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.
Stephen and Jim,
Sorry, indeed I did mix ppmv and PgC where it should be either PgC or ppmv.
Doesn’t matter for the basic reasoning but matters for the calculations…
From
“If we use dC/dt=2ppm/yr (4.24PgC/yr) and a Te of 4 years from Dr. Ed’s paper.
Outflow=430ppm/4yr=107.5 ppm/yr
Inflow= 107.5ppm/yr+ 2ppm/yr =109.5ppm/yr
Balance Level = 109.5ppm/yr(4yr)=438ppm”
The IPCC’s natural carbon cycle between atmosphere and land was 108 PgC/yr, that was my confusion.
Good, then again:
If we use dC/dt = 2ppm/yr (4.24PgC/yr) and a Te of 4 years from Dr. Ed’s paper and assume that the total increase of the basic inflows and outflows increased from 79 ppmv/year to 94 ppmv/year then
Inflow = 94 ppmv/yr + 5 ppmv/yr FF CO2 = 99 ppmv/yr
Outflow = inflow – dC/dt = 97 ppmv/yr = 94 ppmv/yr + 3 ppmv/yr
dC/dt = 2 ppmv/yr is fully caused by the inflow of FF CO2
The inflow increases first by the human input, the increase in output follows later. Not reverse.
That is the essence of the story, the rest can be calculated in the same way as in my previous comment.
Total outflows are, of course larger than total inflows, no matter if one splits the inputs and outputs in “natural”, which hardly changed over the years with 79 ppmv/yr and the rest all human caused (as mass, not as remaining FF CO2 molecules).
For the underlying differences in model as used by Dr. Ed and me, see next comment…
Jim Siverly, July 18, 2025 at 10:52 am
“The “outgassing” data from 1990 to 2000 are OK. But the plot assumes H(1) is true and it plots the O2 effect as if human caused all the CO2 increase shown on the horizontal axis.”
I still am waiting for the explanation of Dr. Ed why that figure doesn’t show that half of human emissions (as mass) gets about fifty/fifty in oceans and vegetation…
Nowhere the plot assumes H(1) is true.
The plot is quite simple:
At the right side are the calculations of O2 use and CO2 release from FF burning if all these changes remained in the atmosphere.
At the left side are the observed CO2 increases and O2 decreases in the atmosphere for each year.
At the bottom is the calculated uptake in the biosphere, based on the O2 release and the difference is what the oceans absorbed. Of that difference, the part that was absorbed in the ocean surface also is measured at about 10% of the increase in the atmosphere, but not separated in the plot.
Further, the “outgassing” is the change in O2 caused by the warming of the oceans and is only for the difference between the two arrows, not the observed CO2/O2 changes.
Ferdinand,
Your numbers and percentages don’t add up.
Inflow = 94 ppmv/yr + 5 ppmv/yr FF CO2 = 99 ppmv/yr
Outflow = inflow – dC/dt = 97 ppmv/yr = 94 ppmv/yr + 3 ppmv/yr
dC/dt = 2 ppmv/yr is fully caused by the inflow of FF CO2
If human CO2 is 5ppm/99ppm then it can’t be less than 5% of the outflow because it mixes in the atmosphere. This puts human CO2 outflow at 4.89ppm, not 3ppm. That means that of the 2ppm increase in dC/dt, only 0.11ppm is human CO2 and 1.89ppm is natural CO2.
Ferdinand Engelbeen
July 18, 2025 at 10:54 am
“The inflow increases first by the human input, the increase in output follows later.”
That is Magic Math slight of hand. Never mind the equivalence principle. It reminds me of alarmists explaining why CO2 lags interglacial warming. First CO2 causes a little warming which is followed by more CO2-caused warming. The tail wags the dog, making the dog wag more.
“Total outflows are, of course larger than total inflows…which hardly changed over the years with 79 ppmv/yr and the rest all human caused (as mass, not as remaining FF CO2 molecules).”
Let me try and repeat that back: Beginning with 79 ppmv/year, natural inflows have hardly changed, but total inflows rose to 97 ppmv/year, the increase all human caused. (Each mass of 4 FF carbons emitted got replaced with a mass of 5 natural carbons regardless of the source of the molecules).
Feel free to expound on that.
Jim,
I have looked back on the discussion of the last few weeks to see if there is anything I could have said better. I concede that my description of exchanges between the surface and deep oceans did not get to the heart of the difference between residence time and adjustment time. Further, Ferdinand has not been able to convince you there is any difference, and your conversation with him seems to have gotten bogged down in minutia missing the big picture.
Let’s go back to your July 1 10:38pm comment:
“….Apparently, we both agree that the industrial carbon is not largely left in the atmosphere. Your terrestrial biomass growth is one sink. The oceans are an obvious second. The deep ocean is basically an infinite sink. We also agree on where the extra carbon is coming from. The only disagreement is on how much of the observed increase in atmospheric CO2 is caused by industrial carbon or an additional natural component.”
I agree with your breakdown of where we agree and where we disagree. We agree that the “extra carbon” from fossil fuel burning is spread all over the place, acidifying oceans and stimulating biomass growth. But you say that since the present atmosphere contains little “human carbon”, fossil fuel burning is not responsible for much of the atmospheric growth. Tell me if I am missing something, but I believe that is your (and Ed’s) ONLY argument.
I have said repeatedly that mainstream science, while attributing all of the atmospheric carbon level change to human emissions, still predicts low levels of atmospheric “human carbon” in the present atmosphere. This is because of those balanced exchanges, also known as disequilibrium isotope fluxes, also known as Seuss effect dilution, that I urged you to understand. The issue neither you nor Ed ever address is why you think that, despite all the mixing going on (which is changing only the carbon makeup of the reservoirs, not their levels), the present composition of the atmosphere should naively be taken as measuring the human and natural contributions to CO2 growth. It does not.
Jim,
I have looked back on the discussion of the last few weeks to see if there is anything I could have said better. I concede that my description of exchanges between the surface and deep oceans did not get to the heart of the difference between residence time and adjustment time. Further, Ferdinand has not been able to convince you there is any difference, and your conversation with him seems to have gotten bogged down in minutia missing the big picture.
Let’s go back to your July 1 10:38pm comment:
“….Apparently, we both agree that the industrial carbon is not largely left in the atmosphere. Your terrestrial biomass growth is one sink. The oceans are an obvious second. The deep ocean is basically an infinite sink. We also agree on where the extra carbon is coming from. The only disagreement is on how much of the observed increase in atmospheric CO2 is caused by industrial carbon or an additional natural component.”
I agree with your breakdown of where we agree and where we disagree. We agree that the “extra carbon” from fossil fuel burning is spread all over the place, acidifying oceans and stimulating biomass growth. But you say that since the present atmosphere contains little “human carbon”, fossil fuel burning is not responsible for much of the atmospheric growth. Tell me if I am missing something, but I believe that is your (and Ed’s) ONLY argument.
I have said repeatedly that mainstream science, while attributing all of the atmospheric carbon level change to human emissions, still predicts low levels of atmospheric “human carbon” in the present atmosphere. This is because of those balanced exchanges, also known as disequilibrium isotope fluxes, also known as Seuss effect dilution, that I urged you to understand. The issue neither you nor Ed ever address is why you think that, despite all the mixing going on (which is changing only the carbon makeup of the reservoirs, not their levels), the present composition of the atmosphere should naively be taken as measuring the human and natural contributions to CO2 growth. It does not.
David,
No, we don’t agree that extra carbon from FF is acidifying the ocean. What we have said that according to Henry’s Law, the amount of a gas in the liquid is proportional to the partial pressure of the gas above the liquid. Since fossil fuel only accounts for 5% of the partial pressure increase, it only accounts for 5% of the acidification, if there is any.
David,
Also, Suess effect dilution is bad science. Dr. Berry’s model falsifies Suess Effect dilution.
David Andrews
July 19, 2025 at 11:28 am
“…I believe that is your (and Ed’s) ONLY argument.”
Of course, I can’t speak for Dr. Ed, but I think he would agree that one argument is the relatively minor amount FF emissions contribute to atmospheric growth compared to natural emissions. The other issue I have is the adjustment time. It’s ambiguous, unmeasurable, and most likely based on incorrect physical science.
The issue you think hasn’t been addressed has been addressed over and over. The “mixing” is accompanied by increasing levels. It follows from what the models yield. The model I use is a one compartment model, a slim version of the multi-compartment model that Dr. Ed explains in the article we are discussing. My model allows me to examine the known data and justify how it could happen in light of standard physical processes and mathematics, like first-order diffusion and differential equations. The data doesn’t compute without including a substantial gradually increasing contribution from natural emissions.
If it helps for you to attribute all the excess carbon to humans, I can understand that to a certain extent. However, I make a distinction between the FF carbon which can be accounted for, an additional human-caused natural contribution that cannot be accounted for, plus an additional contribution that is wholly natural, also unaccounted for. Examples of some non-FF human-caused natural emissions are land use change and cement manufacture, but those are still considered industrial carbon and accounted for. The 8 billion population increase probably accounts for more of the non-FF human-caused natural emissions than has been accounted for. Other sources of increasing natural emissions could be the warming oceans, volcanoes, forest fires, etc.
The bottom line is that it is not naive to decipher the human and natural contributions to CO2 growth and the present composition of the atmosphere. It’s being diligent and scientific. There are two groups of modelers, the linear ones and the non-linear ones. The latter use a combination of Te and Tau. The former use only Te. The references to Ed’s articles make that clear. I’m with the linear modelers, because they make the best arguments.
Jim,
You have given me the goal of trying to make a clearer exposition of adjustment time.
What makes you think that the FF emissions make a “relatively minor” contribution to CO2 growth compared to natural emissions? Is it the present composition of the atmosphere, or is it the ~20x larger gross number, or is it something else? Where are natural absorptions in your model, and is their magnitude constrained by the measured positive net global uptake?
David Andrews
July 19, 2025 at 11:28 am
“The deep ocean is basically an infinite sink”
Atmospheric CO2 sinks with the surface ocean. It doesn’t bypass the surface and go directly into the deep ocean.
“We agree that the “extra carbon” from fossil fuel burning is spread all over the place, acidifying oceans”
The oceans are not acidifying. They are not acid and never will be. Saying the oceans are acidifying is alarmist propaganda. designed to create hysteria. The only people who say that are socialist political activists. There is no science in any of this, it is anti-science.
It is impossible for humans to control atmospheric CO2 concentrations. Atmospheric CO2 concentrations are controlled by Henry’s Law and Henry’s equilibrium ratio which in turn is controlled by sea surface temperatures. If humans add CO2 to the air, that is mixed with the CO2 already in the air and the oceans will absorb more to keep the ratio in balance. If humans remove CO2 from the air the oceans will put it back.
“adding more CO2 to air does not change the Henry’s Law coefficient for combination CO2 gas and ocean water. . . . evidenced by experimentation in thousands of published studies since the mid 1800’s. This is well known established science, and it is the fundamental underlying science of the multi-billion dollar per year instrumentation industry of gas chromatography. . . . Henry’s Law coefficient (a ratio) is dependent on the temperature of the ocean surface, which is the interface between CO2 gas in the air and CO2 gas in ocean surface.”
Bromley, Bud 2023 EPA Submission Document; Comment submitted by Clare Livingston “Bud” Bromley III; Posted by the Environmental Protection Agency on Aug 10, 2023; https://www.regulations.gov/comment/EPA-HQ-OAR-2023-0072-0504; Attachment 3 Comment by Bud Bromley on the proposed rule by the Environmental Protection Agency; New Source Performance Standards for Greenhouse Gas Emissions from New, Modified, and Reconstructed Fossil Fuel-Fired Electric Generating Units: Emission Guidelines for Greenhouse Gas Emissions from Existing Fossil Fuel-Fired Electric Generating Units; and Repeal of the Affordable Clean Energy Rule
https://www.regulations.gov/document/EPA-HQ-OAR-2023-0072-0001
Sorry for the delay in my replies for now…
“There are two groups of modelers, the linear ones and the non-linear ones. The latter use a combination of Te and Tau. The former use only Te.”
That indeed is the heart of the matter, as that is quite different, depending of the model one has in mind.
For the “one-way container / lake / bath tube” model, as used in many engineering programs for chemical reactions, the inputs dictate the level in the atmosphere and the level in the atmosphere dictates the outputs.
The residence time Te and the adjustment time Tau are equal and one may reverse the formula for Te without problems:
Te = mass/ sum(outputs)
Tau = extra mass / sum(extra outputs)
Here such a “classic” model of the atmosphere:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/mass_fluxes_classic.jpg
In that case, and only in that case, Tau = Te and one may revert Te to get the output:
Output = mass / Te
In that case, and only in that case, one may assume that Te also represents Tau.
In the case where part of the outputs are recycled back to the inputs, independent of the mass in the atmosphere, the situation is completely different and Te and Tau are largely to completely independent of each other. That is the “fountain” model, where large amounts of CO2 are cycling in and out, independent of and without affecting the CO2 level in the atmosphere.
Then still:
Te = mass / sum(outputs)
Where outputs = outputs to the cycles + non-cycling outputs and outputs to the cycles are inputs back to the container(s).
Tau = extra mass / sum(extra outputs), where extra outputs are only the non-cycling outputs.
The latter is what changes the mass in the container, not what cycles in and out…
Here the real world flows (based on 2020 IPCC estimates for the different exchanges):
https://www.ferdinand-engelbeen.be/klimaat/klim_img/mass_fluxes_real.jpg
Which model and which Tau is the real world one?
In the case of the “classic” model, any “marker” in the inputs never can exceed its ratio in the inputs in any further part of the flows: neither in the container, nor in the outputs.
In the case of the “fountain” model, any extra inflow of a “marker” in the inputs can asymptotically go up to 100% of the mass in the container, because part of the “marker” is recycled back to the container.
With 1% to 5% FF CO2 of the inputs (1958 – 2020), the atmosphere already contains over 10% FF CO2 in the atmosphere and 6% FF CO2 in the ocean surface and a similar (hard to measure exactly) increase in the biosphere and a small “traced” increase in the deep oceans:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
That means that the “classic” model is at odds with the real world and one may not use Te as Tau.
“The other issue I have is the adjustment time. It’s ambiguous, unmeasurable, and most likely based on incorrect physical science.”
The formula for Tau is the exponential decay rate, or the time for any dynamic process in disequilibrium to go back to equilibrium where the remaining disequilibrium gets 1/e (~37%) of the initial disequilibrium.
If (and only if) the net removal rate is in exact ratio to the height of the difference, then the period over which Tau is calculated plays no role.
Tau can be calculated from the distance to the equilibrium and the resulting net removal rate. If the equilibrium is not exactly known, one can back calculate the equilibrium where the net removal rate is zero.
David Andrews
July 19, 2025 at 8:39 pm
Again, my model gives a lower bound to the industrial carbon contribution which is twice the natural “new” carbon added annually. Yet it’s only 5% of the total carbon which is equivalent to 14% of the rise, assuming a rise of 140 ppm. That means half the annual increase from natural carbon contributes 86% of the rise. I’m still trying get my head around that. It must be related to the 20x larger annual.
Natural absorptions are the usual uptake by plants and ocean. Their magnitude is determined by the average annual sink of about 25% of the carbon in the air.
I look forward to your version of adjustment time. Notice I am vehemently opposed to the notion that the “normal” equilibration point is still 280 or 290 something. Those days are gone.
Ferdinand Engelbeen
July 20, 2025 at 4:28 am
“That is the “fountain” model, where large amounts of CO2 are cycling in and out, independent of and without affecting the CO2 level in the atmosphere.”
What causes CO2 to cycle in and out of the atmosphere? Why would Henry’s law not be active in this process?
DMA, July 20, 2025 at 8:23 am
“What causes CO2 to cycle in and out of the atmosphere? Why would Henry’s law not be active in this process?”
Temperature is the main cause of the huge, mostly seasonal inflows and outflows:
In spring/summer: increasing temperatures and more sunlight increases photosynthesis far beyond any influence of the CO2 pressure in the atmosphere: some 120 PgC nowadays is sucked out of the atmosphere.
The influence of the pCO2 of the water in the plant’s leaves plays a minor role: while the pCO2 in the atmosphere increased with some 50%, the seasonal uptake by plants since about 1750 increased only with 13%.
About half of it is already recycled back into the atmosphere at night, by soil (bacterial) and plant respiration. The other half is recycled back in fall/winter and these processes are completely independent of the CO2 pressure in the atmosphere: fungi, bacteria and animals produce a lot of CO2 out of plant parts, no matter how much CO2 is in the atmosphere.
That is not completely in balance: some 2.5 PgC/year nowadays is removed into more permanent vegetation and soils. That is what is the real influence of the CO2 increase in the atmosphere and that gives the real e-time…
Here a graph of the influence of vegetation on the CO2 level in the atmosphere: that goes from minimum to maximum in a few months time, as can be seen in the opposite δ13C and CO2 changes in the atmosphere:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/seasonal_CO2_d13C_MLO_BRW.jpg
Exact CO2 changes, due to the uptake/release by vegetation can be calculated from the O2 changes, after taking into account the O2 drop by burning fossil fuels:
https://tildesites.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
Figure 7, last page…
For the oceans: also temperature, in reverse order as for the biosphere:
Increased SST in spring/summer increases the pCO2 of the ocean surface, releasing some 50 PgC/year in spring/summer and a similar cooling induces a similar uptake in fall/winter.
See Figure 2 in:
https://tos.org/oceanography/assets/docs/27-1_bates.pdf
The pCO2 (ocean) figures for BATS (Bermuda station) are monthly figures and give the clearest view of the changes over a year.
The overall difference over a year also is about 2.5 PgC/year and that is the real influence of the 50% increase of pCO2 in the atmosphere on the ocean’s total uptake per Henry’s law…
Jim,
So you are modeling absorptions separately from emissions, rather than using the empirically positive net global uptake as a constraint. What does your model yield for net global uptake?
Brendan,
I agree that a better description of the ocean situation is that the added carbon there is making them “less basic” rather than “acidifying”. My point is simply that oceans are clearly one of the net sinks contributing to the positive net global uptake. Your comments suggest you agree. Those who argue that the atmospheric carbon increase is coming from warming oceans have a problem explaining why the oceans are getting less basic, i.e. contain more carbon. Those who argue that the atmospheric carbon increase is coming from decaying vegetation have a problem explaining how plants manufacture carbon. They don’t. They temporarily borrow it from the atmosphere.
I looked at the EPA testimony you linked. It was unsubstantiated opionion. It gave me nothing to argue with.
Ferdinand Engelbeen
July 20, 2025 at 4:28 am
Are you familiar with the adage, “You are entitled to your own opinion, but not your own facts?” I think in an original version it was no right to be wrong in your facts. I am referring to your description of the classic model as “the case where part of the outputs are recycled back to the inputs, independent of the mass in the atmosphere.” That is your opinion of how the atmosphere works and it has been demonstrated wrong by a host of authors noted in Dr. Ed’s references. Your Tau, as being different from Te, is a creation of what you opine as atmospheric reality.
To show that your view of reality is correct, you will need to demonstrate how the linear modelers are wrong, with better data than anecdotes, Magic Math, and a fountain model which allows no increase in “what cycles in and out…”
Is there a paper or textbook somewhere that explains this sentence? “In the case of the “fountain” model, any extra inflow of a “marker” in the inputs can asymptotically go up to 100% of the mass in the container, because part of the “marker” is recycled back to the container.”
“The formula for Tau is the exponential decay rate….”
Back on July 12, 2025 at 7:41 pm, I explained that if you add more reactant to an A to B reaction, the decay rate, i.e. relaxation time, does not change. The concentrations of each moiety will increase, but the new equilibrium will be established in the same time frame. Your model suggests that the decay rate depends on the difference between the reactant concentration and the concentration of the product at the time additional reactant was added. In fact, the reaction rate always depends on the absolute concentration. The reaction continues even at equilibrium where an equal amount of product reacts reversibly in proportion to its concentration and corresponding rate constant.
Statements such as, “If the equilibrium is not exactly known, one can back calculate the equilibrium where the net removal rate is zero,” are best illustrated by experimental data, not observational anecdotes.
David Andrews
July 20, 2025 at 10:37 am
For net global uptake in the last year of my model’s data (2018), I have -2.58 ppm. That is total sink – total sources. Maybe that should be 2.58 ppm, total sources – sink.
Jim Siverly, July 20, 2025 at 11:53 am
“That is your opinion of how the atmosphere works and it has been demonstrated wrong by a host of authors noted in Dr. Ed’s references.”
My response to DMA is still in moderation, and explains in detail why the residence time Te is NOT the real decay rate of an extra CO2 input into the atmosphere.
But here a summary of my latest email to others than here in this discussion:
The formula that shows Ed’s “e-time” is:
Te = level / outflow.
Where Te in general is called “residence time” or “turnover time” by about any engineer in this world. Even the IPCC uses that definition.
Te shows how long an individual CO2 molecule “resides” in the atmosphere before being removed out of the atmosphere, either with an equal change in CO2 mass or without a change in mass, by simply replacing it with a CO2 molecule from another reservoir.
The latter difference is an important one, as that is the exact difference between the model of Berry and the model used in our work for the CO2 Coalition.
e-time or as most is used: Tau is the time that is needed to reduce an extra input of some reactant in a dynamic process back to 1/e (~37%) of the original extra input. That is expressed as:
Tau = extra level / extra outflow.
Where “extra” even may be positive or negative, compared to the equilibrium level where inputs = outputs.
Te and Tau are very clear, different, definitions for different times, even when these times may be equal in specific circumstances.
If (and only if!) all inflows, container and outflows are unidirectional from inputs to outputs, without any direct or indirect recycling from outputs back to inputs, then (and only then!) Te = Tau.
Then Berry reverses that formula:
Balance level = inflow * Te
Again, one may do that if (and only if!) all flows are unidirectional and there are no returns from the outputs back to the inputs.
That was the original approach of Berry, until a few years ago.
His newest approach is to use all Te’s back and forth between the atmosphere and the other reservoirs.
If the three outflows out of the atmosphere would have remained in ratio to the increase in the atmosphere, then the Te’s didn’t change over time. That is not the case:
The increase in CO2 level in the atmosphere was about 50% since 1750.
The increase in CO2 outflow from atmosphere to ocean surface was only 33%
The increase in CO2 outflow from atmosphere to land was only 13%
Thus any calculations based on fixed Te’s (used as Tau’s) over time don’t reflect reality.
To the contrary, one can calculate the real Tau, based on the increase of CO2 in the atmosphere, compared to the “historical” equilibrium of ~280 ppmv, increased to ~295 ppmv for current times for the increase in sea surface temperature. That gives around 50 years e-time (Tau) over the period 1958-current:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
Where A is the total FF emissions since 1750, the measured increase in the atmosphere, the calculated increase of pCO2 of the ocean surface with the formula of Takahashi and the resulting pCO2 difference between atmosphere and ocean surface. That is the driving force for any extra CO2 uptake by the ocean surface,
If there is no difference, then inputs and outputs are equal and there is no net exchange (but still a lot of exchanges).
B is the observed net sink rate and
C is the calculated Tau, based on the polynomial though the net sink rate.
One can back calculated the zero-net-exchange to obtain the recent equilibrium, here by colleague David Burton:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Several others have done that: Peter Dietze (already in 1997!), Lindzen, Spencer, myself,… All obtained an equilibrium between 280-300 ppmv and a Tau of around 50 years.
Here from Peter Dietze:
https://www.john-daly.com/carbon.htm
Thus not only Te doesn’t reflect reality, it largely changes over time, thus never may be used to calculate what the equilibrium level should be. No matter how many references Dr Ed refers to with the same opinion.
Then your:
“K = [B] / [A]. If more reactant is added after the initial equilibrium is reached, a new equilibrium is reached with K = ([B] + x) / ([A] + (1-x)]. Assuming no change in temperature or pressure, K will remain the same. But both reactant and product end up at larger concentrations.”
Of course that is true, but only as long as you add an extra amount of reactant. If you stop adding that extra, the reaction will go back to the old equilibrium.
In the case of CO2 in the atmosphere, humans add more reactant each year, but the sinks don’t follow as fast, thus any new equilibrium will be above the current disequilibrium.
For a constant input of 5 ppmv FF CO2/year:
With a Tau of 4 years:
Old equilibrium: 425 – 2.5 * 4 = 415 ppmv
New equilibrium: 425 + 2.5 * 4 = 435 ppmv
With a Tau of 50 years:
Old equilibrium: 425 – 2.5 * 50 = 300 ppmv
New equilibrium: 425 + 2.5 * 50 = 550 ppmv
In both cases, with halving the human input, there will not be any further increase of CO2 in the atmosphere and with zero FF input, the CO2 levels will sink back to the old equilibrium, wherever that may be.
So your model says natural sources exceed natural sinks. Your model is falsified by data. You know, that “Magic Math.”
David Andrews
July 20, 2025 at 1:05 pm
No, my model is not falsified. You did not include human emissions that are part of the total emission sources that exceed the combination of both in the sinks. It was 4.74 FF + 91.9 natural – 94.1 sunk. There is no purely natural sink like a FF emission or a sequestration. It’s your Magic Math that fails.
Jim,
OK, I missed the “total” before sources. The Magic Math did not fail. It told us net global uptake in your model is positive, as measured. Great!
Now to another earlier question:
“What makes you think that the FF emissions make a “relatively minor” contribution to CO2 growth compared to natural emissions? Is it the present composition of the atmosphere, or is it the ~20x larger gross number, or is it something else?”
Ferdinand Engelbeen
July 20, 2025 at 1:04 pm
You are repeating the same mantra without validating your assertions. Not one example of data showing Tau is longer than Te. You make predictions about equilibrium conditions without evidence of what they will be. That is not scientific.
Your Tau being different from Te is a concoction of your perception that things will return to an old equilibrium. There are scenarios that can be imagined, like net zero FF while continually increasing natural emissions. Or halving FF. Or another ice age. But all static scenarios subject to a constant Te will result in a new equilibrium in less than 30 years as reservoirs adjust to their balance levels. If inputs continue to change, their will never be a new balance level because the level keeps changing to adjust to the new inputs.
I just entered zero FF and a return to 65 ppm/year input in my spreadsheet. It goes to 280 ppm in 25 years. Of course, my model could be wrong. But it is based on the universally accepted 4-year Te, IPCC estimates of reservoir content, and correlation with Mauna Loa data. Do you have a model that meets all that criteria?
Regarding the A/B reaction you wrote, “Of course that is true, but only as long as you add an extra amount of reactant. If you stop adding that extra, the reaction will go back to the old equilibrium.”
There is no “but only.” There is an initial reaction starting with a known amount of reactant. It goes to equilibrium with a Te = Tau. Adding extra reactant creates a disturbance which returns to equilibrium with the same Te = Tau and both reactant and product at larger concentrations. The equilibrium ratio is the same, the Te is the same, but the old concentrations are not. My point being, there are new CO2 concentrations in the atmosphere and the reservoirs and using 280 ppm as a reference is no longer valid. All Tau = 50-year projections are based on that, as far as I can tell.
“In the case of CO2 in the atmosphere, humans add more reactant each year, but the sinks don’t follow as fast,…”
The data seems to indicate sinks have been keeping up for decades now.
“…thus any new equilibrium will be above the current disequilibrium.”
Isn’t that my point?
David Andrews
July 20, 2025 at 5:38 pm
“What makes you think…?”
I honestly don’t have a good answer for that. My estimated incremental increase in natural emissions is less than the annual FF carbon input. The “minor” claim refers to the relative amounts remaining in the atmosphere, like only 14% of the rise. The cliché trying to get my head around it applies. I’ll need to sleep on it.
Jim Siverly, July 20, 2025 at 9:35 pm
“But it is based on the universally accepted 4-year Te, IPCC estimates of reservoir content, and correlation with Mauna Loa data.”
The 4-year Te is universally accepted as the residence time and has zero connection with Tau, the universally accepted adjustment time of around 50 years. Universally accepted, except by you and a group around the Science of Climate Change…
“Not one example of data showing Tau is longer than Te. You make predictions about equilibrium conditions without evidence of what they will be. That is not scientific.”
Sorry, but have you not even looked at the observations and back-calculation towards the real world equilibrium?
Here from Peter Dietze, already from 1997:
http://www.john-daly.com/carbon.htm
Here from David Burton from last year:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Lindzen, Spencer and many others come to a Tau of around 50 years and a basic equilibrium of around 280-300 ppmv, based on observations, but you say that they do that without any evidence?
The IPCC uses much longer Tau’s, but they include a saturation of the different reservoirs for CO2, which is only the case for the ocean surface, not until over 1,000 ppmv for the biosphere and not in sight ever for the deep oceans.
That is the reason that the ocean surface follows the atmosphere with a Te of less than a year and its pCO2 follows the atmosphere with only 7 μatm difference, thus its “new” equilibrium pCO2 remains near the atmospheric pCO2.
Te is the residence time and may be used as Tau if (and only if!) the resulting change in output and new equilibrium is caused by the extra input of one of the reactants. If there are processes involved that are largely to completely independent of the height of the inputs, then Tau and Te have no connection with each other at all.
That is the case for the output into vegetation and the return of CO2 from all life on earth. That is already half the universally accepted Te of 4 years… And half the universally accepted Tau of 50 years, which is the only figure of interest, as that shows how much NET CO2 is removed each year out of the atmosphere in direct ratio to the extra CO2 in the atmosphere…
And one can calculate the increase in the atmosphere with any Tau one likes. The difference is, that with a Tau of 50 years, the basic equilibrium didn’t change (except for the influence of temperature) and with a Tau of 4 years, the basic equilibrium increases with the CO2 level in the atmosphere…
“The data seems to indicate sinks have been keeping up for decades now.”
Not at all: CO2 increased with 50% in the atmosphere, while the sinks in the oceans increased with only 33% and in the biosphere with only 13%. Thus Te was not constant and may not be used as fixed ratio at all.
The NET change (inputs – outputs) remained in ratio to the NET change in the atmosphere, thus Tau remained constant…
I have sent my “model” already to Ed, but here again the references:
https://www.ferdinand-engelbeen.be/klimaat/klim_doc/Ed%20Berry_challenge.docx
and the accompanying Excel sheet with the calculations is here:
https://www.ferdinand-engelbeen.be/klimaat/klim_xls/Berry_fluxes.xlsx
The spreadsheet was made for periods of 10 years, as Berry asked for, but I (still) am working on a general spreadsheet over the full period from 1850 on…
David Andrews
July 20, 2025 at 10:53 am
“Those who argue that the atmospheric carbon increase is coming from warming oceans have a problem explaining why the oceans are getting less basic”
That is an extremely weak argument. It is alarmist’s propaganda based on one measurement off Hawaii with volcanoes spewing CO2 into the water. Measurements from other sites around the world show the opposite. Ocean Ph over coral reefs goes up and down like a yo yo on a daily basis. There is no global measurement. Liu et al 2009 shows South China Sea Ph higher than it was 6,000 years ago and has been rising for the past 50 years. And there is no experimental data anywhere showing CO2 being absorbed from the atmosphere is the cause of the oceans being less basic.
“I looked at the EPA testimony you linked. It was unsubstantiated opionion. It gave me nothing to argue with.”
You’re doing nothing more than avoiding inconvenient truths. Did you read Attachment 3 in full?
Bud Bromley is a world renown expert on Henry’s Law. It was his profession. He used it every day for his entire career. He was speaking from his knowledge gained from a lifetime of experiments and conducting experiments. He was also speaking from many hundreds of references that he did not quote in his submission. You can read them all from his web site. https://budbromley.blog/2022/05/20/correcting-misinformation-on-atmospheric-carbon-dioxide/
He is well published.
Brendan,
David Burton and I have had a lot of discussions with Bud Bromley in the recent past and he has quite remarkable ideas about Henry’s law…
Take from your reference:
“Ocean surface demonstrates the capacity to rapidly absorb orders of magnitude more CO2 than humans produce, and then recover to trend.”
Wow. The observed (yes, observed!) uptake in the ocean surface is only 10% of the increase in the atmosphere. Not orders of magnitude. Observed at seven monitoring stations, which measure a lot of sea surface constants over the years.
See: https://tos.org/oceanography/assets/docs/27-1_bates.pdf
Figure 3 and Table 2.
The drop in pH over the years is small, but again is measured in all seven stations. See Figure 7 in the reference.
Then he produces pages and pages and pages of text, without much meat until about the Pinatubo eruption:
“Nature rapidly absorbed the added CO2 and then more rapidly accelerated again to reset its CO2 concentration to trend. ”
Which is not what happened: human emissions were NOT fully absorbed, still increased, but at a lower speed during the Pinatubo eruption. Here for the increase in the atmosphere over the 1991 Pinatubo and 1998 El Niño episodes:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/wft_trends_rss_1985-2000.png
Only a few ppmv less increase around a 100 ppmv trend since 1958 caused by 170 ppmv fossil fuel emissions over the same period.
Then: “By elimination, there is no other known, logical or physically possible sink for such a large amount of CO2 to be absorbed so rapidly other than ocean surface.”
He never heard of the biosphere? The influence of the Pinatubo was far more pronounced by the extra uptake of CO2 by the green earth, as a lot of leaves, normally part of the day in the shadow of other leaves now received scattered sunlight from the fine aerosols that the Pinatubo emitted.
How do we know the difference? Because the 13C/12C ratio changes in opposite direction for vegetation uptake or release of the biosphere and in parallel for the oceans.
See: https://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_dco2_d13C_mlo.jpg
And his whole CO2 calculation was completely at error, as he used ppm as “mass” ratio, while ppm, as used by NOAA and the whole scientific world, uses ppm as volume ratio…
Better look for more reliable sources…
Ferdinand,
“Where Te in general is called “residence time” or “turnover time” by about any engineer in this world. Even the IPCC uses that definition.
Te shows how long an individual CO2 molecule “resides” in the atmosphere before being removed out of the atmosphere, either with an equal change in CO2 mass or without a change in mass, by simply replacing it with a CO2 molecule from another reservoir.”
Te is “e folding time.” It isn’t residence time or adjustment time or Tau. It arises from the solution to the continuity equation. Tau does not arise anywhere. We’ve shown you from the solution to the Continuity Equation that the 2ppm yearly rise is mostly natural. That’s all there is to it. This is when you need to reach across the table, shake hands and resign. You are just digging a hole.
Ferdinand,
Also, it seems you are trying to apply Chemical Equilibrium concepts to Atmospheric CO2. What is your A and what is your B?
Ferdinand,
So typically, if A is in equilibrium with B, the equilibrium constant k=[B]/[A]. What is the equilibrium constant and what are A and B?
Stephen P. Anderson, July 21, 2025 at 8:57 am
“Te is “e folding time.” It isn’t residence time or adjustment time or Tau. ”
According to Dr. Ed:
“Outflow = L / Te (2)
where Te is the “e-time,” so defined because it is an exponential time. Berry’s e-time Te is the same as IPCC’s turnover time, T (IPCC, 2007, p. 948).”
But the IPCC’s “turnover time” or “residence time” (RT) is simply:
RT = L / outflow. That is not the e-folding time of an extra input of CO2 (whatever the source). Only if all flows are unidirectional, then Te = RT
Dr. Ed uses Te = RT throughout all his calculations, while the IPCC uses an overall RT of about 4 years and increasing slower Tau’s (Te’s) for each exchange between compartments apart, and includes saturation levels for each compartment.
“We’ve shown you from the solution to the Continuity Equation that the 2ppm yearly rise is mostly natural.”
We have shown that the 2 ppmv/yr rise can be only caused by the 5 ppmv/yr supply of FF. The 5 ppmv FF is supplied directly into the atmosphere for 100% as mass and nowhere else.
Other compartments only can remove 3 ppmv/yr CO2 as mass out of the atmosphere, no matter what the outgoing mix of natural and FF CO2 is. Dr. Ed’s and your carbon mass balances don’t fit at all: if the increase is partly natural, and part of the FF increases the total carbon mass in other compartments, where does that extra CO2 in the atmosphere comes from?
Have a look at this graph:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/demetris_1b.png
The dark blue line are FF emissions (without land use changes).
The red line the observed increase in the atmosphere, which may be 100% human caused or 100% natural or any mix in between.
The green line are the sinks in the case that the increase in the atmosphere is 100% human.
The light blue line are the sinks in the case that the increase in the atmosphere is 100% natural.
The light blue sinks in nature are twice as deep as the increase in the atmosphere for a 100% natural increase…
So where does the natural CO2 that causes any increase in the atmosphere comes from?
A is CO2 in the atmosphere, B is CO2 in the oceans.
A is in equilibrium with B when the concentrations in atmosphere and ocean surface have an equal pCO2 per Henry’s law.
That is at a concentration ratio constant of about 0.85 in water, compared to air at 25°C, if I remember well.
When A gets increased with a one-shot 50%, 90% of the ocean surface reacts very fast with a Tau of less than a year, but get saturated at 5% of its own carbon level, which is near equal to the carbon level in the atmosphere (~900 PgC).
pCO2 levels at the ocean “edges” (polar and equatorial) hardly change and remove/release CO2 with a difference, caused by the 50% extra CO2 in the atmosphere with a Tau of about 125 years…
If anyone want to wade through the specious waffle from Uncle Bert at July 21, 2025 at 6:26 am you are welcome.
He starts with a paper that is a pal reviewed CAGW biased paper. It assumes that the oceans only absorb human CO2. Ocean acidification in the title. Ocean acidification is a pseudoscientific lie. Cherry picks a short times series for ocean pH from selected sites that calculates, not measures, pH in the DIC, not the oceans. The DIC is a piece of chemistry invented by the CAGW alarmists because it produces confirmation bias results.
A meaningless undescribed chart. And all wrapped up in yet more specious meaningless waffle.
It is Uncle Bert’s desperate attempt to falsify the Pinatubo experiment conducted by Bromley and Tamarkin.
Bromley & Tamarkin 2022; Correcting Misinformation on Atmospheric Carbon Dioxide; https://budbromley.blog/2022/05/20/correcting-misinformation-on-atmospheric-carbon-dioxide/
They examined data following the explosive volcanic eruption of Pinatubo on the island of Luzon in the Philippines in June 1991. This eruption emitted large amounts of aerosols into the atmosphere blocking sunlight and reducing SSTs and surface temperatures. This altered the Henry’s Law ratio causing a reduction in oceanic emissions lowering the atmospheric concentrations. There was a large natural movement down in atmospheric concentrations of CO2 post the eruption, followed after that by an even larger natural movement back up.
The large movement down in CO2 concentrations post the eruption occurred despite the fact that during this same period, human emissions of CO2 continued unabated. Natural emissions also continued from, e.g. biosphere decay & ocean emissions. During 1991-1992 there was an El Nino event which caused increased emissions from a warmer Pacific Ocean. On top of that, the volcano itself added large amounts of CO2 gas to the atmosphere. In spite of all these emissions, overall SSTs dropped post the eruption causing a large drop in atmospheric CO2 concentrations.
“despite the CO2 additions by humans, natural sources, a volcano and an El Nino. Nature rapidly absorbed the added CO2 and then more rapidly accelerated again to reset its CO2 concentration to trend.”
“The environment, mostly ocean surface (since ocean about 71% of Earth’s surface,) demonstrated rapid CO2 absorbance capacity which is 239 times larger than maximum possible net human emissions. We conclude that net human emissions are trivially minor, negligible, and absorbed and re-emitted along with the 239 times larger change in natural CO2.”
“In the 2 years following the June 15, 1991 eruption of the Pinatubo volcano, the natural environment removed more CO2 than the entire increase in CO2 concentration due to all sources, human and natural, during the entire measured daily record of the Global Monitoring Laboratory of NOAA/Scripps Oceanographic Institute (MLO) May 17, 1974 to June 15, 1991. Then, in the 2 years after that, that CO2 was replaced plus an additional increment of CO2.”
Uncle Bert has tried to take on the world’s foremost expert on Henry’s Law and failed miserably.
Uncle Bert. Dr Ed has said you are out of your depth on the subject matter you are discussing with him, you are way out of your depth on Henry’s Law as well.
Ferdinand,
I can’t believe you’re debating me about this. Why don’t you read Dr. Ed’s first paper? His model is mathematically derived. Te is “e folding time.” It is the time it takes Lb to move 1-1/e the distance to L. I’ve followed Dr. Ed the whole way (for years) and taken the time to read and re-read all his works. It appears to be the same as IPCC’s turnover time. Not sure what residence time is. Dr. Ed has talked about adjustment time before, but it is not derived from the solution to the continuity equation-it is essentially several “e times.”
Also, I’ve shown you mathematically that the dC/dt=2ppm can’t be all FF. It isn’t even 10%. Your Fountain Model doesn’t allow any mixing in the atmosphere and somehow keeps carbon segregated. You’ll need to specifically explain how nature does this “cycling.” Also, you need to explain what is A? What is B? And, therefore what is k? I would think the Climate Coalition would be searching for the truth.
Ferdinand Engelbeen July 21, 2025 at 2:49 pm
Dear Ferdinand,
Even though we disagree on climate physics, I appreciate your effort to clarify your position.
Indeed, I use IPCC’s turnover time and use the same reference you supplied (IPCC, 2007, p. 948). I began with equation (2) because that is how systems models work. That’s why my flow formulas derived from (2) reduce to electric circuit theory. I found later that IPCC had already defined (2) as turnover time.
Also, Stephen is correct that turnover time is also known as e-folding time.
Eq (2) is fully reversible in the way I use it. Again, this is standard systems theory that is proven to work. Dalton’s Law of Partial Pressures follows (2).
There are examples where outflow does not follow (2). Flow of water over a dam, and flow of water out of a hole in the bottom of a container, do not follow (2).
While I have not read every word the IPCC has published, I am not aware that the IPCC uses any formula for outflow for its carbon cycle than (2).
I replicated IPCC’s Fig. 6.1 data for IPCC’s natural carbon cycle. This is a necessary calibration point for any carbon cycle model.
I do not see that you have replicated IPCC’s natural carbon cycle with your formulas. Why not?
IPCC does not define residence time the same as turnover time. IPCC specifically uses a different definition for residence time, as my 2019 paper explains.
I do not see that IPCC “uses” 4 years for any calculations. The only reference that I found where IPCC refers to “4 years” is in its definition of turnover time it say it is about 4 years.
My replication of IPCC’s natural carbon cycle shows that IPCC’s data from its Fig 6.1 produces an e-time of 3.5 years. This is what IPCC is referring to when it says about 4 years.
In my opinion, you have no physical basis for your Tau. You are using data that happen to be close to their balance level, and you think the progress to their balance level has slowed down. You think that carbon just swished around without changing the levels. No proof. Just a bad idea. My simple model explains all the data that you claim need a Tau.
You even confirm this when you say later that Tau is the time for the level to move 63% of the way to its balance level. That proves your Tau is the same as my Te.
So, if you begin with Te and you end with Te, then everything in between is also Te.
Your model is imaginary and not connected to reality. Your model does not represent reality. You have tried to develop your model as a curve fit to the data that you have.
You have no model structure that does what my equations (1) and (2) do.
We must always begin with a mathematical structure for our hypotheses. Then we can check to see how our hypotheses fit the data. Without such a structure, we can’t predict anything, which means we not have a valid hypothesis.
You say, “We have shown that the 2 ppmv/yr rise can be only caused by the 5 ppmv/yr supply of FF. The 5 ppmv FF is supplied directly into the atmosphere for 100% as mass and nowhere else.”
That is nonsense. First, the data you use do not prove in any way that your interpretation of the data is correct. That claim violates the scientific method.
Second, my model explains the data.
You claim, “Dr. Ed’s and your carbon mass balances don’t fit at all: if the increase is partly natural, and part of the FF increases the total carbon mass in other compartments, where does that extra CO2 in the atmosphere comes from?”
First, please show me where you think my formulation does not fit the data.
Second, I have no obligation as a scientist to explain where the extra CO2 is coming from.
My formulation and calculations, using valid data, prove the extra CO2 is NOT coming from human CO2.
The null hypothesis that we must follow in our research is that all changes are natural until proven to be human. The burden of proof is on you to prove the CO2 increase is human caused.
I looked at your graph:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/demetris_1b.png
It does not prove the CO2 increase is human caused. The first failure is it uses sinks. Sinks are not valid data. Sinks are not part of a systems model. To model using sinks is like saying a capacitor is an electron sink without know the size of the capacitor. The so-called net natural contribution has no meaning at all because it is based on fiction.
Real models are based on outflow, not inflows.
The real comparison of annual human emissions with annual change in the CO2 level has been done my Munshi. He showed there is no correlation. Therefore, there can be no cause effect relationship of human CO2 with the CO2 increase. You objected that Munshi’s calculations are detrended, but there you are wrong. All correlations of time- series data must be detrended.
Munshi’s proof that human CO2 cannot have caused the CO2 increase is not rebuttable.
So, really, the only conclusion we can draw from your graph is that human CO2 did NOT cause the CO2 increase.
Brendan Godwin, July 21, 2025 at 5:32 pm
Brendan, if you can’t make a distinction between data as they are observed and the interpretation of these data, then we can’t have a real discussion about the data.
The pH, and other data from seawater can be calculated from any pair of measured data, even from the far past.
pH measurements in the past were based on glass pH meters and had an accuracy of +/- 0.1 pH unit. By far not accurate enough to measure a change in seawater of 0.1 pH unit in 170 years time.
Modern pH measurements are based on colorimetric measurements and are far more accurate.
In several stations one has plotted the colorometric pH measurements and the calculated measurements together. That is the case for e.g. ALOHA (Hawaii) station:
https://www.pnas.org/doi/pdf/10.1073/pnas.0906044106
Figure 1 shows the pCO2 level in the atmosphere, as measured at Mauna Loa , thus not far away and the calculated pCO2 of the ocean surface and included water vapor pressure near the surface, which in average was about 15 μatm lower than in the atmosphere. That means that in average CO2 is entering the oceans from the atmosphere, even if in some summers the oceans were net emitters.
CO2 dissolving in the oceans lowers its pH, no matter if you call it “acidification” to scare people or lowering the alkalinity.
That is reflected in the pH drop over different depths of the surface (not the deep oceans) over a period of 15 years.
They plotted the calculated pH, based on DIC and TA (total alkalinity) together with colorometric direct measurements. These in general match each other within a fraction of a tenth of a pH unit…
If all seven stations show a similar pH drop over time, then that pH drop, no matter how small, is real.
“The DIC is a piece of chemistry invented by the CAGW alarmists because it produces confirmation bias results.”
If you don’t even know that DIC is simply the sum of dissolved CO2 + bicarbonates + carbonates, what are you then discussing at all? And it is impossible to measure a pH from salts. One can only measure the pH of solutions, in this case thus seawater.
“In spite of all these emissions, overall SSTs dropped post the eruption causing a large drop in atmospheric CO2 concentrations” and
“the natural environment removed more CO2 than the entire increase in CO2 concentration due to all sources, human and natural”
As you believe what Bromley says, then give me the data where the CO2 levels in the atmosphere dropped, besides the “normal” drop in the NH spring/summer, thanks to vegetation growing new leaves…
And besides the “normal” spring/summer uptake, the extra uptake by vegetation after Pinatubo, thanks to scattered sunlight, was much stronger than by the oceans. Even both together did NOT remove more CO2 than emitted by human FF fuels use, as the increase in the atmosphere slowed, but did NOT drop.
Have a look at their Figure 11 of your reference of their work: in the years after the Pinatubo, the increase in the atmosphere was a lot smaller than in previous and following years, but still an increase, not a drop.
Your source of what Henry’s law means is not very reliable, to say the least…
Stephen P Anderson, July 21, 2025 at 5:41 pm
“Te is “e folding time.” It is the time it takes Lb to move 1-1/e the distance to L”
I do completely agree with that, I only disagree with Dr. Ed using the residence time of the IPCC as Te. Te is NOT the 4 years residence time of the IPCC. Te (or better Tau, as used by the whole scientific community) is 50 years, as can be calculated from the increase in atmospheric data and increase in NET sink rate. And L also can be calculated from atmospheric data over the past 67 years and is between 280 and 300 ppmv. Not 315 ppmv for the current 325 ppmv in the atmosphere… That is the main difference between Dr. Ed’s opinion and our opinion…
“I’ve shown you mathematically that the dC/dt=2ppm can’t be all FF. It isn’t even 10%. Your Fountain Model doesn’t allow any mixing in the atmosphere and somehow keeps carbon segregated. You’ll need to specifically explain how nature does this “cycling.””
If humans add 5 ppmv/year to the atmosphere, for the full 100% as mass, completely independent of any other inflow or outflow, and there are practically no human CO2 sinks as mass, then the human 5 ppmv/year do fully increase the total mass in the atmosphere with 5 ppmv/year.
The observed increase in the atmosphere is only 2 ppmv/year. Thus the total of other transfers of CO2 mass in and out the atmosphere must remove 3 ppmv CO2/year as CO2 mass to fulfill the carbon mass balance. No matter how much % FF CO2 is already in the atmosphere or in the outputs or inputs. The full increase of CO2, as mass, thus is caused by the one-way addition of 5 ppmv/year FF CO2 and nothing else.
As already several times explained: both the oceans as the biosphere are net sinks for CO2, whatever the isotopic composition in any of the compartments. It is about carbon mass transfer, not where the FF molecules go. Even if the isotopic changes give a good indication of where to the human FF is transferred and resides. Once in the atmosphere, all FF is mixed with the rest of the CO2 and what goes out (and comes back) is a mix of natural and FF CO2. As good as the “fountain” model will rapidly mix the small extra input with all what is already in the basin.
In the period 1958-2025, the total mass of CO2 in all compartments increased from the supply of some 170 ppmv FF emissions. In the atmosphere with 100 ppmv, in vegetation with about 35 “ppmv” (PgC is of course a better metric), in the ocean surface with some 7 “ppmv” and about 28 “ppmv” disappears for a long time into the deep oceans.
If one assumes that any of the 100 ppmv rise in the atmosphere comes from the other reservoirs, then show me the detailed mass balance, where that CO2 originates…
Ed,
Can you confirm that the ONLY result of your calculations which suggest that the atmospheric CO2 increase over the last century has natural causes is the modest percentage of “human carbon” in the present atmosphere?
Dr. Ed, July 21, 2025 at 7:58 pm
Dear Dr. Ed,
“Also, Stephen is correct that turnover time is also known as e-folding time.”
That is where we already disagree. The turnover time is the average time that a CO2 molecule “remains” or “resides” in the atmosphere. That also cán be the e-folding time if (and only if!) all flows are one-way in to out. Not when 95% of all CO2 flows return to the inputs in the same year, but in another part of the day or in another season.
The IPCC agrees that in 1750 some 168.4 PgC of CO2 cycles in and out the atmosphere which contains 589 PgC, or a residence time of 3.5 years, with equal inflows and outflows thus at its dynamic equilibrium.
In about the year 2000, including 240 PgC extra in the atmosphere (at 829 PgC), the outflows increased to 200.4 PgC/year. That gives a residence time of 4.1 years. Which, according to your theory is impossible: Te must remain the same as the fixed factor between the driving force and the output.
Then we have the difference between inflows and outflows, which is the only metric of interest that shows that the process is above its equilibrium: only 4 PgC/year more output than input for 240 PgC extra in the atmosphere.
The exponential decay towards its dynamic equilibrium, for this process gets:
Te = 240 / 4 = 60 years.
An order of magnitude slower than the residence time…
“IPCC does not define residence time the same as turnover time. IPCC specifically uses a different definition for residence time, as my 2019 paper explains.”
Sorry, the IPCC has very clear definitions of turnover time vs. residence time vs. adjustment time:
https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_AnnexVII.pdf page 2237 for “lifetime”:
“Response time or adjustment time (Ta) is the time scale characterizing the decay of an instantaneous pulse input into the reservoir.”
“In simple cases, where the global removal of the compound is directly proportional to the total mass of the reservoir, the adjustment time equals the turnover time: T = Ta.”
“Carbon dioxide (CO2) is an extreme example. Its turnover time is only about 4 years because of the rapid exchange between the atmosphere and the ocean and terrestrial biota. However, a large part of that CO2 is returned to the atmosphere within a few years. The adjustment time of CO2 in the atmosphere is determined from the rates of removal of carbon by a range of processes with time scales from months to hundreds of thousands of years.”
“Turnover time (T) (also called global atmospheric lifetime) is the ratio of the mass M of a reservoir (e.g., a gaseous compound in the atmosphere) and the total rate of removal S from the reservoir: T = M/S. For each removal process, separate turnover times can be defined. In soil carbon biology, this is referred to as mean residence time.”
While we don’t agree at all with the time scales of hundreds to thousands of year of the IPCC, they make it clear that one can’t use the 4 years turnover/residence time of CO2 in the atmosphere as the e-time to remove an extra mass of CO2 out of the atmosphere…
That is part 1…
Dr. Ed,
Part 2.
“You have no model structure that does what my equations (1) and (2) do.”
Nobody disagrees with (1). We only disagree with (2), as the real world Te is around 50 years, not 4 years.
Here -again- what our real world model shows:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/mass_fluxes_real.jpg
The only important difference with the IPCC flows is that we don’t isolate the deep oceans from the atmosphere, but split the flows in 50 PgC/season back and forth between atmosphere and ocean surface and 40 PgC/year back and forth directly between the atmosphere and the deep oceans. That is what bypasses the extreme long e-times of the IPCC.
The turnover/residence time still is exactly the same as your turnover/residence time at 3.8 years, but the adjustment time is the real one: about 50 years. Which fits the past 67 years within one ppmv. I have send you the Excel sheet calculations for the years 2010-2020 and the graph:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/berry_2010.png
“First, the data you use do not prove in any way that your interpretation of the data is correct. That claim violates the scientific method.”
Sorry Dr. Ed, but I don’t think that any bookkeeper in this world will agree with you. If one adds 5 PgC/year directly into the atmosphere and the measured increase in the same atmosphere is only 2 PgC/year, then the 5 PgC supply is the one and only cause of the increase in the atmosphere. No matter how much CO2 cycles between the reservoirs. That is called a mass balance. A simple matter of bookkeeping…
“First, please show me where you think my formulation does not fit the data.”
With a Te of 4 years, the increase in the atmosphere caused by human FF is only a few % of the measured increase. That gap should be filled with “natural” CO2 from other reservoirs, but the other reservoirs also increased in carbon, thus can’t be the source of the extra CO2 in the atmosphere…
“Second, I have no obligation as a scientist to explain where the extra CO2 is coming from. ”
If your carbon balance doesn’t fit the observations, as a scientist you have the obligation to show why that is…
“It does not prove the CO2 increase is human caused. The first failure is it uses sinks. Sinks are not valid data. Sinks are not part of a systems model.”
Any movement of CO2 in/out the atmosphere must obey the carbon mass balance at any second of the day to eternity (except radioactive 14C). As good as the total energy in an electric system must be conserved, no matter where it flows or resides.
That implies that the quantities per year in that graph above and below zero must be exactly the same for each year. We know two quantities with quite good accuracy: human emissions (based on sales/taxes) and increase in the atmosphere. We know the difference between these two with quite good accuracy, thus then remains the question, what is the net sink rate for 100% human increase and for 100% natural increase. In the latter case, the sinks must absorb every gram of human emissions and the net sink rate is twice the increase in the atmosphere. Very remarkable…
“The real comparison of annual human emissions with annual change in the CO2 level has been done my Munshi. He showed there is no correlation.”
I think that Munshi is a she…
Of course there is no correlation in the variability, if one variable has hardly any variability. The cause and effect is exactly in the trends, not in the variability…
How do you prove that the increase of CO2 in the atmosphere is not caused by the twice as steep slope of FF emissions but by temperature without a slope?
By detrending, thus effectively removing the cause of the slope of the increase in the atmosphere…
Some 20 years ago I did made the proof of the pudding for a similar discussion: I mixed two variables: one with a steep trend and no variability at all and one double sinus with only variability and no trend at all. The dependent variable was 0.5 x the first variable + all the variability of the second one with a small lag, to make it as “real” as can.
Then I asked some “attribution” program (don’t remember which one, Anova?) to show me the relative contributions of the two inputs to the result. That failed completely, because the program attributed near all contribution to the double sinus… Can be repeated for any attribution program…
Ferdinand,
[Ferdinand]:
“I do completely agree with that, I only disagree with Dr. Ed using the residence time of the IPCC as Te. Te is NOT the 4 years residence time of the IPCC. Te (or better Tau, as used by the whole scientific community) is 50 years, as can be calculated from the increase in atmospheric data and increase in NET sink rate. And L also can be calculated from atmospheric data over the past 67 years and is between 280 and 300 ppmv. Not 315 ppmv for the current 325 ppmv in the atmosphere… That is the main difference between Dr. Ed’s opinion and our opinion…
“I’ve shown you mathematically that the dC/dt=2ppm can’t be all FF. It isn’t even 10%. Your Fountain Model doesn’t allow any mixing in the atmosphere and somehow keeps carbon segregated. You’ll need to specifically explain how nature does this “cycling.””
If humans add 5 ppmv/year to the atmosphere, for the full 100% as mass, completely independent of any other inflow or outflow, and there are practically no human CO2 sinks as mass, then the human 5 ppmv/year do fully increase the total mass in the atmosphere with 5 ppmv/year.
The observed increase in the atmosphere is only 2 ppmv/year. Thus the total of other transfers of CO2 mass in and out the atmosphere must remove 3 ppmv CO2/year as CO2 mass to fulfill the carbon mass balance. No matter how much % FF CO2 is already in the atmosphere or in the outputs or inputs. The full increase of CO2, as mass, thus is caused by the one-way addition of 5 ppmv/year FF CO2 and nothing else.”
1) Dr. Ed doesn’t use Te as residence time. He explained IPCC describes Te as turnover time.
2) If the whole scientific community uses Tau=50years, then our whole scientific community is in serious need of psychotherapy. Tau doesn’t exist.
3) Currently L is 430ppm.
4) Human CO2 and natural CO2 mix in the atmosphere. Sinks can’t differentiate them. Outflow is proportional to L for all CO2. I’ve shown you mathematically if dC/dt=2ppm = Inflow – Outflow, then most of the 2ppm is natural. Read Dr. Ed’s paper.
5) You flunk physics with your inaccurate mass balance assuming that human and natural CO2 don’t mix in the atmosphere and that nature can differentiate.
Ferdinand Engelbeen July 22, 2025 at 8:49 am
Dear Ferdinand,
Since you think you are a better statistician than Jamal Munshi, who is a professional statistician, I posted his paper above – just below your paper – for all to read.
Munshi concludes human CO2 emissions and increases in atmospheric CO2 are uncorrelated. Do you have a defense?
(This is only part 1. I will follow with another comment on your other claims.)
Just a note of another paper that is pertinent to this discussion. It is discussed and linked in this article https://mailchi.mp/climatedn/cdn_newsletter_250716?e=98e02c0608
It discusses the isotope arguments for FF being the whole cause of the increase being called into question with the better quantification of CO2 emissions from river systems as that CO2 has the same makeup of isotopes as fossil fuels.
DMA, July 22, 2025 at 1:42 pm
That paper is discussed out at WUWT:
https://wattsupwiththat.com/2025/06/25/under-reported-old-carbon-is-not-the-source-of-increases-in-atmospheric-co2/
Ferdinand Engelbeen July 22, 2025 at 2:25 pm
Dear Ferdinand,
Your WUWT paper does not discuss this article that DMA referenced:
https://climatediscussionnexus.com/2025/07/16/matthew-wielicki-on-co2-isotopes/
Also, your WUWT paper does not dicuss these:
https://scitechdaily.com/scientists-were-wrong-plants-absorb-31-more-co2-than-previously-thought/
https://www.nature.com/articles/s41586-025-09023-w
https://www.nature.com/articles/s41561-024-01476-4?fromPaywallRec=false
Dr. Ed, July 22, 2025 at 12:56 pm
According to Munshi:
“A key relationship in the theory of anthropogenic global warming (AGW) is that between annual fossil
fuel emissions and annual changes in atmospheric CO2. The proposed causation sequence is that
annual fossil fuel emissions cause annual changes in atmospheric CO2 which in turn intensifies the atmosphere’s heat trapping property.”
Most of my statistics knowledge is from 60 years ago, but someone who writes that annual (!) emissions must correlate with annual (!) changes in atmospheric CO2 must never have heard of noise around a trend.
This is really stupid. 98% of the correlation between the variability of maximum 2 ppmv around a trend of over 100 ppmv is caused by temperature variability, but temperature gives less than 10 ppmv increase in the atmosphere from warming ocean surfaces since 1958 and zero trend in the derivatives. Temperature is responsible for all the temporal (2-3 years) variability, but not responsible for the bulk of the CO2 increase in the atmosphere…
Here the response for the trends since 1960 with temperature:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_co2_1960_2012.jpg
Compare that with the response to summed FF emissions:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1960_cur.jpg
Or since 1900 from ice cores – firn – MLO and FF emissions:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_1900_1911.png
But of course there is no correlation between FF emissions and increase of CO2 in the atmosphere, according to a professional statistician.
Case closed.
Dr. Ed, July 22, 2025 at 3:05 pm
The second paper in following:
https://climatediscussionnexus.com/2025/07/16/matthew-wielicki-on-co2-isotopes/
is what is discussed at WUWT
And the text contains a grave error:
“devoid of 14C and depleted in 13C”
The “devoid of 14C” is right, “depleted in 13C” is just the opposite:
Most is carbonate rock at near zero δ13C. After dissolution in river water and release in the atmosphere, it is at about -6.5 per mil δ13C and still higher in δ13C than the current atmosphere at -8.2 per mil δ13C…
One can see these two as a positive feedback for the human influence on the isotopic changes for 14C and a negative feedback for δ13C.
Then the second of your references only shows that the human emissions probably were larger than estimated too: if the sinks in pants are greater than expected and the net sinks remains the same, then the sources also are underestimated…
The third reference again is the article discussed at WUWT
The fourth reference is about old 14C depleted carbon, which figures were used in the third reference.
In general: all these new findings are from CO2 flows that are already going on for thousands to many millions of years. These are already in the “basic” CO2 (isotopic) fluxes and only substantially changed when the natural environment changed.
For the 14C level that changed only with solar activity in very small steps over the past 60,000 years.
The 13C/12C ratio changed only with -6.5 +/- 0.4 per mil δ13C over the past 800,000 years
The 14C level dropped together with fossil fuel use, so that correction tables were needed for radiocarbon dating from 1870 on.
The 13C/12C ratio dropped to below -8.2 per mil in the atmosphere and similar in the ocean surface since 1850 in complete ratio to FF emissions.
It would be very remarkable that something in nature would mimic FF emissions in exact ratio and time…
Ferdinand Engelbeen
July 22, 2025 at 3:08 pm
You won’t understand Munshi’s work if you stop your study of it at making fun of what you mistakenly expected it to say. Briefly his work shows there is no correlation between the rate of change of FF emissions and the rate of change of temps proving that the correlations you demonstrate are spurious and no more meaningful that the correlation of FF emissions and shark attacks on nurses.
Dear Uncle Bert.
“if you can’t make a distinction between data as they are observed and the interpretation of these data, then we can’t have a real discussion about the data”
It is impossible to have a real discussion with you about anything. The data is the data. If that disagrees with your world view then. IYO, that data must be interpreted in a way that agrees with your world view. You start with an answer then devise specious constructs that agree with your answer.
“In several stations one has plotted the colorometric pH measurements and the calculated measurements together. That is the case for e.g. ALOHA (Hawaii) station”
Your reference once again used pseudoscience in the title. Can’t you produce real references from real scientists?
Your Figure 1 is a cherry picked short timeline of 18 years to show your confirmation bias, There are large gaps in the real measurements which were all from the DIC. That’s not the same as the oceans.
pCO2 is not concentration and it is misleading to use it to try and show atmospheric CO2 is being absorbed in the ocean. The DIC is different from the ocean. The d13C isotopic ratio for the DIC is -.5 to +2.0 per mil. The oceans are -10 per mil.
“CO2 dissolving in the oceans lowers its pH”
Where is your experimental data?
Warming oceans lowers the pH.
“the extra uptake by vegetation after Pinatubo, thanks to scattered sunlight, was much stronger than by the oceans”
You really are full of it aren’t you. As far as you’re concerned vegetation is the only thing that absorbs CO2 and you avoid the oceans like the plague. The oceans are a real inconvenient truth aren’t they? The oceans are far and away the largest emitter and absorber of CO2.That’s an inconvenient truth for you.
“DIC is simply the sum of dissolved CO2 + bicarbonates + carbonates”
The DIC is dissolved inorganic carbon. That is different from dissolved organic carbon which is different again from the oceans.
“give me the data where the CO2 levels in the atmosphere dropped, besides the “normal” drop in the NH spring/summer”
Perhaps you should read Bromley and Tamarkin’s paper.
Their experiment demonstrated that nature’s measured impulse absorbed 239 times the human-produced CO2 impulse. To be specific, this is the specific impulse calculation of CO2 that was removed from the atmosphere in 2 years after Pinatubo. Their experiment demonstrated that nature is controlling CO2 concentrations, not humans.
This comment will generate yet another page of specious waffle which is endless. I don’t have time to wade through all your nonsense, I have a life to live. This dialog started with me responding to David Andrews. He has either asked you to reply because he lacked the knowledge himself, or you have just barged in. Socialist political activists are 24/7 devoted to their cause. Normal people have lives to live.
Ferdinand Engelbeen
July 21, 2025 at 2:49 pm
In response to Stephen, you asked, “…if the increase is partly natural [emissions], and part of the FF [emissions] increases the total carbon mass in other compartments, where does that extra CO2 in the atmosphere comes from?”
It’s a seminal question. If natural emissions have not remained roughly the same as in preindustrial times, then what changed to introduce the extra carbon, other than FF emissions? I previously suggested some increase was caused by the expanding population which continues to plow fields, cut down trees, and dig holes to build homes and bury garbage. The other likely increase comes from the deep ocean mixing with the warmer surface. In addition to being warmer than 300 years ago, the CO2 content may be greater than what is being sinked these days.
Your math, your model, and your mind set is committed to defending your position which depends on no biosphere expansion other than what results from sinking FF carbon. What does your math and model predict, if FF continues to add 10 Pg/year and the natural emissions continue with a constant 200 Pg/year? What will the subsequent CO2 concentration be in twenty years? And what will the increase from the previous year be?
Ferdinand,
Dr. Ed is not required to explain why natural CO2 is increasing to falsify the human-caused CO2 theory. He isn’t one to guess. That’s not how science works. Maybe if all the money that had been spent supporting this fraudulent science had been spent toward objective research, then maybe we would know the answer. One thing I will say is that nothing about this world is constant other than nature constantly varies. So the idea that Mother Nature was in perfect balance at 280ppm doesn’t make much sense.
To Everyone,
I added a new paper by IvanR. Kennedy, John Runcie, Angus N. Crossan, Raymond Ritchie, and Jennifer Marohasy.
It is now the third PDF file above.
Their paper offers a new unique alterative hypthesis to explain how nature may increase the CO2 level.
In an ongoing email conversation, Gregory R. Wrightstone, Executive Director, CO2 Coalition, wrote to Jennifer Marohasy about this paper:
“If we accept all that you have just provided, you must explain why and how this abiogenic CO2 source suddenly began increasing and continues to increase. This is contrary to how geologic processes work. Increases or decreases to any mantle-derived CO2 or CO2 from weathering would occur over much larger time scales.
And the increase just happens to mirror human emissions.”
Jim,
“What makes you think that the FF emissions make a “relatively minor” contribution to CO2 growth compared to natural emissions? Is it the present composition of the atmosphere, or is it the ~20x larger gross number, or is it something else?”
You were fooled by the present composition of the atmosphere, weren’t you. Just like Mr. Ed.
DMA, July 22, 2025 at 4:00 pm
Even in my rusted knowledge of statistics, I remember that one need to be aware of spurious correlations between variables that have a similar trend. That is the reason that in many cases the correlations are taken from de-trended data.
That goes good in many cases, but fails completely, if the bulk of the trend is caused by a variable with hardly any variability and a huge trend. As is the case for human emissions and the increase in the atmosphere.
In the case of the increase in the atmosphere, indeed the variability in rate of change is fully caused by the variability in rate of change of temperature. But we know from the formula of Takahashi for the influence of temperature on the ocean surface pCO2 per Henry’s law, that the pCO2(aq) increased with less than 10 μatm, while the observed increase is 100 μatm and the supply of FF by humans some 170 μatm over the same period.
So the question then is if the extreme good correlation between FF emissions and increase in the atmosphere is plausible or not and if another (known or unknown) cause may be involved.
As FF emissions are 1.7 times the observed increase in the atmosphere, there is a huge possibility that they are the cause of the increase, simply based on the carbon mass balance.
The two other main probable sources, oceans and biosphere, are proven net sinks for CO2, thus can’t be the cause of the increase and all other known sources are either too small or too slow.
Remains some unknown sources as recently the discovery of extra 14C-free CO2 releases from rivers.
The point is that such releases are already going on for millennia (like coal seam fires) to as long as the earth has liquid water and some solid land. These CO2 emissions, including their 14C and δ13C “fingerprints” are already included in the pre-industrial CO2 levels and isotopic compositions.
Only if they changed completely in parallel with human emissions, then they are of interest, which is partly the case for the river emissions, where they act as a feedback to the human caused increase in the atmosphere.
What I don’t accept of Munshi is that he only looked at yearly (!) variability, that is looking at the noise around de-trended data and then concluding that there is no correlation, implying that there is no correlation between the trends.
If he had looked at e.g. 5 year intervals (or 5 year moving averages), he would have seen that the effect just fades away and only leaves a very small trend for temperature.
Brendan Godwin, July 22, 2025 at 5:19 pm
Brendan, I am only interested in the data, no matter who did measure them or the titles they use to describe them.
“Your reference once again used pseudoscience in the title. Can’t you produce real references from real scientists?”
Thus if you don’t like the title, then the data are pseudoscience?
And again, they don’t measure the pH of DIC, they measure the pH of seawater, even as it passes continuously from the intake of (commercial) sea ships, fully automatically:
https://www.mdpi.com/1424-8220/18/8/2622
“pCO2 is not concentration and it is misleading to use it to try and show atmospheric CO2 is being absorbed in the ocean. The DIC is different from the ocean. The d13C isotopic ratio for the DIC is -.5 to +2.0 per mil. The oceans are -10 per mil.”
Brendan, this only shows that you have not the slightest knowledge of ocean chemistry…
The deep oceans are near zero per mil δ13C and ocean surface between +1 and +5 per mil δ13C and carbonate rocks (dropped by coccoliths out of DIC) also are near zero per mil.
It is at the ocean-atmosphere border that δ13C changes dramatically with -10 per mil δ13C from ocean water to air and -2 per mil from air into ocean waters. Net change -8 per mil δ13C if both flows are in equilibrium.
Or a near constant -6.5 +/- 0.4 per mil δ13C over the past 800,000 years in the atmosphere:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_d13C_lgm_cur.png
And a near constant +4.95 +/- 0.2 per mil δ13C over the past 600 years in coralline sponges (~DIC):
https://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
Until humans started their significant use FF from 1850 on.
“As far as you’re concerned vegetation is the only thing that absorbs CO2 and you avoid the oceans like the plague”
I only look at what the data say:
On short term vegetation is dominant:
Seasonally: -5 ppmv/°C (negative!)
Year-by-year: 3.5 ppmv/°C (positive)
Long term, the oceans are dominant: 4.2%/°C (both directions)
“Their experiment demonstrated that nature’s measured impulse absorbed 239 times the human-produced CO2 impulse.”
I have read their paper and did see Figure 11, which contradicts what they say in the same paper.
Ans 239 times the the human CO2 impulse during a few days has an immeasurable effect on the CO2 increase in the atmosphere…
Bye bye (as long as it lasts)
Dr. Ed, July 22, 2025 at 8:44 pm
Besides what Gregory Wrightstone writes, several items in that paper just don’t add up.
From the abstract:
“Our findings reveal that warming waters absorb atmospheric CO2 by promoting calcium carbonate formation, acidifying seawater and boosting CO₂ release to the atmosphere in late autumn and winter, when atmospheric CO₂ becomes highest”
As far as I know, seawater gets warmer in spring/summer, releasing some 50 PgC CO2 in a few months. Reverse in fall/winter. Kennedy’s findings just do the opposite…
Then we have the oxygen balance: this new find doesn’t involve any interaction with oxygen. Only biological processes do involve huge O2 changes and these show that the biosphere is the main cause of the decrease of CO2 in the atmosphere in spring/summer and increase in fall/winter.
Processes like found by Kennedy et al. only can have a very small influence.
https://www.ferdinand-engelbeen.be/klimaat/klim_img/bender_dO2.jpg
The measurements at Barrow give the clearest indication of the seasonal changes in CO2 and O2
And last, but not least, one can never deduce a long term trend from the variability within a year or a few years, until the trend is significantly larger than the noise…
Stephen P Anderson, July 22, 2025 at 8:42 pm
“Dr. Ed is not required to explain why natural CO2 is increasing to falsify the human-caused CO2 theory. He isn’t one to guess. That’s not how science works. ”
No, but he must explain as a scientist how an increase of CO2 of about half the FF emissions in the oceans and biosphere can have increased any CO2 in the atmosphere, as his model only allows for a (small) part of the increase due to human FF emissions. That is while the CO2 sinks in both oceans and biosphere exceed sources from the same reservoirs. His carbon mass balance doesn’t fit the observed increase in the atmosphere…
“Maybe if all the money that had been spent supporting this fraudulent science had been spent toward objective research, then maybe we would know the answer.”
Still most of all field research is of high quality, but the interpretation of the data is manipulated by a small group of “scientists” with an agenda…
“One thing I will say is that nothing about this world is constant other than nature constantly varies. So the idea that Mother Nature was in perfect balance at 280ppm doesn’t make much sense.”
Nobody says that Nature is constant: for the current SST, the CO2 in the atmosphere should be around 295 ppmv. Only that the change in CO2 ánd isotopic composition nowadays is much faster than in the far past, up to at least 800,000 years (ice cores) or several millions of years (foramins).
Jim Siverly, July 22, 2025 at 7:22 pm
“What does your math and model predict, if FF continues to add 10 Pg/year and the natural emissions continue with a constant 200 Pg/year? What will the subsequent CO2 concentration be in twenty years? And what will the increase from the previous year be?”
The Excel sheet with the calculations for all 20 years is here:
https://www.ferdinand-engelbeen.be/klimaat/klim_xls/Jim_fluxes.xlsx
Starting conditions:
905 PgC in the atmosphere, 200 PgC/year cycling in and out (only natural), 628 PgC equilibrium in the atmosphere for the current SST and 50 years Te for net removal.
Assumption: cycles increase in ratio with the increase in the atmosphere (as mix of natural + FF) . Natural remains 200 PgC, difference is FF “caused”, but does not indicate the ratio of FF/natural within the cycle.
Several starting conditions can be changed, including a small increment per year in the FF emissions.
The calculations are based on a fixed equilibrium and a fixed Te. I still am working on a “floating” equilibrium and the full database since 1850…
Results:
Year 0:
Atmosphere: 905 PgC
In: 200 PgC + 10 PgC = 210 PgC
Atmosphere: 915 PgC (temporarily)
Net out: (915 – 628) / 50 = 5.7 PgC
Out: 210.0 – 5.7 = 204.3 PgC
Atmosphere: 909.3 PgC
Increase in atmosphere: 4.3 PgC
Year 1:
Atmosphere: 909.3 PgC
In: 200.9 + 10 PgC = 210.9 PgC
Atmosphere: 919.3 PgC (temporarily)
Net out: (919.3 – 628) / 50 = 5.8 PgC
Out: 210.9 – 5.8 = 205.1 PgC
Atmosphere: 913.4 PgC
Increase in atmosphere: 4.2 PgC
Year 10:
Atmosphere: 944.0 PgC
In: 208.6 + 10 PgC = 218.6 PgC
Atmosphere: 954.0 PgC (temporarily)
Net out: (954.0 – 628) / 50 = 6.5 PgC
Out: 218.6 – 6.5 = 212.1 PgC
Atmosphere: 947.4 PgC
Increase in atmosphere: 3.5 PgC
Year 20:
Atmosphere: 975.8 PgC
In: 215.6 + 10 PgC = 225.6 PgC
Atmosphere: 985.8 PgC (temporarily)
Net out: (985.8 – 628) / 50 = 7.2 PgC
Out: 225.6 – 7.2 = 218.5 PgC
Atmosphere: 978.6 PgC
Increase in atmosphere: 2.8 PgC
As one can see, the net sink rate increases with the distance to the (old) equilibrium and a new equilibrium will be reached when extra output = extra input with extra CO2 in the atmosphere at extra input * Te
That is at Lnew = 628 + 10 * 50 = 1128 PgC
When the extra input stops, the extra output will exponentially go back to zero and the level in the atmosphere back to the “old” equilibrium of 628 PgC.
Why search for a reason that atmospherc CO2 is increasing? It is staring us in the face. Human emissions are two times larger that atmospheric accumulation.
David Andrews
July 22, 2025 at 9:23 pm
What does your math predict, if FF emissions continue to add 10 Pg/year and the natural emissions continue with a constant 200 Pg/year? What will the subsequent CO2 concentration be in twenty years? And what will the increase from the previous year be?
Ferdinand,
His model does explain that human CO2 is about 20-30 ppm of L which is 430ppm.
David,
Your assumptions are not evidence.
Jim,
The best prediction I can make, assuming constant human emissions of 10 Pg/yr for the next 20 years, would be to also assume that the “airborne fraction” remains around 45% as it has for 75 years. That is, each year the atmosphere would gain 4.5 Pg, so after 20 years it would be up by 90 Pg. Notice that the constant natural emission rate assumed (your 200) doesn’t matter since, by my assumption of a constant airborne fraction, I have guaranteed that net natural absorption is a constant 5.5 Pg/yr. (Note that once again you have focused on natural emissions, forgetting about natural absorption.)
One could certainly be concerned that, going forward, the natural processes that have until now been mitigating the atmospheric CO2 rise might saturate, causing the CO2 growth rate (and airborne fraction) to increase. That is a legitimate concern motivating some research. But for the PAST 75 years the data on the airborne fraction are in. They leave no room to argue that the natural processes are causing the increase.
I am glad you phrased the question in terms of steady rates. You have often referred to “exponentially increasing” rates with no justification except to make your model work. Indeed the human emission rates have been increasing, and that accounts for the positive second derivative of the Mauna Loa curve. But all it takes is steady human emissions to maintain steady growth in atmospheric CO2.
Jim,
I see that my response and Ferdinand’s are different. That is probably the outcome you wanted. His model effectively has the airborne fraction decreasing with time quite dramatically in 20 years, with constant human emissions. While I recognize that “airborne fraction” is only a convenient summary of data and represents nothing fundamental, I am skeptical that it could fall to 28% in 20 years.
Ferdinand Engelbeen
July 23, 2025 at 1:26 am
FE says “If he had looked at e.g. 5 year intervals (or 5 year moving averages), he would have seen that the effect just fades away and only leaves a very small trend for temperature.”
Munshi in fact followed his first work with another that did the same analysis for different time intervals and came to the same conclusion as he had on this referenced paper. I will look for that paper and get a link. I think it is likely already cited in Dr. Ed’s work.
I found Munshi’s work on other time intervals:
https://chaamjamal.wordpress.com/2018/12/19/co2responsiveness/
David Andrews
July 23, 2025 at 7:25 am
DA’s question “Why search for a reason that atmospherc CO2 is increasing? It is staring us in the face. Human emissions are two times larger that atmospheric accumulation.”
Because all the policies recommended to cure the “Climate Crisis” are based on the assumption that we can control atmospheric CO2 by ending our use of fossil fuels. I don’t think there is a “Climate Crisis” but am convinced there is a Climate Policy Crisis that costs dearly in coin and life.
If you and EF are correct will ending the use of fossil fuels end the rise in atmospheric CO2?
DMA,
Yes. Solid science says that ending the use of fossil fuels would end the rise in atmospheric CO2. There is some disagreement on the rate of fall after “net zero”. Ed’s opinions are very much outliers.
To Everyone:
Today, I took some time to review our progress in these debates. This comment is a result of this review. I will make this part of my rebuttal paper as well.
I will appreciate your suggestions on how I can improve this explanation.
A major source of confusion is between those who follow my calculation of the human and natural carbon independently, and those who do not. There is a precedent in physics my method. It is the Partition Principle.
The Partition Principle is used in Statistical Mechanics and Quantum Physics, but it also applies to classical physics. In many cases, including this one, it is the only way to calculate the corrrect answer.
The way I calculate the carbon cycle by separating human carbon atoms from natural carbon atoms follows the Partition Principle of physics.
This separation is necessary to correctly calculate the human carbon cycle and thus the effect of human carbon atoms on the CO2 level as distinct from the effect of natural carbon atoms on the CO2 level.
All calculations made without this separation are fundamentally wrong.
Therefore, In the manner that I defined the “Climate Equivalence Principle,” I now define the “Climate Partition Principle.”
The Climate Partition Principle is a special case of the Partition Principle … an extremely simple case.
There are only two parts to the partition. The variables are continuous. Human carbon atoms and natural carbon atoms are identical. They follow the same rules. There are no substitutions between the partitions. Human and natural carbon atoms do not interact or replace each other.
Neither carbon cycle interferes with the other. Their levels and flows are independent.
Human and natural carbon cycles have their own equilibriums, which represent the maximum entropy for the number of carbon atoms in each partition.
Each carbon cycle has continuing flows from each reservoir to adjacent reservoirs. At equilibrium, these counter flows are equal, but the flows continue.
IPCC defines its natural carbon cycle at equilibrium. This equilibrium results in certain percents of the total atoms residing in each of the four defined reservoirs: land, air, surface ocean, and deep ocean. This equilibrium also allows the calculation of the Te for each outflow node, using Te = Level / Outflow (at equilibrium).
Because human and natural carbon atoms follow the same flow rules and have the same Te’s, their equilibrium percentages are equal.
If either carbon cycle gets new carbon atoms, this adds to the total mass and lowers the entropy in this carbon cycle.
When a carbon cycle is not at its maximum entropy, the carbon cycle will change its flows in a manner that allows the carbon cycle to approach equilibrium as fast as possible.
This is the correct way to calculate the changes in each carbon cycle and to calculate the effect of human carbon on the CO2 level.
All calculations so far presented by the CO2 Coalition representatives are wrong because they have not properly formulated their carbon cycles.
In my opinion, most of the disagreement in these discussions is because the CO2 Coalition reps do not use correct physics. Until the CO2 Coalition reps wake up to proper physics, we will never agree.
Ferdinand Engelbeen
July 23, 2025 at 7:20 am
Thank you for your spreadsheet showing the twenty year future. It’s great. I think I deciphered your formula correctly, but I would like you to confirm it. Meanwhile, I will update my dropbox app so that I can show you the result of back calculating your formula to earlier years.
La_end = (La_begin + Ff_start) – F_netout
F_netout = [ (La_begin + Ff_start) – La_base ] / Te
F_in = Fn_start + Ff_start
F_out = F_in – Fnetout
DMA, July 23, 2025 at 10:25 am
Thanks for the link…
The first point that immediately did attract my attention, is his use of different scales for the different graphs.
For the emissions, the same scale for the 1 to 5 year trends.
For the increase in the atmosphere, smaller scales, so that it is not directly visible that the variability gets smaller.
The same for the “airborne fraction”, to a lesser extent.
And why not plotting emissions and increase in the atmosphere together?
The same visual trick was used for the de-trended data, with a difference in scale of a factor 3.
Nevertheless, as already said: there is absolutely no correlation between the variability of the FF emissions and the variability around the trend of CO2 in the atmosphere, for the simple reason that the FF emissions have hardly any variability. Thus looking at the (temperature caused) variability gives a completely spurious answer.
Just the opposite of the warning that one must be aware of spurious correlations between two similar up going variables…
I am pretty sure that Munshi’s approach would fail with my test of 20 years ago with two variables, one with a slope and no variability at all and another with a double sinus and no slope at all…
And again, in this case, it is entirely possible ánd plausible that the trend of FF emissions is the cause of the increase in the atmosphere, as these emissions are fully added directly into the atmosphere and only can be removed into other reservoirs.
His work does contain a link to another of his works, where he explains why one must use detrended data to avoid spurious correlations. That link doesn’t work, but I probably have found the paper:
https://download.ssrn.com/16/10/12/ssrn_id2851418_code2220942.pdf
That contains following sentences:
“In this kind of empirical evidence, the theoretical time scale at which the proposed causation works must match the time scale of the correlation (Box, 1994). Thus a correlation between emissions and changes in atmospheric and oceanic carbon dioxide must exist at an annual time scale and a correlation between emissions and warming must exist at a decadal time scale.”
Wow. I never have heard of such short time scales.
Because of the relative huge temperature induced noise, one need at least 5 years of data to have certainty about the CO2 trend and as far as I know, climate is at least over a period of 30 years…
With that kind of definitions, one never can obtain any sea level change observation, as there is absolutely no correlation per minute, day, year or even 20 years (only a statistical one) between the real sea level and the observations…
David Andrews
July 23, 2025 at 10:05 am
Thank you for your prediction, as I’m hoping it will get us on the same page. In other words, understanding why we insist on our positions, as I expect we will.
July 23, 2025 at 10:17 am
No worries about not having the same answer as Ferdinand. There are no certainties about the future, because no one has been there yet.
im Siverly, July 23, 2025 at 2:45 pm
Completely right…
Ff_incr eventually can be added each year to make it even more realistic…
and the increase in inflow each year is in ratio to the increase in the atmosphere, but plays no role in our calculations, which is based on the net outflow.
Dr. Ed
July 23, 2025 at 2:30 pm
Thanks for hosting this educational debate. So often do new concepts get introduced that I never realized would apply to this discussion.
I have trouble with this statement, “Because human and natural carbon atoms follow the same flow rules and have the same Te’s, their equilibrium percentages are equal.”
First, there will never be equilibrium as long as inflows and outflows continue to evolve.
Second, why is it necessary for percentages to be equal, even if some type of pseudo equilibrium could be defined? Take a simple reversible chemical reaction. At equilibrium, it would be some coincidence if the percentage of the product turned out the same as the reactant. I’m pretty sure you meant something different than what you wrote.
It’s clear to me that choice of models cause the main disagreement of the two camps participating in this discussion. Your model is linear. Maybe that’s implied by the Partition Principle. That’s a new concept for me to review.
Ferdinand and others use non-linear models. What makes them non-linear is assuming a constant atmosphere concentration in the past as what determines the rate of mass transfer. For example, one model says,
Outflow = (pCO2now – pCO2then) / Tau or ==> 2.8 ppm/year = (420 ppm – 280 ppm) / 50 years.
Linear models use mass transfer proportional to absolute concentration. Those model’s solutions require solving differential equations, not simple math.
Jim,
Let me build on the little model you suggested. (You understand that the numbers I use are nominal only.) That model was:
10 Pg/yr human emissions (measured)
4.5 Pg/yr atmospheric accumulation (measured)
5.5 Pg/yr net global uptake (deduced)
200 Pg/yr natural emission (guesstimated)
205.5 Pg/yr natural absorption of ALL carbon types (deduced from guesstimate)
Thus 200 Pg/yr of carbon is counter-flowing in both directions and COMPLETELY BALANCED. The only imbalance between natural inflow to the atmosphere from land/sea reservoirs and outflow from the atmosphere to land/sea reservoirs is the 5.5 Pg/yr “net global uptake” that mitigates the rise is atmospheric carbon and increases the land/sea reservoir levels. The 200 Pg/yr balanced flow does NOTHING to the levels in the atmosphere or land/sea reservoirs. But it is 20x bigger than human emissions and it does do something. It mixes the atmospheric carbon with the land/sea carbon. Anthropogenic emissions into the atmosphere mean “human carbon” concentrations are higher there than in the land/sea reservoirs. So the mixing moves “human carbon” from the atmosphere to the land/sea reservoirs. While these balanced mixing flows move exactly zero net carbon, they change the composition of the atmosphere by reducing the “human carbon” therein.
The positive net global uptake tells you where the atmospheric CO2 rise is coming from: us. The mixing (which you will recognize either as a “disequilibrium isotope flux”, or what I have been calling the mechanism that dilutes the Seuss effect) hides the evidence that we are responsible. Balanced exchanges just scramble the atmospheric carbon composition without changing the overall carbon levels. The net flow of “human carbon” out of the atmosphere does not correspond to a net flow of carbon. That is why hardly anyone besides Ed bothers to track “human carbon”. Its concentration in the present amosphere does not tell you what Ed thinks it tells you.
Ed,
Your proclamations, which appeal only to the authority of yourself, are just plain silly.
“All calculations made without this [human/natural] separation are fundamentally wrong.” This is nonsense. You are certainly free to do the calculation your way. The 99% of scientists who didn’t do it your way are still correct and gained insights that you missed. In particular you missed the “mass balance” (carbon conservation) argument. Physicists appreciate analyses that use conservation laws, whose elegant simplicity can sometimes appear “Magical”.
“Because human and natural carbon atoms follow the same flow rules and have the same Te’s, their equilibrium percentages are equal.” (?) I don’t think this is what you meant to say, but I have no idea what you did mean to say.
“All calculations so far presented by the CO2 Coalition representatives are wrong because they have not properly formulated their carbon cycles.” The total carbon cycle envisioned in invoking carbon conservation is well formulated. There is no need for a lot of detail. Inputs of carbon to the atmosphere come from human and natural emissions, with the human emissions adding long sequestered carbon to the fast cycle. Natural processes remove carbon from the atmosphere and put it in land/sea reservoirs without any bias on the source of that carbon. Human processes that remove carbon of any type from the atmosphere are negligible. You know the consequences of this simple formulation.
Jim Siverly July 23, 2025 at 4:20 pm
Dear Jim,
IPCC’s model has four main carbon reservoirs. Such a model will have an equilibrium if no new carbon is added to any reservoir. Equilibrium has constant levels and constant outflows. At equilibrium, the carbon will be distributed among the reservoirs with certain percentages.
Human carbon will try to move to these same percentages. If the inflow of human carbon stopped, the human carbon cycle will flow to these same percentages. Then the levels will be constant.
Imagine four ponds connected by tubes. Pour water into one pond and the water will flow to the other ponds until the system is at equilibrium.
IPCC defined its natural carbon cycle at equilibrium, with atmospheric CO2 at about 280 ppm. These flows and levels let us calculate the six Te for this model. Once we know these Te, we can calculate how human carbon flows through the carbon cycle. Human and natural carbon will have the same Te because their carbon atoms are identical.
This model may not apply to chemical reactions. However, I do know that pharmacological models follow the same model that I use
My equation (2) makes my model linear. Outflow is proportional to the first power of the level. Double the level and we double the outflow.
The Climate Partition Principle is an addition to the above description. It means that we must do our carbon cycle calculations by putting natural carbon in one partition and human carbon in another partition, and carbon does not flow between these partitions.
Just for completeness to all with an interest, excluding the argumentative one. Although this will be treated with the usual distain, denial ignorance wrapped up in another specious waffle argument.
Carbon Isotope Ratio Formula 17Jun25 https://www.researchgate.net/publication/392822758_Carbon_Isotope_Ratio_Formula_17Jun25
Further at Page 767-2, https://www.researchgate.net/post/The_physical_processes_of_global_warming_and_climate_change–How_can_alternative_viewpoints_be_resolved/767
Philip Mulholland explains how NOAA measured -10‰ δ¹³C CO2 in the oceans.
DMA, July 23, 2025 at 10:25 am
In addition to what I have already said about Munshi’s work:
Munshi only looked at the difference between the variability one independent variable (FF emissions) with the dependent variable (CO2 increase in the atmosphere).
In the real world, there are two independent variables which influence the CO2 increase in the atmosphere: FF emissions and temperature, the latter can be huge over long periods like ice ages.
As there is a huge (mostly) short-time correlation between temperature variability and CO2 rate of change variability in the atmosphere, all what Munshi did prove is that there is no correlation between FF emissions and temperature…
Brendan Godwin, July 23, 2025 at 9:24 pm
“These two groups are separated by δ13C values of -8.7 0/00 (Air) and -10 0/00 (Ocean) measured for atmospheric and oceanic mobile carbon dioxide gas respectively.”
Mulholland uses following link of NOAA for the -10 per mil for CO2 from the oceans:
https://gml.noaa.gov/outreach/isotopes/mixing.html
That doesn’t contain any direct measurements of CO2 in the ocean waters, but it is known from physics that at the water-air border (and reverse) the heavier isotopes escape slower from one medium to the other medium, which makes that there is a discrimination of about -10 per mil δ13C for CO2 going from the oceans to the atmosphere and about -2 per mil δ13C in opposite direction. Or in average -8 per mil if both flows are in equilibrium.
See: https://scope.dge.carnegiescience.edu/SCOPE_16/SCOPE_16_1.5.05_Siegenthaler_249-257.pdf
“Now the fractionation factors can be computed numerically from eqs. (2):
α(as) = 0.9984= 1 – 1.6‰
α(sa) = 0.9905= 1 – 9.5‰”
I can’t make much of the second link as that discussion is mainly about the influence of the sun on climate, not the topic here.
And I see that you are a Postma believer. Maybe of interest for you:
https://climateofsophistry.com/2023/01/31/ferdinand-engelbeen-another-zeta-5th-columnist/
And that second link does contain some very good advise:
“It is also surprising how emotional this subject has become for many people. Pejorative name-calling and labeling abound within many internet forums. Please — such things are not welcome here. Pejorative language is not conducive to successfully resolving alternative viewpoints.”
Maybe Brendan can learn something of that advise?
Dr. Ed, July 23, 2025 at 2:30 pm
“This separation is necessary to correctly calculate the human carbon cycle and thus the effect of human carbon atoms on the CO2 level as distinct from the effect of natural carbon atoms on the CO2 level.
All calculations made without this separation are fundamentally wrong.”
Sorry, but here we do completely disagree. There is no fundamental difference in any way between human induced and natural CO2 in any process where amounts, pressure or temperature are involved. Only a small (!) differentiation in isotopic composition for biological processes and at physical borders.
Once human FF emissions are supplied to the atmosphere, in all following processes of mass transfer they behave in exact the same way as natural emissions, thus there is not the slightest need to separate them in “natural” and exact the same “human” parts. That “separation” can be theoretically done, but is only of academic interest and makes everything more complicated without purpose.
“Human and natural carbon cycles have their own equilibriums, which represent the maximum entropy for the number of carbon atoms in each partition. ”
This sentence doesn’t make any sense.
The equilibrium level must be exactly the same, or you violate the equivalence principle. In the following texts, you do confirm that principle.
“All calculations so far presented by the CO2 Coalition representatives are wrong because they have not properly formulated their carbon cycles.”
We didn’t use any carbon cycle in our work, as that was not necessary for the overall calculations of the carbon mass balance, the O2 balance, the 13C/12C balance and the 14C balance: we only used the differences between ins and outs, as what goes in must remain in the atmosphere or go out. No matter the source or height of what goes in and or where it goes.
How much carbon cycles between the different compartments is not of the slightest interest for the changes in the atmosphere or any other reservoir: only the difference between ins and outs is what changes the carbon mass in a reservoir and that is quite exactly known for the atmosphere from atmospheric and FF emission data. That shows that more FF CO2 is coming in than as difference is going out as net sink and that difference is exactly known, but of no interest where that goes or how it is partitioned between oceans and vegetation.
Our approach matches the carbon mass balance and doesn’t violate any observation. Your calculations violate the carbon mass balance, as the calculated increase in the atmosphere is much smaller than observed and the main reservoirs that should supply the extra “natural” CO2 also increased in carbon, while they should have decreased…
Ferdinand Engelbeen July 24, 2025 at 2:42 am
Dear Ferdinand,
Thank you again for your comments. It is clear that we disagree on the fundantals of physics.
You have made your points clear. There is no more to discuss. I appreciate your participation in this debate.
I trust that you feel like you have had the opportunity to freely make your points.
Ed
David Andrews July 23, 2025 at 8:35 pm
It is surprising that you taught Thermodynamics and yet you have no appreciation of how and when to use the Partition Principle.
Ferdinand,
It isn’t about agreeing or disagreeing. The math isn’t on your side.
David Andrews,
I thought it was 97% of scientists. Is it now 99% of scientists? You chastise Dr. Ed for appealing to his authority, but then you invoke the authority of the 99%. The problem is that Dr. Ed is correct, and your 99% are wrong. You and your 99% haven’t made one salient point.
Jim,
Dr. Ed is stating that the human carbon cycle is independent of the natural carbon cycle. Human carbon cycle doesn’t affect the natural carbon cycle and vise versa. Nature treats them both the same. I think the Partition Principle is another way of looking at the Equivalence Principle. We would not be here if nature didn’t conform to those two Principles.
David,
Yes, humans are adding about 5PgC to the atmosphere every year, but that causes only about 20PgC of the total carbon in the atmosphere. We’ve shown you the solution to the continuity equation. I think you stopped being a scientist a long time ago and became a politician. I think many of your 99% fit that bill.
Brendan Godwin, July 23, 2025 at 9:24 pm
I have looked at the references in Philip Mulholland’s work: NOAA did only say in that reference that the CO2 out of the oceans (not IN the ocean waters!) is at -10‰ δ¹³C.
That indeed is the case: with an average near zero δ¹³C in the ocean waters, at the water – air border, the lighter (and faster) 12CO2 escapes faster than 13CO2, which gives a change of -10‰ δ¹³C between CO2 in the water and CO2 in the atmosphere. The same happens in opposite direction with a difference of -2‰ δ¹³C, thus leaving +2‰ δ¹³C behind in the atmosphere. Average -8‰ δ¹³C, if the flows are equal.
Calculated here:
https://scope.dge.carnegiescience.edu/SCOPE_16/SCOPE_16_1.5.05_Siegenthaler_249-257.pdf
From the abstract:
“Isotopic fractionation factors for the CO2 transfer between atmosphere and ocean are calculated, taking into account equilibrium and kinetic fractionation. Diffusion of CO2 into the water, which is rate limiting for mean oceanic conditions, fractionates the carbon isotopes only little. 13C/12C fractionations are found to be -1.8 to – 2.3‰ for atmosphere-to-ocean transfer, and -9.7 to -10.2‰ for ocean-to-atmosphere transfer.”
Stephen P Anderson, July 24, 2025 at 7:10 am
Stephen, even the nicest math and fancy formula’s fail on simple facts like adding 10 PgC/year to the atmosphere and looking at the result, which only shows a 5 PgC/year increase, that proves that the 10 PgC/year is the cause of the 5 PgC/year…
Dr. Ed, July 24, 2025 at 4:40 am
Indeed we are at the point to agree that we disagree on the fundamentals of this discussion like the carbon mass balance.
As I have a lot of other problems to solve for the moment and need to prepare for a (similar!) debate in Oslo, I stop here with my reactions, but still are working on the “split” CO2 flows…
Thank you indeed for your hospitality, which indeed is quite rare nowadays…
Ferdinand Engelbeen
July 23, 2025 at 1:26 am
FE says “If he had looked at e.g. 5 year intervals (or 5 year moving averages), he would have seen that the effect just fades away and only leaves a very small trend for temperature.”
The Munshi paper cited above says:
A rationale for the inability to relate changes in atmospheric CO2 to fossil fuel emissions is described by Geologist James Edward Kamis in terms of natural geological emissions due to plate tectonics [LINK] and by Viv Forbes in terms of the natural Henry’s Law equilibrium with much larger store of CO2 in the ocean [LINK] . The essential argument is that, in the context of much larger natural flows of carbon dioxide and other carbon based compounds, it requires circular reasoning to describe changes in atmospheric CO2 only in terms of fossil fuel emissions. It is shown in a related post, that in the context of large uncertainties in carbon cycle flows, it is not possible to detect the presence of fossil fuel emissions without the help of circular reasoning [LINK] .
Carbon cycle flows cannot be directly measured and they must therefore be inferred. These inferred carbon cycle flows contain large uncertainties. The essence of this argument is that the in climate science mass balance of the carbon cycle with and without fossil fuel emissions, the declared uncertainties in carbon cycle flows are ignored. In the related post cited above [LINK] it is shown that when the declared uncertainties are taken into account, the much smaller fossil fuel emissions cannot be detected net of uncertainties in the much larger carbon cycle flows because the carbon cycle balances with and without fossil fuel emissions within its uncertainty bounds.
I believe these quotes and others in Munshi paper address the criticism you mentioned. Do you have an answer to Munshi’s claim or a refutation of his work? I just can’t see how if FF emissions are the cause of ALL of the increase there is not a correlation id the detrended data.
FE
I apologize for this last post. I think you have addressed it above but none of todays comments came into my view until I posted it.
DMA, Brendan, Ed, Stephen, etc.
I don’t think I can do better than my explanation to Jim (on 7/23 at 8:16pm) on why the low level of “human carbon” in the present atmosphere does not tell us human emissions are unimportant. Indeed, the explanation is somewhat more subtle than the other one you are all unable to understand: that a positive net global uptake unambiguously means we, not nature, are the source of the CO2 rise.
So I will move on. Your inability to understand is your problem, not mine.
DMA, July 24, 2025 at 1:25 pm
No problem at all. I think there is some delay if one doesn’t use the refresh button (Ctrl+F5) and only sees the changes after a restart and there is a delay for (too long?) replies which need moderation…
As a final comment, the main point of disagreement:
There is no fundamental difference between our and Dr. Ed’s ideas of the fundamental physics involved.
The main difference is at the process side:
Dr. Ed assumes that all outputs of all reservoirs involved are directly proportional to the CO2 levels/pressures in the different reservoirs. Therefore one can use output = level / Te where Te = RT, the turnover/residence time.
In that case, the small extra input from fossil fuels use has little influence on the CO2 level in the atmosphere.
We assume that the largest parts of the outputs are not proportional to the CO2 levels/pressures in the different reservoirs, but depend mainly of temperature, sunlight and biological processes, both for the outputs as for the inputs, which makes that a large part of the outflows of the atmosphere into other reservoirs are simply recycled in reverse and have little influence on the CO2 level/pressure in the atmosphere.
In that case, the small extra input from fossil fuel use is the main driver for the increase of the CO2 level in the atmosphere.
The correlation coefficients between atmospheric CO2 and climate (and atmospheric CO2 change and climate change) demonstrate these factors are uncorrelated over the most recent 550 million years of evidence.
550 million year correlation coefficient (CO2 and climate): 0.29
550 million year correlation coefficient (CO2 change and climate change): 0.10
No correlation means causation is impossible!
Therefore, changing CO2 cannot be the cause of climate change.
Fact: Oceans are the greatest storehouse of carbon dioxide on the planet.
Science: A warming global climate will raise ocean temperatures which, as a consequence, will outgas relatively more CO2 to the atmosphere, thus climate change CAN cause increasing atmospheric CO2.
Q.E.D.
End of story.
Bob,
End of story? I don’t think so. If ocean outgassing was dominant, CO2 atmospheric accumulation rates would exceed human emission rates. They don’t. Measured carbon levels in the ocean are increasing; that is a probem if you think oceans are a net source rather than a sink. Higher atmospheric carbon levels push carbon INTO the oceans, especially in the cooler polar regions.
Ferdinand Engelbeen
July 25, 2025 at 12:27 am
“There is no fundamental difference between our and Dr. Ed’s ideas of the fundamental physics involved.” And “We assume that the largest parts of the outputs are not proportional to the CO2 levels/pressures in the different reservoirs.…”
Those statement are hugely contradictory. However, the disagreement between your camp and Dr. Ed’s will go on ad infinitum I’m afraid. That is sad, because it’s not an either-or situation. There is only one set of true physical principles at play. One cannot pick and choose what “processes” one wants to use to make the data fit to one’s idea of reality.
I’m on dropbox again and I finished working on back calculating your model, Dr. Roy Spencer’s, and my spreadsheet based on Spencer’s model. I added the natural emissions missing from the former two models. Spencer’s model back calculates perfectly. Your model seems to have a bug, because I expected it to back calculate ok, as well, but it didn’t. Maybe you can explain my error.
https://www.dropbox.com/scl/fi/hckovmziez0g1rpzvu97c/Jim_fluxes.xlsx?rlkey=jxl8bnq5tpwd9wt3r32rqy7d5&dl=0
My spreadsheet was modified from my original upgrade of Spencer’s. I used the Mauna Loa data to back calculate the 1959-2018 years using the formula NEn = Cn – Cn-1 * ( 1 – 1/Te ) – HEn where NE and HE are natural and human emissions, respectively. Astute observers will notice that as a form of Magic Math:
D = Eh + En – Sn.
From 1750 to 1958, I used my original estimate of exponentially increasing natural emissions. That was simply a process of extrapolating the fit to Mauna Loa data assuming there was a constant e-time (or residence, turnover, etc.). Because the Mauna Loa data is confined to a relatively narrow time interval, the extrapolation can be made to end at 280 +/- ? ppm without deviating much from a best fit. I also used a best fit to the Mauna Loa values to do the back calculation for the 1959 – 2018 years.
The takeaway from this exercise is to notice both the Spencer model and my model fit the data. Therefore, the question is, which model most likely represents a physical realistic process? It makes no sense to me that the net amount of carbon sinked annually is proportional to the difference between what the pCO2 is now versus what is was in 1750. That’s what the Spencer model says and does. My model says the amount sinked is proportional to the current atmosphere content. Period. That is standard physics and a fundamentally different concept than the one Spencer’s model is based on.
You can play around with different scenarios of net zero, net natural or various increasing amounts of both in future years. More data from 2018 on can be added as a check on how well my model performs.
David Andrews
July 23, 2025 at 8:16 pm
Your description of the human flow supplementing a constant inflow of natural carbon seems like a good first-glance explanation of what’s going on. Magic Math confirms it. Here’s the problem. Look at Ferdinand’s “Jim’s fluxes” spreadsheet that I amended and linked to below. In Spencer’s model, I tabulated the Te values for the whole period 1750 to 2018. Those values gradually increase from 3.14 years to about 4.3 years. What physical processes were changing during the past three centuries that would cause residence time to increase that much?
You wrote, “The net flow of ‘human carbon’ out of the atmosphere does not correspond to a net flow of carbon.” What does that mean and what difference does it make, even if you could support it with some model more explanatory than simple math?
I showed how increasing natural emissions supplement FF emissions and enable correlating the Mauna Loa data with a physically realistic constant e-time. I proposed various sources for where the extra carbon comes from. Now where is your evidence that there is no extra carbon and natural emissions have remained the same for centuries?
David Andrews
July 25, 2025 at 8:55 am
You never stop do you.
“Measured carbon levels in the ocean are increasing”
Why because you have cherry picked MLO data showing that. One location is not the world. MLO is surrounded by volcanoes that are constantly spewing CO2 into the oceans.
CO2 in the oceans at Grays Reef is falling.
https://www.pmel.noaa.gov/co2/story/Grays+Reef
Jim,
None of my arguments have been about time constants, and you give me no reason to start looking at them now. Getting them right is important, but they have no bearing on the question of where the atmospheric carbon rise is coming from. They are a distraction.
Carbon conservation plus data on human emissions and atmospheric accumulation tell us WITHOUT DOUBT that natural processes are removing carbon from, not adding it to, the atmosphere. You thought you saw a loophole in that argument but have failed to identify it. All you have been able to do is to reproduce Ed’s (and Hans Suess’s, Skrable’s, mainstream science’s, and my own) conclusion that what Ed calls “human carbon” is but a minor component of the carbon in the present atmosphere. That by no means implies that human emissions are but a minor contributor to atmospheric carbon rise. That is Ed’s biggest conceptual error, and you seem to be all-in with it.
I don’t think I need to again go through the arithmetic of my 7/23 post. My statement “The net flow of ‘human carbon’ out of the atmosphere does not correspond to a net flow of carbon” should be self-explanatory. In my analysis I separated the natural exchanges between atmosphere and land/sea reservoirs into the (unbalanced) net global uptake component removing carbon from the atmosphere, and the remaining EXACTLY BALANCED exchanges that homogenize the carbon composition of the various reservoirs but don’t affect AT ALL the total carbon levels in any of them. Why does that matter you ask? The simple “net global uptake” analysis shows that human emissions are responsible for the increase. The mixing represented by exactly balanced exchanges (aka “disequilibrium isotope flues, aka as “Seuss effect dilation mechanism”) changed the composition of the reservoirs without changing levels and fooled you, Ed, and Skarble into naively thinking that “human carbon fraction in the present atmosphere” equals “human contribution to the atmospheric CO2 rise.”
Nowhere in the above is there any need to invoke “extra carbon” or changes in natural emissions over the past few centuries. I don’t need to respond to whatever fudge-factors your undocumented model requires to agree with Mauna Loa data.
What do you find difficult about the consensus view? I could say that it wins by Occam’s razor, but the case is much stronger than that. But I know that the notion of “consensus” is red meat to those who have declared themselves to be on Ed’s side.
Jim Siverly, July 25, 2025 at 10:54 am
Jim, the essence in this case is in the model, in that sense that Ed (and you and many others) assume that all outflows are only CO2 level/quantity/pressure dependent in the different reservoirs.
That is a fundamental error, as at least half of the total yearly outflow, the one into vegetation, is near completely independent of the actual CO2 level/pressure in the atmosphere.
Only depends of temperature and sunlight. Even so much, that it goes from minimum to maximum within a few months, sucks so much CO2 out of the atmosphere, that the CO2 level in the atmosphere drops, despite the opposite extra supply of CO2 from the warming oceans.
Of the (1750, natural) 108 PgC and (2000, human caused extra) 14 PgC that all bio-life releases over a year, mainly in fall and winter, only 2 PgC is stored in more permanent vegetation and soils. The net difference, which is the result of the 240 PgC (human caused) increase in the atmosphere thus only caused a very meager 2 PgC extra uptake by the total biosphere…
That makes that your back-calculation, which is based on the absolute CO2 pressure in the atmosphere is completely at odds with the real world.
In both my and Spencer’s series, you use a fixed in/decrease of CO2 based on the original level of 628 PgC and the calculated 50 years adjustment time.
The real net removal rate of some extra CO2 above the 628 level is in ratio to the difference between the actual CO2 level and the original equilibrium, which makes that in back-calculation the removal rate reduces to zero when the 628 PgC is asymptotically reached again.
Brendan Godwin, July 25, 2025 at 6:27 pm
Congratulations Brendan. You were able to find a negative (?) trend of the pCO2 in seawater within corals which show a seasonal change in pCO2 of the oceans between 250 and 750 μatm.
Can you show me how large that trend is?