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.
Jim, indeed it is a matter of model…
I was looking at Ed’s model in figure 3 and that is the “classic” model of a container where all fluxes go one-way into the container, increase the level in the container and the level in the container determines the outflow. When outputs equal inputs the level remains the same.
That is the classic “lake/bath tube” model.
The most used formula for the residence time is:
Te = mass / output
For the current atmosphere:
Te = 890 PgC / 215 PgC/year = 4.1 years.
Everybody (including the IPCC) agrees on a Te of around 4 years.
The formula for the adjustment time is:
Tau = disturbance / effect
Where Tau is the time needed to reduce the disturbance to 1/e (~37%) of the initial disturbance.
That formula only is true, independent of the time period over which is measured, if the effect is directly proportional to the disturbance. That is the case for both the net uptake in oceans and vegetation.
Where the disturbance can be a one shot extra CO2 or a continuous increasing source of extra CO2, that doesn’t matter. Tau only depends of the distance of a process to the (dynamic) equilibrium of that process without disturbance.
For the “classic” one-way model, Tau is equal to Te and never can exceed Te. That is what Dr. Ed used.
If there is a cycle at work, which recycles CO2 from the outputs back to the inputs, completely independent of the level in the container, the situation is completely different.
That is the “fountain” model, where lots of water are cycling over the fountain, completely independent to the level in the basin and opening a small supply valve determines the water level in the basin.
The real world is far more like the fountain than the lake: 95% of all CO2 is just cycling in and out, largely independent of the CO2 level in the atmosphere. Only 5% is directly affected by the CO2 pressure difference between atmosphere and ocean surface waters or plant alveoles water.
How much is cycling is only of interest for the residence time Te, but doesn’t affect Tau at all, as that only depends of the net outflow into the other reservoirs and the difference in pCO2 between the reservoirs.
In the case of the “fountain” model, Tau and Te are completely independent of each other…
My colleagues and I are working on a clear overview of the differences between Te and Tau and the results for the different fluxes, including on isotopic decays and the IPCC’s Bern model.
Meanwhile, you can download the sheets that I have made for a similar discussion at a Clintel workshop in Athens last September, where things were worked out already:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/on_the_co2_residence_time.ppsx
——-
Then a few short reactions:
– One can split the Feely equation, but the difference is that the net transfer between atmosphere and oceans can be calculated from observations, while the individual in- and outfluxes are rather estimates with large error margins.
– The same for the transfer between atmosphere and vegetation: individual CO2 fluxes are very hard to obtain, but the overall net transfer is easily calculated from the O2 mass balance.
– The difference between uptake by the ocean surface and the deep oceans…
That is where the IPCC goes wrong: the Bern model assumes an uniform ocean surface at average 7 μatm below the pCO2 of the atmosphere, following the atmospheric increase very rapidly (half time less than a year).
That is true for 95% of the ocean surface, except at the main sink places near the poles, where the cold surface waters are at ~ 150 μatm and the atmosphere currently at ~425 μatm. The opposite happens at the upwelling places near the equator: ~750 μatm for water, ~425 μatm in the atmosphere. That is what drives far more CO2 into the deep oceans than in the ocean surface.
Because of the small average difference in pCO2, the large ocean pCO2 changes due to SST changes over the seasons give near the same CO2 fluxes in and out for the ocean surface, mainly in the mid-latitudes.
Further, watch the absolute CO2 transfer calculations that will follow at the end of this discussion…
Sorry, see a “Not Found” error when clicking the reference to the Excel file…
Thus can’t (yet) see what you have exactly done and how to match what you have done…
Please try this link:
http://edberry.com/excel-file/
Ten people have downloaded my file, so far.
The Bern Model assumes half the human CO2 moves out of the atmosphere with an e-time of 4-5 years but half the human CO2 has a very long e-time, many many decades. And, it assumes all the natural CO2 has an e-time of 4-5 years. I ask people if it is possible for a long e-time CO2 to become a short e-time CO2? If not what natural mechanism partitions the long e-time CO2’s and the short e-time CO2’s? And, how does one human CO2 have a different e-time than another human CO2? How can nature tell one human CO2 molecule from another human CO2 molecule? Is there a law of nature we don’t know about? How do you write a differential equation with the Bern Model as the solution?
The Bern model assumes that the different reservoirs get saturated.
That means that the uptake is quite fast, until saturation is reached and then it stops, and another (slower) reservoir must take over.
That is only true for the ocean surface, which is saturated at about 10% of the change of CO2 in the atmosphere.
That is not true for most of vegetation, that increases its growth for 93% of all (C3-type) plants up to 1,000 ppmv and more.
That is absolutely not true for the deep oceans, which are far from saturated. If all human emissions up to now ultimately get into the deep oceans, that would increase its carbon content with 1%. That would lead to 1% increase of CO2 in the atmosphere in equilibrium, or 3 ppmv. That is all.
The Bern model simply is wrong…
BTW, the Bern model and most models and our calculations look at the increase of total CO2, not at “human” CO2 alone. No matter what caused the increase of CO2 in the atmosphere…
Ferdinand,
Dr. Ed uses that simple model to illustrate what pharmaceutical scientists call a one-compartment model with intravenous infusion, dC/dt = Io/V – keC . Io is constant infusion into a constant volume V. The constant, ke, represents the “elimination” rate constant. The sign is negative, because at equilibrium, Io/V = keC representing the situation where inflow equals outflow at the constant level C. Obviously, it doesn’t apply to the multiple compartment Earth, but it illustrates the physical first-order process that governs most mass transport processes occurring in nature. Rearranging Io/V = keC gives 1/ke = CV/Io which is analogous to Te = mass/Io = mass/inflow = mass/outflow. So far so good.
Here is where you lose me. I understand disturbance can be a one-time injection or a continuous input that may or may not be constant. Tau is defined as time to reduce the disturbance to 1/e. What is e? Also, what is the “effect” that is required to be proportional to the disturbance? Finally, what are the equations that show how Tau only depends on the “distance of a process to the (dynamic) equilibrium of that process without disturbance.” I don’t understand what distance means. I interpret dynamic equilibrium as the same situation I described in my two-reservoir diffusion model where the flux is equal, but not zero, on both sides.
Dr. Ed’s simple model uses the equivalent of ke = 1/Te for explaining the concepts involved (at least I presume he does). But the full blown Berry Model uses around six rate constants to demonstrate why, using IPCC’s own estimates, H1 is false.
Using lake or fountain analogies is fine for people to get a feel for what you’re doing, I need more. What are the underlying equations? I completely reject the 95% cycling fountain model, simply because raising the water level should affect the rate of circulation. That doesn’t happen with the fountain model unless you install a feedback mechanism that adjusts the circulation to maintain the level. That is what nature is doing automatically by increasing mass transfer rates in response to the increase in concentration gradients (disturbance).
I wish you well on your progress toward a clear overview of the differences between Te and Tau.
My responses to your short reactions in same order: 1) Of course. 2) Yes, but using Berry-type models, one can draw conclusion about the individual fluxes. 3) You should be rewarded, if not applauded, for working on surface and deep ocean interactions.
Meanwhile, I will review Tau model literature.
The difference: the out that is recycled has zero influence on the water level in the lake.
The water that that gets the overflow of the basin is removed out of the lake, thus influences the water level…
Sorry, but that is not what Figure 3 shows. Figure 3 shows all fluxes in one direction: from ins to container to outs.
Neither is the calculation of the real adjustment time based on Figure 3, but on the net removal of CO2 out of the atmosphere, which is around 50 years. The residence time of about 4 years is based on the sum of all outflows together, not the net outflow…
Jim,
With all respect, I think a program to add up all the natural emissions AND THE NATURAL ABSORPTIONS OF ALL CARBON TYPES is hopeless. The indirect measurement of absorption – emissions, deduced from industrial emissions – atmospheric accumulation and appropriately called “net global uptake”, is the best that we can hope to do. The data on that is solid; see the previously referenced Ballantyne et al. Nature article and the tight constraints on this quantity, especially when integrated over 50 years.
I am puzzled by your statement “We also agree on where the extra carbon is coming from [ fossil fuel reserves]. The only disagreement is on how much of the observed increase in atmospheric CO2 is caused by industrial carbon or an additional natural component.” If we agree that moving carbon previously sequestered in oil/gas/coal reserves into the atmosphere, and from there into ocean and biomass stocks, (i.e. into the fast cycle), aren’t we done? Apparently, you think that the industrial carbon content of the present atmosphere is relevant, even though you understand that equilibrium isofluxes (essentially mixing) erases past differences without effecting carbon levels. Yes, I am puzzled.
Dear Uncle Bert,
You said “the fluxes between ocean surface and atmosphere are measured”
Your PMel reference cites Feely et al which states 940,000 measurements of surface water pCO2. This is pCO2 not CO2. And they are not measurements. pCO2 is estimated/calculated for the entire ocean using actual CO2 measurements from land based stations. This is politicised junk science, just what I expect from you. A wild goose chase.
Then you get carried away with the DIC. The only scientists that I see researching DIC are those pushing climate alarmism. What’s happening in the DIC is microscopic compared to what’s happening with the dissolution of CO2 in the ocean waters. Most CO2 in the ocean is CO2Aq. Your discussion on the DIC is nothing more than a side show waffle.
The hydration equilibrium constant for carbonic acid at 25 °C is Kh = [H2CO3]/[CO2] = 1.70 × 10−3. Hence, the majority of the carbon dioxide is not converted into carbonic acid, but remains as CO2 molecules. In the absence of a catalyst, the equilibrium is reached quite slowly.
https://www.sciencedirect.com/topics/chemistry/carbonic-acid
R.C. Ropp, in Encyclopedia of the Alkaline Earth Compounds, 2013
5.1.1 Carbonic Acid
Indeed there are about 2,000 CO2 molecules for each H2CO3 (carbonic acid molecule) in water
“Aquatic Chemistry Concepts” by James F. Pankow.
In reality, the conversions between the three forms of Dissolved Inorganic Carbon, CO2 or H2CO3, HCO3- and CO3– are almost instantaneous (less than one minute)
Veyres, C., Maurin, J. Cl. Revisiting the carbon cycle International Journal of Earth Sciences Vol. x, No. x, 2021, pp. x-x. doi: 10.11648/j.xxx.xxxxxxxx.xx.
When I pop the top off my 20 year old Dom Pérignon I don’t have to wait for an eternity for the CO2 to fight it’s way out of the DIC, the CO2Aq bubbles out instantly.
Your comments are specious waffle.
David,
People have been working on mathematically accounting for all the carbon for a long time. Skrable and Berry are not the first. Simple math is not “the best that we can hope to do.” As I wrote before, simple math is ambiguous.
Here are a couple papers in my “file” on carbon dioxide models. “A box diffusion model to study the carbon dioxide exchange in nature,” H Oeschger et al., 1974. Even earlier, “Changes in the Carbon Dioxide Content of the Atmosphere and Sea due to Fossil Fuel Combustion,” Bolin and Eriksson, 1959.
“…aren’t we done?” We can quit anytime as long as you admit defeat! (Just kidding). Communication is a miracle, one of my mentors used to say.
This whole discussion is about how much of the increase in CO2 since the beginning of the industrial era has been CAUSED by industrial emissions. Some, like you I gather, think all 33% was caused by them. Dr. Ed is claiming only 8% percent. I have tried to explain how the growth in natural emissions since 1750 may account for the other 25% of the rise by increases in ocean out gassing and extra decomposing vegetation due to population growth. In other words, in 1750, I estimate natural emission recycling was on the order of 136 PgC/year. Today it could be 204. Let me know if you are still puzzled.
Jim,
The simple math shows unambiguously that natural processes remove more carbon from the atmosphere than they add. Your calculation showed that in the process of LOWERING total carbon in the atmosphere, natural process can add “natural carbon” at the expense of “industrial carbon”. So what? Both are greenhouse gases.
Now you say “extra decomposing vegetation” is a source of atmospheric carbon growth. You must be a disciple of that crazy Greek hydrologist, Demetris Koutsoyiannis, who says the same thing. Do you think trees make carbon? No, they do not. They remove it from the atmosphere when they are growing and return it to the atmosphere when they die and decay. The little formula defining “net global uptake” incorporates carbon conservation. You need to ask yourself in all the instances where you identify possible emitters, what the source of the carbon they emitted was. That too enforces carbon conservation. If you discipline yourself to do that you will be a step ahead of Ed and Demetris.
David,
“So what, both are greenhouse gases” is not the topic of this discussion, which is H1. Whether or not increasing CO2 causes global warming would be H2.
I haven’t seen the work of Koutsoyiannis, but I’m going to add him to my todo list, because I need to be able to document reality to support my speculations. Thank you for that. Compared to 1750, today there are 8 times more people in the world cutting down trees and plowing fields, which may prematurely release CO2 into the air. Thus adding more CO2 than would otherwise be if nothing had changed since 1750.
Asking myself what the source of the carbon was from all of the emitters is the discipline of carbon cycle modelers. I’m way behind Ed and others and trying to catch up. I encourage you to get in the game. It’s hard, but fun.
Dave A, that’s all very obviously correct, but who is “DMA”?
Jim,
Please read some peer-reviewed science too. I am sorry I put you on to Kousoyiannis.
Dave B,
I do not know who DMA is; just somebody who follows Ed. My middel initial is E.
The CO2 Coalition’s cavalier attitude towards the rest of climate science bothers me. Celebrating atmospheric CO2 as plant food and ignoring its warming effects bothers me. I do not think that our present atmosphere is necessarily “optimal” for humans, but change can be very costly even if we are not facing an “existential” threat. I am more conversant on the carbon cycle issues than on radiative forcing, etc., but I see flaws in Happer’s saturation argument. “Extreme weather” problems, especially involving the increased water content of tropical storms, seem to me very likely real and linked to CO2. The poor quality of the denier arguments that I have focussed on, ever since stumbling on the Berry/Harde/Salby confusion between deltaC14 and concentration, makes me very skeptical of other skeptics and inclined to believe the consensus. After all, predictions made 25 years ago turned out to be quite accurate. (Predictions were on the high side for awhile, with the warming perhaps masked by sulphur aerosols, but not any longer.)
Brendan, I have no idea who Uncle Bert is, but what part of the formula:
F = k•s•DeltapCO2
don’t you understand?
From Feely: http://www.pmel.noaa.gov/pubs/outstand/feel2331/maps.shtm
From the next section:
“This map yields an annual oceanic uptake flux for CO2 of 2.2 ± 0.4 PgC/yr.”
And dissolved CO2 + H2CO3 together are only 1% in seawater, 90% are bicarbonates and 9% are carbonates. High time to refresh your chemistry. Learn here about the Bjerrum plot:
https://en.wikipedia.org/wiki/Bjerrum_plot
My thoughts on Tau vs Te after considering comments provided by Ferdinand Engelbeen. Tau equals disturbance / result (outflow) which means, when applied to ocean atmosphere fluxes, Outflow = [pCO2(atm) – pCO2(ocean)] / Tau. Generalizing this formula to carbon distribution between the atmosphere and its adjoining reservoirs requires a huge assumption which I believe is untenable. The assumption used by some researchers seems to be that the disturbance is proportional to the level difference, or pressure difference, between the existing level or pressure and what that level or pressure was in pre-industrial times. In other words, pCO2(now) – p(CO2)then. Roy Spencer writes, “[My] model assumes an anthropogenic CO2 source, and a constant yearly CO2 sink rate proportional to the excess of CO2 over a baseline equilibrium value determined by the Mauna Loa data.” https://www.opastpublishers.com/open-access-articles/enso-impact-on-the-declining-co2-sink-rate.pdf
Dr Spencer obtains a best fit to the Mauna Loa data using a “net” sink rate, 0.02/year, of the difference in the CO2 concentration in a given year compared to a fitted 1750 “baseline” value. That “net” amount is actually the relatively small difference between yearly input and outputs that are two orders of magnitude greater than their difference. The flaw in any model using a “baseline” is that the atmosphere does not remember what its “baseline” value was. It is extremely likely that pCO2(atm) and pCO2(ocean) may never return to their pre-industrial values. The only levels nature remembers are the ones they experience in the present time and places. There is no going back to the way things were in 1750 or 1850 or any other year in the distant past.
How does this affect calculations of Tau? If new baseline equilibrium levels were to be estimated today based on the current magnitude of inflows and outflows, assuming no further perturbations from fossil fuel emissions, then two possible situations remain. Either the baseline remains unchanged from some pre-industrial date, or a new baseline results at greater levels of inflows and outflows. I don’t think lesser levels are realistic given the growth in world population. In the former case, Tau would remain about the same as Dr Spencer predicts at 50 years, i.e. (420 – 280) ppm * 0.02/year = 2.8 ppm/year. But what if the baseline equilibrium is greater than 280? For example, a baseline of 320 ppm makes Tau = 1/0.028 or about 36 years. Therefore, Tau is overestimated if baseline equilibrium conditions have evolved due to increasing natural flows.
It makes sense that estimations of Tau vary widely among researchers. No one really knows what the current equilibrium level is or will be.
More specious waffle from Uncle Bert.
Ferdinand Engelbeen reminds me of the singer Engelbert Humperdinck who I always called Uncle Bert for short. I always shorten long names.
Uncle Bert previously said CO2 over the oceans was measured now he agrees that it is calculated and based on CO2 measurements over land.
And he’s dived back into the DIC for another wild goose chase.
Jim Silverly
You said:
“It is extremely likely that pCO2(atm) and pCO2(ocean) may never return to their pre-industrial values. The only levels nature remembers are the ones they experience in the present time and places. There is no going back to the way things were in 1750 or 1850 or any other year in the distant past.”
CO2 rose to 450ppm twice during the last 200 years from instrumental measurements accurate to 1%-3%
See the chart at https://www.researchgate.net/publication/366823612_Lunar_Forced_Mauna_Loa_and_Atlantic_CO2_Variability/figures?lo=1
which is Figure 2 from:
Yndestad Harald, 2022b: Lunar Forced Mauna Loa and Atlantic CO2 Variability; Science of Climate Change, Vol. 2.3 (2022) pp. 258-274; https://doi.org/10.53234/scc202212/13 ; https://scienceofclimatechange.org/wp-content/uploads/Yndestad-2022-Lunar-Forced-CO2-Variability.pdf
CO2 also rose to 400ppm 12,000 years ago based on Stomata proxy measurements.
Steinthorsdottir 2013
The ice core proxy is very monotonic and does not show all the up and down extremes in CO2 measurements.
I just finished reading Koutsoyiannis, Demetris & Johnson, Mark. (2024). The superiority of refined reservoir routing (RRR) in modelling atmospheric carbon dioxide. https://tinyurl.com/bdd4fhyb
Their equations in Annex A. explain in detail the difference between Tau and Te; they support my view that a sink rate proportional to [pCO2(now) – p(CO2)then], although empirically based, “may be a result of the coincidence of increasing human and natural CO2 emissions. The latter, caused by the biosphere expansion, are totally neglected in this relationship.”
My thanks to David Andrews for introducing me to this work. It seems to support Dr. Ed’s multi-compartment analysis and the conclusion that H1 is false.
Happy Fourth of July, all.
Brendan, a calculated flow, based on quite good observations is as valid as direct observations. These observations were over all oceans: some 960.000 to be exact.
And all you have demonstrated is your complete lack of understanding chemical equations.
And please, shouting at someone only shows that you have no real arguments.
Jim,
Indeed here we are at the crux of the matter. Thanks for your insight!
You have noticed the right difference between Te, used by several skeptics and Tau as used by several other skeptics and most “mainstream” scientists, including the IPCC.
Now the main remaining point is what happened with the equilibrium in current times.
From the past (ice cores) we know that the equilibrium changed with Antarctic temperatures at about 8 ppmv/°C or for global temperatures somewhere between 15-20 ppmv/°C. CO2 are direct measurements, be it averaged over 560 years (Dome C) and 600 years (Vostok), while T is derived from dD and D18O and mainly reflect the temperature where the snow was formed, thus near Antarctica.
https://www.ferdinand-engelbeen.be/klimaat/klim_img/vostok_t_co2.png
The discrepancies with the trend are largely caused by the (very) long lags of CO2 changes after T changes, especially during cooling periods, for which is not compensated.
Higher temperatures on land in general increase vegetation (more land available), that is a negative feedback for CO2.
For recent temperatures, we have the formula of Takahashi to calculate the change of CO2 as result of SST changes.
That gives not more than 13 ppmv since the LIA and 3 ppmv since 1958. The real increase since 1958 is over 100 ppmv together with 170 ppmv human emissions over the same period…
Then the possible increase of the equilibrium over the past decades.
That is completely true for about 90% of the sea surface: the pCO2 of the ocean surface follows very closely the pCO2 of the atmosphere. That means that the ΔpCO2 remains about the same (currently at ~7 μatm) and, together with chemical restrictions, that is reflected in the small increase of DIC at about 10% of the change in the atmosphere. For the current increase of about 5 PgC/year in the atmosphere, most of the ocean surface absorbs ~0.5 PgC/year.
That is not what happens at the extremes of the oceans: at some 5% of the ocean surface, the waters are sinking directly into the deep, due increased density from to low temperatures and salinity. That is at the edge of the sea ice, where SST is slightly negative. pCO2 there reaches ~150 μatm, far below the atmosphere. Moreover, that hardly changes over time, as long as there is sea ice. The same at the other 5% of the ocean surface, where deep ocean waters are upwelling, the temperature hardly changes (thanks to clouds!), thus the pCO2 remains high at around 750 μatm. That means that the equilibrium pCO2 between atmosphere and deep oceans hardly changed over the past few millions of years…
The difference between ocean surface and deep oceans is demonstrated by the difference in CO2 uptake: with only about 5% of the sea surface, the deep oceans absorb some 2 PgC/year, 90% of the surface absorbs only 0.5 PgC/year…
See: https://www.ferdinand-engelbeen.be/klimaat/klim_img/bern_balance.png
Thus, besides the straight forward linear uptake by vegetation, the ocean uptake also remains linear with the “old” equilibrium…
Jim,
Further, the rather stable equilibrium pCO2 of the oceans (and vegetation) is demonstrated by the small changes in Tau over the period 1958-current.
The total emissions are known, these are the cause of the CO2 increase in the atmosphere, but play no role in the pCO2 difference between atmosphere and the rest of nature.
The only assumption is that the base equilibrium since 1850 changed with SST with the formula of Takahashi. If one disagrees with that base, one can start with SST and CO2 in 1958, which makes hardly any difference:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
Where [A] is the sum of all FF emissions (without land use changes), the observed increase in the atmosphere, the calculated influence of SST on the pCO2 of the oceans and the resulting ΔpCO2 between atmosphere and oceans.
[B] is the observed net sink rate and
[C] is the calculated Tau, based on the polynomial through the net sink rate, to avoid the influence of short time SST variations.
Jim,
In recent discussions with Koutsoyiannis (last September during a workshop in Athens for Clintel) he used temperature anomaly as the base for his calculations of the CO2 increase/year. Temperature(anomaly) is of a different order than the CO2 increase/year, but has the same variability as temperature change/year, with a pi/2 shift. T(anomaly) has a slope, while T(change)/year has not:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/wft_T_dT_dCO2_trends.jpg
WfT has the emissions not in their database, but the slope is about twice the slope of the CO2 increase in the atmosphere…
Not the first to use T(anomaly) as base and use its slope to calculate the increase in the atmosphere, while ignoring the twice as fast increasing slope of human emissions…
The net effect of his calculations violate the carbon mass balance, but can be corrected by increasing the natural sinks:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/demetris_1b.png
The increase in the atmosphere may be between 100% natural and 100% human. In the latter case, the net natural contribution is the net sink rate in nature. In the former case, the total sinks remove every gram of what humans have added (as mass, not the only the original FF molecules) out of the atmosphere. Quite remarkable.
In that case, net natural sinks are twice the net natural addition in the atmosphere. So how can nature be the cause of the atmospheric increase?
Then, have a look at table 4:
He calculates the residence time from both the change in temperature over the seasons, and from the year by year variability: both between 3 and 4 years. Except that the seasonal change of CO2 is negative for temperature and the year by year change positive… That makes no difference for the residence time, but makes a huge difference for the adjustment time…
Then in equations [66] and [67] he calculates the remaining human CO2 in the atmosphere. He gets around 6%, Harde found about 10%, based on the 13C/12C ratio. While Harde is right, that only shows the remaining FF molecules in the atmosphere, not what the IPCC says as “airborne fraction” which is about the remaining total mass of CO2, caused by FF emissions (the difference being exchanged with CO2 molecules from other reservoirs).
And how can he explain that only 1.5 to 5% of FF in the supply 1960-2020 causes over 10% FF in the atmosphere in the same period with his one-way supply?
Below equation 48 he writes:
“Proposition 1. The IRF equals the probability density function of the residence time for the case
that the input is an impulse function.
Corollary 1. The mean and median response time equal the mean and median residence time for
the case that the input is an impulse function”
Which is only true for a one-way “classic” input-container-output (“lake/bad tube”) model.
Completely at odds with the real world, where 95% of all CO2 fluxes are independent of the pCO2 in the atmosphere…
Dear Ferdinand,
Thank you very much for your many explanations of your hypothesis that says human CO2 caused all or most of the CO2 increase.
Thank you also for your response to my request to show your calculations in my suggested Excel format. My two takeaways are:
(a) that you acknowledge that this method of doing a time-step calculation is valid (and not an Invalid “model” as Dave Burton has called it) and
(b) Your numbers indicate that our major difference is in the Te that we insert for our calculation.
Of your many links, I recommend this one as your best summary of your argument in 42 slides:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/on_the_co2_residence_time.ppsx
With all your work, you deserve a thorough reply to your argument, so I will try to do that in my next comment and in an update in my draft post above. I will show that your arguments, as summarized in your 42 slides — that conclude the true Te equals a tau of 50 years — will not fly.
After that, I will get back to the comments of David Andrews and others. But since your work is the focus of my post, you deserve my priority to recieve my best repies to your comments.
Ed and Jim,
The net effects of the differences between Te and Tau demonstrated for the past 175 years…
For the current atmosphere:
Dynamic equilibrium: for the current average SST, the equilibrium pCO2 between ocean surface and atmosphere would be around 295 ppmv. Can be calculated with the formula of Takahashi [1], if an equilibrium of the past is known. Some 13 ppmv since the LIA (worse case for the largest T increase reconstruction). Some 10 ppmv since 1850 and a few ppmv since 1958, if one doesn’t trust ice cores…
Situation in 1850 (IPCC, 2013):
628 PgC in the atmosphere
Sum of outputs: 168,4 PgC/year.
Net output: 0 PgC/year.
Te = 628 / 168.4 = 3.7 years
Tau = N/A
Situation in 1960:
673 PgC in the atmosphere
Sum of outputs: ~180 PgC/year [2]
Net output: 1.0 PgC/year
Te = 673 / 180 = 3.7 years
Tau = (673 – 628) / 1.0 = 45 years
Situation in 2020:
880 PgC in the atmosphere
Sum of outputs: ~236 PgC/year [2]
Net output: 4.7 PgC/year
Te = 880 / 236 = 3.7 years
Tau = (880 – 628) / 4.7 = 53 years
Looking for the zero net output (that is the equilibrium):
CO2(eq) = CO2(2020) – [CO2(2020) – CO2(1960)] / [Fnet(2020) – Fnet(1960)] * Fnet(2020)
CO2(eq) = 880 – [880 – 673] / (4.7 – 1.0) * 4.7 = 617 PgC
or about 290 ppmv. Not far from the situation in 1850. Not bad for a rough calculation.
The same calculations were done by Peter Dietze (1997!), Lindzen, Spencer and myself years ago…
My colleague, David Burton, used all recent figures to calculate the zero-net-sink equilibrium CO2 level at:
https://sealevel.info/Global_Carbon_Budget_2023v1.1_with_removal_rate_plot2.png
Then what is the real CO2 outflow caused by the absolute CO2 pressure in the atmosphere?
Also easy to calculate even with only two observations at 1960 and 2020:
F(abs) = 880 / (880 – 673) * (4.7 – 1.0) = 15.7 PgC/year.
Some 16 PgC/year of the CO2 outputs from the atmosphere into oceans and vegetation together is caused by the absolute CO2 pressure in the atmosphere. The rest of the over 200 PgC/year outputs are completely independent of the CO2 level in the atmosphere…
[1] (pCO2)seawater @ Tnew = (pCO2)seawater @ Told x EXP[0.0423 x (Tnew – Told)]
http://www.sciencedirect.com/science/article/pii/S0967064502000036
[2] Assuming that the outflows increase with the increase in the atmospheric, but also the inflows, thus only speeding up the cycles.
According to the IPCC, that is true for the ocean surface (but haven’t seen any explanation why that should be), but the expansion of the biosphere, and thus the expansion of the short seasonal bio-cycle, is a lot slower than the increase in the atmosphere, about half of it…
Thanks Ed,
Only one remark:
Te and Tau are completely different things:
Te is how long a single CO2 molecule (of whatever origin) resides in the atmosphere, before being completely removed (as mass) or exchanged with a CO2 molecule of another reservoir (no change in mass).
Tau is how long it takes to reduce a (one-shot or continuous) extra injection of CO2 as mass (of whatever origin) out of the atmosphere, back to (dynamic) equilibrium.
Tau is <= Te only if all in- and outflows are unidirectional (that is the "lake / batch tube" model)
Tau is completely independent of Te if cycles are involved that bring back CO2 from the outputs to the inputs (that is the "fountain" model).
I am working further on the spreadsheet to put it in about the same form as you have made…
Brendan,
I have had years of discussions with the late Ernst Beck about the historical measurements, until his untimely death in 2010.
The historical measurement methods were not too bad (+/- 9 ppmv), but where was measured was a mess. Midst of towns, forests,… completely unsuitable to know the real “background” CO2 levels of that time.
The late Ernst Beck lumped them all together: the good, the bad and the ugly. The real range of measurements was from near the bottom of the graph to (far) over the ceiling.
When one did choose only the measurements over the oceans or at the coast, with wind from the seaside, all these measurements are on or below the ice core measurements:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/beck_1925_1955.jpg
With one exception: at a slope of the Alps where was measured in the morning and extreme CO2 values were found.
To show the problem: there is a modern station at Linden/Giessen (Mid-West Germany) at a few km of the historical station that makes the largest influence on the CO2 “peak” around 1940.
Here for a few days under inversion, compared to the same (raw) data of Barrow, Mauna Loa and the South Pole:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_background.png
Stomata data are local proxies which are calibrated to ice core values. If the average differs from the ice core values over the resolution of the ice core, then the stomata data must be recalibrated. Not reverse…
See further my comment of Beck’s latest, posthumous published work:
https://scienceofclimatechange.org/ferdinand-engelbeen-about-historical-co2-levels-discussion-of-direct-measurements/
Ferdinand,
I appreciate your kind remarks and responses to my suppositions.
At JULY 4, 2025 AT 1:42 AM, with regard to 90% of the sea surface you wrote, “ΔpCO2 remains about the same (currently at ~7 μatm)” and, for the other 10%, “equilibrium pCO2 between atmosphere and deep oceans hardly changed over the past few millions of years.” With respect, those are arguments by assertion. The obvious rebuttal is the fact that the surface ocean contains about 10% more carbon than it did pre-industrial. Somewhere recently I read where terrestrial mass is also increased, in other words, more vegetation to decompose. In the words of Koutsoyiannis and Johnson, the result is biosphere expansion. Therefore the “disturbance” decreases with time, but the amounts sourced and sinked increase yearly due to the always increasing driving force of extra carbon in the air. You could call my comments just assertion also, but I worked on a spreadsheet that I copied from Dr Spencer modified by changing Tau to Te and adding in realistic sources and sinks. It accomplishes the same results as models based on Berry, Skrable, Bolin & Erickson, and many others. Those models work, because the flow rates in nature stay relatively constant while the reservoir concentrations evolve. There is no need to explain why Tau wanders all over the place.
JULY 4, 2025 AT 2:54 AM you wrote, “Further, the rather stable equilibrium pCO2 of the oceans (and vegetation) is demonstrated by the small changes in Tau over the period 1958-current.” What stable equilibrium? The anomalous disturbance that ebbs and flows all the time everywhere? I propose small changes in Tau are an artifact of your flawed model.
“The total emissions are known, these are the cause of the CO2 increase in the atmosphere, but play no role in the pCO2 difference between atmosphere and the rest of nature.” I assume by this you mean the remaining industrial emissions playing a negligible role? This makes no sense. The addition of industrial carbon and possible incremental increases in natural emissions CREATE the pCO2 difference that causes nature to return to a new equilibrium. Perhaps you could summarize the equations that produce graphs A, B, and C. I’m working on a way to demonstrate how the simple math you and David Andrews rely on can give ambiguous results based on somewhat arbitrary choices of variables.
Ferdinand,
Apparently, Koutsoyiannis’ Research Gate article is not the one you referenced above. I’ll try to locate it and explain why you may have incorrectly concluded, “The net effect of his calculations violate the carbon mass balance….” Different models can account for the same mass balance data. What is important is using equations that employ the correct physical processes involved.
DEAR Dr. Ed
The carbon dioxide molecule excited by the IR photon loses its charge in max. 1 secundum and is capable of absorption again. This is a fact! So what are the prominent representatives of climate science arguing about?
Csaba Huszar
If the total emissions is the sum of each of the individual emissions: Et= E1+E2+E3…., and Quantity (Q) in the atmosphere is what is there now plus the total emissions minus the total sinks. It seems very reasonable to say that sink rate for the total would match the rate of sink for each individual emission source.
The crucial point of this discussion is: If we reduce our emissions will it cause the growth in Q to stop?
Dr. Ed’s approach says NO, only slow slightly. The opposition approach says YES. Both sides here seem to agree that growing CO2 concentration is not a problem but if Dr. Ed’s work is correct and it would certainly be a huge hurtle for those that espouse Net Zero.
The irony is that all this fuss about burning fossil fuels (CO2 increase) is a huge mistake. The only greenhouse gas that has a significant effect on climate is water vapor. Global WV is measured by NASA/RSS and the trend has been increasing about 1.4% per decade which is substantially faster than possible from just temperature increase of the planet (net effect of all forcings and feedbacks). WV has increased more than 3 molecules (more than 5 at ground level) for each molecule of CO2 increase. The WV increase is substantially more than possible from just planet warming (more than twice as fast). The WV increase can account for all of climate change attributable to humanity with no significant net contribution from CO2. https://watervaporandwarming.blogspot.com
The atmospheric process that partially explains why CO2 increase has no significant effect on climate is documented at Theory of Redirected Energy: https://energyredirect3.blogspot.com
Ferdinand,
I looked briefly at the parts of https://www.mdpi.com/2073-4441/16/17/2402 that relate to your critique of Koutsoyiannis’ model.
“…he used temperature anomaly as the base for his calculations of the CO2 increase/year.”
Including a temperature factor in one’s analysis makes sense, although I suspect he doesn’t use that to conclude all of the rise in CO2 is due to temperature. That would be the equivalent of saying nature causes all of the rise.
A “twice as fast increasing slope of human emissions…” compared to the temperature anomaly slope is arguing causation by correlation.
“So how can nature be the cause of the atmospheric increase?”
What my primitive model (converting Roy Spencer’s Tau spreadsheet to Te version) indicates is that natural emissions since 1750 have been increasing logarithmically from about 70 ppm in that last pre-industrial century to about 90 ppm today. Almost all of that is sinked each year. However, the net gradually increases each year. The explanation is, as we have discussed, an expanding biosphere. The oceans contain more CO2 and they are warmer. People have prematurely cut down trees and them decomposing and being burned creates extra emissions that otherwise wouldn’t have been without human’s influence.
Skipping down to your last point, a Proposition 1 and Corollary 1 being “only true for a one-way ‘classic’ input-container-output (‘lake/bad tube’) model [and] completely at odds with the real world, where 95% of all CO2 fluxes are independent of the pCO2 in the atmosphere…”
Koutsoyiannis’ model seems to be along the same lines as the multi-component models of Dr. Ed and others like that. Again, they are using rate constants applicable to real world flows/fluxes in each direction. They account for the amounts and concentration of CO2 in each reservoir. There is no need to deal with an adjustment time, because no one knows what the future holds as far an unsure of changes in industrial emissions and probably natural sources too.
“Large parts of the carbon cycle are just cycling in and out of the atmosphere, largely independent of the CO2 level in the atmosphere.”
This is the Bern Model. This makes no sense. The carbon cycle is CO2. Nature cannot differentiate CO2 molecules. As Dr. Berry described in his first paper, it violates the Equivalence Principle. Te is “e folding time.” Tau is “Bern Time” for a sink that doesn’t exist.
I agree CO2 in and out Sets a balance that varies over the years however for me the argument is CO2 has a diminishing effect on heat as concentration increases. The only method of transferring energy through space is radiation and this decreases on a log base after the first 20ppm. It’s written up by the university of Pensylvania that over 340ppm no measurable heat was found, ergo more CO2 has an insignificant effect on temperature. That being so net zero will have no appreciable effect CO2 is not a problem. I understood from Prof Happer that CO2 has little effect as concentration increases. Perhaps his point is that even if man converts oils or coal any increase is without importance on Global temperatures?
Ed, you keep insisting that we err by ignoring anthropogenic removals of CO2 from the air. But that’s not an error, it just reflects what the data show: that anthropogenic removals are negligible.
Approximately 59 kt (= 0.059 Mt = 0.000059 Gt) of CO2 per year are removed from the atmosphere by Direct Air Capture projects, worldwide. That’s about 0.00015% of anthropogenic emissions. That’s obviously negligible. Those projects are scams.
Approximately 50 Mt (= 0.050 Gt) of CO2 per year is captured and stored by operational CCS facilities, but 99.9% of that is captured at the sources, so it’s really avoided emissions, not removals. But I suppose you could make the case that if estimated emissions are calculated from fossil fuel use then carbon capture at sources should be counted as removals. Still, that’s less than 0.2% of anthropogenic emissions, which is insignificant compared to the error bars.
What else? Cement carbonation?
According to GCB (2024), cement carbonation is estimated to remove about 214 MtC from the atmosphere per year, globally, which is about 0.784 Gt of CO2. (The claimed uncertainty is something like ±20%, but that’s surely optimistic.)
That’s conventionally considered a natural removal process, but you could make a good case for calling it anthropogenic removal. But it’s only about 2% of anthropogenic CO2 emissions, so even that is still much smaller than the error bars on anthropogenic emissions.
What else? Lumber?
Lumber production is roughly 2 billion cubic meters of wood per year, which contains about 2 PgC. That’s equivalent to the carbon in (2 × 3.66419 =) 7.3 Gt CO2. That’s a lot, but it’s carbon which was already removed from the atmosphere by trees (nature). That is, it’s carbon moved from a different “carbon reservoir” (the terrestrial biosphere), not from the atmosphere.
What else? Other agriculture?
Crops remove a great deal of carbon from the air. On a windless, sunny day, a healthy cornfield can almost completely deplete CO2 from the air at ground level by noon! But the nearly all of carbon removed from the air by crops (other than lumber) is soon returned to the air, through decay and digestion.
The bottom line is that anthropogenic CO2 removals from the atmosphere are roughly zero. Or, more precisely, they’re much smaller than the uncertainties in anthropogenic emissions of CO2, so they can be ignored in our calculations.
If you think that’s wrong, then tell me: what other anthropogenic processes do you think remove CO2 from the atmosphere?
Data references:
https://sealevel.info/Global_Carbon_Budget_2024_v1.0_with_ten_yr_avgs2.xlsx
https://www.perplexity.ai/search/globally-how-much-carbon-did-c-sWWftiSbTrqTCQyc8S2sfQ
Stephen,
The Bern model is as bad as Ed’s model, both are completely at odds with reality.
Ed’s model assumes that all CO2 inputs together cause the level in the atmosphere and the level in the atmosphere causes the outputs. That is the “classic” lake/bath tube/container model, where all inputs are unidirectional through the container to the outputs.
Te then is the time that any molecule of CO2 resides in the atmosphere, before being removed out of the atmosphere.
Te = mass / output
Te = ~4 years
In the real atmosphere 95% of all CO2 flows are just cycling between oceans – atmosphere – vegetation in spring/summer and back in fall/winter. These move large amounts of CO2, but remove zero CO2 mass out of the atmosphere, as long as the fluxes from oceans to vegetation and back are equal.
That is the “fountain” model: huge masses of water cycles over the fountain, but the level in the basin only changes when the small supply valve is opened by the maintenance man.
These are not equal anymore: humans add increasing amounts of CO2 directly into the atmosphere, one-way, without appreciable human induced sinks. That adds to the overall level of the atmosphere. The increase in CO2 level pushes more CO2 into oceans and vegetation and reduces the ocean output to the atmosphere.
These amounts are much smaller than what the temperature and sunlight do for the natural fluxes: that is the difference between all huge natural influxes + human influx – (natural + human) outflux. Where one can fight over what the “human outflux” is, but that is completely unimportant.
What is important, is that the net total outflux is smaller than the total influx. The increase in the atmosphere is smaller than the human input, thus the mass balance (and any bookkeeper worth his money) shows that the small increase in the atmosphere is from the human input.
That difference between inputs, outputs and what remains as mass in the atmosphere forms the “adjustment” time, that is the time to bring any extra CO2 (of whatever source) in the atmosphere above the “old” equilibrium (for the current average SST around 295 ppmv) back to 1/e (~37%) of the original extra CO2.
The formula for adjustment time (Tau) for a linear process is:
Tau = disturbance / effect
Where the disturbance = the distance to the equilibrium and effect = the net removal rate of CO2
And is currently around 50 years.
See: https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.png
The Bern model assumes different Tau’s for different reservoirs, which combined gives the right answer at the start, but then assumes saturation of all reservoirs at different levels, which is only true for the ocean surface, not until over 1,000 ppmv for vegetation and non-existing for the deep oceans. That makes that the alarmists speak about “hundreds to thousands of years” to remove any extra CO2 above equilibrium.
Dr. Ed,
Was (and still am) busy with the calculation sheet and did just read your reply to David.
Sorry, but you are getting much too personal, while simply ignoring what David wrote.
Our work was read by a lot of people, including Will Happer and many others, before being published.
The adjustment time of near 50 years is exactly what happens with the extra mass of CO2 in the atmosphere and that was found by Peter Dietze, already in 1997, in a discussion with the inventor of the (faulty) Bern model, Fortunat Joos:
https://www.john-daly.com/carbon.htm
and the discussions with Joos and others:
https://www.john-daly.com/dietze/cmodcalc.htm and
Many others, including known skeptics like Lindzen and Spencer found similar adjustment times.
Your calculations are about the 4 years residence time which only shows how long an individual CO2 molecule “resides” in the atmosphere, before being removed or swapped with a CO2 molecule from another reservoir. In the latter case, that doesn’t remove one gram of CO2 out of the atmosphere, as long as ins and outs are equal. 95% of all CO2 fluxes just swap molecules, 5% is what humans add and only 2.5% is what the fluxes do remove as mass out of the atmosphere…
Jim,
I know of the difficulty of dealing with huge cycles and small one-way additions…
There is indeed one and only one possibility that the natural fluxes are the cause of the increase in the atmosphere: if, and only if, they increased in exact the same ratio as the human emissions.
If that is not the case, then you violate the equivalency principle for any CO2 molecule in the atmosphere.
Human emissions increased a 4-5 fold between 1958 and current. Total flows (natural + human) increased maybe 50% or 1.5 times for the ocean fluxes (for which I didn’t find any explanation) and some 20% in vegetation. Thus the only possibility for a natural caused increase is rejected.
Indeed the biological cycle moves a lot of CO2 in and out and increased a lot, but as said before:
1. It removes first and releases only what was first removed out of the atmosphere, most of it diurnal and seasonally and a little bit over longer periods (mostly 1-3 years and the rest longer).
2. A cycle doesn’t net remove anything, only the difference between ins and outs does change the content of a reservoir.
3. The total biosphere since about 1990 is increasingly removing more CO2 than adding to the atmosphere.
Then all one-direction models like that of Koutsoyiannis and many others, have one point against them: any marker in the inputs never can exceed the ratio in the inputs in the further flows: the containers or the outputs.
Human FF emissions were 1-5% in the inputs 1958-2020, but are over 10% in the atmosphere and over 6% in the ocean surface. One-way model completely rejected.
Further, there is little doubt that the “equilibrium” CO2 level did not change a lot over time. One can shift it somewhat higher or lower, but a range of 30 to 60 years for the adjustment time still is an order of magnitude higher than de residence time of 4 years. Even the “thinned” levels of 14C (14-20 years adjustment time) or of the 13C/12C ratio adjustment time of around 15 years is way higher than the residence time.
Last but not least, with a residence time of 4 years, the table in Ed’s spreadsheet (tab: Test) shows the human caused increase in the atmosphere of 2020 at 72.47 PgC or an increase in the atmosphere of 40,71 ppmv.
The basic natural CO2 level was/is (IPCC) 589 PgC or 276 ppmv. Together some 337 ppmv.
Observed for 2020 is 414 ppmv???
From where comes the difference? Both the oceans as vegetation increased in carbon level, thanks to the short residence time…
Jim,
Sorry should have been more clear: the (larger) human emissions play no role in the calculation of the adjustment time…
The simple math is in play in both the residence time as in the adjustment time.
In the case of the residence time, the math is always simple, whatever the direction of the flows.
In the case of the adjustment time that is only simple of the decay rate is in linear ratio with the distance between pCO2 of the atmosphere with the pCO2 of the oceans and plants. Which for both is the case.
As good as the carbon mass balance is simple bookkeeping of ins and outs…
Have a view on the (rough) carbon balance of the different flows (PgC/year) and net changes seen from the atmosphere side:
Human emissions: 10 in, 0 out; net change in the atmosphere: +10 (calculated from FF sales)
Atmosphere: 215 in, 210 out; net change in the atmosphere +5 (measured as increase)
Vegetation: 120 in, 122.5 out; net change in the atmosphere: -2.5 (measured via the O2 balance)
Ocean surface: 50 in, 50,5 out; net change in the atmosphere: -0.5 (measured as DIC in the surface)
Deep oceans: 40 in, 42 out; net change in the atmosphere: -2.0 (not directly measured, difference between total ins and outs of the atmosphere and difference with total for the oceans minus ocean surface, see Feely et al.).
All known other sources and sinks either much smaller or much slower in exchange rate…
The cycles give you the residence time, but even if these double, that doesn’t change the adjustment time with one year, only halves the residence time…
But please show me your calculations…
Not my best knowledge, but as far as I know, the opposite may be happening too: high energy O2 and N2 molecules may excite CO2 to emit IR by collisions:
I asked Google:
“can high energy O2 and N2 excite CO2 molecules to emit IR radiation”
And their AI responds with:
“Yes, high energy O2 and N2 molecules can indirectly excite CO2 molecules to emit IR radiation. While O2 and N2 don’t directly absorb or emit infrared (IR) radiation themselves, they can transfer energy to CO2 molecules through collisions, causing them to vibrate and emit IR radiation”
Dr. Ed,
On page 5, there is an indented paragraph with a quote by “Robert.” The end quote is inside the period rather than, by custom, outside.
Another nit pick on page 16, 4th to the last paragraph, “It also says each individual gas flow independently.” Should be “flows,” no? Or “It also treats each individual gas flow independently.”
The 4th paragraph on page 18 is “IPCC’s true human carbon cycle shows human CO2 causes only 8% of the CO2 in the atmosphere. This proves IPCC’s H(1) that claims human CO2 is 33% of the CO2 in the atmosphere is wrong.”
Shouldn’t it be “…8% of the increase of the CO2…” Also in the next sentence, “…human CO2 is (or causes) all of the 33% of the increase of the CO2…”
Where is 8% calculated? I see the 8% shown in Figure 9, but it isn’t specifically explained previously, unless I’m mistaken. The present article does not suffer from brevity, but perhaps adding that explanation or a reference to it in past papers would be appropriate.
David A wrote, “It is easy to find data showing that an ‘Ah’ term is negligible. This would measure human processes removing carbon from the atmosphere…”
Ed replied, “There are no such data!”
David A. is right. I included the data in a comment, here:
https://edberry.com/co2coalition/#comment-112419
Ed, your “Ah,” i.e., the anthropogenic processes which deplete the CO2 from the air, are negligible. More precisely, they are much smaller than the error bars on anthropogenic emissions, so they can be ignored in “mass balance” arithmetic. Even if you count cement carbonation, anthropogenic CO2 removals are still only about 2% of anthropogenic CO2 emissions.
Ed wrote to David A, “You are not debating physics. You are only debating your emotions.”
That’s untrue. The only part of what David A. wrote which is not rock-solid science is his expressed belief that removing CO2 “helps.” That’s a value judgement with which I disagree, but it is not our topic here.
Fredinand,
I don’t think natural fluxes have to increase in the same ratio as human emissions. The latter are zero order and the former first order. No violation of the equivalency principle.
Regarding 1., the biological cycle doesn’t remember when it recycled itself. Whether is was diurnal, yearly, or from fallen trees hundreds of years old.
As for 2., cycling is everything, otherwise nothing moves in and out.
“3. The total biosphere since about 1990 is increasingly removing more CO2 than adding to the atmosphere.”
Yes, but if you figure in a fraction of the removal was industrial sourced, the natural sink minus source eventually flips negative as the industrial content of the atmosphere increases.
I fail to understand why you claim the compartmental models are unidirectional. The only unidirectional model I can imagine is molecular escape from the atmosphere to space. In other words, the sentence “any marker in the inputs never can exceed the ratio in the inputs in the further flows: the containers or the outputs” is incomprehensible to me.
“Further, there is little doubt that the “equilibrium” CO2 level did not change a lot over time.”
That is totally argument by assertion and circular logic. You are using assumptions about an unvalidated Tau model as evidence against the Te models which suggests an expanding biosphere.
“From where comes the difference?”
Well, you explained it yourself. From the increasing ocean and terrestrial carbon levels. 276 ppm seems a bit low, but makes 414 ppm a 50% increase. Of that, the 41 ppm contributed by humans is 29%, leaving 71% or 97 ppm contributed by the growth in natural emissions. Unless proven otherwise, the null hypothesis on H1 stands.
Jim,
“Shouldn’t it be “…8% of the increase of the CO2…” Also in the next sentence, “…human CO2 is (or causes) all of the 33% of the increase of the CO2…”
Is exactly where it goes wrong: 8% (meanwhile over 10%) of all CO2 in the atmosphere (and over 6% of the ocean surface water CO2) is from fossil fuel origin, as the decrease in 13C/12C ratio shows and the other possible main source of low-13C, vegetation is growing, this leaving more 13C behind in the atmosphere…
That doesn’t disprove that FF is the cause of the 33% increase in the atmosphere, only that some 2/3 of the original FF molecules were exchanged with CO2 molecules from the deep oceans, “thinning” the FF “fingerprint”:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/deep_ocean_air_zero.jpg
Dr. Ed,
This page was linked to as a source for “Fig. 11” however, there are only 10 figures!
Also, the historic evidence is all we need to prove CO2 is NOT a climate change force!
Using the geologic evidence going back 550 million years, correlation coefficients can be computed for the relationship between CO2 and Climate (temp) and changing CO2 and changing Climate. The former calculates to 0.29 (uncorrelated). The latter to a mere 0.10 (highly uncorrelated).
No correlation means causation is impossible. Q.E.D.
That is correct. I first learned about this from Prof. Will Happer, when I met him for the first time in 2014, when he taught a colloquium in the Physics Dept. at UNC in Chapel Hill.
I arrived uncharacteristically early for the colloquium, and was surprised and disappointed to learn that the UNC Physics Department had made no arrangements to record it. So I took the middle pair of seats on the front row and used my phone to record the audio. Prof. Happer kindly gave me his PowerPoint slides, and I combined the audio with the slides to make a usable video, which I posted on YouTube.
The sound quality is mediocre, and we don’t get to see his smiling face, but it is a lot better than nothing. You can find the PowerPoint slides and a link to the video here:
https://sealevel.info/Happer_UNC_2014-09-08/
Afterward, I exchanged emails with Professor Happer, and he generously answered my questions. That email exchange is on my website, and it is instructive:
https://www.sealevel.info/Happer_UNC_2014-09-08/Another_question.html
At temperatures and pressures normally found in the troposphere, air molecules, including CO2, are continually and very rapidly colliding with one another, and thus trading energy back and forth. Those collisional transfers are far more frequent than radiative emissions of photons (the other way that CO2 molecules have of giving up energy), so those collisional energy transfers keep the various constituent gases of the atmosphere in local thermal equilibrium.
When a CO2 molecule has been vibrationally excited with 82.66 meV of energy (which is the energy of a 15 µm photon), on average it takes about one full second(!!) before the molecule will emit a 15 µm photon! In contrast, the time before a CO2 molecule in the troposphere would lose that energy by collisional transfer to another air molecule is measured in nanoseconds, though it depends on altitude and temperature.
So even if a particular radiatively active gas in the atmosphere is absorbing lots of radiation, the effect of that absorbed radiation will be simply to warm the bulk atmosphere. It really doesn’t matter which gases absorb the radiation, nor what wavelengths the absorbed radiation was, the effect is just to warm the air. The N2, O2 & Ar are warmed to the same extent as the “GHGs” which absorbed the radiation.
The very rapid collisional energy exchanges (compared to radiative emissions) do NOT mean that emissions from CO2 are small or inconsequential. But they do mean several interesting things:
1. There are MANY energy transfers, back and forth between air molecules, for each emitted LW IR photon.
2. A CO2 molecule is far more often vibrationally excited with 82.66 meV of energy via collision with another air molecule than via absorption of a 15 µm IR photon, even if there’s a lot of incoming IR.
3. In the lower atmosphere, the constituent gases of the atmosphere all stay at almost exactly the same temperature, even though some of them are absorbing and/or emitting IR, and others are not.
4. The amount of IR emitted by the CO2 in a volume of air is determined by just two factors: the amount of CO2 it contains, and the temperature.
5. The amount of IR absorbed by the CO2 in a volume of air is NOT one of those two factors!
It is the temperature of the air (and the amount of gas) which determines the intensity of radiative emissions. Notably, the strength of radiative emissions from CO2 (or another GHG) is almost completely unaffected by the amount of radiation absorbed by that GHG (except indirectly, as the absorption of radiation warms the air).
As it happens, the Earth’s LW IR emission band peak is similar to the molecular bending mode energies of some gases, including CO2. But only triatomic (and higher) molecules have bending modes, so only molecules with three or more atoms can be “greenhouse gases.” That’s why, for example, O3 (ozone) is a GHG, but O2 (diatomic oxygen) is not a GHG.
Ferdinand,
My operating system is no longer compatible with dropbox where I used to share access to files. I’m thinking of not sharing publicly anywhere anymore anyway. I will try to include all the necessary information for you to understand my calculations. They come from modifying a spreadsheet shared by Roy Spencer some four or five years ago at drroyspencer.com. The concept is similar to Dr. Ed’s “test” spreadsheet except, like Dr. Spencer, I’m only considering the atmosphere with all the other reservoirs combined into one.
I added a column to Dr Roy’s spreadsheet between column C, (anthro CO2 INFLOW), and column D, (“anthro” OUTFLOW), naming it Natural inflow. That column accumulates yearly based on the formula = 64 ppm + 1.3*(1E-17)*EXP(0.02*year). That formula calculates the value of natural inflow for all of the values for each year from 1750. It is an artifact of fitting the Mauna Loa data. Instead of Dr Roy’s 0.02 (1/Tau) and 295 ppm value for 1750 CO2 level, I used 0.23 (1/Te) and 280 ppm. The formula for each successive new value of total atmospheric CO2 (Cn) is Cn-1 + EHn + ENn – Cn-1 / Te.
This results in 2018 values of 4.74 ppm industrial in (from Boden et al.), 91.9 ppm natural in, 94.1 ppm total output. The calculated CO2 is 411.6 ppm compared to the actual 408.5 ppm, but the overall correlation with the Mauna Loa data is, if I don’t say so myself, better than Dr Roy’s. You can find his spreadsheet here: https://www.drroyspencer.com/2019/04/a-simple-model-of-the-atmospheric-co2-budget/
I learned that I can maintain a good correlation even with other values of initial CO2 and Te, but never without some increasing increment from other than the industrial source.
Dear Jim,
Thank you for finding more English errors in my draft, which are now fixed in the next update I will post. Regarding you final suggestion, my text now is:
Berry (2019, 2021, 2023a) derived IPCC’s natural carbon cycle as explained above. Since IPCC’s human carbon cycle must use the same e-times as IPCC’s natural carbon cycle, according to the Climate Equivalence Principle, Berry calculated IPCC’s “true” human carbon cycle.
IPCC’s true human carbon cycle shows human CO2 causes only 8% or 33.6 ppm of the 420 ppm of CO2 in the atmosphere. This proves IPCC’s H(1) that claims human CO2 is 33% or 140 ppm of the 420 ppm of CO2 in the atmosphere is wrong.
Dear Dave,
If you tie a weight to a string, and whirl the weight around, then stop whirling and let the string wind up on your steady finger… what makes the weight speed up?
Ed
Ed,
As I have said many, many times before, neither me, nor Ferdinand, nor Dave Burton, nor Jerry Elwood, nor the IPCC has claimed that your “human carbon” is 140 ppm of the present atmosphere. We all know it is much less. I have told that to Skrable, to Koutsoyiannis, to Harde and Salby, to Ato and to others in the parade of deniers that has come through [junk] Science of Climate Change. I have told that to Jim on this thread. I explicitly told you in our “debate” in SCC in 2023. If you read the Seuss paper from the 1950’s, you will see that he was well aware that balanced exchanges (aka “disequilibrium isofluxes”) between the atmosphere and land/sea reservoirs would dilute his effect. I provided a link on this thread to a Radiocarbon paper showing the (diluted) Seuss effect, measured before atmospheic nuclear testing complicated things in the 1950’s. You continue to either willfully misunderstand, or intentionally misrepresent, good science.
That good science leaves no doubt where the atmospheric carbon increase is coming from : Us.
That’s a remarkably random question, Ed. (And I think you meant angular velocity, rather than “speed,” right?)
What does that has to do with anthropogenic CO2 uptake (your “Ah”)? And, what anthropogenic processes do you think remove CO2 from the atmosphere?
(Never mind; I see that “DMA” is the handle of one of the participants here.)
In addition to what David Andrews said (and many skeptics endorse)…
Take an example:
In Europe, each country that uses the Euro has its own 1 and 2 euro coins. One side is the same with the value, the other side is different for each country. Coins from small “countries” like Andorra (between France and Spain) and the Vatican are very rare and real collectors items.
See:
Now, one day, I bring 300 Andorran one euro coins to the local bank. Coins are not that frequently used anymore in the bank transfers, so they have only 600 coins of different countries in stock. Together that gives a sudden increase to 900 coins in total, of which 300 from Andorra.
There are a lot of transactions of coins each day in the bank, which exchange some 180 one euro coins per day. Exchange, not remove.
While at the start 33% of the coins going out are from Andorra, few will come back, as the total number of one euro coins outside the bank is enormous and doesn’t contain much Andorran coins. So the number of one euro coins in the local bank will get reduced very fast with a “residence” time of about 4 days.
At the start there is a 50% increase of all one euro coins in the local bank, that number will slowly get reduced to the “normal” local level of 600 coins at a much slower speed of about 50 days “adjustment” time for any increase of coins from any country.
That results in following graph:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/andorra_decay.jpg
As you can see: the part of Andorran coins is dropping very rapidly, while the number of total coins only slowly get reduced.
Or the difference between the residence time and the adjustment time.
Just replace FF CO2 for Andorra and all CO2 for total coins and make it years for days…
The number of observed FF molecules remaining in the atmosphere is what the input and the residence time caused.
The amount (pressure) of total CO2 in the atmosphere above equilibrium and what is net changing, is reflected by the the adjustment time, independent of the residence time.
First graph:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/andorra_euro.jpg
Dear Dave,
It has nothing to do with the effect of human CO2 on atmospheric CO2.
It is just a simple question to you to see if you can answer a simple question, simply, without making it very complicated with stuff that is irrelevant.
At least two meteololgy books I have read answered this question and related it to what makes the wind in hurricanes speed up as the air gets closer to the eye wall.
Just thought you were up on this simple physics.
Dear David,
Well, let’s review what we are talking about in this post. The CO2 Coalition’s special document we are discussion says in its abstract:
“Since the beginning of the Industrial Revolution in the late 1700s, the average concentration of Earth’s atmospheric carbon dioxide (CO2) has increased by about 140 parts per million by volume (ppmv) to the current amount of about 420 ppmv. This is much higher than concentrations of the past 800,000 years, which rarely exceeded 300 ppmv, according to ice core data. In this document, the CO2 Coalition presents multiple lines of scientific evidence demonstrating conclusively that the modern increase in CO2 is mainly due to anthropogenic emissions.”
And in its introduction:
“That is, nature is removing CO2 from the atmosphere rather than adding to the total. Since nature is removing large amounts of the gas nearly every year, it follows that the rise in atmospheric CO2 cannot be from natural causes.”
“We use multiple lines of scientific evidence to demonstrate that nearly all the increase in
atmospheric CO2 is from human emissions, most of which are from fossil fuel use.”
So, David, do you agree with these CO2 Coalition statements, or do you disagree?
Do you agree or disagree with the arguments by the authors of this special document?
Dear Ferdinand,
David Andrews tried a similar stunt to your in our 2023 debates. Andrews boasted that the solution could be found in Monte Carlo calculations. He was trying to dump on my equation (2). So, I showed David how the balance levels that I derive from (2) produce a quick and more accurate solution than a Monte Carlo calculation.
Your challenge is similar and easily answered by my (2). So, thank you for supporting (2) and thereby all of its derivations.
Ed,
What’s odd about your argument is that you are telling us what we think. You did the same when you wrongly told us that our “natural absorption” term left out the natural absorption of industrial carbon. WE, not you, get to define what OUR terms mean. You consistently try to create straw men by misrepresenting valid arguments.
Dear David,
Amazing. I ask you two questions, that are normal for a debate, and you refuse to answer them:
“So, David, do you agree with these CO2 Coalition statements, or do you disagree?”
“Do you agree or disagree with the arguments by the authors of this special document?”
Further, you claim:
“What’s odd about your argument is that you are telling us what we think.”
Have you truly lost your mind?
Dear Dave,
Here’s my point.
You claim my equation (2) is wrong and that your (and Ferdinand’s) tau is correct.
Yet, nothing you say contradicts (2).
So, your argument are meaningless.
But your tau cannot explain how inflows set balance levels. Your tau cannot explain how nature held a CO2 level before human carbon had any influence on the CO2 level.
Therefore, you tau is a product of your imagination. It adds nothing to your explanations of anything relevant to how carbon flows through the carbon cycle.
You do not have any equation that might substitute for (2). You don’t even realize that you must provide such and explanation to justify all your handwaving about more data that is nice but proves nothing relevant to the core of your message or to the core of our debate.
So, where is your replacement equation for my (2)?
Dear Dave,
Surely, you are not saying that Will Happer supports your irrational arguments in your special document and in your claims in these comments.
I can’t believe Happer would support such nonsense.
Dear Ed,
Your equation (2) only shows how many Andorran coins are left over time, the increase in total coins from 600 to 900 coins anyway was caused by the supply of 300 Andorran coins, no matter how fast these in the next days were replaced by equation (2) by coins from other countries.
That is completely irrelevant for the cause of the increase in coins and how fast the extra number of coins about the “equilibrium” of 600 coins are removed.
The decline of the total number of coins (of whatever country) or the “adjustment time” of the total number of coins back to 600 is all what is of interest…
Exact the same points as for CO2 in the atmosphere…
Dear Ferdinand,
This is in reply to one of your comments far above in these comments.
Your definition Tau is meaningless because you define Tau not as a (level / outflow) but as a (difference in levels / an unspecified and invalid outflow).
You have not provided a substute for my (2). Therefore, you have no rational model. You have no way to calculate how nature could have produced an equilibrium in the levels before we assume human carbon interferred with this equilibrium.
You have not proved there is any need for a Tau that differs from Te, or that your Tau brings anything to the table to explain how carbon flows in the carbon cycle. In other words, your Tau does not even describe nature, let alone the effects of human carbon.
Your use of “removal” rate is not physics or even science. Removal rates have physics backwards. The only way to structure a carbon cycle model is to use the equation (2) Outflow = Level / Te.
You tell your story about how flows continue without changing levels but you do not realize that this is properly explained by (2). Your story does not justify using a Tau to replace Te.
You claim for 2020 that the total carbon outflow from the atmosphere is 15.7 PgC/year.
Even the IPCC recognizes the carbon outflows (as of 1750) were about 108 PgC to Land and 60 PgC to Ocean, for a total of 168 PgC/year outflow.
Your CO2 Coalition-approved model is one of the biggest frauds in climate history. The CO2 Coalition is way left of the IPCC’s position on climate.
You reference other publications (Dietze, Lindzen, Spencer) in your attempt to prove your claims, without realizing that these publications are also wrong.
How can the people in the CO2 Coalition get science so wrong?
Your Tau model cannot explain how D14C, after 1970, declined back to its original balance level of zero.
This D14C decline may be the most important accidental set of data relevant to our discussion of the effect of human carbon on the observed CO2 increase.
Yet, you do not address this subject in a manner supported by physics.
Your formulation does not recognize or calculate balance levels. Because of that omission in your model, you misinterpret the data. (Same for David Andrews, by the way).
Perhaps your most glaring error of all, is your twice-repeated claim in these comments:
“Where Tau is the exponential decay rate to reduce a disturbance (like the addition of extra CO2 from whatever source) to 1/e of the initial disturbance.”
You don’t get it that only my (2) properly explains the 1/e decrease (found in the D14C data) and which properly explains how carbon flows in the carbon cycle.
So, your argument has come full circle.
You allow that (2) expains the initial D14C decrease, but then you claim (2) does not explain this D14C decrease when D14C gets closer to its balance level.
You then claim you need Tau to explain the decrease closer to the balance level. Yet, you don’t even know what a balance level is, or how to define it.
Then you claim:
“Where Tau is the exponential decay rate to reduce a disturbance (like the addition of extra CO2 from whatever source) to 1/e of the initial disturbance.”
Which means you are recognizing, without knowing it, that (2) indeed explains the complete approach of a level to its balance level.
All your CO2C claims are delusional junk science because, in the end, you indeed recognize, in your 1/e claim, that (2) is the correct explanation of carbon flow.
Dear Ferdinand,
You better stick to the carbon cycle. Your attempt to make your point using coins fails.
You have not shown in any of your arguments that your tau produces a more valid explanation of the carbon cycle than (2).
Dear Dave,
I am looking for ANY calculations that you have done properly. That’s why I gave you the chance to answer a simple physics question that is at the freshman level of physics.
For example, you calculated the e-time of D14C to be 20 years.
https://sealevel.info/Graven2020_nofossil_logscale_1970-1995_annot6.png
You used data for about 1972 to 1986 from a log plot of D14C. You further claim others are wrong and you are correct.
There are two key problems with your calculation:
(a) The log plot does not give the correct answer because it does not relate to a balance level that D14C is decaying to.
(b) You are not using the full range of available data.
See Figure 9 of my paper above. It shows a proper curve fit to the D14C data using (8) that is derived from (2), and which shows that a proper curve fit to the D14C data must use two parameters: e-time and balance level. The curve fit in Figure 9 shows Te = 16.5 years and a balance level of zero. And it uses all the available data after 1970.
Figure 9 proves your calculation is invalid. In fact, Figure 9 supports (2), which proves just about everything you are claiming about the carbon cycle is wrong.
Common Dr. Ed, have you never heard of an exponential decay rate for a disturbance of a process in equilibrium? Or Le Chatelier’s principle?
Te and Tau have completely separate definitions.
Te indeed is the residence or “turnover time” that can be expressed with the simple formula:
Te = mass / output
That shows how long a single molecule of CO2 (of whatever origin) in the atmosphere resides in the atmosphere before either being removed, with or without a change in total mass in that reservoir, or being swapped with a CO2 molecule of another reservoir, thus without a change in total mass within that reservoir.
Wiki gives a nice definition for the residence time:
https://en.wikipedia.org/wiki/Residence_time
Tau is how long it takes for a process in equilibrium that is disturbed by an extra input of one of the reactants to get back to 1/e of the original disturbance.
Again from Wiki for an exponential decay:
https://en.wikipedia.org/wiki/Exponential_decay
and of Le Chatelier’s principle:
https://en.wikipedia.org/wiki/Le_Chatelier%27s_principle
These two, Te and Tau can be equal if, and only if, all flows are unidirectional.
The real world shows that 95% of all CO2 fluxes are bidirectional: half the day or half the year CO2 inputs get outputs and reverse that in the other half.
That is our model, which reflects the real world.
Many before me have calculated the equilibrium between the ocean surface and the atmosphere as 280-300 ppmv for the current average sea surface temperature. That is where Tau is based on: the effect of the difference between the CO2 pressure (pCO2) in the atmosphere and that equilibrium. That gives a small real NET output of only half human emissions in both oceans and vegetation together. No matter how much CO2 circulates through the atmosphere. No matter how high the CO2 outflows (thus Te or your formula (2)) get. Completely unimportant for the NET outflow, which is the only part in the total ins and outs that changes the CO2 level in the atmosphere and other reservoirs.
Your model includes a 3.5 years decay rate for all CO2 molecules and for all isotopes alike.
The decay rates for 14C in the atmosphere are calculated between 12 and 20 years.
The decay rate for the 13C/12C ratio is about 15 years.
The decay rate for 12CO2 and 13CO2 mass, back to equilibrium at around 295 ppmv is about 50 years.
Completely independent of and much slower than your residence time…
Thus your formula doesn’t calculate what the observations show.
The only reason for a faster decay rate of the 13C/12C ratio or the 14C of the bomb tests, compared to the mass of 12/13CO2 is that the isotopic ratio’s are redistributed over all reservoirs and a lot of “old” seawater from the deep oceans from long before the use of fossil fuels or atomic bomb tests is coming back with the old isotopic composition.
With your residence time of only 3.5 years, your calculated increase in the atmosphere gets far lower than what is observed. In your spreadsheet (tab: Test) the human caused increase in the atmosphere in 2020 is 72.47 PgC or an increase in the atmosphere of 40,71 ppmv.
The basic natural CO2 level was/is (IPCC) 589 PgC or 276 ppmv. Together some 337 ppmv.
Observed for 2020 is 414 ppmv.
From where comes the difference? Both the oceans as vegetation increased in carbon level, thanks to the short residence time, thus can’t be the source of the increase in the atmosphere…
Then a few points as direct answer:
“Your definition Tau is meaningless because you define Tau not as a (level / outflow)”
The whole world defines Tau as the time needed to reach 1/e of a disturbance of a process in equilibrium…
“You claim for 2020 that the total carbon outflow from the atmosphere is 15.7 PgC/year. ”
I did claim, based on observations, that the part of the outflows caused by the absolute pressure of CO2 in the atmosphere is 15.7 PgC/year. The rest of the outputs is NOT caused by the absolute pressure of CO2 in the atmosphere. These are caused by temperature, photosynthesis, life and pCO2 differences, largely to completely independent of the CO2 pressure in the atmosphere. I did not claim that all carbon outflow from the atmosphere is 15.7 PgC/year.
“Which means you are recognizing, without knowing it, that (2) indeed explains the complete approach of a level to its balance level. ”
Except that the real speed to reach the balance level is 50 years for any excess CO2 in the atmosphere, not 3.5 years. You simply don’t see the difference between the residence time of an individual molecule CO2 (of 3.5 years) based on the sum of all outflows and a mass removal time (of 50 years) which is based on the NET outflow, that is the difference between all inflows and all outflows.
Dear David,
Replying to your comment on July 1, 2025 at 10:25 pm
Your reference https://www.cambridge.org/core/services/aop-cambridge-core/content/view/193CDF1F705B269BC975AF178CEF1AC3/S0033822224000274a.pdf/discussion-presentation-of-atmospheric-14co2-data.pdf
does not in any way “rebut” my papers.
My section 2.8 discusses the Suess Effect because it is part of my calculations. I note
The Suess Effect is not a cause. It is a result of human CO2 inflow that dilutes natural CO2. Berry’s accurate curve fit shows human CO2 causes no significant “Suess effect dilution.”
Your referenced Figure 2 indeed shows a Suess effect of a few percent. That agrees with my calculations of the expected Suess effect. It shows human CO2 in the atmosphere is about 8%. In other words, your Figure 2 supports my (2) and its calculations using IPCC’s data and my Figure 9.
Even the IPCC knows its carbon cycle data is not perfect, so no one expects perfection in carbon cycle calculations. I notice that your D14C data extends to 2020 whereas my data ends in 2015. So, I will upgrade my data and make some minor revisions to my calculations. But we are not looking at any data that will substantially change my conclusion that human carbon emissions have little effect on the CO2 level.
But your paper is lacking something very important, as shown in my Figure 10, which shows the likely reason 14C increased since, say, 1955 is because 12C inreased while the D14C balance level remained near zero.
The balance level is the critical factor because it represents the continuing inflow of natural carbon (or CO2) into the atmosphere.
Since the D14C balance level has remained near zero even while the bombs increased 14C, the balance level is the best measurement we have of the effect of human carbon on atmospheric carbon. And it clearly shows the inflow (and balance level) of human carbon is somewhere between zero and 8% of the total carbon in the atmosphere.
Seems to me that you agree with (2) even though you cannot bring yourself to admit it.
Sometimes my English is too phonetic… Common is of course Come on Dr. Ed…
No problem, there, Ferdinand. Your English is excellent.
Dear Ferdinand,
I put your comments in quote.
The only definition of Te that is important is equation (2).
Te (2) and the continuity equation (1) fully explain the carbon cycle.
No other definition matters because equation (2) governs the carbon cycle model.
Te explains the real world and Tau does not.
The many before you were wrong. We now have a new carbon cycle generation defined by (1) and (2).
Tau is irrelevant because Net output is irrelevant to a carbon cycle model.
No, my “model” which is (1) and (2) does not specify any value for Te.
IPCC’s data for its natural carbon cycle show the overall Te for carbon in the atmosphere is 3.5 years.
However, carbon isotopes 14 and 13 have a larger Te. For example, D14C data show the Te for 14CO2 is close to 16.5 years.
NO. Data reject your claim.
No, the isotopes follow their own independent carbon cycles with their own Te. Otherwise their carbon cycle are the same.
NO. You have no basis in data to make that claim.
My carbon cycle exactly replicates IPCC’s data for its natural carbon cycle at equilibrium. Your model cannot do this.
Therefore, the data reject your model and accept my model.
My Test spreadsheet used in inflow of 10 PgC/year which DOES NOT represent real data.
There’s no difference because these were not real data.
YES. But only Te repesents the 1/e value. Tau cannot. Case in point: D14C data.
You refuse to recognize that (2) produces the equilibrium that matches real data.
Figure 5 shows that Te is the time it takes for the level to move 63% toward its balance level, no matter where we start. Te properly defines the “speed” to reach the balance level.
You simply have not measured the speed to balance level correctly.
Nonsense. Forget about your “individual molecule” thing. Te fully describes how fast a level moves toward its balance level. Your Tau adds nothing but confusion and errors.
Einstein said we must keep things as simple as possible to explain a physical system. You are adding complexity that is not needed.
To Everyone,
The dark side uses clever ways to promote its invalid claim that H(1) is true.
Figure 11 (in my paper above) is a replot of a figure in CO2C. It has a logical error in the way its data are plotted.
CO2C does not catch this error, which means the CO2 Coalition reviewers are not very concerned about republishing junk science.
I could have explained the error in Figure 11, but I thought I would give you a chance to find it on your own.
Will you be the first to find the error in Figure 11?
Ed, it is ironic that in your quiz question, to evaluate my freshman-level physics chops, YOU got it wrong: you said that the spinning weight speeds up, but it does not. Only its angular velocity increases.
Hopefully your mistake was just sloppy wording, rather than an actual misunderstanding. So I asked whether that’s what you meant—but you didn’t answer. So, again: Is that what you meant?
Regarding the atmospheric lifetime of “bomb spike” 14C, 15-17 years is what you get if you forget to take into account Suess Effect dilution. The log-linear plot is useful because that produces a straight line from an exponential decay process, such as the approximately constant-rate mixing of atmospheric carbon with other major carbon reservoirs, which is the dominant process decaying the radiocarbon bomb spike. But you needn’t use a log-linear plot to reach that conclusion. Here are two examples, using two datasets, which yield (approximately) the same result; one of them is linear, and the other is log-linear:
https://sealevel.info/ndp057_Fruholmen_d14CO2_hairlines3.png
https://sealevel.info/logc14_two_half-lives2.png
The reason for preferring the earlier 14C measurements is that there are two different processes shrinking the 14C bomb spike: one is dilution by mixing, through carbon exchanges between the atmosphere and other carbon reservoirs (mostly oceans and terrestrial biosphere). The other is Suess Effect dilution, due to the addition of 14C-depleted fossil carbon to the atmosphere.
The former process is the one we’re trying to characterize.
In the years immediately following the cessation of atmospheric H-bomb tests, dilution by mixing was the major process contributing to the bomb spike decay. But as the years passed, and anthropogenic CO2 emissions accelerated, Suess dilution became a bigger and bigger contributor.
What’s more, the quantification of Suess dilution is dependent on models, which I, frankly, don’t really trust.
So, by confining our analysis to the first couple of half-lives, we maximize the portion of the decay which is due to the process that we’re interested in, and minimize the portion due to Suess dilution and the possible modeling errors.
When you do that, you find a 14C lifetime of about 20 years.
Now, back to the question at hand: What anthropogenic processes do you think remove CO2 from the atmosphere?
Ed,
Of course I agree with the CO2 Coalition’s conclusion that the rise in atmospheric CO2 is anthropogenic. But we are all also on record as saying that does not for a minute imply what you seem to think it implies, that today there should be ~140 ppm of C14 devoid “human carbon” in the atmosphere. We all understand disequilibrium isofluxes. You quite obviously either do not understand, or do not want to.
I have to say that it is rather sad that you spent such an effort over the years showing that “human carbon” is not abundant in our atmosphere, when all you had to do was have a conversation with Hans Suess some 70 years ago to anticipate it would not be.
Dear Dave,
You get a blue ribbon for your answer on the weight on a string. But my wording was meant to trap you. However, your answer is not perfect. You should have mentioned that energy is conserved, therefore. the speed of the weight cannot increase because that is the more fundamental reason the speed cannot increase.
Check my website menu: About/Adventure in Physics – Weight in a String.
https://edberry.com/an-adventure-in-physics-an-untold-story/
You will see that I published the first paper on this subject in the American Journal of Physics in 1963. I corrected the Scienfic American and two books on meteorology. After my publication, at the encouragement of one of my advisors, I did a simple experiment to further prove my point that the speed of the weight is constant.
Back to calculating the Te for Delta14C and for 14C.
My curve fit using (8) automatically takes into accout the Suess effect dilution because it requires setting the balance level as well as the curve fit. If the dilution were 10%, the balance level would have been -100 rather than zero. My figures 9 and 10 explain my point.
The D14C data show the Seuss effect is only a few percent at best. This means the human carbon is only a few percent of the total carbon in the atmosphere. Therefore, the human CO2 emissions add only a few percent to atmospheric CO2.
Your argument that claims the real amount of human CO2 in the atmosphere is much larger than that indicated by the Suess effect is junk science. It is not backed by data or testable hypotheses. It it imaginary handwaving that contradicts physics.
My curve fit with (8) follows the Delta14C data very closely, leaving little room for controversy or an alternate hypothesis.
Ed wrote, “…the human carbon is only a few percent of the total carbon in the atmosphere. Therefore, the human CO2 emissions add only a few percent to atmospheric CO2.”
It has been explained to you over and over why that is wrong. Exchanges of carbon between reservoirs do not change the amount of carbon in those reservoirs, but they change the distribution of 14C-depleted fossil between those reservoirs.
Ed wrote, “Your argument that claims the real amount of human CO2 in the atmosphere is much larger than that indicated by the Suess effect is junk science.”
Please don’t put words in my mouth. I haven’t said that. In fact, that doesn’t even make any sense, because the Suess effect does not “indicate” how much human CO2 remains in the atmosphere.
Using just GCB (2024) best estimates, ignoring CIs for economy of expression…
From 1750 (roughly the start of the Industrial Revolution) through 2023, human emissions added roughly 232 ppmv of fossil CO2 to the atmosphere + very roughly 105 ppmv of CO2 from land use changes, a total of 337 ppmv. Over the same time period, the amount of CO2 in the atmosphere increased by a net total of about 143 ppmv. Over that time period human removals of CO2 from the air were negligible (even if you count cement carbonation as anthropogenic, it was at most 3-4 ppmv). That means that nature removed (337 – 143) = roughly 194 ppmv of CO2 from the atmosphere.
But that does not mean that “the amount of human CO2 in the atmosphere” is 337 ppmv, or 232 ppmv, or 143 ppmv. The amount of anthropogenic CO2 remaining in the atmosphere is far below 143 ppmv, because of exchanges of carbon between the atmosphere and other carbon reservoirs, which reduce the amount of “human CO2” in the air without reducing the amount of CO2 in the air.
Now, Ed, will you PLEASE answer the question about your “An”? What anthropogenic processes do you think remove CO2 from the atmosphere?
So, you still think that the 4% human carbon inflow can cause 33% of the CO2 level in the atmosphere even as you agree that the Suess effect has never been greater than 8% and likey never greater than 4%.
Good luck with that one, David.
Brendan, average sea surface temperatures (SST) are believed to have risen only about 0.5 °C over the 2/3 century since 1958 (when precise CO2 measurements began). Yet over that same 2/3 century period atmospheric CO2 levels rose by 35% (110 ppmv):
https://sealevel.info/co2.html
Now, consider the relative effect of a 0.5 °C SST increase (since 1958) and a 35% atmospheric CO2 level increase (since 1958) on the CO2 fluxes between ocean and air. We know from the temperature dependence of Henry’s Law that a 0.5°C water temperature increase will reduce CO2 solubility in water by about 2%:
https://sealevel.info/CO2_solubility_in_water_vs_temperature_showing_effect_of_1C_warming5.png
But a 35% increase in CO2’s partial pressure in the atmosphere will increase CO2 dissolution into the ocean by 35%. Since 35% > 2%, it is correct to call the “35%” the “main effect.” That’s not confirmation bias, it’s just what the numbers show. It means that the net effect of the two changes (temperature and atmospheric CO2 level) must be an acceleration in ocean uptake of CO2.
Also, note that global temperatures and presumably sea surface temperatures (SSTs) declined in the 1950s, 1960s, and early 1970s. Yet CO2 levels nevertheless kept on rising. Obviously rising water temperatures didn’t contribute to rising CO2 levels when water temperatures were falling.
https://sealevel.info/newsweek_old.htm
The socialists have an agenda that relies on all CO2 emitted in the last 150 years came from humans and that CO2 never rose above 300ppm until humans started burning fossil fuels. Any evidence to the contrary has to be somehow destroyed at all costs, no matter what the costs.
I said that CO2 rose to 450ppm twice during the last 200 years from instrumental measurements. I never mentioned Beck. But Uncle Bert immediately went on the attack against Beck.
Beck compiled some 200,000 instrumental CO2 measurements from 901 different locations from many dozens of highly qualified and notable scientists. Beck never made any measurements, he just collected them. He is the messenger. Yet the socialists choose to attack him vigorously. Don’t attack the science or the measurements, shoot the messenger.
Uncle Bert has just written more totally unverifiable specious waffle including false statements. Harro Meijer and Ralph Keeling have tried to falsify the 1812 to 1961 instrumental record and failed miserably. Now Uncle Bert’s having a crack. The socialists never give up when their narrative is in jeopardy.
Uncle Bert said:
“When one did choose only the measurements over the oceans or at the coast, with wind from the seaside, all these measurements are on or below the ice core measurements”
False.
Figure 7 from:
Yndestad Harald, 2022b: Lunar Forced Mauna Loa and Atlantic CO2 Variability; Science of Climate Change, Vol. 2.3 (2022) pp. 258-274; https://doi.org/10.53234/scc202212/13 ; https://scienceofclimatechange.org/wp-content/uploads/Yndestad-2022-Lunar-Forced-CO2-Variability.pdf
Shows CO2 in a range from 370ppm to 300ppm from 1820 to 1960. 50% of these measurements were over the ocean.
Nothing in all of his comment or links on July 4, 2025 at 3:04 pm did anything to falsify the 1812 to 1961 instrumental record. He’s done much the same as Meijer and Keeling, cherry pick one or two locations and claim these measurements can’t be correct, therefore all the remaining 900 locations are all wrong too. In his attack on the measurements in the supplied link he keeps referring to a background layer. Charles Keeling demonstrated with his measurements that there was no difference between CO2 measurements at the surface to 4,300 metres up on mountain tops.
I.e. His measurements demonstrated there was no such thing as a background layer. There was only a difference if the measurement location was in the middle of a forest. Out of the 901 locations in the 1812 to 1961 instrumental record, Charles Keeling only found one. The 1812 to 1961 instrumental record demonstrated the same as Keeling’s own measurements.
There was no difference over the oceans. Keeling falsified his own background layer nonsense. The background layer is a red herring.
Uncle Bert tried to say that Beck did not interpret the measurements correctly. You can’t interpret measurements. A measurement is a measurement.
Uncle Bert, along with Meijer and Keeling, are all saying the measurements are wrong and the proxies are right. There is complete ignorance with the monotonic ice core record. It shows an average and does not show the up and down extremes in the record. To see the extremes you need to look at Stomata proxies. Then Uncle Bert comes out with the astonishing comment that “Stomata data are local proxies which are calibrated to ice core values”. What a load of nonsense. This comment demonstrates just how desperate Uncle Bert’s specious waffle has become. In addition, CO2 rose to 400ppm in 500 AD. See Figure 14 in:
Mixing Proxy and Measured Data
DOI: 10.13140/RG.2.2.19788.95360/1
https://www.researchgate.net/publication/354144035_Mixing_Proxy_and_Measured_Data
This is CO2 from plant stomata for the past 1,800 years. Chart adapted from Kouwenberg et al 2004 by Dr Robert Holmes in his video presentation The Ice CO2 Record is “Probably Wrong” Too.
Holmes, (2019b) https://www.youtube.com/watch?v=WNEQo6lk9ko&t=2s “The Ice CO2 Record is “Probably Wrong” Too YouTube video with many references to the literature, accessed 20/11/2023.
Uncle Bert, along with Meijer and Keeling, are trying to falsify a measurement because it is an inconvenient truth and destroys the socialist narrative. A measurement is a measurement. You can’t re-interpret it or falsify it to suit your predetermined narrative.
Finally, Figure 2 from:
Yndestad Harald, 2022b: Lunar Forced Mauna Loa and Atlantic CO2 Variability; Science of Climate Change, Vol. 2.3 (2022) pp. 258-274; https://doi.org/10.53234/scc202212/13 ; https://scienceofclimatechange.org/wp-content/uploads/Yndestad-2022-Lunar-Forced-CO2-Variability.pdf
is the average from 901 locations from all over the world, most were over the oceans. Many locations were on mountain tops, one even higher than Mauna Loa. Many along beaches. The key to the accuracy of these measurements is the 3 year overlapping period of 1958, when Mauna Loa began and 1961 when the 1812-1961 instrumental record ended. For that 3 year period the two different measurements mirrored each other and were almost identical.
I’ll probably be locked out of this discussion yet again for another week. I anticipate this will be my final comment. Good luck to those with the patience to sift through Uncle Bert’s specious waffle. I’ve had the experience before and it is not pleasant. The socialist political activists are 24/7 in their political endeavors. We normal people have lives to live.
Dear Ed,
With an input of only 1 to 5% FF in total inputs, the observed ratio of FF in the atmosphere is already over 10% and over 6% in the ocean surface. The rest of the FF molecules gets into vegetation and the deep oceans, where it is more difficult to measure. The speed at with the FF molecules are exchanged is caused by the residence times. No problem with that. That is about CO2 molecules.
The speed at which the total mass in the atmosphere get reduced to the equilibrium with the ocean surface is of a complete different order: an observed year by year increasing NET removal of CO2 mass (of whatever origin) out of the atmosphere. NET removal. That is observed (!) as only half the current human emissions. Or a Tau of around 50 years.
Moreover, the sum of all FF emissions over time is near twice the observed increase in the atmosphere:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_co2_mlo_t_1960-cur.png
Thus nature removed about half of the FF emissions as mass (and 2/3 of the FF molecules were replaced by molecules from other reservoirs). Thus nature is not the cause of the CO2 increase in the atmosphere. Human emissions of FF CO2 are.
Each year the calculated (quite exactly known from taxes!) FF emissions are average twice the observed increase in the atmosphere over a year, be it with huge year by year variations in net sink rate (not net source rate!):
https://www.ferdinand-engelbeen.be/klimaat/klim_img/dco2_em2.jpg
With the exception of a few borderline (El Niño) years.
Any bookkeeper worth his/hers money will tell you that FF emissions are the cause of the increase in the atmosphere. No matter your formula (2)…
Dear Ed,
I don’t see any error in that plot:
All what was plotted at the left part of the curves, is the observed combination of O2 and CO2 measurements.
Observed.
At the right side there is a plot of the calculated drop in O2 by burning FF for each type of fuel and the sales for that type and the increase in CO2 if all that FF derived CO2 remained in the atmosphere.
Then one subtracts the calculated O2 release by plants, that is the difference between the above calculated O2 use and what was observed, which is caused by their CO2 uptake, which gives a stoichiometric release of O2 for each CO2 molecule absorbed.
Then one subtracts the calculated CO2 uptake by plants from the FF drop. The remaining gap in CO2 uptake is what the oceans did absorb.
The graph has the ocean and vegetation uptake in reverse order for clarity of the graph, but anyway, without ocean uptake, it would end at the same height as the observed O2 level, with a minor difference, caused by the out-gassing of O2 by the warming oceans. Maybe you have a different sink available than the oceans, but as DIC measurements in the ocean surface show: the oceans are net sinks for CO2.
So I am very curious what the “glaring error” could be, as I don’t see any error in that graph.
Dear Ed,
Only one remark, which is at the essence of our dispute:
Me: ” In your spreadsheet (tab: Test) the human caused increase in the atmosphere in 2020 is 72.47 PgC or an increase in the atmosphere of 40,71 ppmv. ”
You: “My Test spreadsheet used in inflow of 10 PgC/year which DOES NOT represent real data.”
It does for the years after 1800, but in your tab “HumanBB” anyway you use the real data of FF emissions and the calculated increase in the atmosphere, caused by these emissions, according to your formula (2) for all flows.
For the years 2010 and 2020 your calculations show:
Year Lg La Ls Ld Total La ppm
2010 154.35 57.05 29.98 112.77 354.14 26.91
2020 196.10 70.18 37.95 147.32 451.55 33.11
The observed CO2 levels were:
2010: 390 ppmv
2020: 414 ppmv
Or an observed increase in La vs. 1750 of:
2010: 114 ppmv
2020: 138 ppmv
Your calculations with formula (2) don’t match the observations and give much too low results for the observed total increase of CO2 in the atmosphere… That is because your individual Te’s are about a factor 4 too fast…
The tabs in the results disappeared…
Anyway, your results from equation (2) in human ppmv increase are:
2010: 26.29 ppmv
2020: 33.11 ppmv
The observed increases are:
2010: 114 ppmv
2020: 138 ppmv
Equation (2) doesn’t reflect reality…
Dave A wrote, “The poor quality of the denier arguments that I have focussed on, ever since stumbling on the Berry/Harde/Salby confusion between deltaC14 and concentration, makes me very skeptical of other skeptics and inclined to believe the consensus.”
I quite understand, and you didn’t even mention Principia Scientific‘s crackpottery. But why doesn’t the abundant nonsense from climate alarmists also make you very skeptical of alarmists and their claims?
For instance, you say that “‘Extreme weather’ problems, especially involving the increased water content of tropical storms, seem to me very likely real and linked to CO2.” But, as I trust you know, those problems are merely predicted, and there’s been no detectable increase in extreme weather, thus far.
Hurricanes & tropical cyclones have not worsened:
Graph: https://sealevel.info/global_major_freq_hurricanes_2022-02-28_ryanmaue_1941x1017_annot1.png
References: https://sealevel.info/learnmore.html?0=hurricanes#hurricanes
Nor have tornadoes:
Graph: https://sealevel.info/tornadoes-1955-2024.png
References: https://sealevel.info/learnmore.html?0=tornadoes#tornadoes
Nor have nor’easters, droughts or floods, or any other class of extreme weather:
Graph: https://www.ncdc.noaa.gov/temp-and-precip/uspa/wet-dry/0
References: https://sealevel.info/learnmore.html?0=droughts#droughts
Do you know where the prediction of worsening “extreme weather,” and, in particular, worsening tropical storms, came from? It was from this book:
https://www.amazon.com/Storms-My-Grandchildren-Catastrophe-Humanity/dp/1608195023
Storms of My Grandchildren: The Truth about the Coming Climate Catastrophe and Our Last Chance to Save Humanity, by Dr. James Hansen, “the world’s leading climatologist.”
In 2011 Dr. Hansen did a publicity tour to promote his book, and on the Dave Letterman show he explained why global warming will cause worsening storms. He said that AGW would warm the tropics more than high latitudes, and the resulting “increasing temperature gradient” [between high & low latitudes] would “drive stronger storms.” Listen to it here:
https://www.youtube.com/watch?v=SOKBOFLhgqM#t=7m25s
I trust you know that the “increasing temperature gradient” between high & low latitudes is nonsense. The temperature gradient is decreasing, not increasing. (Aside: “Arctic amplification” is the happy fact that “global warming” isn’t really very global, because it disproportionately warms chilly high latitudes, especially in winter. The tropics and summers are affected less—which is nice, because they’re warm enough already.)
That’s just as Arrhenius predicted over a century ago.
Hansen’s mistake was not minor, it was the basis of his book! Yet, as far as I know, not a single prominent climate activist or alarmist institution criticized Hansen’s error, or suggested that the decreasing temperature gradient between high & low latitudes could drive weaker storms. Not even one.
THAT is the most striking difference between climate alarmists and skeptics of climate alarmism. As you’ve seen, prominent skeptics and lukewarmers devote considerable time and effort to debunking things like the Berry/Harde/Salby confusion about CO2. But nobody on the alarmist side of the debate bothers to debunk nonsense like Hansen’s confusion about storms.
That’s because the driving motivation of the leading scientists who’re skeptical of climate alarmism is that, like you, we are passionate about scientific integrity, and that generally isn’t the case on the other side.
If you doubt it, then explain why people like Hansen and even Guy McPherson generally get a free pass from other climate alarmists? Why doesn’t anyone in the alarmist community put as much effort into debunking Hansen’s errors as the CO2 Coalition puts into debunking the Berry/Harde/Salby confusion about CO2?
This has gotten long, so I’m going to defer discussion of “saturation,” the inaccuracy of alarmists’ predictions several decades ago, and the supposed “consensus,” to another day.
Dear Brendan,
You will not be locked out of these discussions. So, keep commenting.
I am not blocking any opinions from these comments because I want this to be an open discussion.
Sometimes, WordPress does not recognize a commentor’s email address. So, it holds a comment until I approve it.
I am not at my computer 24 hours a day, so sometimes a comment gets put on hold until I arrive. I always approve comments.
It is important that WordPress filters comments because the internet is literally flooded with website comments that insert bad code into a website and take down the whole site.
Thank you for your comment.
Ed
Dear Brendan…
Again a lot of allegations with little real meat…
As I already said, I have had a lot of direct discussions with the late Ernst Beck and therefore I am very reluctant to discuss his work, as he can’t defend his work anymore.
For a good idea how he worked: he did dig out lots of historical data, which was an enormous work and that really is where he should applauded for. The problem is his non-selection and use of all available data, the good, the bad and the ugly.
One can criticize the criteria that Calendar used to select or deselect the historical data for his compilation, but at least he had stringent criteria, including not using any data that were used for agricultural purposes.
That should have excluded the two main series (Giessen/Germany and Poona/India) which are at the base of his 1940-1942 “peak”, which doesn’t exist in any other measurement or proxy.
A peak of some 80 ppmv in only 5 years is only possible if you burn down a lot of forests and regrowth in 5 years simply is impossible.
That are the bad data. The ugly data: in Figure 1 of Yndestad (directly copied from Beck’s work) you see the “atmospheric” CO2 measurements. The northern Atlantic air was really measured and below the average of the ice cores. The mid- and south-Atlantic pCO2 was only measured on the seawater samples at different depths, including at the surface, noticed as 0 meter depth. According to Beck, that were atmospheric measurements, but… from the same samples the pH was measured… Nevertheless, he used these data in his latest work.
Then we have Figure 2 in Yndestad: the peak in temperature around 1940 may have caused the peak in CO2, but that implies a 120 ppmv peak for only 0.6°C change. Or 200 ppmv for only 1°C sea surface increase. Wow.
Moreover a similar increase and decrease after 1950 does not lead to any detectable increase of CO2. Very strange behavior of CO2: it stops its huge reaction on temperature at the exact moment that accurate direct measurements in the atmosphere start…
What makes all the historical measurements suspicious is that in about every year one can find any CO2 level one likes: from below the ice core measurements to 500-600 ppmv in the same year at the same place on earth or at different places.
There is a modern CO2 (and other gases) station at Linden/Giessen at a few km of the historical station that is the main source of the 1942 peak. Here a few days of measurements under inversion, compared to Barrow, Mauna Loa and the South Pole. All raw, uncorrected data:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_background.png
The historical measurements were three times a day, two at the flanks of the peaks:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_background.png
So that are the measurements that caused the “peak” around 1941…
About the calibration of the stomata data: these indeed are calibrated against ice core measurements over the period 1900-1990:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/stomata.jpg
For the same stomata index (SI) of 7%, the CO2 level may vary between 315 and 365 ppmv. I think that the ice core values are somewhat better…
And even in the stomata data, there is no “peak” around 1940:
According to the ice cores, the CO2 level in 1940 was around 310 ppmv. If the “real” CO2 level was at 380 ppmv, according to Beck, then the stomata index would be at the bottom of the graph near 5%. Nothing special can be seen in the calibration around 1940…
See further my opinion of already from 2008 about Beck’s compilation:
https://www.ferdinand-engelbeen.be/klimaat/beck_data.html
Again, stomata data are calibrated against ice cores for local bias over land for the period 1900-1990. But what happened hundreds of years ago with the local bias? That may have changed due to land use changes in the main wind direction over the centuries or even the main wind direction may have changed as was probably the case between the warm MWP and the cold LIA in Europe. In that case, the stomata data need to be recalibrated to match the averages of both over the same period. Not the other way out…
And I have followed the video. What a bunch of nonsense is that. Good to fill a whole page in reaction. He uses the unreliable stomata proxy data to refute the ice core records (while that should be in reverse!) and he uses the remarks of the late Jaworowski, which were already refuted point by point in… 1996 by the work of Etheridge et al. on three ice cores at Law Dome.
See my comment on Jaworowski, again of 2008:
https://www.ferdinand-engelbeen.be/klimaat/jaworowski.html
And please let politics out of the debate: I am very interested in politics, but don’t mix a debate about data with a debate about who is politically biased in your own eyes…
Dear All,
The essence of the arguments, for or against (H1), centers on what the correct equations are that describe the true physical processes governing mass transfer between the global reservoirs. Ed Berry uses Outflow = Level / Te and related equations which embody the first-order nature of Fickian diffusion. Ferdinand Engelbeen adheres to a Tau “model” which ascribes Outflow proportional to disturbance / Tau where disturbance equals the difference between the current atmosphere concentration of CO2 and some equilibrium level that would be restored on suspension of industrial emissions.
Mathematically, both models begin with the math balance equation (1):
(1) dC(t)/dt = Eh(t) + En(t) – Sn(t)
where C is the concentration of CO2, and E, S, h, and n represent emissions, sinks, human, and natural, respectively. Demetris Koutsoyiannis describes Tau model adherents as “lumping” emissions and sinks together by equating [Sn(t) – En(t) to net sinks, NS(t), defined as in (2):
(2) NS(t) = k* [ C(t) – C* ]
where C* represents a value of C(t) at some hypothetical equilibrium. The Te model also starts with equation (1), but expresses net sinks, SN, as in (3):
(3) SN(t) = ke [ S(t) ]
Which of (2) or (3) properly reflects the true physical processes at work in carbon cycling?
According to Koutsoyiannis, “The proponents of the above ‘sceptic’ [Tau] approach may have difficulties to accept this relationship, preferring [Equation (2)], but [Equation (2)] is for the net sink NS(t) = Sn(t) – En(t), while [Equation (3)] is for the natural sink Sn(t) without subtraction of the emission. It would be absurd to assume that Sn(t) would be related to a portion of the atmospheric storage, such as the surplus above the assumed equilibrium state.
The crucial difference between the two models, other than the question of which equations best describe the realistic physical principles at play, is the fact that the Tau model assumes the equilibrium value of S* has not changed since pre-industrial times. The Te model allows for the possible expansion of the biosphere and a potentially larger S*. This would have the effect of shortening Tau.
Unfortunately for the Tau model camp, this dilemma will never be resolved with simple math. We are going to have to rely on more rigorous analysis such as presented here by Dr. Ed or that of Demetris Koutsoyiannis. See Annex A, page 20, https://tinyurl.com/bdd4fhyb
Dr Ed
Thank you.
Brendan
Jim,
In an earlier note to Ferdinand you said “I’m working on a way to demonstrate how the simple math you and David Andrews rely on can give ambiguous results based on somewhat arbitrary choices of variables.” You seem to have been distracted from that goal or maybe have given up. My goal here is to keep you focused on it.
I think we agree on all of the following data-driven conclusions:
• The present atmosphere contains little “industrial carbon”, carbon that once resided in a fossil fuel. (That is Ed’s key result, but it is old news and unimportant.)
• The (fast cycle) carbon content of the atmosphere, oceans, and biomass have all increased since 1950.
• Natural emissions of carbon into the atmosphere from processes such as ocean outgassing and vegetation decay exceed emissions from fossil fuel burning by an order of magnitude.
• Data and “simple math” allow the further conclusion that natural transfers from the atmosphere to land and sea reservoirs (of ALL carbon types of course) exceed natural emissions. This is equivalent to the statement that “net global uptake” is positive. Repeating relevant data from Ballantyne: between 1950 and 2010, integrated human emissions were 350 +_29 PgC, atmospheric accumulation was 158 +-2PgC, making net global uptake 192 +- 29 PgC.
I know you are struggling to accept the consequences of the final bullet point.
You have argued that the larger natural emissions from decaying vegetation in 2025 compared to 1950 (because there is more vegetation to decay) means they are a cause of the atmospheric rise. This is what Koutsoyiannis has also argued, which is why I put you on to him. Several months ago I told Demetris I would nominate him for the Nobel Prize in Alchemy, if he could demonstrate in a laboratory setting how decaying vegetation managed to emit more carbon than it had taken in from the atmosphere while it was growing. He has not responded to me.
I don’t know how your spreadsheets are structured, but as the biomass example illustrates, it DOES make sense to link various emission and absorption processes and focus on net changes in individual caches of carbon, no matter what Demetris says. Stock changes over a defined period are presumably better known than emission and absorption rates. A larger biomass in 2025 compared to 1950, combined with carbon conservation, precludes biomass growth as a source of atmospheric carbon rise. Simple math is not wrong just because it is simple.
So once again I am puzzled how you can look at the 350 PgC hole in fossil fuel reserves made between 1950 and 2010 and have any doubt whatsoever where all the carbon is coming from. But if you have a coherent rebuttal, by all means bring it. Ed has none. Demetris has none.
And good luck to you convincing people net global uptake is negative.
Dear Jim,
I must make one correction to your review comment:
My equation (1) is not as you wrote it. My equation (1) is:
(1) dL/dt = inlfow – Outflow
This applies to any definable set of carbon atoms, including their total.
I apply it separately to natural 12C and to human-produced 12C. I could also apply (1) to the total of natural and human carbon but this has no advantage.
This (1) is the continuity equation designed to keep track of specific atoms (in our case). Your (1) destroys this necessary continuity.
I disagree with your (1) because it does not include -Sh(t), and therefore it assumes the sinks for human carbon outflow are the same as the sinks for natural carbon outflow.
This assumption destroys the intended continuity, messes up the carbon cycle calculations, and messes up the minds of those like Andrews who can’t keep track of what is in their carbon cycle calculations.
The proper physics way to formulate this problem is the way I suggest, e.g., to do the natural and human carbon cycles separately using my (1). We can add them up later, if we wish.
This may be the most important point of disagreement in these discussions.
Ed
Dear Uncle Bert,
More specious waffle. You are obviously running scared from the 1812 to 1961 instrumental record because it thwarts your political narrative. All you have to offer on this occasion is a list of excuses. You can’t falsify anything with excuses and you can’t falsify measurements. They are what they are.
You said:
“That should have excluded the two main series (Giessen/Germany and Poona/India) which are at the base of his 1940-1942 “peak”, which doesn’t exist in any other measurement or proxy.”
I have already falsified this in my previous comment.
Additionally your list of excuses are confusing. You refer to a figure and then talk about something else.
You said:
“A peak of some 80 ppmv in only 5 years is only possible if you burn down a lot of forests and regrowth in 5 years simply is impossible.”
You’re making the same stupid mistake as Ralph Keeling. You are ignoring the oceans. All your excuses are falsified by Bromley & Tamarkin 2022.
Bromley & Tamarkin 2022; Correcting Misinformation on Atmospheric Carbon Dioxide; https://budbromley.blog/2022/05/20/correcting-misinformation-on-atmospheric-carbon-dioxide/ Accessed 28-8-2023
They examined data following the explosive volcanic eruption of Pinatubo on the island of Luzon in the Philippines in June 1991. This eruption emitted large amounts of aerosols into the atmosphere blocking sunlight and reducing SSTs and surface temperatures. This altered the Henry’s Law ratio causing a reduction in oceanic emissions lowering the atmospheric concentrations. There was a large natural movement down in atmospheric concentrations of CO2 post the eruption, followed after that by an even larger natural movement back up.
The large movement down in CO2 concentrations post the eruption occurred despite the fact that during this same period, human emissions of CO2 continued unabated. Natural emissions also continued from, e.g. biosphere decay & ocean emissions. During 1991-1992 there was an El Nino event which caused increased emissions from a warmer Pacific Ocean. On top of that, the volcano itself added large amounts of CO2 gas to the atmosphere. In spite of all these emissions, overall SSTs dropped post the eruption causing a large drop in atmospheric CO2 concentrations.
“According to the results of this study, the second derivative (i.e., the acceleration) of CO2 concentration dropped precipitously in the 2 years following Pinatubo to its lowest point in the pre-Pinatubo Mauna Loa record, despite the CO2 additions by humans, natural sources, a volcano and an El Nino. Nature rapidly absorbed the added CO2 and then more rapidly accelerated again to reset its CO2 concentration to trend.
there is no other known, logical or physically possible sink for such a large amount of CO2 to be absorbed so rapidly other than ocean surface.
The environment, mostly ocean surface (since ocean about 71% of Earth’s surface,) demonstrated rapid CO2 absorbance capacity which is 239 times larger than maximum possible net human emissions. We conclude that net human emissions are trivially minor, negligible, and absorbed and re-emitted along with the 239 times larger change in natural CO2.
In the 2 years following the June 15, 1991 eruption of the Pinatubo volcano, the natural environment removed more CO2 than the entire increase in CO2 concentration due to all sources, human and natural, during the entire measured daily record of the Global Monitoring Laboratory of NOAA/Scripps Oceanographic Institute (MLO) May 17, 1974 to June 15, 1991. Then, in the 2 years after that, that CO2 was replaced plus an additional increment of CO2.”
You said that Beck copied good and bad data. What you meant is that Beck should have cherry picked his data to make it look like your ice core record.
Then you follow Keeling and blame an inversion. Like an inversion occurred at all 901 locations at the precise time they were all taking sample measurements. Even a grade 5 child can see through this.
Then you doubled down on calibrating stomata against ice core proxies. Only you do that. I have a chart that I can’t show you as I have no web link to the chart. You can find it. It is Figure 7-13 in the book Climate Truths. You’ll have to buy the book. http://www.climate-truths.com. We have charted Stomatal birch CO₂ vs Antarctic ice core CO₂ after Steinthorsdottir, 2013. We did not calibrate CO2 to the ice core data but merely charted them together. It shows CO2 going up and down and the ice core flat lining it’s way through the middle like an average.
Then there’s the flimsy excuse that the instruments were too close to vegetation and the plants were expiring CO2. This conveniently ignores that fact that readings were taken during the day when the plants were taking in CO2 and not expiring.
Patrice Poyet points out.
Poyet, Patrice 2021 in ResearchGate Discussion.
Global Warming (Part 1): Causes and consequences of global warming, a natural phenomenon, a political issue, or a scientific debate?
https://www.researchgate.net/post/Global_Warming_Part_1_Causes_and_consequences_of_global_warming_a_natural_phenomenon_a_political_issue_or_a_scientific_debate#view=5ce771de3d48b7330442d974
“A typical example where one confuses measurements (IR spectroscopy since 1959, or chemical since 1812 the accuracy of which we discussed before) with proxies delivering reconstructed values that are the result of a model applied on data coming from a low pass filter (firnification=convolution) that changes both the resolution and the dynamic of the records.
You can only compare ice-records with ice-records.
“Ice cores furthermore are low-pass filters on the temperatures themselves because of the “firnification” process.” [Poyet, P., 2021. The Rational Climate e-Book: Cooler is Riskier. The Sorry State of Climate Science and Policies. Final First Edition, April 19th, 125 Figures, 185 Equations, 473 pp., e-ISBN 978-99957-1-929-6, DOI: 10.13140/RG.2.2.28648.80640
(Ch. 5 Glaciers, Ice-Cores, Arctic and Antarctic, Page 182 on Page 189; Also page 110.)] “It takes decades, sometimes centuries before the air is completely trapped in the ice (before that, slowly decreasing exchanges remain with the atmosphere) and the composition of it is a complex sort of “mixed average” over the time during which the firnification process operates. In fact, ice core data, though providing some information, are not accurate proxies of the atmospheric composition (they depress, for various reasons, CO2 content that leaks when there is drainage during the firnification – and there is – as this gas is very soluble) nor of the temperature. They are just a better than nothing proxy. You can compare them between each others (e.g. Arctic versus Antarctic searching for the location of a volcanic eruption), but mixing apple, oranges and cabbages does not deliver any scientific result.””
Even your precious ice core record is fake. Ice core records have regularly gone over 300 ppm and as high as 500 ppm 3,000 years ago. The Byrd Core, e.g., has undergone intense attacks that really don’t stand up to any scientific scrutiny. Referring to the chart from Poyet 2021 of proxy measurements shows Camp Century Core in Greenland and the Byrd Core in the Antarctic going above 400 ppm.
This is Figure 15 from:
Mixing Proxy and Measured Data
DOI: 10.13140/RG.2.2.19788.95360/1
https://www.researchgate.net/publication/354144035_Mixing_Proxy_and_Measured_Data
which is taken from Figure 75 in Poyet 2021. The Rational Climate e-Book: Cooler is Riskier. The Sorry State of Climate Science and Policies. Final First Edition, April 19th, 125 Figures, 185 Equations, 473 pp., e-ISBN 978-99957-1-929-6, DOI: 10.13140/RG.2.2.28648.80640
Pre-Industrial CO2 concentrations from Antarctica and Greenland ice cores of up to 500ppm that were rejected by authors of various papers because they did not fit with the “man-made climate warming” theory. Poyet 2021.
Byrd Core has come under general attack, including from you above, by stating that the core samples were contaminated with drilling fluid. It has been said that everything Jaworowski said regarding the Byrd Core was refuted by Etheridge et al 1996 by the three ice cores drilled by Etheridge et al in 1996. Yet Etheridge never mentioned Jaworowski or the Byrd Core or drilling fluid in his paper. Etheridge did not refute anything.
Etheridge et al 1996 ice cores were for the last 1000 years and did not cover the 500 ppm period from Neftel et al 1982 which was 3,000 YBP. He was specifically looking at the last 200 years when CO2 increased. His CO2 measurements from his ice cores were based on assumptions and models. His CO2 growth was attributed to humans burning fossil fuels by way of assumption, not measurements.
Jaworowski points out that this criticism of contaminated core samples is valid for all other ice cores from the Antarctic since 1985.
There is no valid criticism of Neftel et al 1982 or Jaworowski 1992a. Both the Camp Century Core and the Byrd Core are valid CO2 proxy measurements.
As pointed out by Poyet, Callendar cherry picked the so called “Gold Standard” Ice Core Record leaving out all data showing CO2 proxy measurements above 300 ppm. Every time data is presented that shows CO2 above 300 ppm before 1750 it gets attacked by those supporting the IPCC’s narrative. These attacks don’t stand up to scrutiny.
And as for politics. The strategy employed by the socialists is infiltration and subversion. Subversion is where they say they are not who they actually are and are not doing what they are doing. Actions speak loader than words. You are actively pushing the global socialist agenda. You have infiltrated the CO2 Coalition.
Dear Ferdinand,
Perhaps to give you some perspective, please look at my Figure 7. The top row shows the natural distribution of natural carbon among the four IPCC reservoirs. Only 1.4% is in the atmosphere. 90% is in the oceans. This is the equilibrium distribution for the fast carbon cycle.
Human carbon has added about one percent to the total carbon in the carbon cycle. If humans ever stop emitting carbon to the atmosphere, the human carbon cycle would move to the same equilibrium percentages as the natural carbon cycle. At that equilibium, human carbon would all only 4 ppm to the atmosphere.
My calculations do perfect carbon accounting because I keep human carbon atoms separate from natural carbon atoms. No one else, to my knowledge, is keeping the human and natural carbon atoms entirely separate in their carbon cycles. Not even you.
My one specific objection to your comment is there is no Tau of around 50 years. My figure 5 shows e-time s the time for a level to move 63% of the way to its balance level. You claim your tau does the same thing. Therefore, you tau is really my Te. There is no difference. Te explains everything you use to justify your use of Tau.
Figure 5 shows how the level approaches its balance level seemingly very slowly as it gets closer to its balance level. You have use that “very slowly” feeling to invent a tau but your tau is still Te.
I think the other weakness in your argument is that you do not yet understand balance levels.
Dear Ferdinand,
In reply to your comment: July 8, 2025 at 4:25 am
You are correct that my calculations in HumanBB show a much smaller increase in CO2 that the total measured CO2.
That is because my HumanBB calculations are only for human CO2. Notice, those calculations begin with zero levels in the reservoirs and only human carbon gets added each year.
The difference is the amount that natural carbon has added to the atmosphere.
You have discovered how I calculated the effect of human CO2 by using IPCC’s own data.
Thus, my conclusion that according to IPCC’s own data, human carbon adds very little to the CO2 in the atmosphere.
Ed,
The mass-balance formula we have long discussed only makes sense when the natural absorption term includes aborption of ALL types of carbon. Jim discovered what you and I already knew and maybe even Brendan has figured out. You are motivated to confuse the issue because correct analysis proves that your separate anaylsis of industrial and natural carbon hid from you an important insight: natural processes are removing substantially more carbon from the atmosphere than they are adding. That makes it very tough for Jim to argue natural processes are a significant source of the rise, but he is trying. I do not expect him to be successful. You might want to look at graphs of human emissions and atmospheric accumulation in your own earlier papers, which you have omitted from the current one.
Your conclusion that industrial carbon levels in the present atmosphere are small is old news, was anticipated in the 1955 Seuss paper, and is not relevant to the question of why atmospheric carbon levels have been increasing.
David,
Thinking only of net sinks obscures the possible increase in atmospheric carbon due to increasing natural sources. Keep in mind that yearly emissions from natural sources are twenty times more than industrial emissions. Your simple math will never distinguish the sign of the difference between annual natural sources and sinks. That’s why I’m working on a method of determining it. The main thing I know is Mauna Loa data cannot be fitted by my model without allowing for an increase in emissions. That is why I agree with Dr Ed’s rejection of H1.
If decaying vegetation wasn’t at least as much as previous amounts absorbed, there would begin to be a deficit.
You miss the point by focusing on where the carbon is coming from, or at least by assuming it’s all from fossil fuel. The problem is determining how it’s being distributed and to what degree fossil fuels have contributed to the rise in CO2 in the atmosphere.
The second reference for the modern CO2 measurements at Giessen (Germany) should be:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/giessen_2005-07-14.png
The historical measurements were at 7 AM, 2 and 9 PM.
That already gives a bias of about +40 ppmv, compared to the ice cores.
Even the modern average at still rural Linden/Giessen is good for average +40 ppmv, together already +80 ppmv for the historical measurements.
Calendar was completely right to reject all historical measurements for “agricultural purposes”…
Jim,
You write “If [carbon from] decaying vegetation wasn’t at least as much as previous amounts [of carbon] absorbed…” You seem to be implying it could be more! Are you vying with Demetris for the Nobel Prize in Alchemy?