and atmosphere remained about the same, as the average pCO2 of the ocean surface closely followed the increase of pCO2 in the atmosphere.”
That’s tantamount to saying there has been an increase in natural emissions. If there has been an increase in natural emissions, then FF cannot be responsible for all the excess CO2. H1 fails.
“As far as I know, [the huge exchanges between ocean surface and atmosphere caused by the seasonal temperature amplitude] didn’t increase over time.”
How could you know that unless assumed based on Magic Math? Even if temperature amplitude didn’t increase over time (although your Takahashi references contradict that), the biosphere has.
I’m still looking for where this Tau logic stems from. And while I think of it, why haven’t you responded to my analogy of A B reaction reaching the same equilibrium ratio while both concentrations increase after additional reactant is added to the system?
I think the speed of CO2 receding during interglacials was much less than 0.02 ppm/year. Largely because the temperature drop controlled the CO2 drop as it does the CO2 increase. So the equilibrium condition is controlled by temperature and changes according to Henry’s Law, etc. Tau has nothing to do with it.
“Even if all these cycles doubled, thus halving Te, that doesn’t affect Tau at all…”
I’m inclined to agree with the antecedent, but argue the precedent is irrelevant because Tau is ambiguously defined.
Ferdinand Engelbeen
July 14, 2025 at 4:07 pm
“natural emissions never, ever were larger than the natural sinks” is not the same as “natural emissions are growing faster than the sinks.” Sinks are larger, but only keeping pace with the increasing emissions.
Ferdinand Engelbeen
July 14, 2025 at 4:22 pm
“The processes that make the 4 year turnaround are in part not the same processes that permanently remove any excess CO2 out of the atmosphere.”
“…the ocean surface is largely responsible for the fast Te, but doesn’t remove much CO2 permanently.
The deep oceans add less than half of the oceanic Te, but are responsible for 4 times more CO2 removal than the ocean surface.”
Do you realize that is a hand-waving argument? You are basically saying that, the atmosphere and surface ocean participate mostly in fast turnover, and the ocean’s small part in Te removes most excess carbon. Actually, I agree with my paraphrase of your scenario. However, I am not sure what statement(s) I made you are objecting to or how it proves H1 true.
Furthermore, what do the other statements at July 14, 2025 at 4:22 pm have to do with my definition of Magic Math?
Jim Siverly, July 14, 2025 at 8:04 pm
It seems quite difficult for some here to understand the difference between Te and Tau.
Per definition:
Te = mass / output (residence time or turnover time)
Tau = change in mass (or pressure) / change in net mass (adjustment time or life time)
The difference is in the words “change” and “net”
For a one-direction process where all inputs flow via a container to outputs and nothing returns from these outputs back to the inputs, Tau <= Te (Stallinga, 2023). Only in that case. In all other cases, where some part of the outputs return to the inputs, Te and Tau are largely to completely independent of each other. That is where Berry, Harde, Stallinga, Salby, Koutsoyannis, you and too many other skeptics get wrong. They all still think that Te = Tau.
Both Te and Tau can be calculated, as far as the CO2 mass flows are known.
For e.g. the biosphere the current uptake is calculated at about 120 PgC/year, of which most is taken in in spring-summer.
That is based on the O2 balance and 13C/12C balance over the seasons.
Half of that, some 60 PgC/year already returns the same day as absorbed during the day at night, as plant and soil (bacterial) respiration. The other half comes back in fall-winter. The diurnal changes are rough estimates, based on direct δ13C measurements within forests.
The overall change is slightly better known, still with a large margin of error (+/- 60%), based on the oxygen changes:
https://tildesites.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
That shows a net uptake of about 2.5 PgC/year extrapolated for current years.
Thus for the current atmosphere – vegetation exchanges:
Te(a-g) = 900 PgC / 120 PgC/year = 7.5 years
For Tau, the net change in mass is the observed net sink rate, the change in plant growth for 93% of all plants on earth (C3-type plants) is directly proportional to the absolute CO2 pressure in the atmosphere, up to over 1,000 ppmv, thus
Tau(a-g) = (900 – 628) PgC / 2.5 PgC/year = 106 years
Te and Tau for vegetation differ more than an order of magnitude of each other…
The same calculations are valid for the deep oceans, where the pCO2 at the sink and source places hardly changed between 1958 and today, thus still with enormous differences for the increase of CO2 in the atmosphere.
The only exception is the ocean surface, where the pCO2 of the surface increased with the pCO2 of the atmosphere from zero in the past at equilibrium to 7 μatm today.
That means that my calculation for Tau(a-s) was way too high. It should be:
Tau(a-s) = 15 PgC / 0.5 PgC/year = 30 years
Still twice Te…
That is not Magic Math, that is calculating Te and Tau on known data. Which shows that using Te for the net removal of any extra CO2 (of whatever source) out of the atmosphere is way too fast…
David Andrews
You were ill-advised to ridicule and abuse Murry Salby based on Wikipedia. They are a socialist propaganda outfit. Whatever they said the truth would be 180 degrees the opposite. That’s an appalling attack by you.
David Andrews
Your abusive comment directed at Murry Salby based on Wikipedia is totally false and all lies.
Murry Salby responds to the attacks on his record
JoNova | August 11, 2022
https://climatecite.com/murry-salby-responds-to-the-attacks-on-his-record/
Murry Salby’s detailed response
https://joannenova.com.au/s3/jonova.s3.amazonaws.com/guest/salby-murry/re_nsf_r.pdf
As Jo Nova says and I concur: “any scientist who responds to a question about Murry Salby’s work with a reference to his employment is no scientist.
https://joannenova.com.au/2011/08/blockbuster-planetary-temperature-controls-co2-levels-not-humans/“
Jim Siverly, July 14, 2025 at 7:14 pm
“Don’t you see that the 1,000-year-old CO2 returns from the deep experiencing a warmer world than in 1750 and somewhat greater biomass?”
Not very relevant for the total CO2 in the atmosphere, which was ~290 ppmv then, somewhat 13 ppmv higher than 400 years later during the LIA. Thus returning waters only slightly higher in CO2 than in 1750.
Very relevant for their isotopic levels, as these were from CO2 sinks into the deep, long before the low-13C and 14C-free FF emissions and the 14C increase from the atomic bomb tests.
“Did you mean the ratio of the level in the atmosphere versus the output increased over time?”
Yes, for the atmosphere its CO2 level increased with about 50%, the outputs to the ocean surface increased with 33%. For vegetation only with 13%… Thus in both cases Te increases, be it less for the oceans than for vegetation.
“That’s tantamount to saying there has been an increase in natural emissions.”
You are still stuck at the idea that the inputs define the CO2 level in the atmosphere. That is only the case for the one-directional “lake” model, not for the real world where huge seasonal cycles are at work.
In NH spring-summer, the CO2 level in the atmosphere even drop some 10 PgC (~5 ppmv) on global level, despite the huge input from the ocean surface… Thanks to warming (and sunny) vegetation that sucks more CO2 out of the atmosphere than the warming ocean surface supplies.
“Even if temperature amplitude didn’t increase over time (although your Takahashi references contradict that), the biosphere has.”
The calculation was only for the ocean surface. The formula of Takahashi shows the same pCO2 difference for the same temperature change. If the temperature change over the seasons didn’t change, the seasonal uptake and release didn’t change either.|
The change in CO2 cycle height (both inputs and outputs) is both for vegetation (+12%) and for the deep oceans (+33%) not for the ocean surface.
“I think the speed of CO2 receding during interglacials was much less than 0.02 ppm/year. Largely because the temperature drop controlled the CO2 drop as it does the CO2 increase.”
The 0.02 ppmv/year was for the “fast” T increase of 5,000 years between a glacial and interglacial period. The opposite change is even much slower.
CO2 changes follow the increase with 800 +/- 600 years delay during warming and several thousands of years in opposite direction. A Tau of 50 years then is peanuts compared to the extremely slow changes in pCO2.
There is even no influence of the change in vegetation visible over the full 800,000 years, until the human use of FF… That is reflected in small changes in 13C/12C ratio at -6.5 +/- 0.4 per mil. The drop since 1850 is around -8.2 per mil in the atmosphere…
That of the A – B reactions I need to look that up…
Jim Siverly, July 14, 2025 at 7:27 pm
“’natural emissions never, ever were larger than the natural sinks’ is not the same as ‘natural emissions are growing faster than the sinks.’ Sinks are larger, but only keeping pace with the increasing emissions.”
Not only contradictory: if the natural emissions are growing faster, but don’t exceed total sinks, then they don’t contribute to the increase in the atmosphere. If they grow higher than total sinks, then the increase in the atmosphere would be larger than of human emissions alone.
And again: you have the order for vegetation in the wrong direction: sinks in vegetation are the first step, caused by temperature and sunlight. The releases of CO2 from vegetation follows later and except for a few El Niño years, are smaller than the uptake… For the oceans it is reverse, but again, the release is smaller than the uptake…
Dr. Ed,
The link to the Roth article comes up as the Robbins article: https://scienceofclimatechange.org/wp-content/uploads/SCC-Roth-Origin-of-CO2-V5-1.pdf. Interestingly, a google “I’m feeling lucky” search comes up the same thing. It must be an SCC Publishing issue. The full search gave me this option: https://scienceofclimatechange.org/roth-about-the-origin-of-co2-in-the-atmosphere/. Furthermore, the google AI comment on the full search has it bass ackwards: “The CO2 Coalition, in their study, argues that the increase in atmospheric CO2 is not primarily caused by human emissions, but the study is flawed and ignores the overwhelming scientific consensus.”
David Andrews June 30, 2025 at 8:50 pm
David,
I deleted your remarks that attack Salby from your above refrenced comment. I will otherwise leave the comment.
My reasons are (a) personal attacks are not part of a science debate, (b) Salby is not here to defend himself, (c) your attacks have no references, (d) your attacks make no contribution to this discussion, and (e) if I leave your attack on Salby, it will set a bad precedant to the discussions on my website.
We are here to discuss and debate climate science. Whatever a person has done in the past, or even accused to have done, is not relevant to the discussion of what the person has published or otherwise presented to the public.
Ferdinand Engelbeen
July 15, 2025 at 2:52 am
“Both Te and Tau can be calculated, as far as the CO2 mass flows are known.”
The calculation of Te is straight forward from first-order principles. Everybody knows how it’s done and understands it clearly. Your Tau is derived from the misconception that a disturbance will be restored to its original equilibrium state. The assumed FF disturbance is conflated by an additional disturbance due to natural emissions. Therefore, your Tau is ambiguous, corrupted, and impossible to document unless you survive human extinction and return in a century to report the situation.
You repeat the same mantra comprising anecdotal data to which I continue to reply, where is the justification of Tau that is based on your premise that preindustrial equilibrium returns with net zero FF?
Ferdinand Engelbeen
July 15, 2025 at 5:57 am
If you check the simple math data, you should find that the rate CO2 is rising is more often less than the output rate.
“You are still stuck at the idea that the inputs define the CO2 level in the atmosphere.”
Do you deny that [ inputs – outputs ] define the CO2 level? Please, no more anecdotal evidence that proves nothing. These are arguments by assertion, not scientific.
“The 0.02 ppmv/year was for the “fast” T increase of 5,000 years between a glacial and interglacial period. The opposite change is even much slower.”
More assertions without presenting data proving it. What 5,000 year periods? The data shows wide variations in rates of CO2 removal which, to my eye balling, all seem much less than 0.02 ppmv/year.
“A Tau of 50 years then is peanuts compared to the extremely slow changes in pCO2.”
Yes, because Tau has nothing to do with gradual CO2 equilibrium totally dependent on temperature. Tau is a fabrication gaslighting those of us bothering to check your math and unnecessarily alarming others about climate change.
Jim Siverly, July 15, 2025 at 7:07 am
Indeed that is an issue at their website. I have the article by Roth downloaded in the past with exact the same reference…
I have uploaded the real article and it can be downloaded at:
https://www.ferdinand-engelbeen.be/klimaat/klim_pdf/SCC-Roth-Origin-of-CO2.pdf
We have asked SCC to retract that article, because it contains so many errors and mispresentations of what we did write, that one can’t name it “science” at all. But they refused, because the author refused to do it…
To give a few examples:
In the abstract he writes:
“In such a system the concentration cannot rise more than the inflow. Therefore, since the concentration has risen by
50 %, the inflow must have risen by at least 50 %. ”
That is based on his idea that the atmosphere is a “lake / bath tube” model.
But the increase of inflows from the oceans increased only with 33% and from the biosphere with 11%. Thus his model of the real world is wrong, not ours…
“Another weakness of the study is its assumption that natural fluxes in and out of the atmosphere have remained unchanged for 250 years.”
Our study nowhere said or implied that the natural fluxes remained unchanged…
Only one point of the many points that show the “quality” of his remarks.
In chapter 13, the oxygen balance, he writes:
“Oxygen is consumed when fossil fuels are burned, and it is produced when plants grow (greening of the Earth). The oxygen mass balance merely reflects the accuracy of our estimates of these two processes; it says nothing about the source of the elevated CO2 concentration.”
In the same chapter the oxygen balance is shown as graph and clearly indicates how much oxygen is used burning FF and how much O2 is produced by the global biosphere, thus how much CO2 the global biosphere has absorbed, the remainder was absorbed by the oceans:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/bolingraph.gif
Which shows very clear that FF burning is the cause of the full increase, only reduced by the CO2 uptake from both the biosphere and the oceans.
If he doesn’t understand the oxygen balance, what does he understand at all?
Then the “new” study of Bernard Robbins.
He makes the same mistake as many before him, by comparing T variability with CO2 rate of change variability and “forgets” to plot the twice as steep slope of human emissions. These simply disappear in space, I suppose. Or they separately sink into oceans and biosphere without leaving one gram of CO2 in the atmosphere…
Here how that works:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/demetris_1b.png
The dark blue line is the human emissions/year, including the 2020 Covid drop.
The red line is the observed increase in the atmosphere, which may be 100% human or 100% natural or anything in between.
The green line is the net sink rate if the increase in the atmosphere is 100% human.
The light blue line is the net sink rate if the increase in the atmosphere is 100% natural.
In the latter case, every gram of what humans emitted is absorbed somewhere in nature. Very remarkable. And nature sinks about twice the amount that it supplied to the atmosphere…
Very, very remarkable…
Jim Siverly, July 15, 2025 at 8:47 am
“where is the justification of Tau that is based on your premise that preindustrial equilibrium returns with net zero FF?”
Except for a slight increase of the equilibrium since pre-industrial times, due to increased sea surface temperatures, the equilibrium can be back calculated from the ratio’s between net sinks and absolute CO2 pressure in the atmosphere. The intercept of zero sink is the equilibrium level in the atmosphere. Calculated by Peter Dietze (1997), Lindzen, Spencer, myself and recent by David Burton:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
That is a straightforward calculation that shows the equilibrium for any disturbance of any kind of dynamic equilibrium…
Ferdinand Engelbeen July 15, 2025 at 10:29 am
Dear Ferdinand,
Thank you very much for your comments and scientific challenges. You are certainly welcome to continue to make your challenges. Your challenges have been admirable.
However, you have proved wrong your special document published by the CO2 Coalition. When you use Dietze, Lindzen, Spencer, and Burton to attempt to enforce your arguements, you merely prove that Dietze, Lindzen, Spencer, and Burton are equally wrong about your claims that H(1) is true.
All these authors are deficient in their understanding of how to do systems models and such expertise is very relevant to this subject. Scientists can be very proficient in their own area of expertise, but few scientists also have the necessary expertise in systems engineering, systems models, probability, Markov chains to properly argue that H(1) is true in the face of my and other scientists proof that H(1) is false.
In addition, the null hypothesis is this debate is that H(1) is false. The burden of proof is on your side and your side has not met that burden of proof.
One other startling error that you made a few days ago, was to claim that it is incorrect to detrend time series data in order to calculate a correlation. On that subject, your claim is overturned by extensive literature in statistics.
Munshi is correct that his statistics prove there is no correlation between human CO2 emissions and the increase in atmospheric CO2. Munshi’s primary calculation was for annual data. He also tried 2-year, 3-year, 4-year, and 5-year data to find a correlation. All these tests failed to find a correlation.
The conclusion, supported by all good science, is when there is no correlation between two time series, there is no cause-effect relationship between these time series variables.
This fact alone proves you CO2 Coalition paper is pseudo science. If I were you or anyone in the CO2 Coalition, I would immediately reject this paper.
Best wishes,
Ed
Ferdinand Engelbeen
July 15, 2025 at 6:06 am
I don’t understand how “Not only contradictory:” applies to my statement that sinks are larger, but only keeping pace with the increasing emissions.
“if the natural emissions are growing faster, but don’t exceed total sinks, then they don’t contribute to the increase in the atmosphere.”
That is not necessarily true and you cannot use Magic Math to prove it so. Increasing natural emissions supplement the FF emissions which contributes to the CO2 rise. This is what the Berry, Harde, Stallinga, Salby, and Koutsoyannis papers are explaining.
“If they grow higher than total sinks, then the increase in the atmosphere would be larger than of human emissions alone.”
That’s Magic Math. Natural emissions and FF emissions are increasing at about the same rate as the sinks are. You should be seeing that for yourself, if you’re working on step-wise integration.
I don’t know where I claimed any order for vegetation being in the wrong direction. I can’t deal with anecdotal data, because I cannot evaluate it out of the context of a full carbon cycle. Something like Dr. Ed and others have demonstrated.
Jim Siverly, July 15, 2025 at 9:14 am
“If you check the simple math data, you should find that the rate CO2 is rising is more often less than the output rate.”
What does that prove? That there is a huge variability in sink rate, not in source rate, because the known source is twice as high as the increase in the atmosphere and the difference also is half the human emissions.
“You are still stuck at the idea that the inputs define the CO2 level in the atmosphere.’
Do you deny that [ inputs – outputs ] define the CO2 level?”
Inputs – outputs = NET output, thus Tau,
Te = mass / output = mass / input when output = input and for a “one way” process, the input dictates the level in the atmosphere and therefore the output…
I did forget to show the Eemian for the equilibrium changes with temperature:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/eemian.gif|
Some 100 ppmv increase for 10°C increase for Antarctic temperatures or between 15-20 ppmv/°C for global temperatures.
According to Takahashi for modern times: about -13 ppmv between MWP and LIA and back +13 ppmv today since the LIA. +3.5 ppmv/°C for 1-3 year events (Pinatubo, El Niño) and -5 ppmv/°C for seasonal changes.
The current increase is over 100 ppmv/°C if temperature was the origin of the increase, which it is not.
Thus the oceans are not the cause of the increase in the atmosphere, neither is vegetation…
Dr. Ed, July 15, 2025 at 11:01 am
One can’t prove that a hypothesis is right, one can only prove that a hypothesis is wrong, if it violates even the smallest, minuscule fact. I haven’t seen any proof that our work violates any observation of any kind. Thus still is getting strong.
The main argument is simply in the carbon mass balance, all the other observations just support the human cause of the increase, but are not even necessary.
The mass balance shows that human emissions are larger than the observed increase in the atmosphere, thus nature is a net sink for CO2 (whatever the combination of natural and FF CO2 in the atmosphere), not a net source.
Any attempt to show that natural emissions are even a part of the increase violate the carbon mass balance.
Then:
“One other startling error that you made a few days ago, was to claim that it is incorrect to detrend time series data in order to calculate a correlation.”
This is really a mathematical joke.
Let us start with two independent variables that cause changes in a third, dependent, variable.
One has no trend and a lot of variability, the other has zero variability, but a huge trend. The net result of both together is a huge trend with huge variability:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_t_em.png
With an error in it: human emissions are labeled as d(em)/dt, while that are just the emissions/year.
Both temperature dT/dt and dCO2/dt are moving 12-month averages with a lot of variability.
dT/dt has zero trend and all variability. Human emissions are all trend and near zero variability.
Now, when analyzing these data, all the CO2 variability of the increase indeed is caused by temperature variability in the derivatives, but as dT/dt has no trend, it is not responsible for the trend in dCO2/dt, while the emissions/year show twice the trend of dCO2/dt…
That means that looking at the variability on the de-trended data shows what is responsible for the variability but effectively removed the cause of the trend of CO2 in the atmosphere!
Simply said, every type of program that looks at the variability for the cause of the increase in the atmosphere is doomed to fail, including the RRR approach of Koutsoyiannis…
At last, here the influence of a few extremes in temperature around the 100 ppmv trend in the past 67 years of accurate measurements:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/wft_trends_rss_1985-2000.png
Ferdinand Engelbeen
July 15, 2025 at 11:10 am
“Inputs – outputs = NET output, thus Tau…”
Yes, Tau. A construct of Magic Math. We will go round and round getting nowhere, I’m afraid.
I suppose, too, you won’t be agreeing that Tau has nothing to do with the interglacial shifts in equilibria. I already acknowledged temperature is only fractionally responsible for the excess natural emissions. Biosphere expansion and FF account for the rest, thus oceans, vegetation, temperature, and FF all contribute to increasing CO2 in the atmosphere.
One of the first papers I saw on this subject was ( http://www.co2web.info/ESEF3VO2.pdf ) by Tom Segalstad in 1998. He addressed much of the mass balance ideas brought out by Ferdinand Engelbeen and others here but concluded the quantification of the processes discussed led to a conclusion that closely matches Dr. Ed’s numbers. He was very critical of the IPCC treatment of ocean chemistry and modeling of CO2 /temperature dependence. He was also critical of the ice core data based on his interaction with Jaworoski who apparently worked on them extensively.
DMA, July 15, 2025 at 1:42 pm
I had similar discussions with Segalstad and others in the early 2000’s with the same arguments. Nothing since then has changed… The main difference: the main use of the residence time to “prove” that humans are only part of the increase. Still violating the carbon mass balance…
Take this one:
“Both radioactive and stable carbon isotopes show that the real atmospheric CO2 residence time (lifetime) is only about 5 years, and that the amount of fossil-fuel CO in the atmosphere is maximum 4%”
The supply of FF was 1% to 5% of the total inputs between 1958 and current, but meanwhile the observed increase in the atmosphere is already over 10% FF and in the ocean surface over 6% FF.
The “life time” of the bomb 14C is between 12 and 20 years, still 3 to 5 times slower than the 4 years residence time…
And about Jaworowski: he never performed a CO2 measurement in ice cores. He was a specialist in radioactive fallout from Chernobyl and looked at the presence (and migration) of these metal ions in relative warm ice fields of Scandinavia (with a lot of water veins. He translated his experience to objections against ice core CO2 measurements, which can’t be compared at all, at least as for the much lower temperatures and the lack of water veins, large enough to pass CO2 molecules…
All his objections from 1992 were rebutted by the work of Etheridge et al. from 1996 on three high accumulation and high resolution ice cores at Law Dome. Despite that he repeated his objections in the early 2000’s…
See: https://www.ferdinand-engelbeen.be/klimaat/jaworowski.html
Jim Siverly, July 15, 2025 at 1:01 pm
Jim, Te is about mass / outflow, not [input – output], which is NET outflow.
Ferdinand,
“The main argument is simply in the carbon mass balance, all the other observations just support the human cause of the increase, but are not even necessary.
The mass balance shows that human emissions are larger than the observed increase in the atmosphere, thus nature is a net sink for CO2 (whatever the combination of natural and FF CO2 in the atmosphere), not a net source.
Any attempt to show that natural emissions are even a part of the increase violates the carbon mass balance.”
If the most that human emissions have ever been is 4-5% of the total emissions every year since 1750, then how can the total amount of human CO2 in the atmosphere be more than 5%? By the way, this is a carbon mass-balance question.
Stephen and Jim,
You both seem to half accept the mass balance argument when you agree that nature is a net sink, and that “of course natural processes are removing more carbon from the atmosphere than they are adding.” But you seem to be hung up on a different point, the same one that has confused Ed for several years. Remember, Ed’s calculations, Jim’s spreadsheet, AND MAINSTREAM SCIENCE all agree that there is little of what Ed calls “human carbon” in the present atmosphere. You seem to think, as Ed did, that cinches the case that the rise is dominated by natural processes (the very same ones that are removing net carbon from the atmosphere!) That is where you and Ed are in disagreement with mainstream science, Ferdinand, and me.
My July 14 posts at 8:10 and 8:16 AM explained why the “human carbon” content of the present atmosphere would be what it is even with 100% of the atmospheric rise coming from human emissions. The only counter-argument against that post so far is Stephen’s “net global uptake is poop”. If that is the best you can do, case closed. But there is also work to be done getting you to understand adjustment times, that I am leaving to Ferdinand.
David,
What are you talking about? I never agreed that nature is a net sink. I believe nature is a net emitter. It has to be. That is the only thing that makes sense mathematically.
David,
Ed Berry has already made the argument with his model derived from physics. He’s already showed net global uptake is poop. dC/dt= Input – Output. Output is proportional to CO2 level. Falsify his hypothesis. If dC/dt=0, input=output, then what is Tau?
If human emissions have never been more than 5% since 1750 then how can human CO2 be more than 5% of the total atmospheric composition?
Stephen,
Data says unambiguously that atmospheric accumulation is only 45% of human emissions. See Ballantyne cited multiple times above. Where does the rest of the “human carbon” go if not into natural land/sea sinks?
None of the stuff being talked about here is new. See:
https://scienceofclimatechange.org/wp-content/uploads/Andrews-2023-Clear-Thinking-about-Atmospheric-CO2.pdf
David,
You don’t answer questions. You just refer to dogma.
Stephen P Anderson, July 15, 2025 at 10:00 pm
“dC/dt= Input – Output. Output is proportional to CO2 level”
1. Output of the atmosphere is NOT proportional to the absolute CO2 pressure, but proportional to what Henry’s law dictates for the ocean surface. Not that it makes much difference, as input – output is a meager 5 PgC/year (~2.5 ppmv/year) at a level of 900 PgC in the atmosphere. For the absolute output that makes some 16 PgC/year. That is all. All the rest of the 200 PgC/year is what other processes absorb and bring back and these processes are largely independent of the CO2 pressure in the atmosphere. Like the uptake by vegetation in spring/summer: 120 PgC/half year only from the sun and temperature. The net effect of the full biological cycle is only 2.5 PgC/year more out than in.
2. Add the human FF emissions / sinks to that formula:
dC/dt = Input – Output + FF – human induced sinks
dC/dt = -5 PgC + 10 PgC – 0 PgC
dC/dt = +5 PgC fully caused by human FF emissions.
That is the mass balance.
That says nothing about what happens with the individual FF CO2 molecules, which may (in part) reside in the atmosphere or may all replaced (NOT removed as mass!) by CO2 molecules from other reservoirs.
3. For input = output:
If input = output, the formula for Tau:
Tau = extra CO2 / extra output
can’t be calculated, because there is no extra output.
At the moment that there is extra CO2 in the atmosphere above the equilibrium with the ocean surface, per Henry’s law, Tau can be calculated and both for oceans and vegetation, that is a linear function: the extra output is directly proportional to the extra CO2 in the atmosphere.
For the current atmosphere that gives:
Tau = (900 – 589) / 5 = 62 years.
The 900 PgC in the atmosphere and the 5 PgC/year inputs-outputs are observed. the 589 PgC in 1750 was based on ice core measurements, but may have shifted over time (as is the case for the average ocean surface).
Thus what is the current equilibrium where inputs = outputs?
That can be back-calculated. As both the (deep) oceans and the biosphere react in ratio to the extra CO2 in the atmosphere, the point of zero difference between inputs and outputs is easy to obtain:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Or about 282 ppmv or 607 PgC, slightly higher than in 1750, due to an increased sea surface temperature.
That makes that the current Tau gets:
Tau = (900 – 607) / 5 = 59 years.
Several others like Dietze (1997), Lindzen, Spencer and others have calculated the current “equilibrium” CO2 level in the atmosphere between 280 and 300 ppmv
What has that to do with Te? Simply nothing. The output may be 20 or 200 or 2000 PgC/year with a calculated Te of 50 or 5 or 0.5 years, that has zero influence on Tau, which can be calculated independently of Te as long as inputs – outputs 0.
Tau is the real removal rate (adjustment time or lifetime) of any extra CO2 in the atmosphere as mass, whatever the origin of the extra mass.
Te is the average time any individual CO2 molecule (whatever the origin) remains in the atmosphere, before being transferred to another reservoir. Either by mass removal or by replacement.
4. How can there be more FF CO2 in the atmosphere than 5% with only 1% to 5% (1958-current) in the inputs?
Quite simple: the 1-5% in the inputs is “fresh” FF CO2. Part of the total FF emissions in the past were distributed into vegetation and ocean surface and now are recycled back to the atmosphere as “old” FF CO2. Thus FF accumulates over time in all three reservoirs…
Only what gets into more permanent vegetation and soils doesn’t return and what goes into the deep oceans returns only after many centuries…
I hope this made it clear what the difference between Tau and Te means…
The sentence
“as long as inputs – outputs 0”
had the smaller than / larger than signs, but these disappeared…
So the text should be:
“as long as inputs – outputs do not equal zero”
David Andrews
July 15, 2025 at 9:01 pm
If you want to get me to understand adjustment times, maybe you should help Ferdinand answer my question about an A to B reversible reaction reaching the same equilibrium ratio while both concentrations increase after additional reactant is added to the system. What is Tau for the time to establish the new equilibrium and why should it be any longer than the original relaxation time?
Ferdinand Engelbeen
July 16, 2025 at 2:51 am
“1. Output of the atmosphere is NOT proportional to the absolute CO2 pressure, but proportional to what Henry’s law dictates for the ocean surface.”
You’ve asserted this countless times here. It disagrees with mainstream scientists who are not fooled by Magic Math. It’s time for you to show a proof of 1. And not with anecdotal data, which is not proof.
I know that you are going to say it is the NET output that is proportional to the difference, as in F = k•s•ΔCO2. Where is Feely’s use of that formula derived from first principles?
Jim Siverly, July 16, 2025 at 6:29 am
“I know that you are going to say it is the NET output that is proportional to the difference, as in F = k•s•ΔCO2. Where is Feely’s use of that formula derived from first principles?”
Jim, I am really surprised that you even question that formula…
From the atmosphere into the oceans, the gas transfer is:
F- = k*s*pCO2(atm)
Where (s) is the solubility in seawater and (k) the kinetic forcing function, the gas transfer velocity.
the opposite transfer is:
F+ = k*s*pCO2(aq)
In both cases a lot of CO2 molecules are going from one medium to the other medium.
The overall transfer then is:
F = k*s*ΔpCO2(atm-aq)
Compared to the [Te(s-g) – Te(g-s)] of Dr. Ed, the influence of the CO2 mass in the atmosphere is about the same, as for any gas mass equals partial pressure. A doubling of CO2 mass in the atmosphere will give a doubling of CO2 transfer from atmosphere to ocean surface.
For the oceans, that is not the case, because of all carbon present in the surface (~900 PgC) only about 1% is pure, dissolved, CO2 which causes the equilibrium pCO2 of the ocean surface. The carbonates, bicarbonates, pH and temperature all influence the pure [CO2] and thus the pCO2 of the surface, but not in direct ratio to their mass.
Thus Te(s-g) is not applicable as surrogate for the CO2 transfer between ocean surface and atmosphere.
In the first formula:
F- = k*s*pCO2(atm)
(s) plays no role, and must be dropped.
Ferdinand Engelbeen July 16, 2025 at 2:51 am
Dear Ferdinand,
Jim, Stephen, and others are correct.
The outflow of carbon from the atmosphere depends only on the level (or pressure) of carbon in the atmosphere divided by an e-time. Since the earth is not sealed with plastic, the carbon cycle easily flows between the carbon reservoirs.
This simple equation is more than physics. This result of the whole field of systems engineering that no one in the CO2 Coalition will even study. I usually reference the book by Jay Forester (MIT): Principles of Systems. Get a copy and read it. If you can’t understand it, as I predict, this means you and everyone else in the CO2 Coalition does not know WTF you are talking about when you attempt to define a carbon cycle.
This is more than physics. This is systems engineering. We have people like you, Burton, Happer, Lindzen, Spencer, and all the rest of the CO2 Coalition clan, who think they know systems engineering but they don’t. So, they screw it up. You and they are way out of your field of expertise when you attempt to deal with a subject like the carbon cycle, which is a system.
To say the ocean determines how much carbon flows out of the atmosphere, is analagous to saying that a charity determiines how much money I send it, when it is obvious that I determine how much money I send to a charity. That is a system. That is how nature works. The reservoir that holds the carbon sets the outflow of its carbon. A sink doesn not determine the outflow of another reservoir. Your focus on sinks misses the whole method to solve the problem.
This is the opposite of govenment taxes that determine how much money I send them. But government is not free flowing system. Government is a forced structure that steals our money.
A key part of a simple system is that Outflow = Level / Te
All pharmcology models use this equation, for example, and it works.
The fact that I could reduce my system equations of for the carbon cycle to an electric circuit proves that my model is physicially correct. It reduces to Ohm’s Law. My carbon cycle model functions like an electric circuit. Your’s does not.
Your and the CO2 Coalition’s handwaving arguments do not even have a mathematical structure. You don’t even know how to define a carbon cycle model. Your so-called mass conservation is a piece of junk from the viewpoint of physics, systems, and simple bookeeping. You have nothing that you can reduce to Ohm’s Law to demonstrate that your hypotheses are truly simulating nature.
You cannot follow the very simple process of separating your mass balance equation into two separate models, one for natural carbon and the other for human carbon. Such separation is fundamental to this problem and the proper way to solve this problem, e.g., calculation the effect of human CO2 on the level of atmospheric CO2.
If I were the teacher and a student could not understand that we need to make this separation in order to solve this problem, I would flunk the student and suggest he pursue another subject, like maybe being a rock star.
When you, and others like Andrews, talk about a natural carbon atom “taking the place of a human carbon atom”, you are so far out in limbo land that you should take up another profession entirely.
The CO2 Coalition should get out of this subject because they claim expertise that they do not posess. As a result, they are destroying the progress of atmospheric physics.
Jim,
I do want to help you understand adjustment time. Here is a little exercise which I hope will convince you that one time constant does not describe the carbon cycle. Unlike Ferdinand’s analysis, mine is mostly qualitative but I hope gives insight.
Start by imagining a two-box system called “atmosphere” and “surface ocean”. (Temperatures are stable throughout.) The CO2 content in one box has reached a Henry’s Law equilibrium with the CO2 content in the other box. Now introduce a steady trickle of CO2 to “atmosphere”. The CO2 concentration there grows, it no longer is in equilibrium with “surface ocean”, and net CO2 is transferred to “surface ocean”. The dynamics could be analyzed with Henry’s Law and a time constant which measures how much “surface ocean” lags “atmosphere”. Let’s guess that time constant is 4 years. After a while, turn off the CO2 trickle into “atmosphere” [net zero!], and in four-ish years the system settles into a new and stable equilibrium with higher CO2 levels than it originally had. In this model, it will stay there indefinitely.
“But wait”, you say, “that model is too simple!” I agree, so we will add a third box called “deep ocean” which exchanges carbon with “surface ocean”. The mechanisms for doing that include the sinking of organic matter, and circulation patterns with vertical components. Since extra carbon has been introduced to “surface ocean”, we can expect the net result is to transfer carbon from “surface” to “deep”. This will reduce the “back pressure” of carbon in “surface ocean” and allow a decrease in atmospheric carbon. Do you care to argue that the time constant for that adjustment is also 4 years? Of course it is not. The physical processes are entirely different. A credible analysis estimates one century. Some older and much longer estimates are, in my view, doubtful. I am not sure if the consideration of biological dynamics in parallel with surface-to -deep transfers reconciles one century with Ferdinand’s 50 years.
You have a few times noted that you had to postulate “exponentially” growing natural emissions to keep up with the Mauna Lua curve. That is because of your too-short time constant.
Ed,
1.You have not been able to tell me how natural processes that remove more carbon from the atmosphere than they add, are nevertheless are responsible for CO2 growth.
2. We agree that there is little of your “human carbon” in the present atmosphere. I have told you why: the dilution of the Seuss Effect, known about since the 1950’s. You have not responded.
I have several times judged high school debates. When one debater ducks question from the other, that debater loses. You lose, Ed.
David Andrews July 16, 2025 at 9:33 am
Dear David,
That is one of the most complicated pseudo explanations of a simple concept I may have read.
First, you have no formula for adjustment time, so it is meaningless in the context of this discussion. It has no bearing on how to calculate or explain the evolution of the carbon cycle. It is a diversion from physics.
Second, the only meaningful time constant is e-time because it has a real formula that predicts things and applies universally to our discusion.
Third, for a simple explanation of how carbon flows in IPCC’s carbon cycle model, see my Figure 7. The top row illustrates IPCC’s natural carbon cycle at equilibrium. Change the numbers if you wish but every set of suggested numbers will have an equilibium distribution. This is the condition where the carbon flows between the boxes are equal.
The second row in Figure 7 illustrates human carbon at equilibrium if all human emissions ended. The human carbon cycle will have the same percentages in each box as the natural conbon cycle because of the climate equivalent principle.
Figure 7 shows human carbon left in the atmosphere at equilibrium is about 4 ppm when human carbon has added about one percent to the carbon in the natural carbon cycle.
Such equilibrium represents a maximum entropy for the carbon cycle.
Figure 7 shows what happens to human carbon that we introduce into the atmosphere. The addition of human carbon to the atmosphere begins in a low entropy condition. Human carbon will flow to the other boxes in a manner that increases the entropy as fast as possible.
Human carbon cannot increase the CO2 level in a manner that would lower the entropy of either the human carbon cycle or the natural carbon cycle.
The CO2 Coalition’s argument that human carbon causes all the CO2 increase, or somehow causes the natural carbon cycle to cause the CO2 increase fail because they lower the entropy of the total carbon cycle, which is an impossible.
David Andrews July 16, 2025 at 9:55 am
“1.You have not been able to tell me how natural processes that remove more carbon from the atmosphere than they add, are nevertheless are responsible for CO2 growth.”
Your question itself shows you do not understand the physics of the carbon cycle. Even in my last comment, I explained the basics of how human carbon affects the carbon cycle.
“2. We agree that there is little of your “human carbon” in the present atmosphere. I have told you why: the dilution of the Seuss Effect, known about since the 1950’s. You have not responded.”
Read my draft paper above.
First, we disagree WHY human carbon is a small part of the present atmosphere. You claim it is because natural carbon atoms “replaced” human carbon atoms in the atmosphere. Your explanation defies physics and would decrease the entropy if it happened.
Second, the Seuss effect is a calculated effect, not a cause. It does not even deserve a special name but you make a big deal of it because you incorrectly believe it somehow strengthens your argument. It does not.
The D14C data show human carbon has lowered the D14C level by less than 8%. That proves human carbon is less than 8% of the atmosphere.
This D14C “dilution” is a result of the continuing inflows of human carbon and natural carbon into the atmosphere. These inflows set balance levels. The dilution is a measure of the human carbon balance level compared to the natural carbon balance level. Period.
At the risk of sounding silly (I’m an old land surveyor who’s expertise is in knowing what to measure and mostly at sea on the technicalities in this discussion) I will ask if the mass of the atmosphere is constant? It seems that the mass balance approach assumes that it is but Dr. Ed’s approach does not. I know that lots of atmospheric gasses are added and removed by natural and anthropogenic processes.
DMA,
A better name for the argument often called “mass balance” is simply “carbon conservation.” If human emissions put 100 units/yr of carbon into the atmosphere, but the measured carbon growth rate is only 45 units/yr, then by carbon conservation, natural processes must be removing 55 units/yr and putting it in somewhere else. The carbon can’t just evaporate. These are good average numbers. Ed is trying to convince you that these same natural processes are somehow adding carbon to the atmosphere, but he never directly tells us how. That is because they are not.
Ferdinand,
“Output of the atmosphere is NOT proportional to the absolute CO2 pressure, but proportional to what Henry’s law dictates for the ocean surface. Not that it makes much difference, as input – output is a meager 5 PgC/year (~2.5 ppmv/year) at a level of 900 PgC in the atmosphere. For the absolute output that makes some 16 PgC/year. That is all. All the rest of the 200 PgC/year is what other processes absorb and bring back and these processes are largely independent of the CO2 pressure in the atmosphere. Like the uptake by vegetation in spring/summer: 120 PgC/half year only from the sun and temperature. The net effect of the full biological cycle is only 2.5 PgC/year more out than in.”
You and David keep repeating stuff that has no scientific basis. That is not Henry’s Law. You know it is not Henry’s Law. I’ve shown you that it is not Henry’s Law, but you continue to insist it is Henry’s Law. Read any Chemistry 101 textbook and it will recite Henry’s Law exactly like I have stated. Dr. Ed showed in his first paper that C14 bomb data supports his hypothesis, L/Te = outflow. How is it possible to debate people who refuse to accept natural law? You don’t accept the Equivalence Principle. You don’t accept the gas laws. You don’t accept scientific method. You refuse to answer my questions. You and David are so chained to your beliefs that you can’t accept that they are wrong.
David Andrews
Aren’t the units computed as a percentage of the atmosphere? If that mass is changing the units aren’t the same. Human emissions are tons of CO2 but total CO2 is in tons computed by multiplying a measured percentage times a figure that maybe not constant.
Ferdinand,
So, for input=output, Tau has no meaning then what is Te?
David Andrews July 16, 2025 at 11:27 am
David,
There you go again:
“… then by carbon conservation, natural processes must be removing 55 units/yr and putting it in somewhere else.”
You have physics backwards. “Natural processes” don’t “remove” human carbon from the atmosphere, like a dump truck removes garbage.
Human carbon flows out of the atmosphere toward its equilibrium distribution in the carbon cycle, thereby increasing its entropy.
Simple calculations based upon human emissions and reasonable Te for the six flow nodes, show human CO2 cannot cause all, or even most, of the CO2 increase because human carbon added to the atmosphere flows to the other boxes too fast to allow human CO2 to cause all the CO2 increase.
You are trying to tell people that human emissions cause all the increase in the face of carbon cycle data, including D14C data, that prove your claim is impossible.
I don’t need to prove how nature would cause the CO2 increase. You need to prove that human CO2 caused the increase.
Science requires we use the null hypothesis which says all changes are natural until proven otherwise. The burden of proof is on you to prove otherwise.
You have not and cannot do that.
Stephen Paul Anderson, July 16, 2025 at 11:40 am
Stephen. if the ocean surface in average, per Henry’s law, is in equilibrium with the atmosphere, that is when in average there is a fixed ratio between CO2 in the atmosphere and the ocean surface waters, then still a lot of CO2 can be exchanged, because some parts (near the equator) are warmer, thus release CO2 and some parts are colder, thus absorb CO2. That is called a dynamic equilibrium. CO2 is removed near the poles and that sinks with the cold waters into the deep oceans, to return some 1,000 years later near the equator, releasing its CO2 again.
At that moment there still is a
Te(a-d) = 589 PgC / 25 PgC/year = 23 years.
For the reverse flow:
Te(d-a) = 37,100 PgC / 25 PgC/year = 1,484 years.
Tau is not calculable as (input = output) and division by zero is not possible.
There is no usable information in Te(a-d) or Te(d-a), as the only point of interest is if the input and output flows are equal and neither of these two gives us that information.
In the current atmosphere the CO2 mass is already 900 PgC which makes that the outflows (and also inflows) into the deep oceans increased (let us assume in ratio, thus + 50%):
Te(a-d) = 900 PgC / 40 PgC/year = 22.5 years
Te(d-a) = 37,100 PgC / 40 PgC/year = 928 years
The output from the atmosphere to the deep oceans increased in ratio, thus Te(a-d) remained about the same, but as the carbon content of the deep oceans hardly changed, Te(d-a) did change a lot.
Again, that doesn’t give the slightest information of the actual change of CO2 in the atmosphere or deep oceans.
What happened to Tau? Yet it is calculable: the estimated net sink rate from the atmosphere into the deep oceans (input – output) is 2.0 PgC/year. That gives for Tau:
Tau(a-d) = (900 – 589) PgC / 2 PgC/year = 155 years
If Tau doesn’t change over time, which is the case for a linear decay, then we can calculate the carbon increase or decrease in the atmosphere, ocean surface, deep oceans and vegetation for the past and the future – if human emissions and temperature are known…
Tau gives us usable information, Te doesn’t.
Dr. Ed, July 16, 2025 at 11:58 am
“Simple calculations based upon human emissions and reasonable Te for the six flow nodes, show human CO2 cannot cause all, or even most, of the CO2 increase because human carbon added to the atmosphere flows to the other boxes too fast to allow human CO2 to cause all the CO2 increase.”
Simple calculation indeed shows that human FF is readily distributed over all reservoirs, which all increase in carbon content. But as human emissions (according to your Te’s) are fast getting out of the atmosphere, where is the rest of the observed increase in the atmosphere coming from?
Something doesn’t add up in your carbon mass balance…
Ferdinand Engelbeen
July 16, 2025 at 7:13 am
I know your mind is made up, but humor me while I try to understand your interpretation of F = k•s•ΔCO2.
Do you agree that output from the atmosphere is equivalent to – dCO2/dt, where CO2 is the concentration of CO2 in the atmosphere (the minus sign indicates output is reducing CO2)?
Second, by splitting Feely’s equation, do you agree that F- = k*p(CO2) = – dCO2/dt?
Also, that F+ = k * s * pCO2(aq) = + dCO2/dt?
Finally, at equilibrium, although there is no net transfer, do those forward and reverse rate equations still apply?
Ferdinand Engelbeen July 16, 2025 at 1:04 pm
Since human CO2 can’t cause all the CO2 increase, the only other possibility is natural CO2 increased.
However, I don’t need to show or prove how nature is doing that.
(This is somewhat like an astromoner finding something is causing a planet to deviate from its expected orbit. The astronomer does not have to find WHAT is causing the deviation in order to prove his calculations are correct. Typically, someone else finds the cause.)
Science requires we use the null hypothesis which says all changes are natural until proven otherwise. The burden of proof is on you to prove that my calculations are wrong or the numbers I use are wrong.
Ferdinand,
So, Te = L/outflow=589PgC/25PgC/yr=23.6 years. Where did you get your outflow from?
Ferdinand,
Also, what Te(c) vs. Te(a-d)?
DMA
July 16, 2025 at 11:05 am
July 16, 2025 at 11:45 am
Although there are gasses entering and exiting the atmosphere, their concentrations remain relatively constant except CO2 which has been gradually increasing. Fortunately, we have the Mauna Loa and other places monitoring it. It’s more difficult to measure CO2 in other reservoirs. The mass balance has to do with where the fossil fuel carbon went. I have no idea why David Andrews doesn’t see the obvious that whatever is no longer in the atmosphere is somewhere distributed between the other reservoirs. The hard part is what Dr. Ed did, to use estimates of reservoir content and mass transfer rates to figure out what went where when. David Andrews’ simple math is insufficient to explain all the data correctly using the correct physical principles involved.
“Aren’t the units computed as a percentage of the atmosphere?”
That’s a good question. The volume of the atmosphere is constant and the mass is easily determined by C * V. Ocean concentrations are measured, but the volumes vary widely and it’s impossible to know concentrations and volumes of the land.
That’s why Dr Ed’s methods are so useful. It allows a way to evaluate the estimates and synchronize them with the known values which are mainly just the changing concentration of CO2 in the atmosphere. If there’s any missing carbon, you can be sure to find it somewhere in a tree or on the ocean floor.
David Andrews
July 16, 2025 at 9:33 am
I will just add two things to Dr. Ed’s answer at July 16, 2025 at 10:16 am. First, the long 50-year Tau is an artifact of using the preindustrial value of CO2 as the equilibrium concentration if net zero ever happened. Because of bioexpansion, the new equilibrium will be at a much larger CO2 value.
Second, yes, I postulated “exponentially” growing natural emissions to keep up with the Mauna Loa curve using an e-time of about four years. I also tried no change in natural emissions and postulated slowly increasing e-time to maintain the agreement with Mauna Loa data. But that required deviating greatly from the universally accepted constant e-time of about 4 years. I couldn’t make it correlate with both constant natural emissions and constant e-time. Can you demonstrate a scenario matching Mauna Loa data using a 4-year e-time without increasing natural emissions?
Ed,
Must I go back to your old papers and identify plots which show human emissions greater than atmospheric accumulation? The world understands: those plots mean net global uptake has consistently been positive. The world understands: that proves natural processes are removing net carbon from the atmosphere. The world understands: that proves human emissions cause the CO2 rise. A dump truck analogy works. Nine dump truck loads move carbon from land/sea reservoirs to the atmosphere. Ten dump truck loads move carbon from the atmosphere to land/sea reservoirs. As a result, natural processes mitigate the increase in atmospheric carbon that humans cause. You know the consistently positive net global uptake falsifies your false theory and that makes you panic.
Please don’t repeat that your calculation shows only a small “human carbon” component in the present atmosphere. That is a correct conclusion in line with mainstream science, anticipated 70 years ago, and not particularly important.
Entropy??? Careful Mr. Ed, I taught thermodynamics. Go ahead, pursue this line. Make my day.
Ed,
Must I go back to your old papers and identify plots which show human emissions greater than atmospheric accumulation? The world understands: those plots mean net global uptake has consistently been positive. The world understands: that proves natural processes are removing net carbon from the atmosphere. The world understands: that proves human emissions cause the CO2 rise. A dump truck analogy works. Nine dump truck loads move carbon from land/sea reservoirs to the atmosphere. Ten dump truck loads move carbon from the atmosphere to land/sea reservoirs. As a result, natural processes mitigate the increase in atmospheric carbon that humans cause. You know the consistently positive net global uptake falsifies your false theory and that makes you panic.
Please don’t repeat that your calculation shows only a small “human carbon” component in the present atmosphere. That is a correct conclusion in line with mainstream science, anticipated 70 years ago, and not particularly important.
Entropy??? Careful Mr. Ed, I taught thermodynamics. Go ahead, pursue this line. Make my day.
Jim,
“universally accepted constant e-time of about 4 years. ” (?!)
…universally accepted by novices that don’t understand the difference between adjustment time and residence time perhaps. So you really think the time constant for surface ocean/ deep ocean mixing is four years? Or do you think that particular mixing time is irrelevant? Can you tell me where I referenced the 1750 equilibrium in my little exercise? You are not making much sense. Explain yourself.
Jim,
I just noticed your comments about the growth in carbon in the ocean (“acidification”) and in the biosphere (the greening that the CO2 coalition talks about.) Of course that results from natural processes moving carbon out of the atmosphere and into those reservoirs. It is where the net global uptake went. What I don’t understand is why you apparently think that supports the wrong notion that natural processes cause the atospheric increase.
Ferdinand,
“Observed: 5 PgC/year = 10 PgC/year + natural inputs – natural outputs
Or natural outputs are 5 PgC/year larger than the natural inputs.
Even if the natural outputs include half the human input of 5 PgC/year human supplied FF molecules, then still the full increase of 5 PgC/year in the atmosphere is caused by the human emissions.
According to your ideas, natural outputs are smaller than natural inputs.
Who is violating the carbon mass balance ánd the equivalency principle here?”
You. You are violating the carbon mass balance and the equivalence principle. You flunk Physics 101. Let me help you.
dCO2/dt = Inflow – Outflow
Inflow=Lb/Te (Lb=Balance Level)
Outflow= L/Te
L=430ppm
If we use dC/dt=2ppm/yr (4.24PgC/yr) and a Te of 4 years from Dr. Ed’s paper.
Outflow=430ppm/4yr=107.5 ppm/yr
Inflow= 107.5ppm/yr+ 2ppm/yr =109.5ppm/yr
Balance Level = 109.5ppm/yr(4yr)=438ppm
Te (eTime) is the time it takes for Level to reach 0.693 the distance from the level to the balance level. So, in 4 years from now, the level should be 435.54ppm.
If inflow is 5ppm human and 104.5ppm natural, then in 4 years when the level is 435.5ppm, human CO2 can be no more than 20ppm of the total. Outflow, which is 107.5ppm/yr, is 4.945ppm/yr human and 102.555ppm/yr natural. So, of the 2ppm/yr increase, 0.055ppm is human and 1.945ppm is natural. Natural emissions are greater than natural sinks. This is conservation of mass and in compliance with the equivalence principle.
David,
Dr. Ed has talked about adjustment time. Te is the time it takes for level to go 0.693 the distance to the balance level. So, in 4 years it will be at 435.5ppm. In 8 years it will be at 437.2 ppm. In 12 years it will be at 438ppm. So, some of the CO2 molecules have very short residence times and some have long residence times. It takes 3 or 4 Te’s to reach the balance level. (Actually, it never does. That is the nature of Euler’s number.) Residence time has nothing to do with the mathematics of the conservation of mass of carbon in the atmosphere.
Ferdinand,
P.S.-This is the solution to the first order linear differential equation. There is no other solution.
Stephen P Anderson, July 16, 2025 at 11:56 pm
“dCO2/dt = Inflow – Outflow
Outflow= L/Te
L=430ppm”
So far so good. Then:
“Inflow=Lb/Te (Lb=Balance Level)”
Say what? Are you saying that soil bacteria which remove plant rests and humans, which exhale 40,000 ppmv CO2 do that in ratio with CO2 in the atmosphere?
“If we use dC/dt=2ppm/yr (4.24PgC/yr) and a Te of 4 years from Dr. Ed’s paper.
Outflow=430ppm/4yr=107.5 ppm/yr
Inflow= 107.5ppm/yr+ 2ppm/yr =109.5ppm/yr
Balance Level = 109.5ppm/yr(4yr)=438ppm”
There it goes completely wrong.
Te has nothing to do with the decay rate of any extra injection of CO2, from whatever source.
Te = mass / output.
Between 1750 and current, both mass and output may have increased with 50% (which is not the case, outputs did increase more slowly), leaving a rather constant (or increasing) Te.
Between 1958 and 2025 dCO2/dt increased a five fold from 0.5 ppmv/year to 2.5 ppmv/year.
Simply said: Te and dC/dt have nothing in common and the 4 years residence time and the real decay rate or adjustment time (Tau) are completely different items.
Why is that? Because most of the outflows are (near) completely independent of the absolute CO2 pressure in the atmosphere. These are temperature, sunlight, bacterial and other biological processes, independent of how much CO2 resides in the atmosphere.
The height of the inflows and outflows has zero impact on the decay rate of CO2 in the atmosphere, only the difference counts: dCO2/dt = inflows – outflows.
dCO2/dt is quite exactly known, outflows only roughly, thus Te is even far from certain.
Then the balance level: that can be back calculated from the level in the atmosphere and the resulting dCO2/dt. Where dCO2/dt = 0, that is the balance level:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Between 280 and 300 ppmv.
“Te (eTime) is the time it takes for Level to reach 0.693 the distance from the level to the balance level. So, in 4 years from now, the level should be 435.54ppm.”
Te is level / output, that “can” be like Tau, the time to reach 1/e of the balance level, if and only if all inflows, container and outflows are unidirectional. That is the “lake / container / bath tube” model. Then Tau is smaller than to equals Te.
If there are back flows, which is the case for 95% of all CO2 flows the real world, then Te and Tau are decoupled and completely independent of each other. That is the “fountain” model, where lots of CO2 are pumped in and out, without any influence on the quantity that is really removed.
The calculated Tau, based on the current 420 ppmv and the calculated balance level of around 290 ppmv and the observed dCO2/dt of 2.5 ppmv/year gets:
Tau = (420 – 290) / 2.5 = 52 years
“So, of the 2ppm/yr increase, 0.055ppm is human and 1.945ppm is natural. Natural emissions are greater than natural sinks. This is conservation of mass and in compliance with the equivalence principle.”
One little problem: the CO2 level, both in the oceans and the biosphere increased with in total about 1 ppmv/yr as mass. Both oceans and biosphere together supplied near 2 ppmv/yr to the atmosphere.
Total increase in all containers together: 3 ppmv/year, with an external (human) supply of 2 ppmv/year. Something doesn’t add up here…
Moreover, with 1% to 5% in the input (1958-current) the observed FF level in the atmosphere is already over 10% and in the ocean surface over 6%… With your calculation that would be less than 1%.
Stephen P Anderson, July 17, 2025 at 12:13 am
“Te is the time it takes for level to go 0.693 the distance to the balance level.”
That is the essence of the discussion here:
Te is NOT the time it takes to decay to the balance level. That is Tau.
Te in this real world has nothing to do with reaching a balance level, it only shows how long an individual CO2 molecule “resides” in the atmosphere, before being removed (with a change in mass) or replaced (without a change in mass) out of the atmosphere. Only 2.5% of CO2 mass is removed per year, while 25% per year is replaced.
Or a difference between 50 years for Tau and 4 years for Te.
David Andrews
July 16, 2025 at 9:38 pm
I can’t immediately tell you what the time constant for surface to deep ocean is, but I’m sure I can get it from Dr. Ed’s paper. It will be different because of the concentration and volume differences. The important point to note is that not all the atmosphere carbon going to the surface is removed to the deep. There is a gradual increase in CO2 there as well, which contributes to the excess CO2 increasing in the atmosphere.
Truck load analogies are not compatible with physical processes. Stick to Magic Math.
July 16, 2025 at 9:50 pm
Better yet, graduate to step-wise integration and compartment modelling. Then you will see for yourself how natural emissions and FF both contribute to atmospheric increase.
Ferdinand,
“Why is that? Because most of the outflows are (near) completely independent of the absolute CO2 pressure in the atmosphere. These are temperature, sunlight, bacterial and other biological processes, independent of how much CO2 resides in the atmosphere.”
Dr. Ed’s hypothesis is based on Henry’s Law, the Ideal Gas Law, and correlates well with C14 bomb data. Te is e folding time which comes from the solution of the differential equation. Your Tau is a mathematical construct. It does not come from the solution of the conservation of mass equation, and it has no basis in math or physics. Its basis is a desired outcome. Dr. Ed’s model is beautifully simplistic and violates no natural laws. Your’s isn’t. Dr. Ed’s solution comes straight from the textbooks that I studied. Your’s does not. Your Tau violates the Equivalence Principle and treats human CO2 and natural CO2 differently. As long as you insist that non-science and non-logic are your basis, we are at an impasse.
Sorry but I have to stop here…
I need to make a presentation for a direct confrontation with Hermann Harde about the same subject for the Scandinavian Skeptics conference and need to transfer all my data to a new computer (thanks to Microsoft, which made Windows 11 not compatible with my only 7 years “old” model), my 3D-printer got broken and I just sold my brand new solar panels that I didn’t use, because of the perfidious change in tariffs they will imply when installed.
Still will finish the A-B item and the Berry challenge within a few days I hope, as promised.
David,
Jim,
“universally accepted constant e-time of about 4 years. ” (?!)
“…universally accepted by novices that don’t understand the difference between adjustment time and residence time perhaps. So you really think the time constant for surface ocean/ deep ocean mixing is four years? Or do you think that particular mixing time is irrelevant? Can you tell me where I referenced the 1750 equilibrium in my little exercise? You are not making much sense. Explain yourself.”
4 years is the universally accepted eTime for outflow from the atmosphere. If you would read Dr. Ed’s paper he says that the eTime for surface ocean to deep ocean is different. I thought we were all talking about atmospheric carbon? The eTime for atmosphere to land will be different than atmosphere to surface ocean, but total eTime is faster than the fastest individual eTime. That’s why the Bern Model is wrong. Thus, we get an overall eTime of 3.5 to 4 years.
Ferdinand,
“One little problem: the CO2 level, both in the oceans and the biosphere increased with in total about 1 ppmv/yr as mass. Both oceans and biosphere together supplied near 2 ppmv/yr to the atmosphere.
Total increase in all containers together: 3 ppmv/year, with an external (human) supply of 2 ppmv/year. Something doesn’t add up here…
Moreover, with 1% to 5% in the input (1958-current) the observed FF level in the atmosphere is already over 10% and in the ocean surface over 6%… With your calculation that would be less than 1%.”
Show your evidence.
David Andrews July 16, 2025 at 9:34 pm
Gee, David, I’m really scared. You may have taught thermodynics but that does not mean you KNOW thermodynamics.
So, challenge me on my comments above about entropy.
Jim,
You have not given us much information about your spreadsheet but assert various conclusions. Some of your comments make me wonder whether it is constrained by carbon conservation. For example “There is a gradual increase in CO2 [in the surface ocean] as well, which contributes to the excess CO2 increasing in the atmosphere.” I imagine your spreadsheet has a row for each year, and columns showing carbon stocks in different places. If you sum all the stocks in a row (year), how does that sum vary year to year?
My other main question about your analysis is one asked before but neither you nor Ed nor anyone else has responded. When you say “Then you will see for yourself how natural emissions and FF both contribute to atmospheric increase” are you simply saying that the present atmosphere contains only a small quantity of “human carbon”? You should know what I think of that argument.
Stephen,
A last comment:
Dr. Ed’s hypothesis is based on Henry’s Law, the Ideal Gas Law, and correlates well with C14 bomb data.
Dr. Ed’s hypothesis should be based on Henry’s Law, which implies a current equilibrium between atmosphere and average ocean surface of 295 ppmv for the current average sea surface temperature. Not 438 ppmv, according to your calculation, which is based on a Te of 4 years only, not the real, calculated from observations, decay rate of 50 years:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
Where A are the FF emissions, observed increase in the atmosphere, the influence of temperature on the equilibrium pCO2 of the ocean surface since 1850, calculated with the formula of Takahashi and the resulting ΔpCO2 between atmosphere and ocean surface.
B is the observed net dCO2/dt with a polynomial to avoid the year by year variability, caused by T variability.
C is the resulting Tau, which is what shows the time to reach 1/e of the ΔpCO2.
The latter is based on every calculation of e-fold decay rates for any process in dynamic equilibrium where one of the components is changed.
https://en.wikipedia.org/wiki/Exponential_decay
Again Te is NOT the decay rate of CO2 to a new equilibrium. That is Tau. Te only shows how long a single CO2 molecule resides in the atmosphere, thus how much CO2 mass is moved through the atmosphere, not how much CO2 mass is REmoved…
And where do we make any differentiation between FF and other CO2? Once in the atmosphere, FF CO2 increases the total mass of the atmosphere with 5 ppmv/year and half that amount as total mass (not the FF CO2 alone) is removed out of the atmosphere. No matter its composition.
Berry’s solution violates the carbon mass balance, because of his use of the much too short residence time, which does not reflect the observed decay rate of about 50 years.
Stephen P Anderson, July 17, 2025 at 7:06 am
Net uptake by the biosphere, based on the oxygen balance and oceans as remaining difference:
https://tildesites.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
“We find the average CO2 uptake by the ocean and the land biosphere was 1.7 ± 0.5 and 1.0 ± 0.6 GtC/yr
respectively”
Increase in the ocean surface, about 10% of the increase in the atmosphere:
https://tos.org/oceanography/assets/docs/27-1_bates.pdf
Figure 3 and Table 2.
Increase in the deep oceans: the remainder of the net sinks for dCO2/dt minus FF emissions.
Increase of FF in atmosphere and oceans:
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2001GC000264
Figure 4.
Based on the drop in 13C/12C ratio: over 10% FF in the atmosphere and over 6% in the ocean surface, calculated for a δ13C level of FF of -25 per mil and an atmosphere at average -6.4 per mil δ13C. Vegetation grows, thus with more CO2 uptake than release, which enriches the atmosphere in 13C at +24 per mil δ13C. Thus is not the cause of the enormous δ13C drop, not seen in the past 800,000 years, when δ13C levels were average -6,5 +/- 0.4 per mil, despite huge changes of 90 ppmv over glacial / interglacial transitions.
Ferdinand Engelbeen July 17, 2025 at 7:38 am
Dear Ferdinand,
You wrote, “Berry’s solution violates the carbon mass balance, because of his use of the much too short residence time, which does not reflect the observed decay rate of about 50 years.”
That is not true because my model begins with the Continuity Equation (1), which ensures my model conserves carbon mass. This conservation is entirely independent of Te.
This negates everything you claimed in your comment because you have based your claims on your fiction about my model.
Your model does not conserve carbon because (a) you have no continuity equation that forces conservation of carbon mass and (b) my Section 3.1, equations (10) and (11) show the critical error in your carbon mass balance equation.
Ferdinand.
“Dr. Ed’s hypothesis should be based on Henry’s Law, which implies a current equilibrium between atmosphere and average ocean surface of 295 ppmv for the current average sea surface temperature. Not 438 ppmv, according to your calculation, which is based on a Te of 4 years only, not the real, calculated from observations, decay rate of 50 years:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
Where A are the FF emissions, observed increase in the atmosphere, the influence of temperature on the equilibrium pCO2 of the ocean surface since 1850, calculated with the formula of Takahashi and the resulting ΔpCO2 between atmosphere and ocean surface.”
It is based on Henry’s Law and the Ideal Gas Law. Henry’s Law doesn’t imply what you say it implies. Your’s and Takahashi’s ΔpCO2 is not part of Henry’s Law. If you keep repeating it is, I’ll keep repeating it isn’t.
Ferdinand,
Is the Scandinavian Skeptic’s Conference in English and is it going to be recorded?
Dr. Ed, July 17, 2025 at 8:18 am
dL / dt = Inflow – Outflow (1)
Agreed
Outflow = L / Te (2)
Upside down…
Te = L / outflow but you may only reverse that formula if, and ONLY if, all flows are unidirectional from input via the container to the output.
How do you calculate the 60 ppmv/year in spring/summer into vegetation with that formula, when the outflow goes from near zero to maximum in a few months, even lowering the L in the atmosphere?
Lb = Inflow * Te (4)
Completely wrong: Lb is not set by the inflows, it is set by the equilibrium between ocean surface and atmosphere per Henry’s law at current SST, that is about 295 ppmv.
Again your formula is true if, and ONLY if, all flows are unidirectional, or the “lake/container/bath tube” model. Not applicable at all for the real world, where 95% of all CO2 flows are just cycling in and out the atmosphere.
Further, one can threat the human and natural flows apart, but that makes no sense at all, as once the human FF is added to the atmosphere, its mass is there for 100% and only can be removed as mass, not apart as “human” and “natural” CO2, even if it is possible to do that.
Sorry I have to go now, I did make some example of how FF accumulates in the atmosphere, but that is somewhere at the beginning of this discussion…
Stephen P. Anderson, July 17, 2025 at 8:36 am
Takahashi’s formula IS the change in ratio of CO2 between atmosphere and ocean waters per Henry’s Law. That is the change in solubility of CO2 in seawater with temperature of about 4%/°C. That is all. Not over 100 ppmv/°C as your calculation shows.
The conference is partly in English, partly in Scandinavian languages, I hope that there is simultaneous translation, although I can understand some Norwegian.
I suppose that there will be video’s of the debates with English translations…
“Completely wrong: Lb is not set by the inflows, it is set by the equilibrium between ocean surface and atmosphere per Henry’s law at current SST, that is about 295 ppmv.”
Staggers the imagination. Maybe Harde can get through to him. He seems like an honest guy but his mind is twisted by years of propaganda.
Stephen Paul Anderson July 17, 2025 at 10:06 am
Thank you, Stephen. Your comments are correct.
Ferdinand has so many incorrect comments that I do not have time to correct them all. And he repeats his incorrect comments over and over.
Perhaps the biggest revelation in all these comments is that the CO2 Coalition, including Lindzen and Happer, support what Ferdinand says.
Where have all the true scientists gone?
Harold Lewis, Emeritus Professor of Physics, University of California, wrote in his resignation letter to the American Physical Society, on October 8, 2010, that IPCC’s climate theory “is the greatest and most successful pseudoscientific fraud I have seen in my long life as a physicist.”
Stephen P Anderson
July 16, 2025 at 11:56 pm
You nailed it. I was struggling with how to use Magic Math to show how natural emissions have added to the excess CO2.
(1) D = Eh + En – k * C
(2) Let En = g * Eh
(3) D = Eh * ( 1 + g ) – k * C
(4) Eh = ( D + k * C ) / ( 1 + g )
Using “g” being approximately 20, according to IPCC estimates, and your numbers:
Outflow = 430ppm/4yr = 107.5 ppm/yr and Inflow = 107.5ppm/yr + 2ppm/yr = 109.5ppm/yr,
Eh equals a quite reasonable estimate of the current annual influx of industrial carbon of about 5.2 ppm.
I don’t want to comment too much on Ferdinand’s views until he is back to respond. However, I agree with Dr. Ed that he asserts the same dogma repeatedly, most which are arguably incorrect. What is most central to his argument is his assertion that “[balance level] is set by the equilibrium between ocean surface and atmosphere per Henry’s law at current SST, that is about 295 ppmv.” This is something we should explore in greater detail. What say you?
Thanks Dr. Ed and Jim.
Jim, I don’t think it really matters if Ferdinand returns. I can cut and paste his replies as if he were here because they don’t change. He seems to revere Takahashi. This idea that 95% of CO2 flows are just cycling in and out of the atmosphere is such a crazy assertion. Anyone who puports to understand the Equivalence Principle would not say that. Dr. Ed’s model aligns with everything I learned in physics, chemistry, math. Dr. Lewis is right. This is a surreal world we live in.
Ferdinand Engelbeen July 17, 2025 at 8:56 am
You wrote:
My model meets those conditions because all its flows are outflows.
You wrote:
It depends upon the time step that I use. If I use annual time steps, then I use annual averages for the data. If I use monthy time steps, I use monthly averages for the data. Etc. No problemo.
You wrote:
Lb is defined by (4). It is not related to any conditions or equilibriums. It is a logical deduction from (1) and (2).
It is clear that you have not even read my description of my model.
Lb is relevant to all flows because Levels always move toward their balance levels. Te is the time a level takes to move (1 – 1/e) of the way to its balance level.
Lb is a critical definition to determining Te or even your Tau. If you don’t define the balance level, you cannot properly calculate Te or even Tau. Since you do not use balance levels to evauate your time constants, all your calculations are wrong and meaningless. Throw them all out. Your math is invalid.
You wrote:
Your claim does not apply to my formula (2).
Please forget about all your lake etc models. My model is none of those. If you can’t understand my model and its uniqueness, then you are not qualified to judge it.
Your remarks make it clear that you have not even read my explanations of my (1) through (8).
Further, there is NO “cycling”. There are only flows. My model, which is only equation (2) and its deriviatives, fully accounts for ALL flows between reservoirs. There is no cycling. That crazy idea is proposed only by those who do not understand the meaning and power of (2).
You wrote:
It not only makes sense to track human and natural flows separately, anyone who does not track these flows separately simply does not know how to use the power of theoretical physics.
Sorry, Ferdinand, you are way out of your field of expertise in this subject. Too bad that Lindzen and Happer agree with you because this means they also are way out of their fields of expertise when they address this subject.
David Andrews
July 17, 2025 at 7:26 am
I don’t have the other reservoirs in my spreadsheet. I downloaded Dr. Roy Spencer’s model and added the exponentially increasing natural emissions to provide a good fit to the Mauna Loa data. So many others have done this analysis, I don’t need to reinvent the wheel. I do find my model useful to test results and conclusions claimed by others. Expanding to more than one compartment involved complications I found too difficult to resolve at the time. For example, one can add a middle layer between the surface ocean and the deep. There is also a model that uses two land reservoirs. Again, others have already done the multi-compartment modelling and I’m satisfied to trust those results.
I don’t know what question neither Ed nor I have answered. The present atmosphere contains approximately the quantity of “human carbon” that results from our model calculations based on the known data and estimates of other data not well-known. For example, it is not well-known exactly what the annual natural emissions are, but it is about twenty times the human input. That amount corresponds to approximately a fourth of the atmosphere sinked every year. The more human carbon that remains in one year, the more that gets removed the next year. The numbers are never exactly known, but the models can track estimates within realistic variability limits.
The only assumptions I use are the 4-year e-time which means sinking ¼ of the carbon per year and that natural emissions are about twenty times the human input. These are IPCC estimates.
Regarding carbon conservation, I just updated my spreadsheet to make sure the total human emissions equaled the current atmosphere content plus the cumulative amounts of human emissions removed annually. That required a formula for the amount of human-sourced carbon sinked annually. In case you wanted to start your own spreadsheet, here it is. Let H = Eh and Ht is the human emissions introduced in year t.
Total H removed = K * ( Ht + (1-K) * Ht-1 + (1-K)^2 * Ht-2 + (1-K)^3 * Ht-3 …., etc.
The (1-K) represents that for each K * Hn removed every year, (1-K) remains in the atmosphere. My spreadsheet shows that in 2018, 20 ppm of human emissions remains, about 5%. This is a lower bound, because it doesn’t include any account of the human emissions that returned from the sinks. That is why I never proceeded to expand my spreadsheet.
Jim,
“What is most central to his argument is his assertion that “[balance level] is set by the equilibrium between ocean surface and atmosphere per Henry’s law at current SST, that is about 295 ppmv.” This is something we should explore in greater detail. What say you?”
It is difficult to decipher what that even means. I believe the 295ppm is the preindustrial level he is using. He is calling that the balance level. All of this since 1750 has raised the level to 430ppm due to FF, which is 135ppm above the balance level of natural inflows and outflows. He calculates Tau as 430-295/2.5ppm/yr= 54 years. The 2.5 is dCO2/dt. So he’s saying the 2.5ppm/yr comes from taking 5ppm/yr (human emission) in half. So, inflow minus outflow would be a negative 2.5ppm/yr. So, it would take 54 years to decay back to the balance level. If it wasn’t for the dastardly human emissions we would be at 295ppm.
However, I will give him some credit because he is saying that more CO2 is good. It is just that his understanding of why is all messed up.
If they could show something that has been derived from the continuity equation or laws of nature that supports the idea that half the CO2 stays in nature, but they can’t even do that. Their model is built to achieve a desired outcome. The Equivalence Principle is a law of nature, but somehow, their natural carbon that cycles in and out of the atmosphere and human carbon don’t violate this Principle. What screwed up pseudoscience. I’m with Dr. Lewis.
Stephen P Anderson
July 17, 2025 at 6:13 pm
I think 295 is the “new” equilibrium value that he expects CO2 to return to in Tau years, the old being 280. He often links to that graph showing a small increase in CO2 due to temperature based on Takahashi’s equation.
The 430-295/2.5 ppm/yr = 54 years is what I don’t get. In words it means Tau = disturbance / (result or effect) implying that we will go to 295 ppm losing 2.5 ppm/year. I don’t think Tau assumes any more human emissions, because that would make Tau infinity. Tau is for net zero and the time to return to yesteryear. That’s what makes this Tau discussion futile. We will never get back there to prove one way or the other.
Yes, there is this magic sink that only acts on human carbon, and when human carbon is gone, it stops.
Ferdinand Engelbeen, July 17, 2025 at 7:58 am
Should have included the “Bolin” graph, which shows the calculated drop in oxygen and related FF CO2 emissions and the calculated increase of oxygen and related uptake of CO2 by the biosphere, the observed O2/CO2 levels and the CO2 uptake by the oceans, filling the gap in the period 1990-2000.
https://www.ferdinand-engelbeen.be/klimaat/klim_img/bolingraph.gif
I have seen a more recent update, but haven’t located it yet.
Jim and Stephen,
“If we use dC/dt=2ppm/yr (4.24PgC/yr) and a Te of 4 years from Dr. Ed’s paper.
Outflow=430ppm/4yr=107.5 ppm/yr
Inflow= 107.5ppm/yr+ 2ppm/yr =109.5ppm/yr
Balance Level = 109.5ppm/yr(4yr)=438ppm”
107.5 ppmv/yr was the original balance level for 0 PgC/yr human input, inflow = outflow and 4 years Te at 277 ppmv. Per year that gives:
Inflow = 107.5 ppmv + 5 ppmv = 112.5 ppmv
Inflow – outflow = 3 ppmv
Outflow = 107.5 ppmv + 2 ppmv = 109.5 ppmv
Increase in the atmosphere fully caused by FF emissions
New equilibrium for a constant supply of 5 ppmv FF CO2:
For a Tau = Te of 4 years and L(o) = 430 ppmv (assuming that L(o) increased to the previous years L)
L(t) = 430 + 2 * 4 = 438 ppmv
For Tau = 50 years and L(o) = 295 ppmv (for the current SST):
L(t) = 295 + 5 * 50 = 445 ppmv
In both cases the new equilibrium is above the current CO2 level in the atmosphere, thus the FF inputs still are above the outputs, until outputs catch up with the extra input.
The main difference is that in the case of a 4 years Tau, the non-extra equilibrium moves up together with the atmospheric level, which is the case for the sea surface, and for both the deep oceans and vegetation, still the “old” equilibrium is working, as the linear response of the net output shows.
Bye for now.
Ferdinand Engelbeen July 18, 2025 at 3:04 am
Dear Ferdinand,
Although your numbers begin similar to my numbers, your description does not make it clear why you got your numbers. Nature is not as complicated as you make it out to be.
Try to describe everthing you just wrote in simple equations that show cause and effect.
My equation (2) (added to my (1) for mass conservation) solves the complexity problem with simple, valid physics.
Equations (1) and (2) are all we need to describe the flows in the carbon cycle. It makes cause and effect clear and it allows intellingent time-step calcuations for both levels and flows.
Ferdinand,
Yes, we concur, human inflow is greater than human outflow, but natural inflow is greater than natural outflow. Also, in Dr. Ed’s model the balance level is set by inflow. We can’t figure out what sets your balance level. The only thing that would make sense is natural inflow sets your balance level, but it is only the natural inflow from 1750. How nature does that you will need to explain. If that is the case, then natural inflow was about 70ppm/year. Now, natural inflow is about 105ppm/yr. Natural inflow has increased by about 35ppm/yr. How do you reconcile that with your model?
Ferdinand Engelbeen
July 18, 2025 at 3:04 am
At the risk of piling on, I have the same question as Stephen. How do you reconcile 107.5 ppmv/yr, “the original balance level for 0 PgC/yr human input…and 4 years Te at 277 ppmv?” 277/4 is less than 70 ppmv/year. We fail to see how the “old” equilibrium is working.
Dr. Ed,
Did you ever reveal the error in your Figure 11? The caption already explains, “Bit (should be But) the plot assumes H(1) is true and it plots the O2 effect as if human caused all the CO2 increase shown on the horizontal axis.”
The only other objectionable thing I could see is with the arrows indicating that about a 15 ppm atmospheric increase was balanced by the same amount of land and ocean uptake. Whereas the uptake was only about half of the “extra” emissions. If that isn’t the error, I look forward to your explanation.