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.
Dear Dr. Ed,
With respect, I’m on your side. My equation one,
(JS1) dC(t)/dt = Eh(t) + En(t) – Sn(t)
is exactly your equation,
(EB1) dL/dt = Inflow – Outflow
with Inflow = Eh(t) + En(t) and Outflow = Sn(t) = SN(t) = [ Sh(t) + Sx(t) ] where Sx(t) equals that fraction of total carbon sinked that was not derived from human sources. I could have included that earlier, but there was no need to clutter up the math with variables that can’t be derived from simple math. In other words, we know Eh(t) and dL/dt from the available data, but calculation or estimation of the relative amounts of Sh(t) and Sx(t) are not possible without model approaches like yours. My primary interest is in resolving the question of which model most appropriately describes the physical processes involved. Although probably a fool’s errand, I would like to see everyone get on the same page here.
You wrote, “I disagree with your (JS1) because it does not include -Sh(t), and therefore it assumes the sinks for human carbon outflow are the same as the sinks for natural carbon outflow.”
Sink rates for human carbon outflow are the same as the sink rates for natural carbon outflow, because of the equivalence principle. I hope my explanation of Sn(t) = [ Sh(t) + Sx(t) ] clears that up.
Dear Jim,
I had only an older version of his RRR approach and couldn’t load your reference in Firefox. But now loaded in the MS browser…
Koutsoyiannis wrote:
“1. The notion of the equilibrium state is incompatible with the recent biosphere expansion, which was documented in the main part of this essay and elsewhere [1,9,25].”
The main effect of temperature on short term is on vegetation at about -5 ppmv/°C for seasonal changes and +3 to +4 ppmv/°C for year by year changes. Over periods longer than a decade the influence of expanding vegetation is near zero and the oceans take over as the main level of equilibrium. Visible as +8 ppmv/°C for Antarctic temperatures and 15-20 ppmv/°C for global temperatures over the past 800,000 years.
That the expansion of the biosphere plays little role can be seen as a very stable 13C/12C ratio of -6.5 +/- 0.4‰ δ13C, until humans start to emit FF. The level today is below -8‰, while vegetation is a net sink of CO2, preferable of 12CO2, leaving relative more 13CO2 behind, thus increasing the 13CO2 level in the atmosphere…
What Koutsoyiannis and many others forget is that a cycle doesn’t add or subtract anything from the atmosphere, only the difference between the ins and outs changes the level of CO2 in the atmosphere. Even if the natural cycle of vegetation doubles (as was at least during interglacial periods), that halves the residence time, but doesn’t change Tau with one second.
“2. The idea that human emissions are the only or the main agent of change is incompatible with the ever-changing Earth’s states, including the atmosphere and climate”
We never said or implied that. Over the past 800,000 years, the changes were huge, but all caused by huge changes in temperature over very long time periods. The warming from a glacial period to an interglacial needed 5,000 years for a change of some 100 ppmv CO2, or some 0.02 ppmv/year…
Even shorter periods like the MWP-LIA cooling don’t show more than 10-20 ppmv/°C.
The current change in the atmosphere is 2.5 ppmv/year, with 5 ppmv/year of FF emissions and suddenly over 100 ppmv//°C. Which violates Henry’s law (maybe +13 ppmv since the LIA…)
According to Koutsoyiannis the FF emissions are not the cause of the increase in the atmosphere…
“3. The importance given to human emissions is disproportional to its share in total (4%).”
Again the idea of the “classic” reactor with unidirectional flows through the container… Indeed, in that case, FF ratio’s in the container and output never can exceed the FF ratio in the input.
But the observed FF level in the atmosphere is already over 10% and in the ocean surface over 6%…
Koutsoyinannis “lake model” is herewith rejected.
Our model more resemples the “fountain model”, where a small input is the only cause of the level and overflow of the basin, no matter how much water flows over the fountain itself… The latter gives the short residence time of 4 years for CO2 in the atmosphere. The former the small net outflow rate of 50 years…
“4. While the proportionality relationship in Equation (A3) has an empirical basis (see below), it may be a result of the coincidence of increasing human and natural CO₂ emissions. The latter, caused by the biosphere expansion, are totally neglected in this relationship. ”
The human input increased a factor 5 between 1958 and today. The biosphere expanded some 20% over the same period. Quite a difference.
As said before: only if both expanded at the same rate, the natural fluxes might be the main cause of the increase.
So, the whole appendix A of Koutsoyiannis fails to reject our approach…
It could be more. If there was an equilibrium before the world population grew from negligible to 9 billion people, a lot of old growth forest has been cut down since.
Brendan,
I agree that data from around the time of the Pinatubo eruption demonstrates that natural processes can affect atmopheric carbon levels. Note that in this case, net global uptake INCREASED because of the cooler weather. That is, atmospheric carbon levels were LOWERED (did not rise as fast) because of the event. This is hardly a convincing demonstration that natural processes are raising atmospheric carbon levels as they remove carbon from the atmosphere.
Jim, about the formula’s:
Koutsoyinannis says:
“It would be absurd to assume that Sn(t) would be related to a portion of the atmospheric storage, such as the surplus above the assumed equilibrium state.”
Well, I suppose that Koutsoyiannis never has heard of the Le Chatelier’s principle?
That shows that Sn(t) – En(t) changes from zero to some value that tries to counter the “disturbance”, that is the change in one of the components of a dynamic equilibrium…
That is exactly what Tau does: with some extra CO2 in the atmosphere, Sn(t) will increase in ratio to the extra CO2 pressure and En(t) may be reduced (in the case of the oceans) or not (or even slightly increase, in the case of vegetation). Thus Sn(t) and possibly En(t) of course change with the extra CO2 in the atmosphere.
95% and more of Sn and En are completely independent of the CO2 level in the atmosphere. The 5% depends of the pCO2 difference between atmosphere and ocean surface. That will go to zero if there were no human emissions or stop increasing if we would halve our emissions, but there is no reason to do that at all…
The math still remains very simple: human emissions are straightforward into the atmosphere, for 100%.
The removal of the extra mass (no matter the original FF molecules) only depends of the total extra CO2 in the atmosphere (not that from one year human emissions) above the long standing dynamic equilibrium with the ocean surface, only with a small change in equilibrium over time caused by SST changes. The observed Tau is around 50 years and has nothing in common with the residence time… Even if all vegetation on earth doubled over time, that does about double S(t) and E(t) and thus halves Te, but doesn’t change S(t) – E(t), thus doesn’t change Tau…
ADMIN NOTICE:
I don’t know if you have the same difficulty as I do, trying to find previous comments that I wish to reply to, and trying to find if there is a new comment that is a reply to a comment days ago.
Because of the large number of comments on this post, I find it difficult to reply to comments that are embedded in comments way above the new comments at the bottom of this list.
So, I am going to try an experiment that is reversible:
WordPress allows me to set the number of sub-comments. it is presently set at the default of 4.
As a test, I am going to reset this to 0.
After this reset, all comments will be reorganized into cronological order rather than in reply order.
This will force us to state the author, date, and time of the comment we are replying to.
But I think it will help us to find the comments we wish to reply to, and help us review all NEW comments since we last looked at this page because they will all be at the bottom of the comment list.
So, if you don’t like this chronological order setup, tell me. It is easy for me to reset the WordPress replies back to 4.
We lose nothing by trying this experiment.
Here we go. Refresh your browser to see the comments in chronological order.
Jim,
It was probably more source than sink until about 1980, due to expanding population and following land use changes. Since at least 1990, the biosphere is a net sink, as can be deduced from the oxygen balance: If there is a net CO2 uptake, then extra O2 is produced or reverse. By measuring the O2 balance, one can calculate the net uptake or release of CO2 by the global biosphere.
Only since about 1990, we have O2 measurements that are accurate enough (less than one ppmv in 21,000 ppmv…) to calculate the net uptake or release of CO2 by the global biosphere. Here reflected in the work of Bender et al.:
https://tildesites.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
The partition of the net CO2 sinks between oceans and vegetation can be seen in Figure 7 at the last page.
From 1994 to 2002 the net uptake by the biosphere was 1.0 +/- 0.6 PgC/year. With the exception of the 1998 El Niño, the biosphere was always a net sink for CO2…
It really is that simple: human emissions are directly, for 100% in the atmosphere. They increase the CO2 level with the full emissions and decrease the δ13C and Δ14C levels for all what they supply.
All what nature does is removing about half what humans added as mass and replace 2/3 of all original FF molecules with CO2 molecules from other reservoirs…
Dr. Ed – July 9, 2025 at 9:52 am
Good idea, I probably missed several comments and reactions, due to the local replies…
Ferdinand Engelbeen July 9, 2025 at 9:33 am
Of course:
“Even if all vegetation on earth doubled over time, that does about double S(t) and E(t) and thus halves Te”
only is true for the biosphere part of the natural CO2 fluxes.
As that is about halve the total natural CO2 flux in and out, then Te is reduced by app. 25%…
Dr. Ed, July 8, 2025 at 9:45 pm
Dear Dr. Ed,
The main question remains:
Human emission are redistributed between atmosphere, biosphere, ocean surface and deep oceans.
The increase in the atmosphere is only a fraction of the observed increase.
What is then the source of the observed difference, as both the biosphere and the oceans increased in carbon content?
Ed, in the comment below addressed to “Dave,” were you talking to me, or to Dave A? In it you complained about my (his?) “tau,” but I’ve said nothing about “tau.”
The model you depicted in your “Figure 3,” labeled “IPCC’s natural and human carbon cycles,” is based on a misunderstanding of Fig. 6.1 from AR5, and it is strikingly unphysical. It shows “human carbon cycle” distinct from a “natural fast carbon cycle,” which is nothing like physical reality, and certainly not what the IPCC’s diagram meant. Notably, your model diagram shows various “human carbon cycle” flows between the atmosphere and both “Land” and “Surface Ocean,” which have no basis in reality. It also shows unbalanced “human carbon cycle” flows from the atmosphere into & from both “Land” and “Surface Ocean,” yet shows zero “human carbon” accumulated in both, which obviously makes no sense.
I’m uninterested in analyzing that model, or the equations based on it. I prefer to focus on the real world.
You claimed that human processes removing carbon from the atmosphere (your “An”) are not negligible. So I discussed those processes, one by one, here:
https://edberry.com/co2coalition/#comment-112419
I showed you that your “Ah,” i.e., the anthropogenic processes which deplete the CO2 from the air, are negligible. More precisely, they are much smaller than the error bars on anthropogenic emissions, so they can be ignored in “mass balance” arithmetic. Even if you count cement carbonation, anthropogenic CO2 removals are still only about 2% of anthropogenic CO2 emissions.
● If you now understand that that is correct, then please acknowledge your error, so that we can move on.
● Or if you still think that’s wrong, then please demonstrate that. Please answer the question I keep asking: What anthropogenic processes do you think remove CO2 from the atmosphere?
“If an honest man is wrong, after being shown his error he either stops being wrong or stops being honest.”
– unknown (related by Andre Bijkerk)
Ed wrote, “So, if you don’t like this chronological order setup, tell me. It is easy for me to reset the WordPress replies back to 4. We lose nothing by trying this experiment.”
One thing you’ve lost is the “reply” button.
IMO, 10 would be better than 4, which was better than zero.
However, it would be better yet if there were a user option to choose to view the comments either in “tree view” (with replies shown immediately following the comments to which they reply), or “chronological.” The default should always be “tree view,” but an option to switch to chronological, to find any new comments, would be helpful.
Ideally, each comment would also show a link to the comment to which it’s replying.
As long as we’re wishing for things, it would be nice if references to .jpg and .png images like this produced scaled, inline copies of the image:
https://sealevel.info/1612340_Honolulu_thru_2025-04_vs_CO2_annot1.png
An “edit” button would be nice, too.
Ferdinand,
“Even if the natural cycle of vegetation doubles (as was at least during interglacial periods), that halves the residence time, but doesn’t change Tau with one second.”
The kinetics of mass transfer of molecules between two reservoirs towards their return to equilibrium (or relaxation) after a sudden modification of the conditions, such as a jump of temperature or of pressure is analogous to how Tau and Te are related by 1/Tau = (K+ + K-) where K+ and K- are the individual rate constants for the forward and reverse directions of flow. A change in either individual rate constants will affect Tau. Making Tau independent of Te is a function of your incorrect model.
“Which violates Henry’s law (maybe +13 ppmv since the LIA…”
Henry’s Law expresses an equilibrium condition where the concentration of gas dissolved in a liquid is directly proportional to its partial pressure. It says nothing about the time to come to equilibrium after an imbalance.
“But the observed FF level in the atmosphere is already over 10% and in the ocean surface over 6%…”
Yes, and therefore “classic reactor” and “lake” simple math models can be rejected.
“The human input increased a factor 5 between 1958 and today. The biosphere expanded some 20% over the same period. Quite a difference.”
The simple math difference between 20% of 100 ppm of natural emissions is 5 times larger than the 4 ppm increase in industrial emissions. Even simple math shouldn’t require any correlation between the two fluxes. Koutsoyiannis hasn’t failed to reject your approach. He led you to water, but he just couldn’t make you drink.
Brendan Godwin July 8, 2025 at 8:32 pm
Brendan, I am pretty sure that you are against measuring temperature in the middle of towns, near airco outlets, asphalt parkways, on asphalted rooftops etc. for the global temperature record.
Then it wonders me why you insist to use CO2 data which are highly contaminated by local CO2 sources. As like the alarmists for bad temperature data, because you like the results?
I do contest both: contaminated data are bad data and should not be used for any record.
There is no need to use contaminated data like these of Giessen and Poona, as there is a quite reliable source of average data over the same periods: ice core CO2 levels, with only one drawback: its resolution, which depends of the local snow accumulation.
For 2 out of 3 ice cores at Law Dome, the resolution is less than a decade. with data over the past 150 years, thus including the 1940 “peak” in the contaminated CO2 measurements of Giessen and Poona. The same ice cores have a direct overlap 1958-1978 with the direct measurements at the South Pole:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/law_dome_sp_co2.jpg
Equal within +/- 1.2 ppmv (1 sigma).
If they correctly reflect the atmospheric data over 20 years, I don’t see any reason that they will not correctly reflect the data of 20 years before 1958. That is for the period 1938-1958, thus including the non-existing peak in the global CO2 data.
And again: stomata data are local data over land. They have the advantage of reflecting local changes very rapidly. Local changes, not global changes.
The historical Giessen data were three times a day, of which one in the middle of the day and two at the much higher levels at the flanks of the nightly degassing. Bias of the measurements: +40 ppmv. Bias of the location (in modern measurements) +40 ppmv. Overall bias, compared to global levels: +80 ppmv. That is your 1940 “peak”…
Have further a read of our specialist in ice core and stomata data: Renee Hannon:
https://co2coalition.org/wp-content/uploads/2024/06/Measurement-of-CO2-Concentrations-Through-Time-2024-June.pdf
Bud Bromley has some strange ideas of what Henry’s law implies. The effect of SST on the CO2 pressure of the ocean surface (in equilibrium with the atmosphere) is only some 10-20 ppmv/°C.
Or for the Pinatubo, only a smaller increase in CO2 than before or after the Pinatubo.
A smaller increase, not a decrease!
In January, compared to the previous year January:
1991: 1.1 ppmv
1992: 1.4 ppmv
1993: 0.8 ppmv
1994: 0.9 ppmv
1995: 1.9 ppmv
Moreover, the reduction of the CO2 increase was mainly caused by increased vegetation growth, thanks to the scattered sunlight by the Pinatubo induced aerosols, giving more light to leaves, normally part of the day in the shadow of other leaves…
How do we know that? Because the 13C/12C ratio increased while the CO2 increase dropped. If the oceans were responsible, the CO2 changes and 13C/12C changes would parallel each other:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/temp_dco2_d13C_mlo.jpg
And I have seen the Byrd contaminated data. Well they did show the whole range of data they have measured at the same depth. For uncontaminated data the spread is about 1.2 ppmv for modern drilling and extraction methods.
If you find drilling fluid, that gives an enormous range, which has nothing to do with the real CO2 data of that time. I should have rejected all these data, the authors only retained the lowest data, as these were probably the real background CO2 of that time. But Poyet (and you) like the high, contaminated data, so the rejection must be wrong…
Then the late Jaworowski.
Indeed Etehridge didn’t refute his objections by using his name, he refuted them point by point, whithout naming him. But everybody knew that Jaworowski’s objections were the target. Except Jaworowski himself, who repeated his objections years later…
Further I confronted him in a personal mail with the fact that he had looked at the wrong column in Neftel’s ice core record: the ice age data vs. the gas age data.
He replied that there was no difference, as there are frequent melt layers in the ice of Siple Dome. In reality Neftel encountered only one melt layer and adjusted the ice age – gas age difference accordingly.
And if you believe Jaworowski, how can one measure 200-300 ppmv in the ice cores when the outside CO2 is over 400 ppmv and in the labs where is measured probably a lot higher, if there is a lot of exchange through “cracks in the ice”?
Let the good old Dr. Jaworowski rest in peace, together with his wrong ideas of CO2 in ice cores…
And how much liquid water do you think remains between the ice crystals at -40°C at the inland cores like Vostok and Dome C?
Ferdinand
To Ferdinand Engelbeen, from July 9, 2025 at 9:33 am
“95% and more of Sn and En are completely independent of the CO2 level in the atmosphere.”
That is completely wrong and utterly opposed to the forces at work between transport across interfaces. Study the derivation of the kinetics of the reaction of A B, which is analogous to interfacial transport. http://brussels-scientific.com/?p=7724 . The transport rates are proportional to the concentration at all times even at equilibrium when the forward and reverse rates are equal. Until equilibrium, the concentrations are constantly changing. There is no static concentration to which the disturbance is heading, such as in the case of your Tau model where the rate is proportional to the current level minus the equilibrium level. That old equilibrium level may never be achieved because of the new equilibrium created by additional carbon added to the system.
Jim Siverly, July 9, 2025 at 11:43 am
Jim,
If I have understand it correctly, both Dr. Ed and I use bidirectional flows to calculate Te or Tau alike. No problem there, except that the time constants of Dr. Ed are based on the total outflows as if these were caused by the absolute CO2 level/pressure in the different containers, while 95% of all outflows (especially from atmosphere into vegetation and back) are completely independent of the CO2 level in the atmosphere. Which makes that his increase of total CO2 mass in the atmosphere is way lower than observed.
I am aware of the time constant for Tau, as that is an observed 50 years. Not 4 years, or there wouldn’t be such an increase in the atmosphere.
Your calculation of the 5 times higher increase of the vegetation inflow violates the equivalency principle for CO2: for nature to be the main cause of the CO2 increase in the atmosphere, it should have increased all in- and outflows a 5-fold between 1958 and today, not 20%…
Koutsoyiannis, Harde and many others use the one-way input – container/lake/bath tube – output model and are completely at odds with reality, thus their results make no sense at all.
Jim Siverly, July 9, 2025 at 1:05 pm
Jim,
“The transport rates are proportional to the concentration at all times”
Yes, for those processes that depend of the CO2 concentration. The calculated output based on the absolute CO2 pressure in the atmosphere is some 16 PgC/year in total into both oceans and vegetation together.
Take the output form the atmosphere into vegetation in spring/summer: 120 PgC absorbed by the biosphere with increasing temperature and sunlight, due to photosynthesis. Going from near zero to 100% in a few months time, near completely independent of the pCO2 in the atmosphere. Even reducing the pCO2 of the atmosphere with some 10 ppmv in the NH. If there was no emission of 60 PgC from the same biosphere at night and 50 PgC from the warming ocean surface, the drop would be 120 PgC or 60 ppmv…
Reverse, there may be some influence of the CO2 pressure in the water of the leaves that respire CO2 at night, but for all other releases by bacteria, molds, animals, including humans, there is zero influence of the pCO2 of the atmosphere in the quantity that is released from decaying organics…
From Ferdinand Engelbeen, July 9, 2025 at 1:21 pm
Ferdinand,
Again you repeat the assertion that “95% of all outflows (especially from atmosphere into vegetation and back) are completely independent of the CO2 level in the atmosphere.” This cannot be supported by experimental data. If so, please present it. Look at the anecdotal data from the CO2 coalition where they subjected trees to several levels of CO2 with arguably a proportional increase in growth rate. If the growth was independent of CO2 level, no significant growth would have been observed.
You completely misunderstand my comparison of your five-fold increase in human emissions and my 20% increase in natural emissions. There is no violation of equivalence principle which applies to first-order uptake. Human emissions are zero order. They don’t follow the rules that must be applied to first order natural emissions and uptake.
“Koutsoyiannis, Harde and many others use the one-way input – container/lake/bath tube – output model and are completely at odds with reality, thus their results make no sense at all.”
Dr. Ed is right. You do not understand his model and the others. You have yet to develop a rigorous model that refutes theirs. Their models are not at odds with reality as they all explain the data and use proper physical principles in doing so. It’s your devotion to a simple math coincidence model that prevents you from understanding their models.
GENERAL QUESTION TO THOSE COMMENTiNG ON PHYSICS:
How familiar are you with the following concepts:
Lagrangian, Hamiltonian, Principle of Least Action, entropy, equilibrium, systems formulation and mathematics, time-step numerical integration, Markov Chains, probability, the significance of stastistical non-correlation, scientific method, and the philosophy of science?
This is not a test and you don’t have to answer this question. But the reasoning you learn in these subjects does help people understand my simple deductive model that is entirely based on (1) continuity equation and (2) outflow proportional to level divided by an e-time.
To Ferdinand Engelbeen, from July 9, 2025 at 1:49 pm, and also from July 9, 2025 at 9:33 am
I may be incorrect in claiming all “transport rates are proportional to the concentration.” You gave examples such as releases by bacteria, molds, animals, including humans, etc. I will give some thought to what degree that would effect a Te model. But certainly, the ocean processes are first order in both directions.
From July 9, 9:33 am
“The math still remains very simple: human emissions are straightforward into the atmosphere, for 100%.”
You are likening human emissions to a “disturbance” and characterizing Tau as relaxation time. That is not an appropriate model in that continually accumulating human emissions, rather than a one-time “dose,” conflated with additional “excess” natural emissions give rise to your ambiguous Tau values. Your estimates of Tau are a consequence of using a flawed model.
“The removal of the extra mass (no matter the original FF molecules) only depends of the total extra CO2 in the atmosphere (not that from one year human emissions) above the long standing dynamic equilibrium with the ocean surface, only with a small change in equilibrium over time caused by SST changes.”
That is assertion based on what equation NS*(t) = K* [ S(t) – Se* ] predicts. Since there will never be cessation of burning fossil fuels in our lifetime, you won’t have any way to verify it.
“The observed Tau is around 50 years and has nothing in common with the residence time… Even if all vegetation on earth doubled over time, that does about double S(t) and E(t) and thus halves Te, but doesn’t change S(t) – E(t), thus doesn’t change Tau…”
Do you have any actual evidence of that?
Jim Siverly quoted Ferdinand saying, “The observed Tau is around 50 years and has nothing in common with the residence time…” and asked, “Do you have any actual evidence of that?”
The roughly 50 year “adjustment time” (a/k/a the 35 year effective first half-life) of CO2 added to the atmosphere is determined from measured data, as I discussed here (section 2):
Burton, D. A. (2024). “Comment on Stallinga, P. (2023), Residence Time vs. Adjustment Time of Carbon Dioxide in the Atmosphere.” OSF Preprints. https://doi.org/10.31219/osf.io/brdq9 (and there’s supplementary material here)
It also cites five other sources reporting approximately the same result: Spencer 2023, Engelbeen 2022, Dietze 2001, IPCC SAR WG1 TS B.1 p.16, Moore & Braswell 1994:
1. Spencer, R. W. (2023). ENSO Impact on the Declining CO2 Sink Rate. J Mari Scie Res Ocean, 6(4), 163-170. https://doi.org/10.33140/jmsro.06.04.03
2. Engelbeen, F (2022). The origin of the increase of CO2 in the atmosphere, http://www.ferdinand-engelbeen.be/klimaat/co2_origin.html (section 3)
3. Dr. Peter Dietze: http://www.john-daly.com/carbon.htm
4. The IPCC’s Second Assessment Report: WG I Technical Summary, section B.1, p.16:
https://archive.ipcc.ch/ipccreports/sar/wg_I/ipcc_sar_wg_I_full_report.pdf#page=29
https://sealevel.info/SAR_TS_p15_50yr_adjustment_time_highlighted.png
Excerpt:
“Within 30 years about 40-60% of the CO2 currently released to the atmosphere is removed.” That implies an adjustment time of 33-59 years, and a half-life of 23-41 years.
5. Moore, BIII, &Braswell, B.H. (1994). The lifetime of excess atmospheric carbon dioxide. Global Biogeochem. Cycles, 8(1), 23–38. https://doi.org/10.1029/93GB03392
Excerpt:
“The single half-life concept focuses upon the early decline of CO2 under a cutoff/decay scenario. If one assumes a terrestrial biosphere with a fertilization flux, then our best estimate is that the single half-life for excess CO2 lies within the range of 19 to 49 years, with a reasonable average being 31 years.”
Also, Prof. Richard Lindzen mentioned it during the Q&A (3rd video) of this excellent(!) lecture:
● Part 1: https://www.youtube.com/watch?v=hRAzbfqydoY
● Part 2: https://www.youtube.com/watch?v=V-vIhTNqKCw
● Part 3 (Q&A): https://www.youtube.com/watch?v=69kmPGDh1Gs (including discussion of CO2 adjustment time / effective atmospheric lifetime):
Dear Ferdin
I am responding to your “Fountain Model” that you described in response to my comment. Your Fountain Model is nothing that exists in nature. When water enters a fountain, it doesn’t cascade over a stagnant pool of water that is only released if a small valve opens from the bottom. The water mixes with all the water in the fountain, and the thoroughly mixed water cascades over the side. Nature doesn’t segregate CO2. Dr. Ed’s hypothesis is that outflow is proportional to level or concentration. This makes sense because as the concentration of CO2 increases in the atmosphere, according to the gas law, CO2 partial pressure increases, and the number of collisions with its surroundings increases. These surroundings include other gases, matter, etc. Some of these collisions are with sinks, thus increasing outflow. A hypothesis has to be derived from logic. Your hypothesis that there is some carbon cycle that exists in nature that is partitioned from the human carbon cycle violates the Equivalence Principle and all manner of logic and common sense that the scientific method derives from. Your notion that there are human sinks and natural sinks has no observable basis. You will need to explain in detail how nature does this.
Dear Uncle Bert,
Re: Your comment July 9, 2025 at 12:47 pm.
You’re looking at ice core data for the last 150 years. You can’t take ice core proxies until firnification is complete. That takes centuries. Take that same data that you’ve presented and conduct a proxy measurement in another 200 to 300 years and it will show the same flat line.
You said: “stomata data are local data over land . . . Local changes, not global changes”. You also say CO2 is a well mixed gas the same everywhere. You say it’s not well mixed if it is measured from stomata. Ice core data is local to the poles and is not global. You thinking is scrambled.
Your Giessen hysteria is based on nothing except your specious waffle, excuses and a wing and a prayer.
You said: “Bud Bromley has some strange ideas of what Henry’s law implies”. Bud Bromley is a world renown expert on Henry’s Law. He worked with Henry’s Law his entire working career. It is his profession. He knows a lot more than you do. You only think you know. You’re once again blaming everything on vegetation growth and ignoring the oceans. It can’t be the oceans no matter what and the only argument you have to back that up is yet more of your specious waffle.
And you’re doubling down on the Byrd ice core data being contaminated. The data was not contaminated. It was only contaminated in your confirmation biased mind. All other ice core data was contaminated.
More from [Poyet, P., 2021. The Rational Climate e-Book: Cooler is Riskier. The Sorry State of Climate Science and Policies. Final First Edition, April 19th, 125 Figures, 185 Equations, 473 pp., e-ISBN 978-99957-1-929-6, DOI: 10.13140/RG.2.2.28648.80640, (Ch. 5 Glaciers, Ice-Cores, Arctic and Antarctic, Page 182 on Page 189; Also page 110.)]
“If I understand well: Oeschger has been unable to answer one single question asked by Jaworowski, but he states that he cannot be wrong because he’s been involved for so long that he cannot be mistaken, and finally the cherry on the cake, the argument of morality, Jaworowski is irresponsible because he dares ask questions. [Page 247]
3. Now, third stage, while drilling and extracting the core, when lifting up the column will let the gas reform from the clathrate and escape the sample throughout the cracks (this is somewhat following similar hysical processes to what happens when oil and gas are extracted by fracking). Furthermore various pollutions, contamination and corruption of the T preservation are unavoidable during the drilling, conditioning and transportation processes. While lifting up the ice core the same mechanisms that led to fractionation when the ice accumulated over time are also at play but in a reverse manner as the gases will transit from their hydrate form to gas again at different P/T (according to the phase diagram) and therefore at different moment and depths thwarting the records in the bubbles. Drilling decompresses cores excavated from deep ice, and contaminates them with the drilling fluid filling the bore-hole. Decompression leads to dense horizontal cracking of cores, by a well known sheeting process. After decompression of the ice cores, the solid clathrates decompose into a gas form, exploding in the process as if they were microscopic grenades. In the bubble-free ice the explosions form a new gas cavities and new cracks as reported by Shoji and Langway (1983) for a 2,037m long ice-core “Deep-ice cores drilled from the Greenland and Antarctic ice sheets undergo volume relaxation due to the expansion of air bubbles with time after core recovery”. These authors also report, and it gives an idea of the stress of the recovered sample, “decreasing rate of hydrostatic pressure of about 5.4bar.min-1 for each core length recovered of approx 1.9m”. Through these cracks, and cracks formed by sheeting, a part of gas escapes first into the drilling liquid which fills the bore-hole, and then at the surface to the atmospheric air. Particular gases, CO2, O2 and N2 trapped in the deep cold ice start to form clathrates, and leave the air bubbles, at different pressures and depth. [Page 249]
As a summary, all these problems arise simply because the ice cores do not fulfill the essential closed system criteria.” [Page 250]
Poyet states on page 251:
“On the other hand, the ice core data from the Taylor Dome, Antarctica, which are used to reconstruct the IPCC’s official historical record, feature a much more flattish time trend and range, i.e. 285 to 245 ppmv (Indermühle, et al. 1999). This difference strongly imply that ice cores are not a proper matrix for reconstruction of the chemical composition of the ancient atmosphere. Furthermore, Jaworowski (1997) claims that many discrepancies affect the ice cores and that (Oeschger et al., 1985) made an ad hoc attempt to explain some of these anomalies without success and further adds a very specific claim “In about ~6,000-year-old ice from Camp Century, Greenland, the CO2 concentration in air bubbles was 420 ppmv, but it was 270 ppmv in similarly old ice from Byrd, Antarctica”. Though, he does not provide the source of this, it is not difficult to find Fig.1 in (Neftel, 1982) to display exactly that sort of anomaly, though the age is more ~7,000-year-old corresponding to 1010 meters at Camp Century, Greenland and 900 meters at Byrd, Antarctica, see for yourself next Figure 108. [Page 252]
So we are left with inaccurate and dubious ice core results as the three fundamental premises are violated because the closed system criteria cannot be met, and which lead the entire CAGW edifice to crumble. Pre-industrial CO2 air concentration of at least 335 ppmv (Slocum, 1955) and pre-Boreal Holocene concentrations of up to 348 ppmv totally invalidate the low and arbitrary cherry picking of Callendar (1938) of 292 ppmv319 which appears more as pathological science (Langmuir, 1989) than anything else. “Callendar was prejudice in selecting from all his data roughly 30%, which showed concentration around 290 ppm, leaving the remaining 70% which showed concentrations over 300 ppm” (Foscolos, 2010) and he made a disservice to science. This practice of arbitrary selection of data sets matching prerequisites is also prejudicial to science and denounced by Jaworowski (1997) for Neftel at al.; Pearman et al.; Leuenberger and Siegenthaler; Etheridge et al.; Zardini et al.; among others.”
From his 2004 paper, Jaworowski, at page 252 in Poyet 2022, states that the IPCC concluded that all CO2 emissions post the industrial revolution were caused by humans burning fossil fuels and that this is based solely on the assumption that CO2 did not rise above 300ppm until after the industrial revolution. Jaworowski says that this assumption, which is based on ice core studies, is false and that IPCC projections should not be used for national and global economic planning.
Additionally Jaworowski says: “. . . they did not measure CO2 in the air bubbles and secondary gas cavities from such larger samples, but only from 1g samples.. . small [sample] size meant that [they were] probably uncontaminated.
Jaworowski (1992a)” Pages 242-243.
You ignore all inconvenient truths and facts. You’ve totally ignored the fact that Etheridge was comparing ice core samples from 2,000 years apart. The 3,000 YBP samples were wrong because they weren’t the same as his 1,000 YBP samples. Biased pseudoscience.
You have a confirmation bias and all arguments must be equal to your confirmation bias. You construct specious waffle arguments to try and make everything equal to your confirmation bias. Your comment on July 9, 2025 at 12:47 pm was nothing more then another bunch of excuses. You’ve said nothing that negates anything that I have said.
Jim Siverly on July 9, 2025 at 3:33 pm and July 9, 2025 at 4:02 pm
Part 1.
Dear Jim,
I will try to show where it goes wrong with the use of Te, compared to Tau, specifically for the biosphere, as the problems are very clear for that part…
To start with: Te and Tau are different things, but may be the same in specific circumstances.
The formula for Te is:
Te = mass / output
The formula for Tau is:
Tau = disturbance / effect
The first is about how long a molecule CO2 resides in the atmosphere, that is the residence time or turnover time.
The second is how long it takes to remove an extra injection of CO2 mass in the atmosphere back to 1/e (~37%) of the original injection. In the case of a linear ratio between disturbance and effect, the time period makes no difference for Tau.
The first is about molecular transfer, the second is about mass transfer. Both for natural and FF CO2 alike.
In the case of a one-way world (container/lake/bath tube model), Tau is always <= Te.
In the case of a bidirectional world (fountain model), Tau is completely independent of Te.
Then the "model":
We can separate the in/outflows in two main parts: atmosphere – biosphere and atmosphere – oceans.
Both show large bidirectional (mainly seasonal) flows.
1. The atmosphere – biosphere flows.
In 1750, according to the IPCC, there was a more or less stable dynamic equilibrium between the atmosphere and the biosphere, with an alternating bidirectional flow of 108 PgC/half year.
That gives for Te:
Te(a-g): 628 / 108 = 5.8 years
Te(g-a): 2500 / 108 = 23.1 years
For Tau:
As there is no disturbance, the effect is zero and Tau can't be calculated.
Remark: Te(g-a) is in fact mostly the effect of the much smaller reservoir of about 550 PgC in living vegetation. That gives a much faster Te(g-a) of 550 / 108 = 5.1 years. For our model, that plays no role at all.
Then we suddenly add 50% extra CO2 in the atmosphere, about the current increase, so that we can compare the results.
The observed increases in fluxes and decrease in the vegetation reservoir (according to the IPCC) gives:
Te(a-g) = 883 / 123 = 7.4 years
Te(g-a) = 2470 / 118.7 = 20.1 years.
Tau = (883 – 589) / (123 – 118.7) = 68.4 years
Remarks:
The increase of CO2 in the atmosphere is far more rapid than the increase in outflow into vegetation, because the biological growth of vegetation needs far more time to follow the extra pCO2 pressure. Even in ideal circumstances, the ultimate growth rate is about 50% of the extra CO2 level. Not 100%.
The back flow of CO2 from vegetation into the atmosphere follows the inflow in vegetation, mostly within the same year in other seasons, minus what is added to more permanent vegetation and soils. As the total level in vegetation + soils hardly changes, Te(g-a) decreases.
That also means that Te is not constant and the reverse formula (2): Outflow = L /Te is not applicable.
That all demonstrates that Tau and Te have very little in common and the results not only differ an order of magnitude, but also are nearly independent of each other. Add to that the Tau for the oceans of a similar order (and more accurate calculations) and then you will find the ~50 years real, observed, adjustment time…
About understanding the different models, please look at my presentation for the Clintel wrokshop in Athens, last September, with a direct confrontation with Harde, Koutsoyiannis, Stallinga and others. If that is not sufficient, we can discuss that here in detail.
https://www.ferdinand-engelbeen.be/klimaat/klim_img/on_the_co2_residence_time.ppsx
And, while Berry started with the same one-way "container/lake" model with only one Te out, he evolved to a two-way model in recent years, which is already more like what happens in the real world. Be it with the decay rates which are not relevant at all. Koutsoyiannis, Harde, Stallinga and others still stick to their one-way models.
"That is not an appropriate model in that continually accumulating human emissions, rather than a one-time 'dose,'"
Sorry, but for any process in dynamic equilibrium, only the distance between the "disturbed" pCO2 and the equilibrium pCO2 counts, no matter if that is a one-time injection or a continuous (increasing) supply. That can be seen in the quite constant Tau, while yearly human emissions increased a five fold 1960-2020 and CO2 in the atmosphere increased with some 30% over the same time period:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
Where A shows the sum of all human emissions since 1750, the observed increase in the atmosphere, the influence of the SST increase since 1850, calculated with the formula of Takahashi and the resulting ΔpCO2 between atmosphere and ocean surface.
B shows the observed net sink rate with a polynomial through the data.
C shows the calculated Tau.
That Tau is observed and not even based on a model is clearly demonstrated by David Burton…
Stephen P Anderson, July 9, 2025 at 5:25 pm
Stephen,
We didn’t separate human and natural CO2 at all in all our works. That is what Dr. Ed did.
In all our calculations, the human input is only handled as a separate, one-way supply into the atmosphere. That is all. In the atmosphere, it is mixed with all what is already there plus what is added by the natural cycles. In all following reactions it is handled as part of the mass changes, not separated at all.
The outputs are directly proportional to the partial CO2 pressure (pCO2) difference (not the absolute CO2 pressure!) with the ocean pCO2 and similar for water in plant leaves. For plants, the bulk of the CO2 uptake is completely independent from the pCO2 in the atmosphere and only depends of temperature and sunlight. Only a small percentage per year is directly proportional to the extra CO2 in the atmosphere. The same for the ocean surface temperatures over the seasons and the resulting in- and outflows.
That are the main differences in “model” that Dr. Ed and we have.
More to see in the sheets that I have made for a workshop in Athens:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/on_the_co2_residence_time.ppsx
Dave Burton, from JULY 9, 4:35 PM
Artifact: Something observed in a scientific investigation or experiment that is not naturally present but occurs as a result of the preparative or investigative procedure.
Your Tau model is an artifact of a self-fulfilling prophecy. The plot you made in your comment on Stallinga, P. (2023), “net natural CO2 removal rate vs. Mauna Loa CO2 level,” follows from Koutsoyiannis’ equation (A3), which is NS*(t) = K* [ S(t) – Se* ] or my equation (2) from July 8, 2025 at 12:32 pm. Your data fits the model, but unfortunately correlation does not equal causation. You even label the graph “fossil only” seemingly unaware of the fact that it violates the equivalence principle.
In short, your logic is flawed. You assume no annual increases in natural emissions and no change in equilibrium conditions. Then you apply an equation that assumes the sink rate is proportional to the disturbance and claim the calculated result is a “measured” adjustment time. That fails the smell test.
Thanks for the reference to the Moore and Braswell reference introducing me to some unfamiliar terms, donor-dependent flux and unit pulse (Dirac Delta) functions. I will investigate them for potential application to this discussion.
Brendan Godwin, July 9, 2025 at 7:38 pm
Brendan,
You have no idea of the differences between ice cores.
Two of the Law Dome ice cores have an enormous snow precipitation per year: 1.2 meter per year ice equivalent.
That makes that at 72 meters depth or ~40 years of snow/ice layers, the gas bubbles are already fully closed in the ice. Until that depth, there is 40 years of gas exchange with the atmosphere, which makes that the average age of the air, at the depth where the gas bubbles fully close, is only 10 years older than in the atmosphere:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/law_dome_firn.jpg
That means that the difference between the age of the ice and the enclosed gas is about 30 years. That is all.
There are differences between the closure time for different bubbles, which makes that the gas content of all bubbles at the same depth has a spread of about 8 years.
As there is a steady increase in CO2 over the past 100 years, the changes in CO2 level is easy to follow and also shows that there is no “leaking” of CO2 or diffusion within the ice core, surely not over such a short period.
That also shows that the compilation of the late Ernst Beck makes no sense: there was no “peak” of 80 ppmv around 1940, or that would have been measured in the Law Dome ice cores as a near equal peak, but with shorter duration.
I never said that CO2 is well mixed everywhere. It is well mixed in 95% of the atmosphere. It is not well mixed in the first few hundred meters over land, where huge CO2 sources and sinks are at work. Thus all CO2 measurements there, historical or not, don’t give you any clue of the real “background” CO2 level.
And Giessen hysteria? It looks more that you are getting hysteric if one shows you that the historical data were not so reliable. Have a look at the monthly averages for the modern station at Linden/Giessen:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_mlo_monthly.jpg
Compared that to what is measured on the top of a volcano…
The standard deviation for the historical CO2 data was 68 ppmv (1 sigma, not a sign of reliability!), of the modern station about half of it and at Mauna Loa a few ppmv (seasonal changes excluded) and at the South Pole less than 1 ppmv…
“Bud Bromley is a world renown expert on Henry’s Law. He worked with Henry’s Law his entire working career. It is his profession.”
Maybe he is, and I am not an “expert” in these matters, but I look at the evidence of what many “experts” tell me and accept their expertise, if what they say is reasonable.
So, what says Bud Bromley: that the recent CO2 increase is caused by Henry’s law because of the warming oceans. In the past 800,000 years, the CO2/T ratio never was above 20 ppmv/°C. Currently not more than 3-4 ppmv/°C for short term temperature changes (Pinatubo, El Niño) and -5 ppmv/°C for seasonal changes.
The change over the past 175 years the increase of CO2 in the atmosphere is over 100 ppmv/°C. That rings some alarm bells: impossible that Henry’s law got berserk.
Thus looking at what other “experts” say, I did see the work of Takahashi on near one million seawater samples and he concluded that the increase in pCO2 (the CO2 level in equilibrium with the atmosphere) with temperature is a simple formula, independent of the start conditions or composition of the seawater:
(pCO2)seawater @ Tnew = (pCO2)seawater @ Told x EXP[0.0423 x (Tnew – Told)]
Or calculated for the SST increase since the LIA (worst case): some 13 ppmv extra.
Since 1850: less than 10 ppmv extra.
Bud Bromley’s expertise indeed is quite strange…
And the ice core from the Siple core (not the Byrd core) indeed was contaminated with drilling fluid:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/siple_01.jpg
“Additionally Jaworowski says: “. . . they did not measure CO2 in the air bubbles and secondary gas cavities from such larger samples, but only from 1g samples.. . small [sample] size meant that [they were] probably uncontaminated. Jaworowski (1992a)” Pages 242-243.”
Which thus is clear nonsense: there is a huge range of 280-500 ppmv at the same depth from multiple samples where drilling fluid was found.
And then the following:
“Particular gases, CO2, O2 and N2 trapped in the deep cold ice start to form clathrates, and leave the air bubbles, at different pressures and depth.”
That indeed is true. But the reverse, does not lead to problems, as ice cores are at least stored for over a year at -20°C to expand. Then most clathrates decompose, as “grenades” that explode, causing cracks in the ice.
As N2 and O2 clathrates “explode” at much lower temperatures than CO2 clathrates, they should escape first, thus leaving higher CO2 levels behind. As the opposite is found, even within current much higher CO2 levels in the ambient atmosphere, that seems no problem at all.
The newest sublimation technique even sublimates everything of a sample under vacuum, leaving no ice at all, freezes water out and cryogenically freezes every gas to measure them later over a mass spectrometer, including the isotopic ratio’s…
The objections of the late Jaworowski are exactly the points that Etheridge et al. have investigated: drilling with three different methods, dry (hot coil) and wet, sampling CO2 top down in air, firn and ice and especially at closing depth both in firn and ice where the bubble closing starts and ends.
Jaworowski was a specialist in the radioactive outfall of Tsjernobyl, including in ice cores, but he never performed any CO2 measurement in ice, only had a lot of comments that were rejected only 4 years later. Still he insisted that he was right in 2002, 4 years after Etheridge’s work. That is your source…
“You’ve totally ignored the fact that Etheridge was comparing ice core samples from 2,000 years apart.”
Not that I know: the Siple ice core is much longer than the three Law Dome ice cores, but all ice cores show the same CO2 levels over the past 10,000 years in overlapping periods with a maximum difference between each other of +/- 5 ppmv:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/antarctic_cores_001kyr.jpg
and
https://www.ferdinand-engelbeen.be/klimaat/klim_img/antarctic_cores_010kyr.jpg
Despite extreme differences between the ice cores in accumulation rate: from 1.2 meter per year for Law Dome to a few mm/year for the inland cores like Vostok and Dome C and between -20°C and -40°C average temperature.
It is up to you who you want to believe… I look at all the evidence, no matter who says it and no matter if I like the data or not…
Jim Siverly wrote on July 10, 2025 at 10:10 am, “Your Tau model is…”
I have no “Tau model.”
There are four commonly mentioned time constants associated with atmospheric CO2, as I discussed in my Comment on Stallinga. The one which matters for climate is the “adjustment time” (roughly fifty years, determined from measurements). I sometimes describe it as the “effective lifetime.” The associated half-life is about 35 years.
The one which Demetris Koutsoyiannis, Ed Berry, Peter Stallinga, and a few others erroneously fixate on is the “turnover time” (estimated from models at at three to five years). It is also sometimes called the “residence time.”
Jim wrote, “The plot you made… follows from my equation (2) from July 8, 2025 at 12:32 pm” (‘(2) NS(t) = k* [ C(t) – C* ]’).
The plot does not follow from any model or the equations derived from any model. It is just data: measured CO2 data, and calculated emissions (from economic statistics). The observed linearity is simply what the actual data show.
That linearity is unsurprising because we know that the main (geophysical & biological) processes which accelerate the removal of CO2 as the CO2 level rises are roughly linear.
Jim wrote, “You even label the graph “fossil only” seemingly unaware of the fact that it violates the equivalence principle.”
Apparently I was unclear. “Fossil only” simply means that the data in the graph includes only fossil CO2 emissions, and does not include estimates of “land use change emissions.”
It is commonly estimated that current CO2 emissions due to land use changes are only about 1/10 the magnitude of fossil CO2 emissions, but the fraction was higher in the past.
Land use changes (clearing forests and draining swamps) cause the release of (non fossil) CO2, but the magnitude can only be estimated from very uncertain models. So there are two ways of accounting for it:
Option #1. We can include very rough estimates of land use change emissions in the estimates of anthropogenic CO2 emissions. This is more “fair,” but at the cost of widened error bars on our estimates of anthropogenic emissions.
Option #2. Alternately, we can count only fossil CO2 as anthropogenic emissions, and consider the land use change emissions as a diminishment of natural CO2 sinks. That has the advantage of resulting in much more precise “anthropogenic emission” numbers, because we aren’t adding the rather large uncertainty of those land use change emissions. But the cost is that our calculated CO2 removal rates are somewhat understated.
Since I have very low confidence in the models used to estimate land use change emissions, in my plot I chose Option #2. That is what “fossil only” means.
I explained that in the paper:
Here’s that plot annotated to identify a few key events associated with “outlier” data points:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot4.png
I also mentioned in the paper what the result is when Option #1 is used:
Jim wrote, “You assume no annual increases in natural emissions and no change in equilibrium conditions.”
Where did you get THAT idea? I said no such thing.
In fact, I can name several natural CO2 sources which I’m confident have increased. So what? There’s nothing remarkable about that. Natural CO2 sinks have increased faster.
It would be unreasonable to think that equilibrium levels cannot change. For one thing, we know from ice core data that CO2 levels at glacial maxima averaged around 190 ppmv, and during interglacial optimums they peaked around 280 ppmv, representing a roughly 90 ppmv shift in equilibrium CO2 level in the air (associated with very drastic environmental changes).
What’s more, the equilibrium between multiple carbon reservoirs depends on the total amount of carbon in the system. So if the total amount of carbon increases (due to burning coal), the equilibrium levels must also increase.
However, the atmosphere contains less than 3% of the carbon in the major carbon reservoirs (ocean, terrestrial biosphere/soil, and air), and our CO2 emissions have increased the total by less than 2%. So the change to the equilibrium levels due to that increase should be small.
Jim wrote, “you apply an equation that assumes the sink rate is proportional to the disturbance and claim the calculated result is a ‘measured’ adjustment time.”
I did no such thing. I just plotted the data. The linearity is obvious.
When you see an obviously linear plot, linear regression yields the equation which characterizes it. The equation follows from the data.
Perhaps I assume too much. Do you understand how to recognize linearity vs. acceleration vs. deceleration in a graph?
Ferdinand, from your comment July 10, 2025 at 4:07 am
The Tau model gets increasingly hard to understand. In your calculations for present day, you have
Tau = disturbance / [a difference in bidirectional flows]
Where is the derivation of this formulation?
In my objection to conflating a constant infusion with a one-time dose you wrote, “Sorry, but for any process in dynamic equilibrium, only the distance between the ‘disturbed’ pCO2 and the equilibrium pCO2 counts, no matter if that is a one-time injection or a continuous (increasing) supply.”
Where is that assumption validated? That could only be known if there was experimental data to confirm. There has been and likely never will be a cessation of burning fossil fuels.
Your graph C in the link you gave was calculated and, therefore, not observed. What is observed is that your calculation is based on a flawed model as Dr. Ed, Koutsoyiannis, Harde, Stallinga and others have been trying to explain to you.
I was unable to load the power point presentation. Can you check to see if the link is correct?
Dave Burton July 9, 2025 at 10:42 am
Dear Dave,
Did you ever learn to read?
Your comment shows you did not even read the legend to my Figure 3, which clearly says that it shows the exact data from IPCC Fig. 6.1.
My Figure 3 exactly represents the key carbon cycle data in IPCC’s Fig. 6.1. Maybe you are so incompetent that you cannot understand IPCC’s Figure. 6.1, and simply follow the numbers that show IPCC’s levels and flows for its Land-Air-Surface-Deep simulated carbon cycle.
The purpose of my Figure 3 is to make it easy to understand what is in IPCC’s Fig. 6.1.
You don’t understand either figure. You call these figures “unphysical.”
If you think you have better data on the fast carbon cycle than the IPCC spent about $500 billion to produce, then where is YOUR competitive carbon cycle diagram and your argument that somehow YOUR data is so much better?
You say my Figure 3 lower row for the “human carbon cycle” “has no basis in reality.”
But you did not even read my text that says the same thing about IPCC’s human carbon cycle. You did not read any of my papers that calculate IPCC’s true human carbon cycle using IPCC’s own natural carbon cycle data, to prove IPCC’s human carbon cycle is wrong as shown in IPCC’s Figure 6.1 and in my Figure 3.
The late Richard Courtney wrote that my work – that uses IPCC’s own data to prove wrong IPCC’s claim that H(1) is true – is the only breakthrough in climate science since 1980. You may disagree with Courtney, but you are not a qualified reviewer like he was.
In any case, I would think that anyone as involved as you are in climate science would have read what I wrote carefully. But you reject my papers that show this, when you have not shown there is any error in my argument.
You simply say, “I’m uninterested in analyzing that model, or the equations based on it. I prefer to focus on the real world.”
The “real world” you say. You are living in a pseudoscience dream world.
Then you change the subject to talk about Ah.
You say, “I showed you that your “Ah,” i.e., the anthropogenic processes which deplete the CO2 from the air, are negligible.”
No, you did not. You did junk science to make your claim.
My argument is simple. I simply assume human carbon follows the same rules as natural carbon follows to flow through the atmosphere, e.g., the climate equivalence principle.
Turns out this approach proves your claim is wrong. Further, there is no valid scientific basis to your claim.
You argue you can “ignore human emission in your mass balance arithmetic.”
You are wrong because when we include it, we get a different answer. We get the correct answer.
My paper above explains why your mass balance arithmetic is wrong, and you have not defended your error.
You don’t understand IPCC data that relates to this discussion.
You don’t understand my paper or its proof that H(1) is false.
You can’t do a correct carbon mass balance because you throw out the most important part of the balance.
Jim Siverly, July 10, 2025 at 12:31 pm
Jim, I think that David Burton has replied to most of your questions…
More details about what Tau means and different calculations can be found at Wiki:
https://en.wikipedia.org/wiki/Exponential_decay
In a former page of Wiki it was shown that for a linear response of a system in equilibrium, the formula:
Tau = disturbance / effect is independent of the time frame over which the ratio is measured. For non-linear decay rates, one need to do the calculation for each time frame again.
Both the uptake by the oceans and by vegetation are quite linear.
Effect in the case of CO2 is the net increase in output when the CO2 level above the equilibrium increases, the net increase in output is the difference between inputs and outputs, for each bidirectional exchange between reservoirs apart as good as for all exchanges together.
And in my opinion, a simple calculation, based on observations, is as valid as a direct observation.
Our idea of the real word is based on real world data, the “one-way” model is rejected by the same data:
If one has only 1.5-5% FF in the input, the one-way model of Koutsoyiannis, Harde, Stallinga,… never can show higher levels of FF in the atmosphere than 5%. In reality, the atmosphere already contains over 10% FF and the ocean surface over 6%.
If you click on the reference, the sheets are automatically downloaded, thus maybe found in your download map.
If that doesn’t work, I will make pictures of the relevant sheets…
Ferdinand,
Wiki is not a scientific reference. It has no scientific credibility. It has site moderators who push agendas. Your Fountain Model, where outflow is proportional to [pCO2(atm)-pCO2(ocean)] has no scientific basis-that is, there is nothing that it is derived from. There is no partial pressure of CO2(ocean). Henry’s Law states that the amount of gas that dissolves in a liquid is directly proportional to the partial pressure of the gas above the liquid. Dr. Ed’s hypothesis that outflow is proportional to level is derivable from Henry’s Law and the Ideal Gas Law. Your model has no natural basis. Also, you continue to violate the Equivalence Principle, although you continue to claim that you don’t, but Dr. Ed does. You don’t make any sense.
Ferdinand,
The partial pressure of CO2 is equal to the mole fraction of CO2 times the total pressure of the atmosphere. It has nothing to do with some imaginative pCO2(ocean).
Dave Burton, in answer to July 10, 2025 at 11:46 am, and Ferdinand Engelbeen July 10, 2025 at 1:41 pm
No, Ferdinand, Dave Burton replied unsatisfactorily to my questions. He claims the “CO2 removal rate vs. CO2 level” plot does not follow from any model. The plot in question has the form NS(t) = k* [ C(t) – C* ] with CO2 removal rate being net sink, NS(t), and CO2 level as C(t). When NS(t) = 0, C(t) = C* or as Dave’s preprint says, the “x-intercept gives an estimate of the equilibrium level, which is 285 ppmv. Like it or not, that is a model equation.
Ironically the explanation of “fossil only” misses the fact that sink rate is calculated from Eh(t) – dC(t)/dt which is another way of saying “fossil carbon not removed” in violation of the equivalence principle.
Furthermore, Dave admits that, “the equilibrium levels must also increase.” Yet his simple math model portrayed by the “CO2 removal rate vs. CO2 level” plot leaves no room for that possibility.
Ed wrote on July 10, 2025 at 1:35 pm, “My Figure 3 exactly represents the key carbon cycle data in IPCC’s Fig. 6.1.”
No, Ed, it represents your misunderstanding of AR5’s Fig. 6.1. They show in red the natural increases in natural CO2 sinks which result from elevated CO2 levels, and you misinterpreted the red as meaning those were “human” CO2 sinks.
Perhaps the AR5 authors should have used a different color, rather than using the same red that they used for human CO2 emissions. It was clear to me what they meant, but obviously it was unclear to you. (The AR6 authors used a quite different diagram for their figure 5.12, which I found less clear, but you might prefer it,)
For instance, the AR5 authors used a red arrow for 20 PgC/year (of the 80 PgC/year) of CO2 absorbed by the ocean from the atmosphere, and likewise a red arrow for 17.7 PgC/year of the CO2 emitted from the ocean into the atmosphere, because those increased fluxes are due to the elevated levels of atmospheric and ocean surface CO2. You interpreted those as “human.” But those are both natural CO2 fluxes.
The reason the AR5 authors drew them in red is because they represent the portion of the natural CO2 fluxes which are due to the rise in atmospheric CO2 level (and the rise in surface water DIC), which they understand (but you deny) is due to human CO2 emissions.
The physical mechanism for those increased fluxes is pretty obvious, too: a 50% elevation in CO2 partial pressure in the atmosphere results in a 50% increase in CO2 air molecules striking and being absorbed by the ocean surface.
Likewise, since the DIC in surface water tracks pCO2 in the air pretty closely, the AR5 authors estimated that that rise increases CO2 fluxes the other direction by 17.7 PgC/year.
Now, can we please discuss the actual, physical anthropogenic CO2 sinks?
You claimed that the human processes removing carbon from the atmosphere (your “An”) are not negligible. So I discussed those processes, one by one, here:
https://edberry.com/co2coalition/#comment-112419
When I say that “Ah,” i.e., the anthropogenic processes which remove CO2 from the air, are negligible, I mean that they are much smaller than the error bars on anthropogenic emissions, so they can be ignored in “mass balance” arithmetic.
1. Approximately 59 kt of CO2 per year are removed from the atmosphere by Direct Air Capture projects, worldwide. That’s about 0.00015% of anthropogenic emissions.
2. Approximately 50 Mt of CO2 per year is captured and stored by operational CCS facilities, but 99.9% of that is captured at the sources, so it’s really avoided emissions, not removals. But if you count it, that’s a little over 0.13% of anthropogenic emissions. Are you counting CCS as part of your “An”?
3. According to GCB (2024), cement carbonation is estimated to remove about 214 MtC from the atmosphere per year, globally, which is about 0.784 Gt of CO2. That’s conventionally considered a natural removal process, but IMO you could call it anthropogenic. But it’s only about 2% of anthropogenic CO2 emissions, so even that is still much smaller than the error bars on anthropogenic emissions. Are you counting cement carbonation as part of your “An”?
Can you identify any other anthropogenic sinks?
● If so, then what are they?
● If not, then please acknowledge that your “An” is negligible, so that we can move on.
“When my information changes, I alter my conclusions. What do you do, sir?”
– John Maynard Keynes (attributed)
Ferdinand Engelbeen, July 10, 2025 at 1:41 pm
The Wiki discourse on exponential decay is boilerplate. It explains the math applicable to a system at rest disturbed by “a quantity is subject to exponential decay if it decreases at a rate proportional to its current value.” Since CO2 increases annually, in part due to the fraction of industrial carbon contributing to it, I contend simple exponential decay does not apply.
Where is the former page of Wiki showing that, for a linear response of a system in equilibrium, the formula [ Tau = disturbance / effect ] is independent of the time frame over which the ratio is measured?
This sentence I do not understand: “Effect in the case of CO2 is the net increase in output when the CO2 level above the equilibrium increases, the net increase in output is the difference between inputs and outputs, for each bidirectional exchange between reservoirs apart as good as for all exchanges together.”
Also, if by “And in my opinion, a simple calculation, based on observations, is as valid as a direct observation,” you mean simple math, I’m not buying it.
Thank you for your patience with my attempts to understand your position. I did get the download of the power point presentation and will have a look now.
(Sorry about the botched </a> in that comment.)
Stephen wrote on July 10, 2025 at 2:55 pm, Wiki is not a scientific reference. It has no scientific credibility. It has site moderators who push agendas.”
I like to say that Wikipedia is untrustworthy for anything controversial. Inevitably, partisans for one side of the argument take over the articles, and turn them into propaganda. Gender issues and climate change are particularly notorious examples, but you really cannot trust Wikipedia for information about anything controversial. Here’s an eye-opening article:
Harvard Students Edit Wikipedia To “Dismantle The Patriarchy”
Since Jimbo Wales is a leftist, his thumb on the scale ensures that that side of the argument generally “wins” on Wikipedia.
But Wikipedia is not completely useless. For topics which nobody argues over it is usually fine.
For instance, it is good for looking up data cable pinouts:
https://en.wikipedia.org/wiki/IEEE_1284
The article on exponential decay is fine, too:
https://en.wikipedia.org/wiki/Exponential_decay
Ed,
I can’t sit quietly by and ignore the ignorance you show every time you mention C14. A year ago, I presented an oral paper at the annual meeting of the NW chapter of the American Physical Society in Bothell, WA, which I called “Challenging the Abuse of Atmospheric Radiocarbon Data “. You were featured, but you had company. A few corrections to your narrative:
• DeltaC14 is a measure of the C14/C12 ratio in a sample, and there is indeed a “balance” involved in determining the reference ratio, the C14/C12 ratio that gives Delta C14 = 0. The amount of C14 in fast cycle carbon is determined by the competition between the mostly constant production rate of C14 in the upper atmosphere, and the decay rate dictated by C14’s 5730 yr half-life. At the “balance level”, as much C14 is leaving the fast-cycle system by decay as is being added by upper atmosphere production. This balance level has nothing to do with flow rates into or out of the atmosphere as you assert.
• If an object containing carbon, say a piece of wood, is sequestered from the atmosphere for a long time because it is no longer growing, some of its C14 decays (to N14), and the C14/C12 ratio in the sample decreases. The magnitude of the decrease indicates the age of the sample. For example if C14/C12 is measured to be half of the reference value, the sample is about 5730 years old. You cannot extract a date from the C14 concentration alone, because without knowing how much carbon was in the sample to begin with, that concentration is meaningless. That is why the isotope ratio is used in dating, not concentration. It is not because Delta14C has a balance level and C14 concentration does not, as you claim.
• Let’s talk about atmospheric C14 concentration, measured say as the molar fraction of the atmosphere. This is the quantity that you and Harde and Salby and a couple of others thought was the same thing as DeltaC14. I believe that is what you mean by “14C” in your Figure 10 plot. You don’t say what the units are but add it to DeltaC14. Real physicists don’t add apples and oranges.
• You do not understand what is meant by “Suess effect dilution”. If you did, you might have called your paper “A calculation of Suess effect dilution.” Seuss effect dilution is what causes the amount of industrial carbon in the present atmosphere to be much less than what would be naively calculated by ignoring disequilibrium isofluxes. Climate scientists are not naïve on this point. You are. To be a credible challenger of the consensus you must understand the consensus first. You do not.
A thought experiment to help you, and others who are uneasy with disequilibrium isofluxes, to understand:
Imagine a short (few decades) stable period in a pre-industrial world, where the atmospheric CO2 level is, say 280 ppm. Solar variability is nil, Milankovitch cycles don’t change much on a decadal time scale, the ocean CO2 content has reached equilibrium with the atmosphere as dictated by Henry’s Law, the Revelle factor, etc., and the biomass is stable. In this idealized world the carbon levels in the major reservoirs are stable except for seasonal variations, but there are still balanced two-way exchanges much like today. Oceans outgas CO2 in one place and absorb it in another. Plants grow by taking in CO2 from the atmosphere and return it when they die and decay. Human emissions are 0. Atmospheric CO2 growth is 0. Net global uptake is 0. Natural emissions are exactly balanced by natural absorption. Now aliens land and use this idealized world to test thermonuclear weapons in the atmosphere. The tests double the atmospheric C14/C12 ratio to 2 parts per trillion, twice the one part per trillion that existed before.
Questions:
1. What happens to the atmospheric CO2? Answer: nothing, unless you want to worry about the effects of a part per trillion increase.
2. How does the C14 /C12 ratio change over time? Answer: it returns to one part per trillion in about a decade, just as it did after 1965 in the real world.
I think this thought experiment is useful because it shows how isotope changes need not be linked to level changes. The real world is more complicated than the idealized world described, but real-world processes like the decay of the bomb pulse can be understood by simple insights.
Dave Burton July 10, 2025 at 4:37 pm
You wrote:
Dear Dave,
Did you read the Figure 6.1 Legend?
IPCC’s Fig 6.1legend reads:
So, it looks like you can’t read, as I assumed in my last comment.
Next you wrote:
Not valid, Dave. Your reasoning is circular.
You assume human carbon outflow is negligible because you already assumed human carbon caused all the CO2 increase. The IPCC assumes the same thing in its red numbers in its Fig 6.1.
The proper physics solution is to treat the human carbon cycle and natural carbon cycle independently but using the same rules. This is a lot easier and far more accurate than the way you are doing it.
The one thing I did, that no one else did, was to recalculate IPCC’s red numbers using the same rules that IPCC used for its black numbers. That’s my breakthrough. It proves H(1) is false.
Einstein said the most difficult part of a physics problem is usually its formulation. I did the correct formulation of the problem. Anyone can repeat my calculations.
Your formulation of the problem is invalid and wrong. That’s why your solution is wrong.
Of course. Human carbon flows into the same “sinks” as natural carbon flows. Total human carbon has added one percent to the carbon in the natural carbon cycle.
Do you honestly think there is a precise fixed limit on these sinks?
You have seen the photo of the four trees that grew up in different CO2 levels. Every tree on the planet will soak up more CO2 if there is more CO2.
Your focus on sinks rather than sources, inflows rather than outflows is unnatural. That’ not how things work.
Your way is like riding a bicycle backward, downhill. You go out of balance and crash.
In summary, you are wrong about the red numbers in IPCC’s Fig 6.1.
You are wrong about using sinks that have, at best, 10% accuracy, to arbitrarily make decisions about human carbon that is only 1% of the total carbon in the carbon cycle.
David Andrews July 10, 2025 at 6:41 pm
Dear David,
Thank you for your comment because you support a lot of what I am teaching.
You agree with my balance levels but do not understand that I consider the natural production of 14C as an “inflow of 14C.”
I claim the reason carbon dating works is because Delta14C has a balance level, which means 14C does not. 14C changes with 12C in a manner that keeps Delta14C at its balance level. Why do you think we disagree?
I, Harde, and Salby may have mis-labeled a chart way back in 2019. We corrected this in our following publications. Are you perfect? You have made a lot of physics errors in your publications.
David. You know I understand the Suess effect dilution. Even my draft paper above explains it. I think you are upset because the Suess effect has turned out to be minimal, proving H(1) is false.
You wrote, “In this idealized world the carbon levels in the major reservoirs are stable except for seasonal variations, but there are still balanced two-way exchanges much like today.” Thank you. That is exactly what my carbon cycle model explains. Please explain that to the CO2C authors.
You say, in your mental experiment, the C14 /C12 ratio returns to its original level in about a decade. That is incorrect. It would return at the same rate Delta14C has returned since 1970, which is with an e-time of 16.5 years. It cannot return to its original value in ten years.
Jim,
I have several times had trouble understanding your thought processes, but what on earth does this mean?
“Ironically the explanation of “fossil only” misses the fact that sink rate is calculated from Eh(t) – dC(t)/dt which is another way of saying “fossil carbon not removed” in violation of the equivalence principle.”
While once you helpfully explained to Ed his error in interpreting the “simple math” associated with carbon conservation, now you seem to suggest that carbon conservation violates the principle that industrial and natural should behave the same??!!?? One way to insure that these two types are treated the same is to just analyze total carbon as all mainstream scientists do. Did you know that Richard Courtney, whose praise Ed repeats over and over, for separating their analysis, had a career in the coal industry? That by itself does not disqualify his opinion, but certainly raises some flags.
You are on record as saying that “you are on Ed’s side.” Perhaps that should explain to me why your logic is so hard to understand.
Ed,
Do you really not understand that the Seuss effect is minimal only because it has been diluted by disequilibrium isofluxes? And that no reputable scientist disagrees with that? And that therefore the small amount of industrial carbon in the present atmosphere says nothing about the cause for the rise? To understand the cause of the rise you have to stop pretending that you don’t understand the mass-balance (carbon conservation) argument.
From Ferdinand Engelbeen, July 10, 2025 at 1:41 pm and Jim Siverly, July 10, 2025 at 4:41 pm
This may be a bit premature, but if I don’t write it now, it may be gone forever.
From Ferdinand’s power point presentation at a Clintel wrokshop in Athens, last September (see his comment on July 10, 2025 at 3:43 am), I saw Tau defined as the usual disturbance / effect. However, there was a slide with the example:
Tau = (415 uatm – 295 uatm) / 2.35 uatm/year = 51 years
I interpret the denominator as the difference between the current CO2 level and what it was in preindustrial times. The numerator is the current CO2 sink rate. While I am still waiting for a formal presentation of the derivation of that equation, I was curious what would happen to my spreadsheet model if I ran it from 2018 (the last year of my available industrial emission data) until equilibrium assuming no further industrial emissions and a freeze of the natural emissions at the 2018 level. My model uses a 4-year residence time (turnover, e-time, etc.) and allows for an exponentially increasing biomass. In other words, the land and ocean reservoirs average more emissions gradually each year from 65 ppmv to 93 ppmv. The increase was necessary to correlate with the Mauna Loa data.
The model simulation resulted in an equilibrium value of 398 ppmv in 2045, down from 410 ppmv in 2018. The 1/e value of about 402 ppmv occurred in 2022 or about four years.
My hypothesis is this: no matter what the equilibrium CO2 level would be, if the world suddenly went net zero, the new CO2 would be at that new level in less than 30 years with a 63% reduction in only four years.
Re: Uncle Bert’s comment July 10, 2025 at 10:13 am
Dear Uncle Bert.
More excuses and specious waffle and totally lacking in any science. The deeper you dig yourself into the quagmire the more difficult it is to make any sense out of anything that you say. Everything you write is specious. Unvalidated assumptions and pseudoscientific rhetoric. I find myself agreeing with Jim Silverly. Your ideas are an artifact of your self-fulfilling prophecy. “the compilation of the late Ernst Beck makes no sense”. Any measurement that doesn’t fulfill your self-fulfilling prophecy makes no sense to you.
200,000 measurements from 901 locations from dozens of highly qualified and notable scientists produce data that doesn’t conform to the confirmation bias of the catastrophic anthropogenic global warming CAGW proponents so they invented a new term. “Background layer”. CO2 is well mixed everywhere unless it’s near one of the accurate scientific instruments from the 1812 to 1961 instrumental record. So the CAGW proponents invented a fictitious “background layer” just to cloud the argument.
“The standard deviation for the historical CO2 data was 68 ppmv (1 sigma, not a sign of reliability!), of the modern station about half of it”
You’re comparing monotonic ice core proxy data to Mauna Loa measurements. All that does is demonstrate you’re not a scientist and have no scientific argument.
“And the ice core from the Siple core (not the Byrd core) indeed was contaminated with drilling fluid”
Jaworowski produced measurements that doesn’t conform to your confirmation bias so you have to invent something wrong with it and attack the man. You fail to admit that all ice cores have drilling fluid contamination. Jaworowski’s had less than ALL the others and probably none at all.
Then the 1812 to 1961 instrumental measurements were not what you wanted so you’ve concocted a specious argument that they were contaminated from all the fly and insect farts. They only thing that’s contaminated is your brain.
“a simple calculation, based on observations, is as valid as a direct observation”
Calculations that give you the confirmation biased results that you are looking for are not measurements. You take real measurements, put them through a calculation and produce fake results.
Uncle Bert. You need to retire to your IPCC cubicle and retire from bring a political agitator. Do something meaningful with your life. Get a life.
I don’t know about the rest of you but I have lost my patience trying to wade through all of Uncle Bert’s specious waffle. It’s endless. It’s like how the Indians say they are drunk. Translated – “my head is eating circles”. As fast as the specious waffle comes around, you chew it up and spit it out but it just keeps coming around and around. They say when you die and go to Heaven, that’s if we all make it there, that life is eternal. I think there’s something after that for Uncle Bert’s specious waffle.
David Andrews
July 10, 2025 at 8:13 pm
David,
The “fossil only” issue arose in my comment (July 10, 2025 at 10:10 am) following Dave Burton’s at July 9, 2025 at 4:35 pm. I said, “You even label the graph “fossil only” seemingly unaware of the fact that it violates the equivalence principle.” Dave explained that “fossil only” meant omitting the land use fraction of industrial carbon. Got that so far?
OK, then I went back to look at the plot equation which is based on Eh(t) – dC(t)/dt = Sn(t) – En(t). The left-hand side basically means “fossil carbon not removed” in year t. It violates the equivalence principle, because the full Eh(t) that year is mixed in with the rest of the atmosphere and much more than half of Eh(t) gets removed.
Am I missing what you mean by carbon conservation? If you mean simple math as in the equation above, then we have a problem. And I think it’s because we don’t share the same understanding of the equivalence principle.
Jim Siverly July 10, 2025 at 9:58 pm
“My model uses a 4-year residence time (turnover, e-time, etc.) and allows for an exponentially increasing biomass. In other words, the land and ocean reservoirs average more emissions gradually each year from 65 ppmv to 93 ppmv. The increase was necessary to correlate with the Mauna Loa data.”
The basic problem is that one can match the Mauna Loa data with any combination of (net) sinks and temperature…
Thus one need to look at the physics behind the math.
The 4 years residence time of today includes all inflows and outflows, whatever their direction. Including two main cycles: from the warming oceans through the atmosphere to increasing vegetation in spring/summer and back in fall/winter. These cycles are near completely independent of the actual CO2 pressure in the atmosphere.
Indeed they did increase over (many) years, as you assume, but from the past to today that is only true in ratio for the ocean surface (according to the IPCC, but they didn’t give any explanation how and why that happens) and less than complete for the biological cycle: some 40% increase in the cycle for the CO2 increase in the atmosphere, despite 175 years time to get the same percentage.
Your thesis implies that the current equilibrium increased at about the same rate as the increase in the atmosphere, matching the 4 years residence time to allow for the difference.
A new equilibrium will be approached with a Te of 4 years at about 398 ppmv in 2045.
So far so good. Only one problem: the 398 ppmv is way above the equilibrium pCO2 of the oceans surface, which would be around 295 μatm (~ppmv, ppmv is in dry atmosphere, μatm in the atmosphere includes water vapor).
If we simply ignore the ice core results and start in 1958, the level in the atmosphere was 315 ppmv.
Assuming an equilibrium pCO2 of the oceans, that also starts at about 315 μatm in 1958.
With the increase in temperature, the pCO2 of the ocean surface increases with the formula of Takahashi:
(pCO2)seawater @ Tnew = (pCO2)seawater @ Told x EXP[0.0423 x (Tnew – Told)]
or with an increase of 0.6°C (HadSST3 global) that increases the overall pCO2 of the sea surface waters to:
pCO2(new) = 315*EXP(0.0423*0.6) = 323 μatm.
Less than 10 μatm increase in equilibrium pCO2 by the ocean surface over the period 1958-2025.
Vegetation hardly plays a role in the equilibrium: they watch and wane with the overall pCO2 in the atmosphere, which is determined by the ocean surface waters over the millennia and the availability of land in between ice ages.
That can be seen in the very small changes in δ13C over the past 800,000 years, despite huge changes of 90 ppmv in CO2 level, until humans started to emit FF CO2:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_d13C_lgm_cur.png
Even with an enormous increase in size between glacial and interglacial periods: that is completely dwarfed by the equilibrium set by the ocean surface temperature and the changes in size were slow enough to get equalized by the deep oceans cycle.
Moreover, if you calculate the equilibrium pCO2 down to where inflows and outflows are equal (thus zero net flow), over the period 1958-current, that shows a level of 285 ppmv. Here from David Burton:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
That is only calculated from the observed net sink rates, thus independent of any idea of the real level of Te or Tau.
Again the “old” equilibrium that didn’t change much over time.
For the underlying equations of the long Tau of around 50 years: already obtained in 1997 by Dipl.-Ing. Peter Dietze in a debate with the inventor of the Bern model, Fortunat Joos:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/Dietze_1997.png
More on that page at the website of the late John Daly:
https://www.john-daly.com/carbon.htm
And the discussion with Joos and others:
http://www.john-daly.com/dietze/cmodcalc.htm
https://www.john-daly.com/dietze/cmodcalD.htm
Jim Siverly, July 10, 2025 at 10:39 pm
Eh(t) – dC(t)/dt = Sn(t) – En(t)
Eh(t) is the human input, for 100% injected into the atmosphere as mass.
That increases the total mass of CO2 in the atmosphere.
– dC(t)/dt removes a certain amount of mass of CO2 out of the atmosphere, no matter the composition, thus original human and natural CO2 molecules alike, and that equals natural sinks minus natural sources, because of a lack of human sinks (again as mass, not in original FF molecules)…
Everybody of the “man-made” CO2 increase is talking about carbon mass transfers, only the “natural-made” CO2 increase people make a differentiation…
Jim Siverly July 10, 2025 at 4:41 pm
Unfortunately, the Wiki page had their simple formula of the decay rate for a linear ratio process on the same page as today for the exponential decay rate, but someone deleted it.
Anyway Peter Dietze in 1997 and many others after him (Lindzen, Spencer) used the same formula to calculate the effective adjustment (or life) time.
If there is a linear ratio between cause and effect, it doesn’t matter over what time frame Tau is calculated. In the case of the recent record since 1958, one can calculate Tau over 1 year (as I have done, be it on the smoothed sink rate) or over a period of 10 years or over the full period, you will obtain the same result. Of course, by using the polynomial, the results are already smoothed…
The sentence:
“Effect in the case of CO2 is the net increase in output when the CO2 level above the equilibrium increases, the net increase in output is the difference between inputs and outputs, for each bidirectional exchange between reservoirs apart as good as for all exchanges together.”
means that one can calculate the different Tau’s for each exchange between the atmosphere and the different reservoirs, if one knows the net outflux (that is difference between inputs and outputs) for each of them.
In that case total Tau(c) can be expressed as function of n exchanges:
1/Tau(c) = 1/Tau(1) + 1/Tau(2) +… …+ 1/Tau(n)
Dr. Ed, July 10, 2025 at 7:19 pm
Dear Dr. Ed,
Only one remark:
“Total human carbon has added one percent to the carbon in the natural carbon cycle”
I think that we all agree that human emissions get into the atmosphere for the full 100%, thus adding some 10 PgC/year to a total of CO2 that circulates through the atmosphere with 200 PgC/year as input and 205 PgC/year as output for the current CO2 cycles.
For the mass balance, the human input is the first cause for the increase of 5 PgC in the atmosphere, or you violate the mass balance. That is about mass transfer.
For the molecular balance, if the FF CO2 is only 1% of all CO2 in the atmosphere and nothing comes back with the return flows, the removal of FF molecules is 2.05 PgC/year, still near 8 PgC/year of FF molecules are added to the atmosphere each year.
Further, as the 2 PgC/year FF molecules are distributed into ocean surface and vegetation via the fast cycles, some of these FF molecules will return from the other reservoirs, increasing the FF molecular level in the atmosphere.
On the other hand, the increase in FF molecules also increases its ratio in the outputs…
The current, measured, increase of FF molecules in the atmosphere is already over 10% and in the ocean surface over 6%. In vegetation and deep oceans also increasing, but difficult to quantify. The former does only return waters with CO2 from ~1000 years ago, that does influence the current 13C/12C and Δ14C levels.
In short: The full input of FF CO2 gets into the atmosphere and gives its full increase in the atmosphere as mass and an enormous drop in 13C/12C ratio. About half that input as mass (whatever the origin) is removed and about 2/3 of that input as original FF molecules is replaced by CO2 molecules from other reservoirs…
Brendan Godwin, July 10, 2025 at 10:22 pm
A last comment to your “science”, as I see that it is just a waste of my time to discuss things with someone who doesn’t want to accept any data which he doesn’t like.
– “200,000 measurements from 901 places”
Of which 198.000 contaminated with local sources and sinks. Completely worthless to know the past global CO2 levels.
Those measurements that were over sea and coastal with wind from the seaside are on or below the ice core measurements. On or below. No peak at all in all the measurements over the oceans. Strange isn’t it?
https://www.ferdinand-engelbeen.be/klimaat/klim_img/beck_1930_1950.jpg
The minima are, not by coincidence, mostly from measurements over the oceans or coastal
That is already 70% of the global surface.
Then we have recent flight measurements, here over the Rocky Mountains:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/inversion_co2.jpg
Once over 700 meters, the CO2 levels are within a few ppmv of the Mauna Loa level for the same days.
In total: 95% of the air mass shows “background” CO2 levels within 10 ppmv from near the North Pole (Barrow) to the South Pole.
But according to Brendan, we should believe the historical (and current?) CO2 measurements in 5% of the atmosphere from highly contaminated areas over land.
– “You’re comparing monotonic ice core proxy data to Mauna Loa measurements. All that does is demonstrate you’re not a scientist and have no scientific argument.”
The ice core data are direct measurements of CO2 in the atmosphere, not “proxies”. Including an overlap of 20 years with the direct measurements at the South Pole. If you have any real “scientific” arguments, why we shouldn’t use these data for historical CO2 levels, then give them…
And I was comparing the historical CO2 data from Giessen:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/kreutz_08.jpg
Which show a range of 240-680 ppmv (wow, what a “background” range – CO2 at that time was expressed as tenths of a percent) and a standard deviation (“streuung”) of 66 ppmv with the
stdev of the modern station at Linden/Giessen of around 30 ppmv
and with the Mauna Loa stdev of some 2 ppmv and
the South Pole data stdev of less than 1 ppmv
and the ice cores with a stdev of 1.2 ppmv
If you have any scientific arguments why we should use the historical data from Giessen as the “real” background CO2 level of that time, be my guest.
– Jaworowski produced measurements that doesn’t conform to your confirmation bias
Jaworowski never, ever did any CO2 measurement in ice cores. He did measurements in ice fields of Scandinavia for the radioactive fallout of the Tsjernobyl disaster.
These icefields are at much higher temperatures than the Greenland or Antarctic ice cores and therefore have a lot of water veins where metal ions can migrate. That is near impossible for CO2 in ice cores at -20°C to -40°C.
Thus his critiques were based on quite different materials and circumstances.
One has calculated the theoretical migration of CO2 in the Siple Dome ice core by looking at the increase of CO2 near a melt layer. The conclusion: at middle depth the resolution increases with some 10% or from about 20 years to 22 years and near the bottom rock it doubles from 20 to 40 years. And near melt layers, on can find higher than average CO2 levels. Melt layers are typical for the Siple Dome ice core and absent in Law Dome and, as far as I know, any other Antarctic ice core.
Simply not important at all for migration and not measurable in any ice core that is colder:
https://catalogue.nla.gov.au/catalog/3773250
Bye bye…
Stephen P. Anderson, July 10, 2025 at 3:12 pm
“The partial pressure of CO2 is equal to the mole fraction of CO2 times the total pressure of the atmosphere. It has nothing to do with some imaginative pCO2(ocean).”
Of course the pCO2 is what you describe, but you are wrong about the pCO2 of the oceans: That is the base for Henry’s law and describes the partial pressure of the oceans in equilibrium with a small volume of air above it. That pCO2 is measured in the small air volume and is used as pCO2 of the ocean water.
When the pCO2 of the oceans and the atmosphere above it are equal, there is no net CO2 transfer between the two (still a lot of CO2 molecules are traveling in each direction, but flows are equal up and down).
The pCO2 of the oceans was measured with meanwhile several millions of samples, even on commercial sea ships with automatic equipment on board…
See further the compilation of Feely et al. for the reference year 1995:
https://www.pmel.noaa.gov/pubs/outstand/feel2331/maps.shtml
for the overall formula to calculate the net CO2 flux between atmosphere and oceans, based on the difference in pCO2 between atmosphere and ocean surface waters.
The whole interesting story starts about at:
http://www.pmel.noaa.gov/pubs/outstand/feel2331/exchange.shtml
Jim (and Ed too),
Ferdinand has responded to Jim’s equivalence principle concern, but I will too. Let’s go back to the beginning.
(change rate of atmospheric carbon) = (carbon addition rate by all processes) – (carbon removal rate by all processes).
Divide the PROCESSES into human and natural and indicate which by subscripts. MAKE NO DISTINCTIONS ABOUT CARBON TYPES OR YOU MAY GET CONFUSED.
Processes which add are E(missions). Processes which remove are A(bsorptions)
dC/dt = En + Eh – An – Ah
En = ocean outgassing, vegetation decay, etc
Eh = human burning of fossil fuels
An = dissolution of carbon into the oceans, photosynthesis, etc
Ah = removal by direct carbon capture technology, sequestration, etc. Unless you can name a human PROCESS which removes carbon of any type on the scale of Petagrams, we will ignore this term.
Then Eh-dC/dt = An – En
It is usually easiest to integrate this over time, and talk about stock changes in a fixed period.
The left-hand side is definitively measured to be positive in the industrial era. Therefore, the right-hand side is too. Natural processes are definitively removing more carbon from the atmosphere than they are adding.
Good luck making a model which says the human influence is small.
David Andrews July 11, 2025 at 9:48 am
Dear David,
Let’s use your equation:
dC/dt = En + Eh – An – Ah ………………(1)
Argument #1
Equation (1) works for natural and human processes individually:
dCn/dt = En – An…………………….(2)
dCh/dt = Eh – Ah…………………….(3)
Assume (2) is at equilibrium, so it is zero. Then we can easily find the six Te from IPCC’s data for its natural carbon cycle at equilibrium.
Then we can integrate (3) from 1750 to 2020 using data for annual human CO2 emissions.
By using the same Te in (3) as found in (2), we can calculate how fast human CO2 flows out of the atmosphere annually.
This is the key.
Human CO2 will flow out of the atmosphere and into the other carbon reservoirs, in proportion to its level, exactly as fast as natural CO2 is already flowing out of the atmosphere.
Human CO2 is a minor part of the total CO2 flows, so it can’t change the rules, or Te.
The sum of (3) from 1750 to 2020 is much less than the measured total CO2 increase.
This means your argument is wrong because you ignored the annual outflow of human CO2.
Therefore, nature did not stay at equilibrium from 1750 to 2020. Nature played a dominant part in the CO2 increase.
Argument #2
Rewrite (1) as follows:
dC/dt = (En– An) + (Eh – Ah) ………………………………. (4)
Integrate (4) from 1750 to 2020 to get:
Total CO2 increase = (Natural CO2 increase) + (Human CO2 increase)………………….(5)
This shows your argument depends on what you assume for Natural CO2 increase.
If you assume the natural increase is zero then you automatically conclude all the increase was Human CO2 increase.
When you drop Ah, you are assuming all the increase was Human CO2 increase. Therefore, your reasoning is circular, and wrong.
Ferdinand Engelbeen July 11, 2025 at 7:59 am
Dear Ferdinand,
Neither of your referenced articles negate my formulation that uses (1) and (2).
The proper use of such information is to fine tune my formulation.
But the proper way to fine tune my formulation might be to begin by expanding the number of land reservoirs and ocean reservoirs. That would allow simulation of different types of land and allow consideration of ocean flow.
The key to doing this is my formulation because it easily allows such expansion to multiple reservoirs and addition of flows between the new reservoirs.
As everyone knows, no model can perfectly describe nature. But my model comes closer than any other model because it is based on only two equations.
Ferdinand Engelbeen July 11, 2025 at 4:36 am AND July 11, 2025 at 7:59 am
Dear Ferdinand,
Please see my reply to David Andrews July 11, 2025 at 9:48 am
All arguments about the carbon cycle or “carbon mass balance” must use equations and numbers. Your use of numbers is not a valid argument because you are not showing where your numbers enter equations.
That’s why we must first agree on the formulation of the problem. Until then, numbers such as you and Dave Burton throw out have no relevance to our discussion.
I have provided the only complete formulation of the problem, and I have provided the way to numerically integrate levels and flows over time.
Until someone does a competing formulation, my formulation is the only game in town.
Ed,
You persist in being willfully ignorant by, once again, conflating human/natural processes with your “human/natural carbon”, despite my BOLD CAPS WARNING that doing so would confuse you. I made the “mass-balance” argument as clear as I could, but evidently it was not clear enough for “Winterberg’s best student”. I hope it was clear enough for Jim, but I am not optimistic. His logic has been kind of shakey recently.
Congratulations, once again. You have confirmed Hans Seuss’s 1955 comments about what are now called disequilibrium isofluxes. Indeed, your “human carbon” is but a small part of the present atmosphere as he predicted. But that is irrelevant to determining the cause of the CO2 increase. The mass-balance argument tells us about that. You have not refuted it. Obviously I have nowhere assumed anything about the constancy of natural processes. Data show clearly that natural sinks are increasing in response to the higher carbon levels in the atmosphere.
Ed, David, and Ferdinand,
Not that you are waiting with bated breath, but I am anxious to respond, busy until later today, and will respond sometime, hopefully.
Dr. Ed,
David Andrews has said it very correct.
But let’s go in more detail again. The whole discussion is about what caused the increase in CO2 mass in the atmosphere. Not where the human FF molecules reside or are transferred to. Even if they are all captured by the next available tree within seconds, that excludes the capturing of a natural CO2 molecule in the same season, except for a small increase in biomass over a year.
dC/dt = En + Eh – An – Ah
Where dC/dt and Eh are quite exactly known and Ah as human induced sink of CO2 mass (not sinks of human FF molecules!) is negligible.
Thus even if we don’t know En and An exactly, and thus the margins of the residence time Te are rather wide, we do know the difference between En and An quite accurately.
For the past years we can make the rough sums (as mass) in PgC/year:
dC/dt = 200 (En) + 10 (Eh) – 205 (An) – 0 (Ah)
Both En and An do already contain a certain percentage of FF molecules, but that is about transfer of molecules, and only of academical interest, as that doesn’t have any influence on the measured transfer of CO2/carbon mass, whatever its composition.
What is sure, is that all FF emissions as mass and as isotopic composition are for 100% injected into the atmosphere.
With 909 PgC in the atmosphere (2025) we have, with Te(c), the overall residence time of CO2 in the atmosphere:
Te(c) = 909 / 205 = 4.43 years
With a difference of CO2 in the atmosphere between 2025 and 1750 we have:
Tau = (909 – 589) / (210 – 205) = 64 years
A little overblown as the zero net outflow equilibrium slightly increased from 1750 to 2025 due to warming oceans from 589 PgC to 628 PgC which gives:
Tau = (909 – 628) / 210 – 205) = 56 years
So, which one is of interest?
Te is based on the sum of all outputs out of the atmosphere, no matter their direction or back flows from the receiving reservoir. Even if the back flows from oceans and vegetation were equal to the outflows from the atmosphere into the oceans and vegetation, Te will not change. But the net CO2 transfer from the atmosphere to the two main other reservoirs would be zero.
As the exact flows between the different reservoirs are only known with large margins of error and the flows between ocean surface and deep oceans not measured at all (that is based on the Bern model!), any calculation of the net outflow based on the residence times is very problematic.
The only time of interest is Tau, which shows how much net CO2 really get transferred from the atmosphere into the other reservoirs. The only point of discussion in that case is the shift of the equilibrium over time since 1750, but that is easily solved by using the formula of Takahashi for the increase of pCO2 of the ocean surface with temperature, confirmed by the back calculation of the measured net CO2 output to zero net output by David Burton and many others in the past:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
DAVID ANDREWS JULY 11, 2025 AT 8:57 PM
Dear David,
My simple demonstration using your own equation proves your interpretation of your equation is wrong.
You responded, as you always do when trapped, by attacking me personally, which is a giveaway that you are wrong.
You wrote:
Irrelevant?
Then show it in math, David. Show it in math.
Your capitalized statement is scientific insanity:
Wow! In theoretical physics, David, we always explore the next level of detail to get as much information as we can. And in this debate, that obvious next level is to consider human and natural carbon independently.
After all, the objective of this debate is to determine the effects of human CO2 emissions, as distinct from natural CO2 emissions. We can’t do that unless we look at each process separately.
We lose no information is this logical separation but we gain more insight. And that separate insight proves you are wrong.
That’s how we do theoretical physics, David. But you never learn.
You refuse to look at each process separately because you realize you lose the debate when we do.
(Yes, I was Winterberg’s best student, by far, as he wrote several times. Care to compare your PhD thesis with mine? My bet is you cannot follow the math and logic in my thesis, which was a breakthrough in climate physics, described in textbooks, exclaimed by Russian physicists, and still gets several citations every year. And, yes, I did score a perfect 800 on my SAT and finished in half the allotted time because the test should have been twice as long.)
Dr. Ed, July 11, 2025 at 12:18 pm
“When you drop Ah, you are assuming all the increase was Human CO2 increase. Therefore, your reasoning is circular, and wrong.”
We didn’t “drop” Ah for circular reasoning, Ah just is minuscule and less than 1% of Eh…
Your calculations should show:
F(a-g) – F(g-a) + F(a-s) – F(s-a) + F(s-d) – F(d-s) = dC/dt – Eh
As you use the overall Te of around 4 years in your calculation, the result is far too small and doesn’t reflect the real increase in the atmosphere.
Again, somewhere lost in the discussion:
With your Te of 4 years, most human emissions are redistributed into vegetation and oceans.
Despite that, there is a measured increase of CO2 in the atmosphere.
What is then the source of that extra CO2, as both oceans and vegetation increased in carbon content?
Ed,
“That’s why we must first agree on the formulation of the problem.”
Yes, we must agree on the formulation of the problem. I think we agree that the problem is to determine: “what has caused the atmospheric CO2 increase over the last century?”
Your formulation is to calculate the “human carbon” in the present atmosphere. Your central conceptual error is to not recognize, or at least not acknowledge, that this is an unimportant statistic determined by the mixing, on a short residence time scale, of atmospheric carbon with that in other reservoirs. Balanced mixing does not change levels, as illustrated by my little thought experiment. I know you care deeply about this unimportant statistic because it is your signature contribution, praised by coal man Richard Courtney. But your separate tracking of human and natural carbon has gotten you nowhere useful. It is the total carbon that matters, and that is tracked by the mass-balance analysis.
Between 1960 and 2010
350 +- 29 PgC of human emissions
158 +- 2 PgC of atmospheric accumulation
Therefore 192 +- 29PgC of net global uptake, because the carbon we added has to be accounted for.
The argument is remarkably simple and makes no assumptions about the constancy of natural processes. If you can discipline yourself not to go off on unnecessary tangents about different carbon types, you will see it too.
Ferdinand Engelbeen July 12, 2025 at 7:10 am
Dear Ferdinand,
Thank you again for your participation in this debate.
As you say, “The whole discussion is about what caused the increase in CO2.”
For this discussion, I have the option to rewrite our (1) as my (4)
dC/dt = (En– An) + (Eh – Ah) ………………………………. (4)
which when integrated over a period of years becomes:
Total CO2 increase = Total (En– An) + Total (Eh – Ah)………….(6)
Which is the same as my (5).
Now, we can insert your “rough sums” to get (6):
Total CO2 increase = Total Natural (200 – 205) + Total Human (10 – 0)………….(6a)
Hmm. It looks like your rough sums say the following:
Total CO2 increase = Total Natural (-5) + Total Human (+10)………….….(6b)
Your rough numbers say nature subtracted 5 and human added 10.
Do you really believe that? I don’t. But those are your numbers.
Further, I don’t agree at all with your definitions and calculations of Te and Tau. We can discuss these disagreements after you fix your numbers to make (6b) believable.
David Andrews July 12, 2025 at 11:15 am
Dear David,
Your physics is clutzy. Please put your numbers into equation (6) that I just wrote in my comment to Ferdinand:
Total CO2 increase = Total (En– An) + Total (Eh – Ah)………….(6)
Using Ferdinand’s numbers, this became:
Total CO2 increase = Total Natural (200 – 205) + Total Human (10 – 0)………….(6a)
Total CO2 increase = Total Natural (-5) + Total Human (+10)………….….(6b)
Ferdinand Engelbeen July 12, 2025 at 10:53 am
Dear Ferdinand,
Your following equation does not properly represent my calculations:
F(a-g) – F(g-a) + F(a-s) – F(s-a) + F(s-d) – F(d-s) = dC/dt – Eh
However, we have a bigger problem.
You claim Ah is less than 1% of Eh.
Your conclusion is based on your other errors. We must begin with IPCC’s natural carbon cycle data, shown in my Figure 3.
Then you have some problems to solve:
1. Your Tau of 50 years does not fit IPCC’s natural carbon cycle data.
2. Your Tau of 50 years does not fit the bomb test data that show Te = 16.5 years with a balance level of zero.
3. Your Tau is the time for a level to move 63% of the way to its balance level. Well, that is exactly Te. So, you have no basis to claim a Tau of 50 years, which is the same as saying Te is 50 years.
4. You assume human CO2 moves out of the atmosphere with a Tau of 50 years and then you conclude from this assumption that “Ah is less than 1% of Eh.”
5. You have not made a valid argument to justify your conclusion. Even IF you think Ah is small that does not justify dropping it from your equation.
6. Salby and Harde found that CO2 flows out of the atmosphere with Te much less than 3.5 years. You can see this in the monthly CO2 data. If your Tau of 50 years were in control, there would be no monthly sawtooth pattern in the CO2 data.
7. Your claim that H(1) is true conflicts with Munshi’s statistical analysis that shows the annual correlation of human CO2 emissions with annual CO2 increase is zero, which proves H(1) is false.
Dr. Ed, July 12, 2025 at 11:27 am
“Total CO2 increase = Total Natural (200 – 205) + Total Human (10 – 0)………….(6a)
Hmm. It looks like your rough sums say the following:
Total CO2 increase = Total Natural (-5) + Total Human (+10)………….….(6b)
Your rough numbers say nature subtracted 5 and human added 10.”
Indeed that is exactly what David and David and I are saying…
There simply is no appreciable human sink in this entire world… The only sinks are natural sinks, which absorb any mix of natural and human CO2 alike.
Even if you integrate all human emissions in the period 1958-2020, that is about 170 ppmv, while the measured increase is only 100 ppmv. Nature removed 70 ppmv CO2 out of the atmosphere into oceans and vegetation…
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_mlo_t_1960-cur.png
Ferdinand Engelbeen July 12, 2025 at 12:41 pm
Dear Ferdinand,
You say,
“Indeed, that is exactly what David and David and I are saying…
There simply is no appreciable human sink in this entire world… The only sinks are natural sinks, which absorb any mix of natural and human CO2 alike.”
That statement sinks your ship.
Even as you admit there are natural sinks, you are saying that there are no human sinks.
Does that begin with the first human CO2 molecule? Or the first ten?
You are saying that the jillions of trees on the planet will not accept the CO2 added by human emissions. This contradicts even the famous picture of four trees grown in different CO2 levels.
So, you are saying that the Te for human CO2 is much greater than the Te for natural CO2. Your argument violates the climate equivalence principle.
With this, I am outa here. Got better things to do today.
Ed,
I hadn’t seen your 10:38 post when I wrote my 11:15 post. Now I see your 11:47 post and later ones too.
A few points:
1. For a semi-quantitative analysis of why your calculation of “human carbon” in the present atmosphere is irrelevant, see my rebuttal to Skrable. https://pubmed.ncbi.nlm.nih.gov/36719939/ The mixing means that only about the last decade’s worth of C14 devoid “human carbon” should be expected to still remain in the atmosphere. That agrees well with the current measured atmospheric radiocarbon specific activity. This is the diluted Seuss effect which you have shown you are uncertain about even though you effectively calculated it. No one ever expected to measure the (undiluted) “Natural + 33% Human” curve in your Figure 9, because the composition of the present atmosphere only gives information about the last decade; earlier information is effectively erased by the mixing. I could make the case that my argument on the Skable analysis shows that, in the last decade at least, the rise is anthropogenic. Similarly the pre-1950 data shows a (diluted) Seuss effect. But a conservative conclusion is just to say that the present atmospheric composition is an unreliable indicator by itself of the atmosphere’s history because of mixing. Interpreting the composition as showing that the CO2 increase is mostly natural as you do, as if mixing doesn’t occur, is naïve and just plain wrong.
2. You make a case for analyzing details in physics, such as studying the human and natural cycle separately. Yes, that is often the case. I think the reason you are the only one doing it here is to be found in the paragraph above. And I am sure you know of many, many physics problems where the smart approach is to apply a conservation law rather than to grind through an unnecessarily detailed analysis. Carbon conservation is a quite useful constraint.
3. On your request that I insert numbers into your (6) to attribute the atmospheric growth to natural or human origins: I will use the Ballantyne numbers again, for the period 1960-2010, omitting error bars this time. The units are PgC
Total Increase = 158
Human input = 350
Natural input = -192
Yes, things would be a lot worse if natural sinks weren’t bailing us out. The ~45% “airborne fraction” has held up pretty well.
4. I see you are still haggling with Ferdinand about “Ah”. He is correct. Did you bother to read how I defined it?
Dr. Ed, July 12, 2025 at 12:37 pm
Dear Ed,
“Your following equation does not properly represent my calculations:
F(a-g) – F(g-a) + F(a-s) – F(s-a) + F(s-d) – F(d-s) = dC/dt – Eh”
Indeed, it shows what your calculations should show, but don’t show…
dC/dt and Eh both are quite exactly known. dC/dt – Eh is the overall removal of CO2 wherever in nature that may be, for human and natural CO2 together, whatever the mix in the atmosphere.
All bidirectional fluxes between the atmosphere and vegetation or oceans together should equal the net sink rate of what is removed out of the atmosphere as mass.
Then the other items:
“You claim Ah is less than 1% of Eh.”
Again… Ah is what humans exactly produce as CO2 mass sinks. That are things like reforestation in some countries, still dwarfed by clear cutting of forests in other countries, CCS (pretty good object for government subsidies, but the largest project did fail), etc. That is not about how much original FF molecules are removed with the increasing outflows into oceans and vegetation.
“1. Your Tau of 50 years does not fit IPCC’s natural carbon cycle data.”
The Tau of 50 years is calculated from the difference between the current CO2 level in the atmosphere with the “old” equilibrium (plus T influence) and the observed net outflow. Tau has nothing to do with CO2 cycles.
“2. Your Tau of 50 years does not fit the bomb test data that show Te = 16.5 years with a balance level of zero.”
The Te of 4 years also doesn’t fit, but you forget the “thinning” of the δ13C and Δ14C signals by the deep ocean returns of ~1000 years ago with 13C/12C and Δ14C of long before the bomb tests and fossil fuel use.
And you forget the 14C-free supply of FF…
That makes that the decay rate for Δ14C is much faster than for 12/13CO2 as mass and that the drop of δ13C is only 1/3 of what it should be if all FF remained in the atmosphere…
“3. Your Tau is the time for a level to move 63% of the way to its balance level. Well, that is exactly Te. So, you have no basis to claim a Tau of 50 years, which is the same as saying Te is 50 years. ”
You did calculate a Te of 4 years by adding all outputs out of the atmosphere together, but didn’t take into account the CO2 cycles that do move a lot of CO2, but don’t remove the same quantity out of the atmosphere than they move.
Some 200 PgC is moving through the atmosphere in half a year and just is cycling back in another half year, hardly affecting the CO2 level. Only some 5 PgC/year is removed by the extra CO2 pressure in the atmosphere or 16 PgC/year by the absolute CO2 pressure in the atmosphere.
“5. You have not made a valid argument to justify your conclusion. Even IF you think Ah is small that does not justify dropping it from your equation.”
Be my guest to find any human sink that can influence the results of our calculations…
“6. Salby and Harde found that CO2 flows out of the atmosphere with Te much less than 3.5 years. You can see this in the monthly CO2 data. If your Tau of 50 years were in control, there would be no monthly sawtooth pattern in the CO2 data.”
This is a good one: the seasonal sawtooth is caused by the influence of temperature on (deciduous forests) vegetation and is negative for temperature: -5 ppmv/°C
The year by year variability is caused by the influence of temperature on (tropical forests) vegetation and is positive for temperature: +3 to +4/°C.
On decades and longer (up to 800,000 years), the oceans surface temperature is dominant and there is the 50 years Tau based on.
“7. Your claim that H(1) is true conflicts with Munshi’s statistical analysis that shows the annual correlation of human CO2 emissions with annual CO2 increase is zero, which proves H(1) is false.”
This is a complete joke: Munshi first de-trended all the data and only looked at the variability of the data. As all the small variability (+/- 1.5 ppmv for the extremes) is caused by temperature and human emissions have hardly any variability, of course you only find a correlation between temperature and none with human emissions.
But if you look at the over 100 ppmv trend since 1958, the human emissions trend is 170 ppmv directly into the atmosphere and temperature has hardly a trend, here for the yearly changes:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em9b.png
Dr. Ed, July 12, 2025 at 12:58 pm
Dr. Ed, David Burton, Dave Andrews and I made it very clear that there are no appreciable human sinks. That is human made CO2 capturing mass sinks, no matter if that “mass” is 100% natural or 100% FF or anything in between. Sinks as mass, not sinks as (specific) molecules.
Again, once human FF CO2 is mixed in the atmosphere, it adds its full mass and 14C-free and low-13C fully to the atmosphere. Nature only removes about half that mass and replaces 2/3 of the FF 13C, thus nature is a sink for CO2, not a source.
Dear Ferdinand Engelbeen, and others using the simple math model to claim H1 is true.
Re: July 11, 2025 at 2:27 am
I think we have reached an impasse. I cannot continue countering what I consider flawed science and logic. In your last comment, you wrote,
“These cycles are near completely independent of the actual CO2 pressure in the atmosphere.”
That is patently false. Ocean outgassing and removal of CO2 are near completely proportional to the concentration gradient at the air-ocean interface. Even some of your colleagues here agree with that (I would hope).
Next regarding the problem you have with “398 ppmv is way above the equilibrium pCO2 of the ocean surface, which would be around 295 μatm.” You made the correct point that temperature does not account for the full difference between the new and old equilibrium pCO2’s. However, one must also take into account the increased CO2 levels in the reservoirs. Consider the first order reversible reaction between A B and its equilibrium K = [B] / [A]. If more reactant is added after the initial equilibrium is reached, a new equilibrium is reached with K = ([B] + x) / ([A] + (1-x)]. Assuming no change in temperature or pressure, K will remain the same. But both reactant and product end up at larger concentrations.
It’s self-fulfilling prophecy to use the “CO2 removal rate vs. CO2 level” plot of Dave Burton to argue no change in equilibrium pCO2. That’s because it’s based on the equation Eh(t) – dC(t)/dt = k * (C(t) – Co) which assumes negligible Ah, because (for some reason) sequestration is considered to be the only way a fossil fuel carbon gets removed. Below, I will derive a simple math model that will explain the correct way to interpret the mass balance logic you are using.
In the following derivation, I will use abbreviated terminology for time constraint reasons. I can explain any misconceptions later. I will shorten the mass balance equation to D = Eh + En – S. This is meant to be the equivalent of dC(t)/dt = Eh(t) + En(t) – Sn(t). I leave off the (t), but all calculations are intended to be valid for any year. For example, D(t) = C(t) – C(t-1).
I make two assumptions. First, that a fairly constant fraction of CO2 is removed and replaced by approximately the same amount each year. Second, that the sink, Sn(t) = S, contains a fraction of the human and natural carbon in proportion to the amounts that were emitted annually. Therefore, I am introducing a factor, f, such that f * S = Eh + En.
I need to show also that S = k * C, but it will have to be assumed for now because the demonstration requires t+1, t, t-1, etc. and there’s no time for that today (tonight now).
(1) D = Eh + En – k * C
(2) S = k * C
(3) f * S = ( Eh + En )
(4) ( Eh + En ) = D + S
(5) f * S = D + S
(6) D = ( f – 1 ) * S
(7) S = D / ( f – 1 ) and from (2) and (7),
(8) D / ( f – 1 ) = k * C
(9) D = ( f – 1 ) * k * C
First, I plotted D versus C to see if the correlation was decent. The intercept provides an estimate of ( f – 1 ) * k.
D = 0.0176 * C – 4.664. That makes the x-intercept 265 ppmv. Let’s put it this way. That correlation is about as good as the one Dave Burton and others use here:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Next, I calculated ( f – 1 ) * k for each of the individual average pairs of D(t) + D(t+1) and C(t) and C(t+1). The average was 0.00435. Next, I calculated f, using k = 0.25, finding an average of 1.017.
Finally, I calculated En(t) from (2) and (3),
(10) En = f * k * C – Eh
En gradually increases from 79 ppmv in 1959 to 99 ppmv in 2017. This is consistent with a pCO2 of 316 ppm that would be expected in 1959, but 396 ppm is a bit less than the 407 ppm I use for the Mauna Loa value in 2017. The use of a four-year turn around value of k = 0.25 suggests that is approximately correct and could conceivably have drifted somewhat. However, no one here seems to claim anything outrageously different than four years.
In summary, this analysis shows the shortsightedness of using the simple math model without consideration of the assumption I made on the basis of the equivalence principle. In every year, the amount of carbon sinked contains a share of both human and natural emissions in proportion to the amounts of each that were emitted. The human amounts have data to back them up. No one knows exactly how much of the natural emissions may have risen. This analysis shows that it is reasonable to expect an equilibrium level of carbon transferring between the various reservoirs to have risen substantially since pre-industrial times.
This is part 1. Part 2 is intended to show how Tau is not substantially different than Te. I know David Andrews will be holding me to it, but don’t hold your breath.
Note: I have not read any comments today, so I will have to catch up on this very interesting debate tomorrow.
Jim,
A few quick comments:
1. Like D (or S) Eh is a measured quantity. I assume you are inputting measured values.
2. Your (1) and your (4) are the same equation, rearranged. A third version is to me the most informative:
Eh – D = S – En The left-hand side is well known and definitively positive in the industrial era. It is “net global uptake”. The individual terms on the right are not well known, but by this equation their difference is. Do you agree it tells us that in the industrial era, more carbon has moved from the atmosphere into natural sinks than has gone the other way?
3. I think making the sink rate proportional to the carbon level would make more sense than making it proportional to emission rates.
4. You write “…(for some reason) sequestration is considered to be the only way a fossil fuel carbon gets removed”. That shows a misunderstanding of the mainstream view which I laid out on July 11 at 9:48 AM (Rocky Mountain time.) The natural sinks take in all carbon without discrimination. There is no equivalence principle problem. Mainstream science generally does not track “human” and “natural” carbon separately.
5. Your model is not far from the mainstream one (except for the time constants.) Therefore I don’t understand your comment about “the shortsightedness of using the simple math model without consideration of the assumption I made on the basis of the equivalence principle”. I think if you look back at my 7/11 post and read how An and Ah are defined, you will understand there is no equivalence principle problem or shortsightedness. Whether you know yet it or not, I think you will find your analysis confirms “H1”.
Jim Siverly, July 12, 2025 at 7:41 pm
“’These cycles are near completely independent of the actual CO2 pressure in the atmosphere.’
That is patently false. Ocean outgassing and removal of CO2 are near completely proportional to the concentration gradient at the air-ocean interface.”
There is an enormous difference between “the actual CO2 pressure”, thus the absolute pCO2 of the atmosphere and the “concentration gradient”. That is the exact point in discussion here.
The current absolute pCO2 in the atmosphere is about 415 μatm.
The (1995) concentration gradient between atmosphere and ocean surface was average only 7 μatm, according to Feely et al., based on near one million sea surface measurements.
The latter, together with chemical restrictions in the sea surface, makes that the sea surface only follows 10% of the change in the atmosphere and that the pCO2 of the ocean surface follows the pCO2 of the atmosphere with an exchange time of less than a year. That also implies that the pCO2 of the ocean surface closely follows the atmospheric pCO2 and thus the difference between ocean surface and atmosphere increases only very slowly.
Even for the deep oceans and vegetation, the uptake is directly proportional to the pCO2 difference with the “old” equilibrium, plus temperature influence, that would be 295 μatm nowadays.
The actual CO2 cycles between all reservoirs are around 200 PgC/year, while the calculated absolute sink rate, caused by the (current!) absolute pCO2 in the atmosphere is only some 16 PgC/year…
The of pCO2 in the receiving reservoirs only plays a role for the ocean surface, that closely follows the atmospheric pCO2, It plays zero role at the sink and upwelling places of the deep oceans and no measurable role in the uptake and release by plants, which simply remain in ratio with the “old” equilibrium.
Then the formula’s:
“(1) D = Eh + En – k * C”
That is for the absolute concentration (or absolute pCO2) in the atmosphere and should be
(1) D = Eh + En – k * ΔpCO2(atm-others)
Based on Feely et al. for the oceans: F = k•s•ΔCO2 between atmosphere and ocean surface.
and similar (but not easy to direct measure) between atmosphere and vegetation. The latter remains proportional to the pCO2 difference with the “old” equilibrium…
That means that your k*C is way to high and your decay rate much too fast…
“(3) f * S = ( Eh + En )”
As David already said: S is not a function of the inputs of one year, S is a function of the increase of actual pCO2 above an equilibrium, wherever that may be. S is completely independent of Eh + En for almost all what is sucked out of the atmosphere by plants in spring/summer (it even reduces pCO2 of the atmosphere) and only for a very small part depends on the extra pressure above equilibrium.
The main difference left is your residence time of 4 years, which is based only on all outputs of the atmosphere, without taking into account that most of these outputs are part of cycles that net removes zero CO2 out of the atmosphere. Only the difference between al inflows together and all outflows together, is the real decay rate of any CO2 mass (whatever its composition) out of the atmosphere and that is the calculated 50 years Tau…
David Andrews, July 12, 2025 at 11:35 pm
Thank you for taking time to critique my model.
1. Yes, I used the Bolen et al. data in Roy Spencer’s spreadsheet.
2. (1) and (4) simply mean S = k * C. Your third version is the slight of hand I’m trying to expose. As long as you believe Sn contains no fraction of Eh you will never understand Dr. Ed’s model.
Do I agree that more carbon has moved from the atmosphere into natural sinks than has gone the other way? Of course. But most of the annual amount remaining in the atmosphere originated from the natural sinks, because nearly all the human emissions are removed annually. That’s what my simple math shows.
3. The sink rate is proportional to the carbon level, S = k * C. But the relative amounts removed are in proportion to the amounts added. S = Eh/f + En/f
4. Not tracking “human” and “natural” carbon separately is what violates the equivalence principle using simple math. I modified the simple math to explicitly account for the equivalence principle.
5. No, my analysis confirms that industrial/human carbon is only a small fraction of the increase in atmospheric CO2 and there has been a large increase in biomass which contributes the majority of the increase in atmospheric CO2.
P.S., from your July 11, 2025 at 9:48 am comment: I laughed out loud at “[Jim’s] logic has been kind of shakey recently.” Give me a break. I have peripheral neuropathy, but so far it hasn’t affected my brain. I hope.
Jim,
You write “As long as you believe Sn contains no fraction of Eh you will never understand Dr. Ed’s model.”
What I called An, which is the same as your Sn, includes the absorption of ALL types of carbon. I made that clear when I wrote in my 7/11 9:48AM analysis “Divide the PROCESSES into human and natural and indicate which by subscripts. MAKE NO DISTINCTIONS ABOUT CARBON TYPES OR YOU MAY GET CONFUSED.”
I thought you understood , but rereading your earler 6/27 8:48pm comment, probably you did not. You wrote
“To be clear, I consider “Ah” as that fraction of atmospheric carbon removed naturally that was originally a fossil fuel. So if At is the total amount removed in a given time interval, At = An + Ah, where An is the non-fossil fuel carbon removed by natural processes.” I responded on 6/27 at 11:38pm “What you call “At” has always been “An” to me” but perhaps you missed that. My 7/11 analysis would make no sense if I used your definition of An. Now you have introduced Sn which is the same as your earlier At and my An.
In summary, we agree that natural absorption processes do not discriminate based on the source of the carbon. The mass-balance argument has NEVER claimed they did; only misinterpretations of the mass-balance argument have caused confusion. I am glad to see that you can say “Do I agree that more carbon has moved from the atmosphere into natural sinks than has gone the other way? Of course.”
But we are not on the same page on everything. You go on to say “my analysis confirms that industrial/human carbon is only a small fraction of the increase in atmospheric CO2”, as if that were important. I agree the present atmosphere has little carbon in it that once resided in a fossil fuel, but human emissions are still the cause of the rise, because natural processes have removed more than they added. I urged you to understand the disequilibriuim isofluxes which can change the atmosphere’s composition without changing levels and offered a little thought experiment. I laid this out again for Ed in my 7/12 1:41PM comment. I do understand his model, and why it is wrong.
Jim Siverly, July 13, 2025 at 7:21 am
In addition to what David said…
“2. But most of the annual amount remaining in the atmosphere originated from the natural sinks, because nearly all the human emissions are removed annually.”
As mass: only half the CO2 mass that humans ad per year are removed (as mix) in the same year.
As original FF molecules: you forget that the two fast cycles: ocean surface and vegetation not only remove FF molecules, but also bring them back in the next season. For vegetation: near fully within a year, for the ocean surface within a few years. Only what goes into more permanent vegetation and the deep oceans is gone for a long period.
“3. The sink rate is proportional to the carbon level, S = k * C. But the relative amounts removed are in proportion to the amounts added. S = Eh/f + En/f”
That is refuted by the observations: between 1958 and 2020, the human input increased from 1% to 5%. The observed ratio is over 10% FF in the current atmosphere and over 6% in the sea surface:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.jpg
and:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/d13C_brw_mlo_spo.jpg
Your simple math is based on the one-way “lake / bath tube” model, which is completely at odds with the real world…
“5. “… there has been a large increase in biomass which contributes the majority of the increase in atmospheric CO2.
The biosphere never can supply more CO2 than it removed first out of the atmosphere… Except for short periods like El Niño’s or when cooling to a new glacial period.
The oxygen balance shows that the biosphere is a net absorber of CO2 and so does satellites which monitor chlorophyll:
https://www.nasa.gov/feature/goddard/2016/carbon-dioxide-fertilization-greening-earth
and
https://tildesites.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
“We find the average CO2 uptake by the ocean and the land biosphere was 1.7 ± 0.5 and 1.0 ± 0.6 GtC/yr respectively;”
That was for the period 1992-2001. Meanwhile the net uptake of CO2 by the biosphere only increased…
Ferdinand,
It seems you and Dr. Ed. are defining Ah differently. Ah is human flow out of the atmosphere. It seems you and David are defining it as carbon capture, sequestration, etc. Ah isn’t trivial. It is essentially Eh.
Also, your answer, “That pCO2 is measured in the small air volume and is used as pCO2 of the ocean water,” is made-up science. That pCO2 is pCO2(atm), not pCO2(ocean). There is no small vapor of atmosphere just above the water that is pCO2(ocean).
Ferdinand,
Also, dC/dt=2ppm annually, based on flows, approximately 5% of that is human and 95% of that is natural. So humans contributed to about 0.1ppm annually of the increase.
David Andrews July 13, 2025 at 10:30 am states:
“I agree the present atmosphere has little carbon in it that once resided in a fossil fuel, but human emissions are still the cause of the rise, because natural processes have removed more than they added.”
How do we know the natural processes removed more than they added? Natural sinks removed less than all the emissions so the atmospheric content grew. There seems to be agreement FF emissions and natural emissions are removed by processes that cannot differentiate between them. It seems possible that if natural emissions are growing faster than the sinks atmospheric content will increase without FF additions. I do not think we have a good handle on the quantity of natural emissions. I think these points lead me to conclude the percent of natural emissions remaining in the atmosphere must closely match the percent of FF emissions remaining.
DMA,
“How do we know the natural processes removed more than they added?”
– Because consistenly over decades, the growth in atmospheric carbon has been only about 45% of human emissions. We can therefore conclude that natural processes absorbing atmospheric carbon into land/sea sinks are larger than emissions from those sinks. If it were the other way around, atmospheric carbon would be growing faster than human emissions. Data say it is not.
“I do not think we have a good handle on the quantity of natural emissions”
-You are correct that we do not, but we do have a good handle on the difference between natural absorption and natural emission rates. That difference, appropriately called “net global uptake”, is the amount of carbon that has “gone missing” from the atmosphere. It is the ~55% of human emissions not accounted for by measurements of atmospheric carbon growth.
“I think these points lead me to conclude the percent of natural emissions remaining in the atmosphere must closely match the percent of FF emissions remaining.”
-This has been one of Ed’s hangups too. There is indeed much more natural carbon around than carbon that was once contained in fossil fuel. And large natural exchanges between air, land, and sea thoroughly mix things up. Ed’s conclusion that the present atmosphere has little “human carbon” in it is correct. But his inference that therefore natural emissions have dominated the increase is wrong. Human emissions caused the growth (see my first paragraph here), but balanced exchanges which did not change levels hid the evidence. The atmosphere had extra “human carbon” after we put it there, but it mixed with the more abundant natural carbon in other reservoirs. These are the “disquilibrium isofluxes” I have discussed elsewhere. This is the “dilution of the Seuss effect”. You cannot understand what is going on without understanding these processes.
Stephen P Anderson, July 13, 2025 at 1:20 pm
You are right, there is some misunderstanding at work. The whole scientific world uses uses An as the fraction of CO2 that is sequestered by humans out of the atmosphere. Be it by planting new forests or carbon capturing ans sequestering (CCS). That are peanuts and the largest CCS project failed:
https://reneweconomy.com.au/chevron-concedes-ccs-failures-at-gorgon-seeks-deal-with-wa-regulators/
Our approach is that Eh, once injected into the atmosphere are part of the total atmosphere as mass and not anymore of interest for what happens with the total CO2 mass, as that is what “may” cause climate change. Only Qt is of interest. No matter how the original FF molecules are redistributed over the different reservoirs. Because Ah is minuscule, the sum of all natural sinks, An, are the only parameter that removes CO2 out of the atmosphere, human and natural molecules alike.
I think that you are mistaken about the pCO2(aq). For Henry’s law there is a (temperature dependent) fixed ratio between the CO2 level (pressure) in the atmosphere and the CO2 level in solution of seawater.
If the pCO2 of the atmosphere doubles, the CO2 level in seawater doubles.
Per Henry’s law, there is no net exchange of CO2 if the dissolved CO2 in seawater has the same apparent pressure as the CO2 in the atmosphere. Of course still there is a lot of exchange of molecules in each direction, but the number of molecules in each direction is equal.
One can theoretically calculate the CO2 content with its apparent pCO2 of the solution, based on alkalinity, salt content, DIC (dissolved CO2 + (bi)carbonates) or much easier by looking at the resulting pCO2 in the atmosphere, when atmosphere and water are in equilibrium.
That is done either by spraying seawater in a small volume of air or the opposite and measuring the pCO2 of the small volume of air.
Thus while strictly speaking, there is no measured pCO2(aq), the pCO2(atm) in equilibrium with seawater is as good as factor to be used in all flow calculations of CO2 transfer between the atmosphere and the ocean surface in either direction.
Stephen P Anderson, July 13, 2025 at 1:24 pm
“Also, dC/dt=2ppm annually, based on flows, approximately 5% of that is human and 95% of that is natural. So humans contributed to about 0.1ppm annually of the increase.”
The 5% is extra CO2 mass and adds its mass directly into the atmosphere. The 95% natural inputs increase to 97.5% (FF + natural) outputs, thus humans are fully responsible for the 2.5% increase of CO2 mass in the atmosphere.
No matter if all FF molecules remain in the atmosphere or every FF molecule is removed out of the atmosphere with the outputs.
For the inputs, the current ratio FF to natural is 5/95. But you forget that the other reservoirs also increased in FF content, the 95% return from oceans and vegetation is not FF free…
That makes that with only 1% to 5% FF input between 1958 and today, the FF content in the atmosphere is already over 10% and in the ocean surface over 6%.
Ferdinand,
Dr. Ed is also saying you can write two independent linear differential equations for natural flow and human flow. Of course you can. Do you know why? Because of the Equivalence Principle.
Ferdinand,
I’m not mistaken about Henry’s law. The partial pressure of the gases in the atmosphere determines the concentration of the gases in the ocean. That’s Henry’s Law. There is no pressure differential from some layer just above the surface to the atmosphere. The only pressure differential in the atmosphere is the hydrostatic pressure differential that causes the lapse rate. There is no radiative forcing that causes the lapse rate. That is also derived from the gas laws.
Ferdinand,
“The 5% is extra CO2 mass and adds its mass directly into the atmosphere. The 95% natural inputs increase to 97.5% (FF + natural) outputs, thus humans are fully responsible for the 2.5% increase of CO2 mass in the atmosphere. No matter if all FF molecules remain in the atmosphere or every FF molecule is removed out of the atmosphere with the outputs.”
It isn’t STATIC. (Caps for emphasis.) Most of the inputs from Natural and Human carbon are flowing out of the atmosphere without going into the math. Dr. Ed has already done a great job of showing you that. (You need to reread all three of his papers.) So, human carbon can’t be more than about 5% of the increase. Most of the increase has to be due to natural carbon. Dr. Ed was very conservative in his second paper and attributed 25% of the increase to humans, but it really isn’t. Humans are only responsible for about 10ppm. Almost nothing.
Stephen,
Ed is not wrong when he concludes from his calculations that “human carbon” makes up only a small part of the carbon in the present atmosphere. He is wrong when he thinks that implies that natural emissions are the dominant cause of the CO2 increase.
In the 1950’s, Hans Suess correctly noted that atmospheric radiocarbon levels were decreasing because of the addition on “cold” (C14 free) carbon from fossil fuel burning. A naive interpretation of the “Suess effect” would predict that if the ~33% carbon increase in the industrial era was from fossil fuel burning, then 33% of the new carbon would be cold. It is clearly not, and Suess in the 1950’s knew why. You are well aware that natural emissions are an order of magnitude larger than human ones. That means that there are large two-way exchanges between the atmosphere and land/sea reservoirs that mix the inventories and “dilute” the Seuss effect. There is a slight imbalance in these exchanges which accounts for atmospheric accumulation being only ~45% of human emissions (natural absorsption is greater than natural emissions) but most of the two way flow is balanced and does not change the atmospheric carbon levels. The balanced flow most certainly still does lower the “human carbon” content of the atmosphere. Ed has unknowingly been calculating the dilution of the Seuss effect rather than finding the cause of the CO2 increase.
I should have said “A naive interpretation of the “Suess effect” would predict that if the ~33% carbon increase in the industrial era was from fossil fuel burning, then the present atmosphere would be a mixuture of 33% cold carbon and 67% carbon with the usual C14/C12 ratio. “
David,
No Dr. Ed isn’t wrong. Dr. Ed’s logic and methods and derivations conform to every upper-level Chemistry, Physics and Math I ever have been taught. It is right out of the Physical Chemistry and Differential Equations textbooks. Now, your logic, doesn’t. I would respond to your Suess effect argument but what is the point? You are so twisted in your ideology that you can’t see science and mathematical truth when it hits you in the face. You continue to regurgitate Big Climate talking points (propaganda) with no science to back it up. Your “net global uptake” is poop. You need to read or reread Dr. Ed’s three papers and also Brendan Godwin’s book and pray to God for some understanding.
Stephen P Anderson, July 14, 2025 at 7:46 am
The CO2 pressure differential is between the ocean surface and the air layer just above it…
“the partial pressure of the gases in the atmosphere determines the concentration of the gases in the ocean.”
In this case it is just reverse: the CO2 concentration in the oceans determines the concentration of CO2 in the atmosphere…
Henry’s law does apply in both directions. The “equilibrium” pCO2 of the ocean waters changes with the sea surface temperature and if it gets higher than in the atmosphere, CO2 is degassing and increases the CO2 pressure in the atmosphere until bot are equal.
That happened over the past glacial-interglacial cycles: (ocean) temperature goes up and CO2 follows…
Stephen P Anderson, July 14, 2025 at 8:01 am
” Most of the inputs from Natural and Human carbon are flowing out of the atmosphere without going into the math.”
If you add 5% human input one-way and the increase in the atmosphere is only 2.5%, how then can the natural inflows have caused the increase?
Both the outputs to vegetation and oceans are larger than their inputs back to the atmosphere. A negative balance which should give an positive result in the atmosphere?
I have read Dr. Ed’s papers and indeed you can split the CO2 flows in “natural” and “human”. But I don’t see any particular reason to do that, as that only makes everything more difficult to follow and more prone for misinterpretations.
Human emissions are going for the full 100% directly into the atmosphere as mass, as low-13C and 14C-free.
All what the natural flows do is removing (not adding!) half of the increase in mass, replacing 2/3 of the FF molecules with CO2 molecules from other reservoirs and diluting the 14C “fingerprint” of FF in the same way.
The main problem for Dr. Ed’s calculations still is that he uses the much too short residence time of 4 years, that is the time that a single molecule CO2 resides in the atmosphere, before being switched with a CO2 molecule from another reservoir. That has nothing to do with the real decay rate of around 50 years for an injection of extra CO2 as mass (whatever its origin), back to the dynamic equilibrium of the pre-industrial times…
Dr Ed’s 4 years residence time violates the carbon mass balance: human FF emissions are very fast redistributed into atmosphere, oceans and biosphere, but there is a large gap between what remains in the atmosphere as calculated and what is observed. That extra CO2 can’t come from the oceans or vegetation, as these increased in carbon content, not decreased… Thus from where is that extra CO2?
Ferdinand Engelbeen, July 13, 2025 at 3:29 am
You wrote, “There is an enormous difference between … the absolute pCO2 of the atmosphere and the ‘concentration gradient,’” but that misses the exact point. We will never come to any understanding while you continue to drag out the same old talking points about what Feely considers an average concentration gradient in 1995. Simply put, if you average out the concentration gradients arriving at a small difference, you are in effect discounting most of the mass transfer that occurred during all the times that difference in concentration were maximal.
We have been over and over this. You are using K * ( pCO2now – pCO2old ) in your math resulting in very small K = 1/Tau. The planet doesn’t remember what pCO2 was in 1750. It only deals with the diurnal and seasonal differences applicable to the current time. We supplement the large amount of natural emissions which together are largely removed annually amounting to about ¼ of the CO2 in the atmosphere. Barring an apocalypse eliminating human life, the expanding biosphere may never end; not in 50 years, 500 years, or 50 million years. That makes Tau irrelevant. The only thing that need be said about a hypothetical net zero is that it will only take a few years for “pseudo” equilibrium to arrive. Te rules.
Having said that, a mea culpa is in order. There is a mistake in my assumption of f * S = Eh + En. Until I rework that assumption, I won’t be responding to comments about model differences with the exception of which physical processes apply.
In that vein, I will respond to your last paragraph,
“The main difference left is your residence time of 4 years, which is based only on all outputs of the atmosphere, without taking into account that most of these outputs are part of cycles that net removes zero CO2 out of the atmosphere.”
You have zero proof of that, only anecdotal evidence. Whether or not any removal process takes place in any specific e-time, the net e-time for the atmosphere is about 4 years as all agree. No process will remove all the annual emissions as long as emissions increase annually whether that be from industrial or biomass expansion.
“Only the difference between all inflows together and all outflows together, is the real decay rate of any CO2 mass (whatever its composition) out of the atmosphere and that is the calculated 50 years Tau…”
Again, there will never be proof of that due to our expected ever-increasing population or an end of the world. “Calculated 50 years Tau” is the operative phrase, because it’s based on the false idea that removal rate is proportional to the pCO2 difference with the “old” equilibrium.
DMA
July 13, 2025 at 1:45 pm
“It seems possible that if natural emissions are growing faster than the sinks atmospheric content will increase without FF additions. I do not think we have a good handle on the quantity of natural emissions.”
Yes and Yes. That summarizes the problem with the simple math. It doesn’t work if natural emissions increase and assumes all excess emissions are industrial emissions. David Andrews and Ferdinand Engelbeen are blind to that reality.
Jim and DMA,
You are completely wrong, and Jim you seem to be backsliding. First of all you should lose your habit of thinking about emissions only and ignoring natural absorption processes (which of course are not particular about whose carbon they absorb.) The method for computing net global updake doesn’t limit what natural emissions are doing. The DATA does allow you to say (for the last century but not always) that natural aborption exceeds natural emissions. If they both increase, net global uptake will still be positive as long as absorptions exceed emissions. You already agreed that more carbon has moved from the atmosphere into natural sinks than has gone the other way. But if natural emissions were to exceed natural absorption then there would be a net transfer of carbon from land/sea reservoirs INTO the atmosphere, and atmospheric accumulation would exceed human emissions. The DATA say that has not happened any time recently.
Stephen P Anderson
July 14, 2025 at 9:00 am
Here is how the Tau crowd rationalize the atmosphere containing a small percentage of fossil fuel carbon (FF) remaining in the atmosphere while causing all the excess carbon accumulating (making H1 true). The fast 4-year turnaround launders FF, but is unable to remove all excess carbon which is no longer identifiable as coming from any source, leaving a deficit of about half of the carbon equivalent to that sourced annually as FF.
Conveniently natural emissions don’t need to be accounted for and all absorptions are considered natural regardless whence they came. They assume an equilibrium remains as it has been since 1750 and use a bastardization of Henry’s Law to explain it. I’m coining the whole analysis Magic Math.
Jim Siverly, July 14, 2025 at 1:52 pm
“The planet doesn’t remember what pCO2 was in 1750. It only deals with the diurnal and seasonal differences applicable to the current time.”
It doesn’t need to. It does see the differences between 425 μatm in the atmosphere and 150 μatm near the poles where the waters with a lot of CO2 sink into the deep oceans, to return some 1,000 years later from the deep and heat up at the equator and increase its pCO2 to 750 μatm. The 150 μatm and 750 μatm of the ocean surface didn’t change much over time, as long as there is ice near the poles and the same maximum temperature near the equator.
Both the level in the atmosphere and the output increased in ratio over time
Te(a-d) = 900 PgC / 40 PgC/year = 22.5 years
Tau(a-d) = (900 – 628) PgC / 2 PgC/year = 136 years
The 2 PgC/year is not directly measured, it is the remaining gap in the net sink rate.
The seasonal differences between ocean surface and atmosphere remained about the same, as the average pCO2 of the ocean surface closely followed the increase of pCO2 in the atmosphere. The huge exchanges between ocean surface and atmosphere are caused by the seasonal temperature amplitude. As far as I know, that didn’t increase over time.
Te(a-s) = 900 PgC / 60 PgC/year = 15 years
Tau(a-s) = (900 – 628) PgC / 0.5 PgC/year = 544 years
The 0.5 PgC/year is directly measured as increase of DIC in the ocean surface
Then the biosphere. The exchange rate expanded from 100 to 120 PgC/year and the net removal rate from zero to 2.5 PgC/year (observed via the O2 balance).
Te(a-g) = 900 PgC / 120 PgC/year = 7.5 years
Tau(a-g) = (900 – 628) PgC / 2.5 PgC/year = 106 years
Overall Te and Tau:
Te(c) = 900 PgC / 220 PgC/year = 4.1 years
Tau(c) = (900 – 628) PgC / 5 PgC/year = 54.4 years.
“Barring an apocalypse eliminating human life, the expanding biosphere may never end”
Based on what happened over glacial and interglacial periods, the total biosphere expanded and did shrink in ratio to the CO2 level in the atmosphere. But that was at a “speed” of 0.02 ppmv/year. There is no reason at all that with a sudden drop in CO2 from 900 PgC back to 628 PgC the whole biosphere will shrink with 25% per year. It will slowly shrink back to the level of around 1750 with a Tau of some 50 years.
“No process will remove all the annual emissions as long as emissions increase annually whether that be from industrial or biomass expansion.”
That is not said or implied by anybody. What is said by the two Dave’s and me is that the both the biomass as the oceans are removing more CO2 than they add to the atmosphere. That is observed both in the biosphere (by the O2 balance) as in the ocean surface (by measuring DIC) and estimated for the deep oceans as difference for the total sinks and confirmed by tracers.
Even if all these cycles doubled, thus halving Te, that doesn’t affect Tau at all…
“It will slowly shrink back to the level of around 1750 with a Tau of some 50 years.”
That is for the overall Tau. The real Tau for the biosphere is:
“It will slowly shrink back to the level of around 1750 with a Tau of some 106 years.”
As that is the real speed of expanding/shrinking of the biosphere…
David,
It also disgusts me to see you insult (postmortem) an intellectual giant like Murry Salby. That’s when I knew you were nothing but a leftist hack. Here is Dr. Salby’s response to Macquarie University:
https://mlsxmq.wixsite.com/salby-macquarie/page-1f
Salby’s only crime was to tell the truth, just like Dr. Ed. They’ve gone against conventional wisdom. Conventional wisdom is usually wrong. How many classrooms still use Murry Salby’s text? Modern climate science is anti-science, anti-truth. It is an instrument of the left.
David Andrews
July 14, 2025 at 3:02 pm
“The method for computing net global updake doesn’t limit what natural emissions are doing.”
No, but it’s convenient to ignore them with Magic Math. If natural aborption and natural emissions both increase, net global uptake will only be positive if emissions exceed absorptions. That is a tautology. The question is how much of the increase is due to either FF or some increase in natural. You assume, or at least your Magic Math assumes, all the increase is FF.
Jim,
It is. It is a mathematical construct built to obtain a desired outcome without a semblance of reasoning or basis.