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.
“Finally, we have the Natural Flux Theorem [postulated July 6, 2025 at 10:23 am]: “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.” This also remains unproven.”
Ferdinand,
So, what are the before and after ratios of human emissions and natural emissions that would support this theorem?
Ferdinand Engelbeen July 29, 2025 at 4:23 am AND
To everything Ferdinand has written in these comments.
Finally, I see the fundamental difference between what Ferdinand, Burton, Lindzen, Spencer, Etc, Etc, are saying versus what I am saying.
Tau will never be the same as Te because thet are completely different concepts.
…….. Outflow = Level / Te …………….. (2)
Te and (2) describe a physical process.
…….. Tau = disturbance / effect
Tau is a curve fit to historical data.
Te and Tau will never be the same thing even if, at times, their values happen to be the same. They are fundamentally different concepts.
The Tau boys and girls are trying to curve fit historical data.
The Te boys and girls are doing the physics that produces and explains the historical and future data.
Never the twain’s shall meet, as they say.
I admit, in all my years of physics, I have never come across anyone, until now, who does not understand that physics is a subject that attempts to explain why things happen. I have always done physics with people who understand physics, until now.
But now, I am dealing with CO2 Coalition people who, frankly, don’t have a clue about how physics works.
So, I have been clearly wrong. The CO2 Coalition boys and girls are freaking physics deprived.
They are so physics deprived that they cannot understand my equations (1) and (2). They don’t get that these equations describe how the carbon cycle works.
Ferdinand claimed (way back in these comments) that I changed my method related to Te.
So, I looked back at my 2019 paper and found that it uses the same (1) and (2) and its derivations as all my later papers. I haven’t changed anything fundamental in my model. I have explained it better in my subsequent papers, but I have not changed my fundamental model and its derivation.
In conclusion, everyone who wants to follow physics can and should reject EVERTHING that Ferdinand has preached in these comments. Ferdinand and his CO2 Coalition are in an entirely different universe that does not understand how to use physics to explain how the carbon cycle works.
To David Andrews and all,
Many comments ago, David Andrews asked me: Why do I not partition my description of the Delta14C data into 12CO2 and 14CO2?
This is a very good question and here is my answer. My Figures 9 and 10 are relevant to this explanation.
Delta14C is about 14CO2 and its connection to 12CO2. The fact that Delta14C remains near zero (really 1000 before they subtracted 1000) has allowed carbon dating.
The constancy of Delta14C even as 12CO2 has gone up and down, indicates the inflow of natural carbon into the atmosphere has a constant ratio of 14C/12C.
So, imagine that this inflow is a like a river. The bomb tests added 14CO2 and this increases Delta14C by almost 70%. Then the bomb tests stopped.
This set up a perfect experiment where 14CO2 was way above its natural balance level set by the natural inflow of 14CO2.
After 1970, Delta14C data show the 14CO2 level approached its natural balance level, defined by Delta14C = zero, exactly following equation (2) Outflow = Level / Te, with a constant Te of 16.5 years.
This happened while 12CO2 was increasing but the same thing would have happened if 12CO2 had remained constant. 14CO2 did not return to ITS original value. 14CO2 returned to Delta14C = zero. My model perfectly explains how this happened.
Therefore, 16.5 years is not only the Te for Delta14C, 16.5 years is also the Te for 14CO2 because 14CO2 caused all the change in Delta14C.
This corrects my previous papers that say the Te for 14CO2 was 10 years. I now see that it is much simpler.
This also makes 16.5 years the upper limit for the Te for 12CO2. Everyone knows that 12C flows through the carbon cycle faster than 14C because 12C is lighter. Maybe no one knows how much faster.
This certainly means the outflows of CO2 cannot ever be 50 years. (We now understand this from my previous comment that explains that Tau is not related to equation (2), but it only a useless curve fit to data.)
There are many papers that indicate the Te of 12CO2 is less than 6 years. The IPCC says the Te of 12CO2 is about 4 years, and IPCC’s data for its natural carbon cycle show this Te is about 3.5 years.
In conclusion, Delta14C was a once-in-a-lifetime experiment that allows us to measure the Te for 14CO2, and this sets an upper limit on the Te for 12CO2.
Delta14C also fully explains why the 14CO2 level has increased since 1950. It increased because the natural inflow or 12CO2 increased while keeping Delta14C equal to zero.
ADMIN NOTE: When we post a comment, this comment list reverts back to previous comments rather than returning to the last comment. To get back, we must click the Newer Comments link. I cannot control this.
Dr. Ed, August 4, 2025 at 12:28 pm
“The Te is NOT 4 years for 14CO2. Do you see the “14” in Delta14C?”
If all CO2 is equal, then the removal rate of 14CO2 should be equal to that of 12CO2 and 13CO2, with maximum a few % change in isotopic ratio. Not an order of magnitude…
For 14CO2 even faster, due to the supply of 14C-free FF CO2.
“You are wrong because I define Te = Level / Outflow …… (2)
That causes a lot of confusion… The “e” in Te is normally used as the e-fold decay rate of some extra injection of CO2 in the atmosphere. Either had used TT (turnover time) or RT (residence time) and things were clear.
And you are using Te as residence time for the bulk of CO2, but Te as decay rate for 14CO2, So which definition did you use for Te for what variable?
“The definition (2) does not say anything about a single CO2 molecule. It says “level” divided by “outflow.” Which obviously does not refer to a single molecule. “
If 25% of all CO2 each year flows out of the atmosphere, then there is a 25% possibility that any individual CO2 molecule flows out of the atmosphere. Thus your Te of 4 years is the residence time of any single CO2 molecule in the atmosphere.
“Furthermore, your implication that (2) is a “one-way process” is further BS. In (2), we need to know only two of the variables to calculate the third variable.”
Which only has some physical meaning if there are no direct returns or processes that are independent of the CO2 level in the atmosphere…
The formula Te = Level / Outflow only calculates the overall Te, no matter if the cause of the outflow is the level in the atmosphere or completely independent of the level in the atmosphere…
In the case of the outflow from atmosphere to vegetation in spring/summer, the outflow (already over half the total outflow) is near completely independent of the CO2 level in the atmosphere and mainly caused by temperature and sunlight.
Thus I am very curious to see your calculation of the outflow from the atmosphere into vegetation, based on your formula outflow = level/Te.
“I reply, your calculation that “shows Te/Tau of 50 years” is not a valid calculation. Your calculation is not based on physics. You have not presented anywhere any valid calculation that Te/Tau is 50 years.”
As far as I have learned a long time ago, an exponential decay rate is calculated as the removal rate of a deviation in a process, caused by the distance to an equilibrium of that process to reach 1/e of the original deviation. No matter if the deviation is positive or negative or the equilibrium is 295 ppmv or zero ppmv…
That is what Wiki shows as exponential decay rate:
https://en.wikipedia.org/wiki/Exponential_decay
If you have a different definition, then I like to see that…
And with the 50 year decay rate we can predict the future CO2 level without problems, as far as human emissions increase linear as they do today: a slightly quadratic increase in the atmosphere at about half total human emissions over time.
“Where’s your data? There are no measurements that can tell the difference between human-caused 12CO2 and natural-caused 12CO2.”
There is no difference between 12CO2 from FF and 12CO2 from natural sources, but there is a difference in 13C/12C ratio between these two:
Over the past 800,000 years the atmosphere in equilibrium with the oceans had a δ13C ratio of -6.5 +/- 0.4 per mil, until about 1850. After that there is an enormous drop to below -8 per mil δ13C, caused by FF emissions and not by decaying vegetation, as vegetation increased over time, thus increasing the 13C/12C ratio of the atmosphere.
Here for the LGM up to today in three parts:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/co2_d13C_lgm_cur.png
Over the past 600 years: 10% in the atmosphere, 6% In the ocean surface, based on the drop in δ13C
https://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
“(2) explains the return of Delta14C to its original level of zero and the small drop below zero caused by human 12CO2 emissions.”
Except that Te for 12CO2 is 4 years and for 14CO2 it is 16 years, while they should be equal…
“(2) can replicate IPCC’s equilibrium at 280 ppm without any need for a Tau of 50 years.”
With a Te (as decay rate) of 4 years the equilibrium does not return to 280 ppmv from 425 ppmv. It does return to a much higher level, as also Jim Siverly assumes.
David Andrew, August 4, 2025 at 8:23 pm
Interesting read that 14C increases as absolute amount in the atmosphere, despite a drop in ratio…
Ultimately that will drop when the two “fast” reservoirs, ocean surface and vegetation, in equilibrium with the atmosphere will drop their 14C content together into the deep oceans (no matter in what way that happens).
But I don’t think that Dr. Ed or Jim do see what that implies for the isotopic ratio’s in the atmosphere…
Ferdinand Engelbeen August 6, 2025 at 5:01 am
Dear Ferdinand,
Once again, you misinterpret the data, when you write, “Interesting read that 14C increases as absolute amount in the atmosphere, despite a drop in ratio…”.
As I clearly wrote, it is NATURAL 14C that follows NATURAL 12C based on the fact that Delta14C stayed at zero even as 12C in the atmosphere increased.
This helps us distinguish between natural and human CO2 in the atmosphere.
Dr. Ed, August 6, 2025 at 2:22 am
“Finally, I see the fundamental difference between what Ferdinand, Burton, Lindzen, Spencer, Etc, Etc, are saying versus what I am saying.”
“Tau will never be the same as Te because that are completely different concepts.”
That is what we were trying to say all the time…
“…….. Outflow = Level / Te …………….. (2)
Te and (2) describe a physical process.”
Te = Level / Output is a physical process, no matter if the Output is caused by Level or by any other process, independent of Level… Thus if only one process (like the output into vegetation) works largely independent of the CO2 level in the atmosphere, you can’t calculate the outflow, because Te is not the real Te for that process…
“…….. Tau = disturbance / effect
Tau is a curve fit to historical data.”
That is an absolutely false accusation. Tau is mostly calculated from the observed distance to the historical equilibrium, but also can be calculated from any time period where the change in disturbance and change in effect is known, without knowing the historical equilibrium. In both cases Tau is around 50 years. That has zero, nothing to do with curve fitting. See:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/acc_decay.jpg
The increase in the atmosphere is measured in the upper graph, the increase of the pCO2 of the oceans since 1850 is calculated with the formula of Takahashi and the difference between these two is used as “disturbance”.
In the second graph, the observed “effect” as result of the increase of CO2 in the atmosphere is plotted together with the polynomial to avoid the (huge) influence of temperature variability in the result.
The lower graph is the resulting Tau, based on the polynomial.
So, where is the “fit” to historical data? In the use of the calculated SST pCO2? We can calculate the same Tau from the difference between 2020 and 1960 for both the increase in the atmosphere and the increase in uptake, without looking at the calculated sea surface pCO2…
With back-calculation from these graphs, one even can find the current equilibrium, which is between 280 and 300 ppmv.
“So, I have been clearly wrong. The CO2 Coalition boys and girls are freaking physics deprived.”
Wow. Only Dr. Ed knows what physics is. All these boys and girls that don’t follow the reasoning of Dr. Ed are physics deprived. Including Dipl.Ing Dietze, Lindzen, Spencer, and many, many, many others, including myself…
Sad, very sad if one needs to accuse others of not knowing physics as an excuse to poison the discussion.
Dr. Ed and others,
I am working on a one-compartment bidirectional model to describe the dispensation of 14C in the atmosphere. It will include inputs from N2 production and the combined reservoirs. The output will just be from a single removal rate constant analogous to 12C. Are there any other inputs to be considered? Would we expect a different input rate from land versus ocean?
Ferdinand Engelbeen August 6, 2025 at 7:01 am
You wrote:
All CO2 is NOT equal because a 14C atom is heavier than a 12 atom. Your use of “removal rate” is unphysical. The “supply of 14C-free FF CO2” is part of the Natural 14C level in (2).
You wrote:
Ferdinand, I am the guy who defined Te, so don’t tell me how it is “normally used.”
I defined it in my equation (2). I called it “e-time.” Later, when I found IPCC’s definition of Turnover Time, I wrote that Te was the same as IPCC’s Turnover time. But since IPCC’s turnover time is confused with residence time, etc., I kept my definition of Te very clear.
(Please see where I have copied IPCC’s definitions of Lifetime above these comments, so you don’t confuse what the IPCC says about the times.)
You prove my point when you wrote:
Everything you write confuses things because you do not follow even IPCC’s definitions of the various Lifetimes.
Equation (2) is Outflow = Level / Te
Te is clearly defined in (2). Te applies to the carbon that is in the respective Level, and it only applies to outflows, not inflows.
Yet, in the case of IPCC’s natural carbon cycle at equilibrium, I can validly calculate the Te for each outflow node by reversing (2) to get Te = Level / Outflow.
This gives me the six Te that apply to IPCC’s natural carbon cycle at equilibrium.
These Te apply to human carbon also because it is identical to natural carbon.
With these Te, I can (and did) calculate the true effect of human carbon on the carbon cycle without confusion with natural carbon.
You wrote:
NO. Your claim is incorrect.
You wrote:
You are trying to curve-fit the data. That is unphysical. Nature is not as complicated as you make it out to be. Equation (2) is based on first principles. Good engineers and scientists who understand models have applied (2) to virtually everything in nature.
I don’t need to justify my use of (2). I defined (2) as a hypothesis. That makes (2) falsifiable by proving it makes a false prediction. This is the way science works.
(2) correctly predicts the return of 14CO2 to its natural balance level. That is a remarkable achievement.
(2) correctly replicates IPCC’s natural carbon cycle data at equilibrium.
(2) correctly predicts any modification of IPCC’s data for its natural carbon cycle.
(2) correctly predicts chemical reactions in pharmacological models.
(2) is the basis of electrical circuit theory and Ohm’s Law.
(2) is the basis of systems engineering itself.
(2) is the basis of Markov Chains.
You wrote:
Sorry, you learned incorrectly.
Thank you for your reference to the WIKI article in Exponential Decay.
I am totally surprised that you do not understand that my Te, Level, and Outflow in (2) are exactly what the WIKI article calls
• Te = Tau = 1 / Lamda = Mean Lifetime
• Level = N(t)
• Outflow = – dN(t)/dt
The WIKI article justifies my carbon cycle model equations (1) and (2), and all its derivations.
I am also surprised that you do not immediately recognize that this WiKI article shows that everything in your model and extensive explanations are WRONG. The WIKI article does not try to curve fit data like you do. Its Tau is NOT your Tau.
Ferdinand, this WIKI article proves that your criticisms of my model are entirely wrong.
I used these concepts in my 1965 PhD thesis, which real physicists still widely cite today as one of the important breakthroughs in climate science.
Yet, you and other unethical members of the CO2 Coalition have censored, trashed, and blacklisted my carbon cycle model because its prediction conflicts with the Coalitions business mantra that claims human CO2 emissions have saved the planet.
I won the People’s Choice Award at the 1993 Microsoft Windows World Open software contest for my model that modeled human body physiological responses to changing weather and environmental conditions, which was the first time anyone used a computer model in a murder trial. My model successfully defended the accused.
As your kindly-referenced WIKI shows, my carbon cycle model based on (1) and (2), uses the same formulation as the following:
Natural sciences
• Chemical reactions: The rates of certain types of chemical reactions depend on the concentration of one or another reactant. Reactions whose rate depends only on the concentration of one reactant (known as first-order reactions) consequently follow exponential decay. For instance, many enzyme-catalyzed reactions behave this way.
• Electrostatics: In a RC circuit, the electric charge (or, equivalently, the potential) contained in a capacitor (capacitance C) discharges through a constant external load (resistance R) with exponential decay and similarly charges with the mirror image of exponential decay (when the capacitor is charged from a constant voltage source though a constant resistance). The exponential time-constant for the process is so the half-life is. The same equations can be applied to the dual of current in an inductor.
• Furthermore, the particular case of a capacitor or inductor changing through several parallel resistors makes an interesting example of multiple decay processes, with each resistor representing a separate process. In fact, the expression for the equivalent resistance of two resistors in parallel mirrors the equation for the half-life with two decay processes.
• Geophysics: Atmospheric pressure decreases approximately exponentially with increasing height above sea level, at a rate of about 12% per 1000m.
• Heat transfer: If an object at one temperature is exposed to a medium of another temperature, the temperature difference between the object and the medium follows exponential decay (in the limit of slow processes; equivalent to “good” heat conduction inside the object, so that its temperature remains relatively uniform through its volume). See also Newton’s law of cooling.
• Luminescence: After excitation, the emission intensity – which is proportional to the number of excited atoms or molecules – of a luminescent material decays exponentially. Depending on the number of mechanisms involved, the decay can be mono- or multi-exponential.
• Pharmacology and toxicology: It is found that many administered substances are distributed and metabolized (see clearance) according to exponential decay patterns. The biological half-lives “alpha half-life” and “beta half-life” of a substance measure how quickly a substance is distributed and eliminated.
• Physical optics: The intensity of electromagnetic radiation such as light or X-rays or gamma rays in an absorbent medium, follows an exponential decrease with distance into the absorbing medium. This is known as the Beer-Lambert law.
• Radioactivity: In a sample of a radionuclide that undergoes radioactive decay to a different state, the number of atoms in the original state follows exponential decay as long as the remaining number of atoms is large. The decay product is termed a radiogenic nuclide.
• Thermoelectricity: The decline in resistance of a Negative Temperature Coefficient Thermistor as temperature is increased.
• Vibrations: Some vibrations may decay exponentially; this characteristic is often found in damped mechanical oscillators, and used in creating ADSR envelopes in synthesizers. An overdamped system will simply return to equilibrium via an exponential decay.
• Beer froth: Arnd Leike, of the Ludwig Maximilian University of Munich, won an Ig Nobel Prize for demonstrating that beer froth obeys the law of exponential decay.
Social sciences
• Finance: a retirement fund will decay exponentially being subject to discrete payout amounts, usually monthly, and an input subject to a continuous interest rate. A differential equation dA/dt = input − output can be written and solved to find the time to reach any amount A, remaining in the fund.
• In simple glottochronology, the (debatable) assumption of a constant decay rate in languages allows one to estimate the age of single languages.
• The core routing protocol on the Internet, BGP, has to maintain a routing table in order to remember the paths a packet can be deviated to.
You wrote:
No, you can’t. You don’t even have a model that can predict. Curve fit predictions are not physical models
You wrote:
Yes, there is an isotopic difference between human and natural CO2, both in 13C and 14C. We already discussed these things, and I showed these differences indicate the amount of human CO2 in the atmosphere is nowhere near 33%. The details are a separate subject than the subject here.
You wrote:
No, they should not be equal. You do not understand this.
Dr. Ed, August 6, 2025 at 3:20 am
“This also makes 16.5 years the upper limit for the Te for 12CO2. Everyone knows that 12C flows through the carbon cycle faster than 14C because 12C is lighter. Maybe no one knows how much faster.”
The isotopic ratio changes somewhat, that can be calculated from the difference in molecular weight, similar to 13CO2, but twice as much.
For a discrimination of about 0.8% in δ13C for 13CO2, compared to 12CO2 flows between the atmosphere and the oceans (bidirectional), that would give a discrimination of around 1.6% between 14CO2 and 12CO2.
No big deal at all and far from the difference between 3.5 years for Te of the bulk 12/13CO2 and 16.5 years for 14CO2.
Can you explain that difference?
And you forget the dilution by the 14C-free CO2 from the use of fossil fuels and the return of “normal” 14CO2 of pre-industrial times from other reservoirs… That makes that the 16.5 years is a minimum limit, not a maximum limit…
About the introduction:
“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.”
It is not my task to defend the IPCC and I do disagree with them on many items, including the “long” Tau’s based on the saturation of the different reservoirs, but please, don’t accuse them of points they didn’t say or implied.
The IPCC (and we) make a differentiation between T (turnover time) and Ta (adjustment time or Tau) and only the latter is what influences the decay of 12/13/14CO2 back to equilibrium, whatever that may be, according to the IPCC (and us). T (your Te) plays no role at all for the IPCC (and us)…
Stephen Paul Anderson
August 5, 2025 at 9:38 am
“Finally, we have the Natural Flux Theorem [postulated July 6, 2025 at 10:23 am]: “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.” This also remains unproven.”
Ferdinand,
So, what are the before and after ratios of human emissions and natural emissions that would support this theorem?
In theory:
Human emissions increased about a five fold between 1960 and 2020. If the natural emissions also increased a five fold over the same time span, then for the same processes that absorb natural and fossil CO2 alike, the increase in CO2 of the atmosphere would be caused by both in ratio to the inputs. Thus far more from natural than from FF.
In reality:
There is hardly any increase in natural emissions: +33% between oceans and atmosphere and a meager 12% between vegetation and atmosphere. Not 500% for both together.
Te even slightly increased, as the increase in mass was higher than the increase in outflows…
In addition to clear up the difference between T/Te (turnover/residence time) and Ta/Tau (adjustment time), here a few graphs to show the difference in flows that cause both. The global seasonal flows graph still needs in part real figures, but the underlying difference is hopefully clear…
Global seasonal flows:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/seasonal_flows_b.png
Both the seasonal outputs into oceans and vegetation are the origin of the 4 years Te, but none of the seasonal flows is dependent of the CO2 level in the atmosphere, except for a small part in the next graph.
Seasonal flows at Mauna Loa:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/seasonal_flows_mlo_b.png
The small net removal rate is what makes the 50 year Ta/Tau
Ferdinand Engelbeen August 6, 2025 at 7:38 am
Dear Ferdinand,
I wrote, “This also makes 16.5 years the upper limit for the Te for 12CO2. Everyone knows that 12C flows through the carbon cycle faster than 14C because 12C is lighter. Maybe no one knows how much faster.”
You wrote, “The isotopic ratio changes somewhat, that can be calculated from the difference in molecular weight, similar to 13CO2, but twice as much.
“For a discrimination of about 0.8% in δ13C for 13CO2, compared to 12CO2 flows between the atmosphere and the oceans (bidirectional), that would give a discrimination of around 1.6% between 14CO2 and 12CO2.
“No big deal at all and far from the difference between 3.5 years for Te of the bulk 12/13CO2 and 16.5 years for 14CO2.
“Can you explain that difference?”
No. I am only talking about the data. At the moment, I cannot explain the reason the data show a large difference between the Te for 14CO2 and 12CO2.
You wrote, “And you forget the dilution by the 14C-free CO2 from the use of fossil fuels and the return of “normal” 14CO2 of pre-industrial times from other reservoirs… That makes that the 16.5 years is a minimum limit, not a maximum limit…”
I totally disagree with your claim. My method of calculating properly accounts for such “dilution” because I separate the human carbon cycle from the natural carbon cycle. Your method puts human and natural CO2 into the same pot and produces confusion. All your conclusions based on your inaccurate physics are wrong.
Dr. Ed, August 6, 2025 at 7:29 am
“I don’t need to justify my use of (2). I defined (2) as a hypothesis. That makes (2) falsifiable by proving it makes a false prediction. This is the way science works.”
Well here are already two items which falsify your hypothesis:
With output = level / Te for the output in vegetation:
1960:
Te(a-g) = 589 PgC / 108 PgC/year = 5.45 year
Output = level / Te:
Output = 589 PgC / 5.45 year = 108 PgC/year
2010 (IPCC in figures 2/3):
Output = 829 PgC / 5.45 year = 152 PgC/year
In reality, the total outflow increased to 122 PgC/year
Thus your Te(a-g) is completely at odds with reality.
Then, again, the difference in Te for 12/13CO2 and 14CO2.
If all CO2 is equal, except for a small (less than 2%) difference in dissolution speed, then an extra injection of 70% 12CO2 would need about exact the same Te as for a 70% extra 14CO2 injection. Not a difference of an order of magnitude…
If one separates the natural and human flows in my previous comment, that makes it not better:
For 2010:
Output(human): 240 PgC / 5.45 year = 44 PgC/year
In reality: 14 PgC/year… a factor 3.5.
Ferdinand Engelbeen August 6, 2025 at 7:50 am
The IPCC (above) explained its definitions of adjustment and residence times, as follows:
“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.”
You wrote that you disagree with the IPCC on many items. No problemo. But we must follow IPCC’s definitions of the terms we use. Otherwise, we produce confusion. You produce confusion when your definitions conflict with IPCC’s definitions.
You wrote that your Tau is an adjustment time that “influences the decay of 12/13/14CO2 back to equilibrium.” and that Te plays no role at all for you or the IPCC.
The IPCC (above) says, “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” … which is also Te.
So, you and your CO2 Coalition buddies are totally confused about how to use Te and Tau and Ta.
Ferdinand, I find your pathetic claims to be junk physics and delusional. You and your buddies are way outside the boundaries of rational scientific discussions. You can’t even get the basics correct.
Whereas my Te and all my calculation agree with the WIKI reference you kindly produced.
Ferdinand Engelbeen August 6, 2025 at 7:01 am
Dr. Ed, August 6, 2025 at 2:22 am
I wrote, “Finally, I see the fundamental difference between what Ferdinand, Burton, Lindzen, Spencer, Etc, Etc, are saying versus what I am saying.”
“Tau will never be the same as Te because that are completely different concepts.”
You wrote, “That is what we were trying to say all the time…” This remark proves you are using junk physics.
Your Tau totally conflicts with WIKI and my Te totally conforms with WIKI.
Doesn’t that ring a bell for you?
You wrote, “Thus if only one process (like the output into vegetation) works largely independent of the CO2 level in the atmosphere, you can’t calculate the outflow, because Te is not the real Te for that process…”
You fail to understand that Te is a first principle that helps explain the data, and that your Tau is an attempt to curve fit data that you THINK Te cannot explain when you don’t even know how to calculate the results of Te.
I wrote “Tau is an attempt to curve fit historical data.”
You wrote, “That is an absolutely false accusation. Tau is mostly calculated from the observed distance to the historical equilibrium but also can be calculated from any time period where the change in disturbance and change in effect is known, without knowing the historical equilibrium. In both cases Tau is around 50 years. That has zero, nothing to do with curve fitting.”
Your Tau has everything to do with curve fitting and nothing to do with physical processes.
You don’t have any equations of carbon flow. You have only Tau, and you think it applies to a 50-year change of carbon levels.
You ignore Te that fully describes these 50-year changes in terms of annual or shorter changes. You think you can apply an overall Tau that describes a 50-year change.
Either you do not understand physics, or you are delusional, or both.
You write, “The … difference … is used as “disturbance” and the “observed “effect” of the increase of CO2 in the atmosphere produces your Tau… based on the polynomial.
You ask, “So, where is the “fit” to historical data?”
It’s right in front of your eyes!
You write, “With back-calculation … (you) can find the current equilibrium, which is between 280 and 300 ppmv.”
You can’t back calculate a process that is moving to its equilibrium because all initial conditions are moving to the same equilibrium.
You wrote, “Wow. Only Dr. Ed knows what physics is. All these boys and girls that don’t follow the reasoning of Dr. Ed are physics deprived. Including Dipl.Ing Dietze, Lindzen, Spencer, and many, many, many others, including myself…
Sad, very sad if one needs to accuse others of not knowing physics as an excuse to poison the discussion.”
Yes, indeed, it is sad that the CO2 Coalition scientists do not recognize their incompetence in this area of physics.
You don’t get it that consensus is not a valid argument in science. Your mistake and the CO2 Coalition’s mistake is to think they know everything about carbon flow and carbon cycle models when they have no expertise in this area.
Your own WIKI reference proves your incompetence in this area.
Worse, you and they do not have the honesty to admit that you and they are wrong on this subject. Rather you and they march off like energizer bunnies beating your own drums, censoring and blacklisting good science that you do not understand.
Your and their behavior is indeed pathetic. When CO2 Coalition scientists claim your special report is valid science, they are not being scientists because they reject the honesty and ethics that must accompany science.
This discussion of your Coalition report has exposed your and their junk science. It’s time for you and the CO2 Coalition to admit you have made a gigantic error in your belief about how the carbon cycle works.
Ferdinand Engelbeen
August 6, 2025 at 9:42 am and August 6, 2025 at 9:53 am
Dr. Ed, August 6, 2025 at 7:29 am
“Well, here are already two items which falsify your hypothesis:…”
Sorry, your calculations are wrong, so your conclusions are wrong.
Dr. Ed, August 6, 2025 at 10:02 am
“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.”
That is your just the opposite in interpretation of what the IPCC says…
The IPCC expects a fast e-time at high level differences and extreme long e-times for the last removals, but none of them are residence times. The overall turnover/residence time of 4 years nowhere is mentioned in the different e-times:
https://wattsupwiththat.com/2013/12/02/is-the-bern-model-non-physical/
They explicitly write:
“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 the atmosphere and the ocean and terrestrial biota. However, a large part of that CO2 is returned to the atmosphere within a few years.”
https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_AnnexVII.pdf
They explicitly reject the equality of your 4 year T/Te with the real Ta’s/Tau’s of between some 3 years and hundreds of years and much longer as they assume. Their Ta/Tau is composed of different Ta’s for different reservoirs, but the fastest: the ocean surface is already saturated at 10% of the change in the atmosphere (and that is a real one…), thus while faster than 4 years, it stops already at 0.5 PgC/year for a change in the atmosphere of 5 PgC/year.
Dr. Ed, August 6, 2025 at 11:04 am
“Well, here are already two items which falsify your hypothesis:…”
“Sorry, your calculations are wrong, so your conclusions are wrong.”
If you don’t show where I am wrong, you can’t conclude that I am wrong…
Ed,
I must laugh at your bizarre claim that 14CO2 has returned to its “balance level.” Figs 1 and 2 in https://www.cambridge.org/core/services/aop-cambridge-core/content/view/193CDF1F705B269BC975AF178CEF1AC3/S0033822224000274a.pdf/discussion-presentation-of-atmospheric-14co2-data.pdf show the following 14CO2 concentrations, where the units are attomoles of 14CO2 per moles of atmospheric gas. (1 attomole = 10-18 moles)
– from 1900 to 1950 the 14C02 concentration grew from ~360 to 370
– the nuclear testing raised it to a peak of over 650 around 1965
– it fell to a plateau a little under 500 after 1990
– it is presently around 510 and rising
This history hardly describes “returning to a “balance level”. There is no mystery in any of this behavior. It is completely understood by mainstream science, and the rise in the 21st century was predicted in 1998 by a group at Lawrence Livermore labs https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/1998GL900010
To understand it you need to understand disequilibrium isotope fluxes which I have explained before. I know you avoid that concept because it also explains why you have been wasting your time calculating the quantity of “human carbon” in the present atmosphere.
Dr. Ed, August 6, 2025 at 10:59 am
Sorry Dr. Ed, but this discussion leads to nothing…
We used the definition of Ta/Tau as used by the IPCC and Wiki and everybody that uses exponential decay in the world. The only difference between you and many other engineers and scientists is the use of the around 4 years turnover / residence time instead of the calculated (from observations) real Ta of around 50 years.
The 4 years turnover/residence time is explicitly rejected by the IPCC as irrelevant for the calculation of the decay rates of any extra CO2 injection in the atmosphere. It is implicitly rejected by Dietze, Lindzen, Spencer and may other skeptics of the alarmist side of “catastrophic” global warming, which use the past equilibrium or current decay rate calculations for their excess CO2 decay out of the atmosphere.
Your 4 years Te is completely bogus, because it is based on outputs that are largely independent of the CO2 level in the atmosphere, thus any decay rate based on current or past levels and outputs has nothing to do with the real decay rates as can be observed/calculated.
That is (probably) my last word here, as I have better and more urgent things to do than trying to convince people that don’t want to be convinced and “forget” to mention the most relevant points of what others, like the IPCC, say to have their point…
Ferdinand,
Do you agree that Natural Emissions are about 100ppmv?
David,
“I must laugh at your bizarre claim that 14CO2 has returned to its “balance level.” Figs 1 and 2 in https://www.cambridge.org/core/services/aop-cambridge-core/content/view/193CDF1F705B269BC975AF178CEF1AC3/S0033822224000274a.pdf/discussion-presentation-of-atmospheric-14co2-data.pdf show the following 14CO2 concentrations, where the units are attomoles of 14CO2 per moles of atmospheric gas. (1 attomole = 10-18 moles)
– from 1900 to 1950 the 14C02 concentration grew from ~360 to 370
– the nuclear testing raised it to a peak of over 650 around 1965
– it fell to a plateau a little under 500 after 1990
– it is presently around 510 and rising
This history hardly describes “returning to a “balance level”. There is no mystery in any of this behavior. It is completely understood by mainstream science, and the rise in the 21st century was predicted in 1998 by a group at Lawrence Livermore labs https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/1998GL900010
To understand it you need to understand disequilibrium isotope fluxes which I have explained before. I know you avoid that concept because it also explains why you have been wasting your time calculating the quantity of “human carbon” in the present atmosphere.”….
Do you even understand balance level? Balance level is (inflow)(Te)=Lb. That is true for 12C, 13C and 14C. It has nothing to do with disequilibrium isotope fluxes.
Ferdinand Engelbeen
August 6, 2025 at 12:48 pm
“Sorry Dr. Ed, but this discussion leads to nothing…”
“That is (probably) my last word here”
Dear Ferdinand,
In case you hang in here long enough to read this comment, I apologize for responding pejoratively to some of your arguments. However, I don’t apologize for my criticisms which I think were largely accurate, but perhaps I could have been more polite.
I hope you will consider a few points to help you make arguments in the future. You repeatedly made assertions here without backing them up, particularly regarding our requests for the physical principles underlying the development of a model. I am still not clear on your claim to have calculated Tau independent of historical equilibrium. The fact that it requires using a correlation and calculating Tau based on a polynomial fit is problematic. Your use of anecdotal data, such as calculating a Te from Level/Output in 1960 and contrasting it with 2010, is troubling.
The most egregious flaw in your presentation is to claim output to vegetation is not concentration dependent. Again, the CO2 Coalition’s tree growth “experiment” is an example. Growth won’t be zero at 280 ppmv, but there will be no growth at zero ppmv.
Dear Ferdinand,
August 6, 2025 at 1:22 pm
I forgot to mention that appealing to the authority of the IPCC and others in the climate “science” community does not go over well with scientists outside the community.
Jim,
I would love to know your take on Figure 2 of the Radiocarbon article previously cited.
Ed,
Analyzing radiocarbon data without referring to disequilibriium isotopic fluxes is a sign of ignornance. In your case it is willful ignorance, since these things have been pointed out to you years ago. Perhaps you can explain why, despite disequilibrium isotope fluxes, the fraction of “human carbon” in the present atmsopsphere is a useful statistic.
David Andrews
August 6, 2025 at 5:22 pm
David,
Thank you for inviting my take on Figure 2 of Schwartz et al. It seems I am not alone being unable to figure out why delta14C has an e-time of 17 or so years. Qualitatively, I would explain the mole fraction curve as the removal of 14C being offset by the 100 ppmv increase in CO2 since 1960. In other words, although delta14C has essentially reached its pre-bomb balance level, the absolute amount of atmospheric 14C increased in proportion to the CO2 increase. I have not worked that out quantitatively yet, but I am working on it.
Stephen P. Anderson, August 6, 2025 at 2:43 pm
“Ferdinand, do you agree that Natural Emissions are about 100ppmv?”
Yes, but I also know that these inflows (and the counter current natural outflows) are caused by temperature, bacteria, fungi, insects, animals,… largely independent of the CO2 quantity/pressure already in the atmosphere.
Most of these huge flows cycle in and out within a year. The only outflow that counts is the net difference at the end of a full year and that is caused by two items: one-way human emissions of FF use and the extra CO2 level/pressure in the atmosphere that causes more uptake than return from the natural sinks and sources.
See the difference in causes for the huge seasonal CO2 flows and the small overall result over a year I did send at August 6, 2025 at 9:04 am
Jim Siverly, August 6, 2025 at 5:01 pm
“I apologize for responding pejoratively to some of your arguments.”
No need for an apology, have had much worse discussions with Greenpeace in the 1990’s about the use of chlorine…
I was a practical chemical engineer in my (long ago) working life, bringing new products (resins for paints, printing inks, etc.) from 1 liter laboratory production up to 17 tons batches in a real factory, with all the practical problems involved. Later on in the direction of process automation, with even less direct engineering theories…
Have several times been confronted with very brilliant people who had troubles to understand what a simple mass budget or other simple things in life imply…
That is the reason that I often use formulas without thinking of the underlying theories and when asked for these theories have to go back in 60-year old memories and sources like Wiki…
That being said:
What Dr. Ed and you used is the 4-year residence/turnover time. That is a simple formula that only looks at what the CO2 level in the atmosphere is and how much per year is going out of the atmosphere.
That doesn’t give you any clue about the underlying processes.
If that are all level/pressure dependent processes, then one may revert the formula to find the output with the calculated Te and then Te = RT or TT or whatever name you give the residence/turnover time.
If a large part of the (in this case all) processes are largely independent of the CO2 level/pressure in the atmosphere, then one may not use Te = RT, as Ta/Tau in that case is completely independent of the residence/turnover time.
That is what the IPCC explicitly and many skeptics implicitly say, but Dr. Ed ignores.
Is that appealing to authority? Or just checking that what they say is right, no matter who says it…
“I am still not clear on your claim to have calculated Tau independent of historical equilibrium. ”
There are two main reservoirs that exchange CO2 with the atmosphere: oceans and vegetation.
For the ocean (surface) the exchange formula is quite simple:
F = k•s•ΔpCO2
No matter if ΔpCO2 is between the current pCO2 and the old equilibrium or between two current pCO2 levels at several years difference.
As the formula for Ta/Tau is:
Ta = disturbance / response
It doesn’t matter over what part of the disturbance you calculate Ta, as for a linear response Ta remains the same. Even for the full disturbance, thus the full distance to the (old or new) equilibrium.
For vegetation, the response is linear too for most plants (with the C3-cycle) between 280 and 1000 ppmv. Below 160 ppmv, all trees and many other plants stop photosynthesis and die out. C4-type plants (some grasses and an important crop: corn) still are growing, but slower with the CO2 level in the atmosphere. Here an overview:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/plant_uptake.png
Again, one can calculate the Ta for plants on any segment of the disturbance/response levels.
There is one problem left: temperature variability also has a huge influence on the yearly uptake, especially in vegetation, of about +/- 2 ppmv on a change of 5 ppmv/year. That is only noise, as the long-term influence of temperature on the CO2 level in the atmosphere is very modest: some 16 ppmv/°C. Therefore it is preferable to use the polynomial through the noise…
“Jim Siverly, August 6, 2025 at 5:01 pm
“I apologize for responding pejoratively to some of your arguments.”
No need for an apology, have had much worse discussions with Greenpeace in the 1990’s about the use of chlorine…
I was a practical chemical engineer in my (long ago) working life, bringing new products (resins for paints, printing inks, etc.) from 1 liter laboratory production up to 17 tons batches in a real factory, with all the practical problems involved. Later on in the direction of process automation, with even less direct engineering theories…
Have several times been confronted with very brilliant people who had troubles to understand what a simple mass budget or other simple things in life imply…
That is the reason that I often use formulas without thinking of the underlying theories and when asked for these theories have to go back in 60-year old memories and sources like Wiki…
That being said:
What Dr. Ed and you used is the 4-year residence/turnover time. That is a simple formula that only looks at what the CO2 level in the atmosphere is and how much per year is going out of the atmosphere.
That doesn’t give you any clue about the underlying processes.
If that are all level/pressure dependent processes, then one may revert the formula to find the output with the calculated Te and then Te = RT or TT or whatever name you give the residence/turnover time.
If a large part of the (in this case all) processes are largely independent of the CO2 level/pressure in the atmosphere, then one may not use Te = RT, as Ta/Tau in that case is completely independent of the residence/turnover time.
That is what the IPCC explicitly and many skeptics implicitly say, but Dr. Ed ignores.
Is that appealing to authority? Or just checking that what they say is right, no matter who says it…
“I am still not clear on your claim to have calculated Tau independent of historical equilibrium. ”
There are two main reservoirs that exchange CO2 with the atmosphere: oceans and vegetation.
For the ocean (surface) the exchange formula is quite simple:
F = k•s•ΔpCO2
No matter if ΔpCO2 is between the current pCO2 and the old equilibrium or between two current pCO2 levels at several years difference.
As the formula for Ta/Tau is:
Ta = disturbance / response
It doesn’t matter over what part of the disturbance you calculate Ta, as for a linear response Ta remains the same. Even for the full disturbance, thus the full distance to the (old or new) equilibrium.
For vegetation, the response is linear too for most plants (with the C3-cycle) between 280 and 1000 ppmv. Below 160 ppmv, all trees and many other plants stop photosynthesis and die out. C4-type plants (some grasses and an important crop: corn) still are growing, but slower with the CO2 level in the atmosphere. Here an overview:
https://www.ferdinand-engelbeen.be/klimaat/klim_img/plant_uptake.png
Again, one can calculate the Ta for plants on any segment of the disturbance/response levels.
There is one problem left: temperature variability also has a huge influence on the yearly uptake, especially in vegetation, of about +/- 2 ppmv on a change of 5 ppmv/year. That is only noise, as the long-term influence of temperature on the CO2 level in the atmosphere is very modest: some 16 ppmv/°C over very long periods. Therefore it is preferable to use the polynomial through the noise…
“Your use of anecdotal data, such as calculating a Te from Level/Output in 1960 and contrasting it with 2010, is troubling”
If the formula of Te = level / output = 4 years and its reverse is right, it should be right for any level of CO2 in the atmosphere, except for any (temperature induced) noise… The fact that the increase in the fast cycle of the biosphere is only 13% and not 50% is a clear sign that you can’t use Te in reverse to calculate the outflows.
“The most egregious flaw in your presentation is to claim output to vegetation is not concentration dependent.”
I did only say that it is largely concentration independent: about 120 PgC is sucked away out of the atmosphere by temperature and sunlight into vegetation in only a few months from minimum to maximum uptake. Only some 2.5 PgC/yr gets into more permanent growth, that is about 2% of the total uptake which is atmospheric CO2 level/pressure dependent…
See the difference in flows I have sent on:
August 6, 2025 at 9:04 am
To myself, David Andrews and Jim Siverly re our recent comments on Delta14C.
First, let’s review the data:
1. Delta14C is about 14CO2 and its connection to 12CO2. The fact that Delta14C remains near zero (really 1000 before they subtracted 1000) has allowed carbon dating.
2. The constancy of Delta14C even as 12CO2 has gone up and down, indicates the inflow of natural carbon into the atmosphere has a constant ratio of 14C/12C.
3. After 1970, Delta14C approached its natural balance level = zero, exactly following equation (2) Outflow = Level / Te, with a constant Te of 16.5 years.
4. Schwartz et al (2024, referenced by Andrews) shows Delta14C is slightly but not significantly below zero.
5. 14CO2 did not return to its original value but returned to near Delta14C = zero.
Now let’s try to explain the above data.
First, my previous comment on this subject said the Te for 14CO2 was the same as the Te for Delta14C was incorrect.
Second, I stand by my calculation that the Te for Delta14C is 16.5 years.
Third, I stand by my published Te for 14CO2 of 10 years (Berry, 2023, Figure 13) because it is an accurate curve fit to the 14CO2 data from 1970 to 1995. Therefore, 10 years becomes the upper limit for the Te of the 12CO2.
Fourth, the increase of 14CO2 after 2000 is caused by the increase of 12CO2 AND the influence of Delta14C very close to zero.
Fifth, the decrease of Delta14C below zero is caused by human emissions of CO2.
David Andrews August 6, 2025 at 12:58 pm, wrote:
Beginning of debate
My phrase, “Returning to the balance level,” properly describes the path of Delta14C because that feature dominates over the decrease in the balance level of a few percent.
The tendency of natural Delta14C to stay close to zero is a better (and simpler) argument than the one proposed in 1998 by the Lawrence Livermore group.
Schwartz et al. say (when translated to normal English) that the addition of 14C-deficient human CO2 into the atmosphere causes more 14C from the land and oceans to flow into the atmosphere, thus increasing 14CO2.
The major problem with Schwartz’s idea is that it assumes human CO2 causes all the 12CO2 increase. The counter assumption that natural CO2 causes most of the CO2 increase is a far better explanation because this natural CO2 immediately brings in 14CO2 with Delta14C equal to zero.
Schwartz’s hypothesis would have a measurable delay in adding sufficient 14CO2 to keep Delta14C near zero. My hypothesis would have no delay, and this is what the data show.
Indeed, all forms of carbon act to return to their own equilibrium percentages, as I have described in my papers. Each form differs in its deviation from equilibrium.
We don’t need to use important-sounding phrases like “isotopic equilibration” and “disequilibrium flux” because 14C seeks its equilibrium like all other forms of carbon.
The natural 12C carbon cycle and the 14C carbon cycle are already close to their equilibrium, but human carbon is far from its equilibrium because its carbon enters the atmosphere and flows toward its equilibrium percentages as fast as possible.
This is why we must calculate the flows of human and natural carbon independently to get correct answers.
The best explanation for the increase in 14CO2 is that nature is the primary cause of the 12CO2 increase.
Ferdinand Engelbeen
August 7, 2025 at 5:16 am
Dr. Ed and I use “the simple formula that only looks at what the CO2 level in the atmosphere is and how much per year is going out of the atmosphere,” because that is all that is necessary to correctly represent the data using well-established physics.
Sometimes and in some places the temperature is sometimes warmer and sometimes colder, but on average at all times concentration drives the mass transfer. This is particularly and completely true for the ocean exchanges. The mass transfer continues in proportion to the concentrations on each side of an interface regardless of whether they in equilibrium or not. You may have come across Fick’s laws somewhere in your science background. Fick’s First Law very simply “describes the rate of diffusion across a surface or membrane. It states that the rate of diffusion is directly proportional to the concentration gradient and the diffusion coefficient.” Notice that it doesn’t describe the rate proportional to the concentration now and what it was in some previous time. If you continue to promote your view of CO2 mass transfer based on my previous sentence, you really should explain the scientific basis for it.
Never have you shown that “a large part of the (in this case all) processes are largely independent of the CO2 level/pressure in the atmosphere.”
“Is [what the IPCC explicitly and many skeptics implicitly say] appealing to authority?” Yes, and using what they say to confirm what they say is circular reasoning.
I can find Dalton’s Law and Fick’s Law in any physical chemistry textbook. Where do I find the science that generated Feely’s Law, F = k•s•ΔpCO2, and where has “No matter if ΔpCO2 is between the current pCO2 and the old equilibrium or between two current pCO2 levels at several years difference” been shown other than in the correlation between delta(pCO2) and pCO2 that you use to calculate Tau?
Where has the formula for “adjustment” time, Ta = disturbance / response, been experimentally demonstrated in any other discipline than climate “science?”
What equations explain the underlying processes beneath the fountain model?
“If the formula of Te = level / output = 4 years and its reverse is right, it should be right for any level of CO2 in the atmosphere, except for any (temperature induced) noise…”
Your figures comparing 1960 and 2010 are wrong in two ways. The black values are preindustrial, not from 1960. The black values were for estimating the equilibrium prior to FF emissions. The total estimated land plus ocean sink was 60 + 108.9, not 108, for an e-time of 3.5 years. The 2010 combined estimated output was 203 Pg compared to 829/3.5 = 238 or 829/203 = 4.1 years. That’s not a bad discrepancy any way you look at.
You wrote, “The fact that the increase in the fast cycle of the biosphere is only 13% and not 50% is a clear sign that you can’t use Te in reverse to calculate the outflows.” Seems like another assertion without good evidence. I have demonstrated Mauna Loa fits using both first-principle and back-calculation models.
“I did only say that it is largely concentration independent: about 120 PgC is sucked away…”
The reason it is sucked away is because temperature changes cause changes in Henry’s Law. A previously equilibrium condition goes out of equilibrium and NET mass transfer begins to takes place. But mass transfer that occurred previously continues to occur at similar rates based 100% on CURRENT concentration gradients having nothing to do with what happened in any previous year.
I saw your seasonal flow diagrams, but as you wrote to Stephen, “The only outflow that counts is the net difference at the end of a full year….”
The link to plant_uptake.png continues not to work.
Ed and Jim,
Neither of you concede that the mass balance/ carbon conservation argument is valid. But even the skeptics on the Trump administration’s climate assessment panel used it to affirm that human emissions are the cause of the atmospheric CO2 increase. Jim claimed to have found a loophole but went quiet, apparently because all he had been able to do is show that “human carbon” is but a small part of the present atmosphere. That was also Ed’s “discovery”, but mainstream science had beaten him to it.
Now you both dismiss disequilibrium isotope fluxes, another easily understood and validated concept used by real scientists. If two reservoirs start with different 14C/12C ratios, and balanced exchanges mix the carbon in the two reservoirs, the reservoir that started with the higher 14C/12C will lose 14C and the other reservoir will gain it, even when no net carbon is exchanged. How do your models manage to avoid this from happening? Do you agree, Ed, with Jim’s bizarre statement that this process violates the equivalence principle???
The Schwartz et al paper was written with the earlier mistakes of Berry, Harde, Salby, and a few others who thought Deta14C was the same as 14C concentration in mind. Ed, you haven’t shaken that mindset. The 1900-1950 pre-bomb data shown in Figure 1 is easily explained by the Suess effect, weakened by the exchanges that must be present as Seuss himself knew in the 1950’s. Note that Delta14C is diverging from Ed’s “balance level”, something that Ed cannot explain. Yes, the values are smaller than Ed’s paper naively believed they should be because of those pesky disequilibrium isotope fluxes.
David Andrews
August 7, 2025 at 12:17 pm
Yes, the mass balance argument is nonphysical. Accounting is not science. I think it is too early to judge the Trump’s panel as affirming that FF emissions cause all or most of the CO2 increase. Have they made statements to that effect? From my reading, The two physicists, I think you are alluding to, have expertise in how much warming extra CO2 will cause, not how much humans are responsible for the increase. I’ll be pleased to stand corrected, if necessary.
I’m not sure what loophole you attribute to me finding. I’ve been a supporter of Ed’s position for quite awhile and I would hardly characterize mainstream science as beating him to what seems to be finding the wrong solution to the problem of “disequilibrium isotope fluxes.” He has been patiently trying to school you and others along his discovery path. His is an exemplary case history of the application of the scientific method.
Your two reservoir problem assumes facts not in evidence, i.e. reservoirs where no net carbon was exchanged. As yet my spreadsheet model isotope work is incomplete and I don’t expect to find it conflicting substantially with Dr. Ed’s model.
But where did I make any bizarre statement of a process violating the equivalence principle? I would like to review it.
I highly doubt any scientist looking closely at the 14C evidence would come to a mistaken conclusion. I would rather jump to the conclusion that somewhere you are mistaken, but I will reserve judgment until finishing my investigation and review what you have written on the subject. Stay tuned!
David Andrews August 7, 2025 at 12:17 pm
Dear David,
You wrote, “Neither of you concede that the mass balance/ carbon conservation argument is valid.”
Well, David, as you should know, my whole model conserves carbon because of its continuity equation (1).
And your “Mass balance” can mean anything you want it to mean.
You claim I “dismiss disequilibrium isotope fluxes,” which you describe as:
Well, you missed the physics in that one, David.
In my model, if two reservoirs are connected, say like land and air reservoirs, these reservoirs will EXCHANGE carbon because the carbon outflow of air goes to land and the carbon outflow of land goes to the air.
For example, suppose land contains only 12C atoms and air contains only 14C atoms, then the outflow of land will send 12C atoms to the air and the air will send 14C atoms to the land.
Eventually, air has enough 12C atoms to send as many 12C atoms to land as land is sending to air. Similarly, with 14C atoms. That is equilibrium
You pound your chest like a happy gorilla and claim this is “disequilibrium isotope fluxes” at work.
NO, it’s my model at work. My model describes equilibrium better than your “disequilibrium isotope fluxes.”
For example, you say, “no net carbon is exchanged.” So, you are a magician as well as a pain in the butt.
Clearly, 12C moved from air to land. That is NOT a net zero exchange, David. Similarly, for 14C.
I have a question for you. How would your “disequilibrium isotope fluxes” apportion the 12C atoms and 14C atoms between land and air in my example?
I will assume you would answer, “equally,” meaning land and air would have at equilibrium the same number of 12C atoms and 14C atoms (assuming we began with an even number of atoms of each).
If you assumed that, you would be wrong, because my model is much more inclusive of physics than your “disequilibrium isotope fluxes.”
In my model, the respective Te’s of land and air would determine how many atoms of each end up in each reservoir when the flows are at equilibrium. Only if the Te’s were equal would we end up with the same number of atoms in each reservoir.
If air’s Te for 12C were lower than the Te for land, then land would end up with more 12C atoms than air at equilibrium.
That’s my carbon cycle model at work.
I put “disequilibrium isotope fluxes” in the same boat as the “flux capacitor”.
Jim Siverly, August 7, 2025 at 10:33 am
“Dr. Ed and I use ‘the simple formula that only looks at what the CO2 level in the atmosphere is and how much per year is going out of the atmosphere,’ because that is all that is necessary to correctly represent the data using well-established physics.”
If already 120 PgC/year, or over half of the total yearly outputs, into vegetation is completely independent of the CO2 level in the atmosphere (even reduces the level in the atmosphere!) and only 2.5 PgC/year depends of the CO2 level in the atmosphere, then you can’t use the residence time in reverse as Dr. Ed and you do.
98% independent of the CO2 level in the atmosphere, 2% level dependent.
“Sometimes and in some places the temperature is sometimes warmer and sometimes colder, but on average at all times concentration drives the mass transfer. This is particularly and completely true for the ocean exchanges.”
Again in very small part: the ocean exchanges are driven by Henry’s law: for a fixed temperature, there is a fixed ratio between the partial pressure (= amount) of gas above a solution and the partial pressure (= amount) of the same (free) gas in solution.
If pCO2(atm) = pCO2(aq), then there is no net transfer, but still lots of CO2 can be exchanged, only there is as much transfer between atmosphere and oceans as reverse.
If there is a difference in pCO2, the net transfer depends of the difference in pCO2 between these two. That is the base of the formula of Feely:
F = k*s*ΔpCO2
Which is true for any part of the oceans and for the oceans as a full dynamic system where lots of CO2 are emitted near the equator and absorbed near the poles (~40 PgC/year), sink there with the ocean waters into the deep oceans, to return some ~1,000 years later near the equator.
And it is true for the seasonal temperature changes which emit ~50 PgC/season in spring/summer to get absorbed again in fall winter.
For the latter see e.g. the seasonal pCO2 at Bermuda monitoring station (BATS), Figure 2:
https://tos.org/oceanography/assets/docs/27-1_bates.pdf
That shows the sea surface temperature induced seasonal change in pCO2 of the ocean waters at Bermuda between 310 and 390 μatm, while the pCO2 in the atmosphere in average over the period of measurements was around 360 μatm and increased with average some 1 μatm/year.
The net result of the CO2 level of 390 μatm in the atmosphere, in the last years of the measurements, on the absorption by the oceans, did lead to a net uptake of 2.5 PgC/year into the ocean waters, of which 0.5 PgC in the ocean surface (see Fig. 3 and table 2 in the reference of Bates) and the rest in the deep oceans.
Or for the ocean surface: 99% of the CO2 output is seasonal temperature dependent, only 1% atmospheric CO2 level dependent.
For the deep oceans: 95% of the CO2 output is temperature difference dependent and only 5% is CO2 level in the atmosphere dependent.
Thus Dr Ed’s and your Te is based on a theoretical world where only the level of some substance influences its output, while in the real world over 95% of the CO2 outputs out of the atmosphere are independent of that level and only less than 5% are CO2 level dependent.
Any calculations based on the 4 years turnover/residence time therefore have no connection with the real world.
As that is the essential base of our dispute, the rest is secondary…
Ed,
Me: “The 1900-1950 pre-bomb data shown in Figure 1 is easily explained by the Suess effect, weakened by the exchanges that must be present as Seuss himself knew in the 1950’s. Note that Delta14C is diverging from Ed’s “balance level”, something that Ed cannot explain. Yes, the values are smaller than Ed’s paper naively believed they should be because of those pesky disequilibrium isotope fluxes.”
I notice your latest comment skipped a discussion of what happened between 1900 and 1950, because your “Delta14C balance level” scheme cannot explain the clearly observed Seuss effect.
Jim
You: “Yes, the mass balance argument is nonphysical. Accounting is not science. “
Wow! Clearly you are not a scientist. When Joule established the equivalence of mechanical energy and heat, did he not do some “accounting”? When Pauli postulated undetected neutrinos to explain the missing energy in beta decays, was that not an attempt to balance the books? I could go on, but you would likely not understand, as you appear to be scientifically illiterate. The fact that human carbon emissions exceed atmospheric carbon growth, along with carbon conservation, tells us unambiguously that natural processes are moving net carbon from the atmosphere to land/sea reservoirs. As the Trump climate assessment task force put it:
“The annual increase in concentration is only about half of the CO2 emitted because land and ocean processes currently absorb “excess” CO2 at a rate approximately 50 percent of the human emissions. Future concentrations, and hence future human influences on the climate, therefore depend upon two components: (1) future rates of global human CO2 emissions, and (2) how fast the land and ocean remove extra CO2 from the atmosphere. We discuss each of these in turn.”
Climate Working Group (2025) A Critical Review of Impacts of Greenhouse Gas Emissions on the U.S. Climate. Washington DC: Department of Energy, July 23, 2025
released 7/29/25
I wrongly gave you more credit for open-mindedness than you deserved. Keep pecking away at your spreadsheets in support of Ed. I won’t bother to comment on them anymore.
David Andrews August 8, 2025 at 6:29 am
Dear David,
I must start addressing you as “Disequilibrium David.”
I just finished showing you how my carbon cycle model explains carbon flow more accurately than your outdated “disequilibrium isotope fluxes.”
Yet, you just wrote:
“The 1900-1950 pre-bomb data shown in Figure 1 is easily explained by the Suess effect, weakened by the exchanges that must be present as Seuss himself knew in the 1950’s. Note that Delta14C is diverging from Ed’s “balance level”, something that Ed cannot explain. Yes, the values are smaller than Ed’s paper naively believed they should be because of those pesky disequilibrium isotope fluxes.”
My model shows how human CO2 balance level lowers Delta14C and explains the Suess effect and 14C flows and levels. It does this more accurately than your math-challenged, outdated “disequilibrium isotope fluxes.”
Ferdinand Engelbeen
August 8, 2025 at 3:14 am
Are you a robot? You keep making the same assertions without proof. Check this box if you are not a robot [].
Anecdotal data of seasonal mass transfers plus scientifically sounding, but invalidated formulas do not equal a coherent argument. Please show how the temperature dependency accounts for the change in CO2 over the whole Mauna Loa period using standard physics and no anecdotes or Magic Math.
Our Te models based on standard physics explain quantitatively within reasonable error the changes in atmosphere CO2. Our “theoretical world” matches the data. Your correlation-derived Tau depends on non-standard physical rules that you have yet to show the scientific basis for. They include your unscientific Temperature Dependency Principle, where temperature drives mass transfer with little concentration dependency, and net mass transfer being proportional to a difference between the current concentration and some equilibrium concentration in the past.
The Feely Formula, net mass transfer proportional to the difference between the current concentrations of pCO2 in the reservoirs, could be correct. But you have not shown how Tau is derived from that relationship. If that is wrong, please refer me to the appropriate date(s).
“Any calculations based on the 4 years turnover/residence time therefore have no connection with the real world” is another assertion without evidence. The Temperature Dependency Principle is simply an observation, not something you have derived from first principles. A Te of about 3 to 5 years was documented by most all scientists who published on this topic. It is only a subset that insist on the unverifiable unfalsifiable 50-year Tau.
Ferdinand,
Stephen P. Anderson, August 6, 2025 at 2:43 pm
“Yes, but I also know that these inflows (and the counter current natural outflows) are caused by temperature, bacteria, fungi, insects, animals,… largely independent of the CO2 quantity/pressure already in the atmosphere.
Most of these huge flows cycle in and out within a year. The only outflow that counts is the net difference at the end of a full year and that is caused by two items: one-way human emissions of FF use and the extra CO2 level/pressure in the atmosphere that causes more uptake than return from the natural sinks and sources.
See the difference in causes for the huge seasonal CO2 flows and the small overall result over a year I did send at August 6, 2025 at 9:04 am…………
Let’s just stick with the math. If natural emissions are around 100ppmv, then how can Te be more than about 4 years? I know Dr. Ed estimated 14CO2 Te at 16.5 years (he was just trying to show that the slowest Te is around 16.5 years based on the only data we have), based on that data, but all the other data suggest 12CO2 Te to be around 4 years. So, your argument is that the estimated 14CO2 Te of 16.5 years is an order of magnitude higher than 4 years and therefore your 55-year Tau (that keeps growing every year) must be correct? Is that your argument? If your Tau was legit and it keeps growing every year it would be a runaway situation.
Stephen Paul Anderson August 8, 2025 at 9:03 am
Dear Stephen,
In a recent comment, I updated my Te:
Te for Delta14C is 16.5 years
Te for 14CO2 is 10.0 years, which is my published Te for 14CO2.
Therefore, Te for 12CO2 is less than 10 years.
Also, for reference, IPCC’s natural carbon cycle data show its Te for 12CO2 is 3.5 years.
Jim Siverly, August 8, 2025 at 8:13 am
” Please show how the temperature dependency accounts for the change in CO2 over the whole Mauna Loa ”
No problem: per formula of Takahashi, based on meanwhile some 3 million seawater samples and Henry’s law for the solubility of CO2 in seawater for different temperatures:
If we assume (wrongly, as the real modern equilibrium is around 295 ppmv), that the equilibrium between ocean surface and atmosphere was established in 1960 at 315 μatm (~ppmv) at that time and the sea surface temperature increased with 0.6°C (HadSST3gl) then the increase in equilibrium (1960-2020) is:
(pCO2)seawater @ Tnew = (pCO2)seawater @ Told x EXP[0.0423 x (Tnew – Told)]
pCO2(2020) = 315 * EXP[0.0423 * (0.6)] = 323 μatm
Or an increase of 8 ppmv in equilibrium per Henry’s law. Not over 100 ppmv as observed, while humans emitted 170 ppmv of FF CO2 over the same time frame…
Vegetation acted as a net sink, as the O2 trends showed and also the increase of chlorophyll as observed by satellites as indication of increasing living organics…
“Anecdotal data of seasonal mass transfers”
The oxygen and δ13C measurements show a mass transfer between atmosphere and vegetation of over 120 PgC/season, half on daily, half on seasonal time scales. Since 1990 accurate enough for the O2 measurements to show the transfers. Nothing “anecdotal”, real, observed data. Here for the δ13C changes:
https://essopenarchive.org/users/529681/articles/606931-the-seasonal-cycle-of-%CE%B413c-of-atmospheric-carbon-dioxide-influences-of-land-and-ocean-carbon-fluxes-and-drivers
https://gml.noaa.gov/education/isotopes/c13tellsus.html
https://boris-portal.unibe.ch/server/api/core/bitstreams/3c99081b-6595-49db-b2ea-71fe69d79cd9/content
And many, many, many others that describe the seasonal (plant induced) δ13C changes.
The seasonal O2 changes are even more important, as these are far less mixed with O2 changes from the oceans than the opposite δ13C changes:
https://bluemoon.ucsd.edu/publications/ralph/3_Seasonal.pdf
https://www.tandfonline.com/doi/full/10.1080/16000889.2017.1311767#abstract
https://geoweb.princeton.edu/people/bender/lab/research_o2n2.html
And many, many, many others that describe the seasonal (plant induced) O2 changes.
Even the diurnal cycle is measured:
https://essd.copernicus.org/articles/15/5183/2023/essd-15-5183-2023.pdf Figure 15…
That are the large outputs of CO2 into vegetation which makes your much too short 4 years Te, largely independent of the actual CO2 level in the atmosphere…
Again: the main problem with Dr. Ed’s and your approach is the use of the turnover/residence time as an e-fold decay rate, while it is a simple division between the amount of CO2 in the atmosphere and the total outputs, not an e-time…
Dr. Ed, August 8, 2025 at 9:16 am
You forget the “dilution” of the 14C “fingerprint” by the 14C-free FF emissions and the return of “old” 14C level CO2 from other reservoirs, which make the 14C decay rate faster (not slower) than for 12CO2.
And the IPCC explicitly rejects the use of the turnover time T as an e-fold decay rate Te…
Stephen Paul Anderson, August 8, 2025 at 9:03 am
“Let’s just stick with the math. If natural emissions are around 100ppmv, then how can Te be more than about 4 years?”
The turnover/residence time is about 4 years. That is the simple formula:
RT = level / output.
No matter if the output is caused by the level or any other process, independent of the level.
In the real world, 95% of the outputs is caused by processes which are independent of the CO2 level in the atmosphere and only 5% are level dependent.
That makes that Dr. Ed’s and Jim’s calculations, based on an exponential decay rate of 4 years is completely at odds with the real world, because Te may not be set equal to the RT of 4 years, as that are two completely separate items.
With a Ta/Tau of around 50 years, the decay of our FF emissions is not fast enough to remove all FF in the same year as emitted, but when FF emissions are halved, that would stop the CO2 increase in the atmosphere and with a full stop, after 35 years (the half life) the extra CO2 drops to around 360 ppmv, after 70 years to 325 ppmv,…
Ferdinand Engelbeen August 8, 2025 at 9:51 am and 10:07 am
Dear Ferdinand,
Contrary to your claims, my model calculates what you call “dilution” of 14C by 14C-free FF emissions, and the recycling of 14C from other reservoirs.
By contrast, your model calculates nothing. It can’t because you have no mathematical formulation of a carbon cycle.
The outflow (that you call decay rate) of 14CO2 cannot be faster than the outflow of 12CO2 from any reservoir.
My Te definition has no dependance on anything the IPCC writes. I formed it from the way systems models are supposed to be formulated, with is fully described in the WIKI reference that you provided.
You wrote, “In the real world, 95% of the outputs is caused by processes which are independent of the CO2 level in the atmosphere and only 5% are level dependent.”
You have made that same claim over and over again. But you have failed to show how your claim changes my (2) that Outflow = Level / Te
While no carbon cycle data are exact, IPCC’s data for its natural carbon cycle is a valid reference for “the real world.” It is the place where all carbon cycle models should begin.
My Te replicate IPCC’s natural carbon cycle. Your claimed carbon cycle cannot replicate IPCC’s natural carbon cycle or any other data that you have presented to this extensive discussion.
So, your claim that Te cannot be set to 4 years, is invalid because it is contradicted by IPCC’s data.
You claim: “With a Ta/Tau of around 50 years, the decay of our FF emissions is not fast enough to remove all FF in the same year as emitted, but when FF emissions are halved, that would stop the CO2 increase in the atmosphere and with a full stop, after 35 years (the half life) the extra CO2 drops to around 360 ppmv, after 70 years to 325 ppmv,…”
No data, used properly, supports your claim. IPCC’s own carbon cycle data prove your claim is wrong.
Ferdinand, it is time for you to stop recycling your invalid claims over and over again, when they contradict both physics and real data.
Ferdinand Engelbeen
August 8, 2025 at 9:43 am
It seems what you have shown is that temperature alone cannot account for the measured rise in CO2 between 1960 and 2020. What you have not shown is how much FF contributed any known amount of that rise, because you rely solely on Magic Math.
Are we to guess how your O2 and 13C references allow you to arrive at the conclusion, “That are the large outputs of CO2 into vegetation which makes your much too short 4 years Te, largely independent of the actual CO2 level in the atmosphere?” I have no clue how you get that.
You see a problem with our approach, because you have invested so much into your approach that you can’t let it go.
The latest kerfufal is the administrations declaration of abandonment of the OCO satellite. The activists siting the quality of the measurements, youth and good condition of the vehicle, and the relatively low cost of maintenance and data gathering. The administration citing the lack of utility for the data. I am a died in the wool proponent of getting the most out of what you have and watching for alternative uses for my tools and information. Has anyone that is participating in this discussion on Dr. Ed’s site analyzed the OCO data to see if it can support either side of this discussion ? My brief introduction to that data revealed that the measured sources of CO2 do not align with the model distribution. The graphic I saw showed barely increased concentration in populated areas except for China. My take on it was that the overwhelming majority of the measured emissions are natural and the human contribution could easily be lost in the noise but that was from just a visual review.
Dr. Ed, August 8, 2025 at 11:12 am
“Contrary to your claims, my model calculates what you call “dilution” of 14C by 14C-free FF emissions, and the recycling of 14C from other reservoirs.”
Yes, your calculations for the 14C decay includes the dilution, but you forget that there is no such dilution is for the decay of a bulk 12/12CO2 injection, thus that the decay rate for a 14C injection is much faster than for a 12/13C injection. Not slower…
“But you have failed to show how your claim changes my (2) that Outflow = Level / Te”
If there is hardly any connection between Level and Outflow, then Te doesn’t tell you anything about the fate of an extra injection of CO2 of whatever source in the atmosphere…
RT/Te is based on outputs alone.
Ta/Tau is based on the difference between inputs and outputs.
The first shows how fast the CO2 mass is moving through the atmosphere.
The second shows how fast an extra CO2 mass injection is removed out of the atmosphere.
From the first you can’t calculate the removal rate of an extra CO2 mass injection, only how fast an individual CO2 molecule is replaced by a CO2 molecule from another reservoir.
“My Te replicate IPCC’s natural carbon cycle.”
Your Te violates the carbon mass balance: if human CO2 is rapidly distributed into oceans and vegetation, then the observed increase in the atmosphere must come from the same reservoirs, which makes that the total increase in atmosphere + oceans + vegetation is much larger than from the FF emissions…
“No data, used properly, supports your claim. IPCC’s own carbon cycle data prove your claim is wrong.”
Even from the start of this discussion, I have sent the calculated CO2 increase with the 50 year Ta/Tau that near perfectly match the Mauna Loa data… And that obeys the carbon mass balance…
https://www.ferdinand-engelbeen.be/klimaat/klim_xls/Berry_fluxes.xlsx
The IPCC’s overall Ta is even worse, going to hundreds of years for a part of the FF emissions…
Jim Siverly, August 8, 2025 at 12:38 pm
“What you have not shown is how much FF contributed any known amount of that rise”
It is pretty sure that all FF emissions are for 100% directly into the atmosphere: as mass and as isotopic composition.
As we measure the change in CO2 mass of the atmosphere and the change of its isotopic composition, we know that about half the FF emissions as mass per year are removed and about 2/3 of its isotopic composition are replaced by CO2 from other reservoirs. That means that FF emissions are fully responsible for the increase in mass and the decrease in isotopic ratio. Only Magic Math can give a different outcome…
“Are we to guess how your O2 and 13C references allow you to arrive at the conclusion, “That are the large outputs of CO2 into vegetation which makes your much too short 4 years Te, largely independent of the actual CO2 level in the atmosphere?” I have no clue how you get that.”
Sorry, but I thought it would be clear from the IPCC’s scheme in Dr. Ed’s Figure 2, that the largest flows are bidirectional and near equal.
Dr. Ed’s and your Te of 4 years only looks at the level in the atmosphere and the output level, but that doesn’t say anything about the cause(s) of the output(s) neither of the input level.
In the case of large cycles within a day/year, the output level doesn’t change at all if input and outputs are equal, thus without any change in level, while the output still is high and the residence/turnover time still is 4 years.
If there is any extra input, of whatever source, then only the difference between inputs and outputs tells you what the real decay rate is and that is Ta/Tau, no matter the height of the inputs and outputs…
If the outputs are not 100% dependent of the level in a reservoir, then the decay rate Te never can be equal to the residence/turnover time. That is the crux of the matter in this whole discussion…
“You see a problem with our approach, because you have invested so much into your approach that you can’t let it go.”
I only see that your approach is based on a model that implies that a change in level causes an equal change in output, while the data show that a 50% change in level only causes a 33% change in output towards the oceans and a meager 13% towards vegetation. Which proves that your model is wrong…
DMA, August 8, 2025 at 5:12 pm
My impression is that the data are not as accurate as they have expected, from the beginning on.
That being said, there are several problems with the CO2 releases that they underestimated: the OCO measurements are only within sunlight, while most emissions out of vegetation are during the night.
https://ocov2.jpl.nasa.gov/science/measurement-approach/
And human emissions are quite small and fast mixed in the total atmosphere. A 5 ppmv increase over a year is 0.15 ppmv / day change. The accuracy of the measurements is 0.8 ppmv over land and 0.5 ppmv over water. Only in tight populated and industrialized regions, that would be measurable…
But stopping these measurements would be a loss of knowledge…
As an end of this discussion, my last contribution:
How much carbon is in a reservoir is not important, as long as it stays there.
How much carbon is exchanged between reservoirs is not important, as long as in and outs are equal.
Only the difference between ins and outs changes the carbon content of a reservoir.
The 4 years Te only looks at the second part.
The 50 years Ta/Tau looks at the last part…
Dr. Ed,
Sorry, I didn’t realize you had a new estimate for 14CO2 Te. When you have mass that is such a minute part of the total mass of the atmosphere, it must be difficult to get an accurate concentration. Also, Ferdinand does not understand that the balance level is some level in the future. It is not the real-time level, but is set by the real-time emission. He either refuses to accept or to understand the continuity equation, which is nothing more than a mathematical description of the natural process.
Ferdinand,
Thanks for the debate. You’ve been a good sport. I do agree with you about one thing. CO2 is good.
Dear Dr. Ed,
I finished a first draft of a one-compartment model for 14C that simulates Figure 2 of Schwartz et al. 2024. I started with the CO2 model where I generated an exact fit to the Mauna Loa data using a solution to the differential equation dC/dt = Eh + En – C / Te. To test my model, I first established equilibrium conditions that would have been in effect prior to 1750. Assuming the atmosphere contained 600 PgC 12C and 600 Kg 14C, I found a 5-year e-time held both amounts constant. Equilibrium for 12C occurs, because no change in net CO2 occurs with the annual exchange of 120 PgC. Equilibrium for 14C occurs because for every 7.5 Kg 14C produced annually from cosmic ray reactions with N2, another 112.5 Kg enters the atmosphere from the 600 PgC emitted by the reservoirs. The reservoirs, in turn, received 120 Kg 14C from the atmosphere. I don’t remember if I tested other e-times, but whatever e-time is assumed requires assuming a lower concentration of 14C in the reservoirs than in the atmosphere, otherwise there would be no equilibrium.
Next, I incremented my spreadsheet as before with an amount of additional CO2 to supplement FF CO2 and maintain the match to Mauna Loa data. The 14C incremented with the same differential equation as 12C such that by 1950, delta14C matched the measured data. In other words, the FF emissions diluted 14C somewhat for over two centuries and the spreadsheet followed that accurately.
Beginning in spreadsheet row for 1955, I manually added enough 14C each year to approximate the rise in 14C from the bomb tests up to the peak in 1966. At that row, I returned to the previous formula operating with the original e-time of 5 years. As might be expected, 14C depleted much faster than the known data. Assuming an additional amount of 14C was being returned to the atmosphere from the newly 14C-enhanced reservoirs, I added an exponentially decreasing amount of 14C to the ongoing increase from the pre-bomb influx formula. Logically that additional amount would be expected to decrease as the bomb carbon dissipated into the deep ocean and returned 14C to its pre-bomb level.
https://www.dropbox.com/scl/fi/qqtwvp85x47fqgxmou2wd/one-compartment-14C-model.png?rlkey=es0h0rfb2mg2xbmd685r97mkx&dl=0
My graph shows two curves for each of the two ways of reporting 14C. The lower curve of each pair represents a formula that avoided including any 14C from the FF carbon emissions. In other words, without distinguishing between natural and FF emissions, the 14C is over counted.
More importantly, the formulas employed to generate the graph reinforce the principles you expound and have demonstrated with your model. There is only one e-time needed to explain the dispensation of bomb 14C. The decay profile is akin to a removal “wave” from the atmosphere impeded by an “echo” of 14C returning from the reservoirs. That phenomena is integrated into the normal exchanges between the atmosphere and the reservoirs resulting in the appearance of an e-time longer than the usual four or five-year e-time.
For the years prior to the bomb tests, the spreadsheet maintains a preindustrial equilibrium and increments 14C accurately using a single formula based on multiple inputs and a constant output rate into and out of the atmosphere to and from other reservoirs. The injection of 14C in the 50’s and 60’s cannot be characterized by a one-compartment model without the manual additions and manipulating a decay profile that matches data. However, those additions and subsequent relaxation of 14C should be adequately described using a two-compartment model similarly derived.
Dr. Ed,
While anticipating push-back on my last comment, I was catching up on popular climate news and came across this at drroyspencer.com: https://www.drroyspencer.com/2025/07/some-thoughts-on-our-doe-report-regarding-co2-impacts-on-the-u-s-climate/
“That same morning I [Dr. Roy Spencer] was called by a particle physicist who heard all of this news [about the Remote Sensing journal editor forced to resign for publishing a Spencer paper] and said something to the effect of, ‘What’s wrong with you climate guys? We have people who believe in string theory and those who don’t, but we still work together.’ We both laughed over the divisive nature of climate science compared to other sciences.”
That struck me as a good summary of this debate. “Climate” science adopts principles not shared by mainstream science. Need I delineate them?
Jim,
From all your work, what did you calculate for e-Times for 12CO2, 13CO2 and 14CO2? Pretty much the same as Dr. Ed’s calculations? Thanks
By the way, this page is a great reference page for future.
Jim,
One of my on-going arguments on Dr. Spencer’s site is that in my view the lapse rate falsifies the GHE. For instance, according to GHE, if greenhouse gases were eliminated from the troposphere, then the troposphere becomes isothermal. My argument is you’d still have a difference in temperature at altitude based on hydrostatic pressure, lapse rate.
Stephen Paul Anderson
August 12, 2025 at 1:21 pm
Stephen,
My Te for 14C is the same for 12CO2, in this case 5 years. However, that maybe somewhat flexible. Most of my time was spent making sure I had equilibrium conditions prior to the introduction of FF and bomb emissions. Until the bomb tests, those e-times had to be the same because of the equivalence principle. After bomb testing, the equivalence principle still applies but the “equilibrium ratio” was thrown off. Then the superposition principle kicks in. That requires a different formula operating. A decay function is superimposed on the normal Te function. The decay e-time I used for the excess amount (the “echo”) emitted to the atmosphere is 15 years, but I am not sure how accurate that is. I should go back and try 16.5 years, because that is what the observed decay rate is.
August 12, 2025 at 1:30 pm
There has been much discussion of what the troposphere would become without IR-absorbing gases (I detest the use of GHG terminology). If you are arguing no change in lapse rate, I agree with you. On which post is that discussion happening?
Jim,
We post on drroyspencer.com. Not much is happening now. It is mostly anti-Trump comments-his takeover of D.C., and Dr. Spencer’s DOE report. They should have had Dr. Berry included on that committee. Thanks for your input on Te. Do you have a webpage where you post your charts?
Stephen,
I adjusted my decay rate to 16.5 years and it reduced the 14C/12C curve to below the observed curve. And then I changed e-time to 5 years and that restored almost a perfect fit.
Also, I have not done any 13C work, but I’m looking into it now. I don’t have a webpage, but I am thinking of writing a paper on the results. It depends on whether anyone else has already done it.
Jim,
I don’t know why I am responding to your 14C analysis, since you don’t even accept the basic fact that data and a little accounting clearly show natural processes are removing carbon from the atmosphere, not adding it. But I will, because there are too many obvious problems with it.
1. Although you generated a 14C concentration curve somewhat similar in shape to the data following the bomb pulse, it certainly does not match the data. The data never gets much below 500 amole per mole before rising, but your two curves bottom out around 400 and 425.
2. I don’t understand why your “mole fraction all CO2 and “mole fraction no FF CO2” curves are different. I trust you are aware that FF CO2 contains negligible 14C, but perhaps you are not.
3. You should look at Figure 4 in the Schwartz paper as well as Figure 2. It shows how 14C moved between various reservoirs (stratosphere, troposphere, biosphere, oceans) after the nuclear testing.
4. You will note from that same Figure 4, that the nuclear testing put about 100 Kmoles of 14C into those reservoirs, and most of it is still there. What time constant do you think determines its removal? Please don’t say four years.
5. You wondered if anyone else had tried an unconventional explanation of the 14C history, as you have done. Harde and Salby did. They realized, unlike you or Ed, that they had to explain an increase in the total amount of 14C in the fast cycle reservoirs. So they postulated new sources which were not credible. See the Appendix in https://scienceofclimatechange.org/wp-content/uploads/Andrews-2023-Clear-Thinking-about-Atmospheric-CO2.pdf Their explanation was aimed at suckers, not scientists, and that is why I earlier expressed my disdain for the (deceased) Murray Salby. He was unethical in his science as well as in his management of grant money.
David,
Thank you for the opportunity to clarify points your questions raise and the benefit your criticisms bring toward improving my model.
First of all, papers like one you cited (Graven et al. 2020) explain how natural processes are removing carbon from the atmosphere AND adding to it. It’s the basis of what is meant by disequilibrium fluxes.
1. It’s true that I am short on how much 14C my spreadsheet predicts following the bomb pulse. I will need to add additional amounts in the lead up to the max around 1966. I will do that and also compare my gross 14C amounts added to what others have published.
2. In both cases, the upper curves represent the calculation that results if one doesn’t take into consideration that FF emissions contain no 14C. That was to highlight the magnitude of the difference FF carbon makes in the whole scheme of things. The lower curve represents the true 14C calculation to within whatever degree my formulas and inherent assumptions are correct.
3. I will generate a Figure 4 type graph from whatever information I can get out of my model. That would be a logical step toward model validation.
4. My one-compartment model only includes the 4-year removal rate constant, because that is the only one necessary. Nature didn’t suddenly change to accommodate bomb carbon. The other rate constant (now 16.5 years) in my model is inferred from what would be necessary to account for the back flux from the first, second, third,…, nth generation return of 14C due to disequilibrium isoflux. However, that inferred rate constant also includes contributions for 14C originally in land and ocean reservoirs from post bomb treaty testing (underground and in the ocean) and subsequently from nuclear energy production. I say inferred, because a one-compartment model can’t handle the contributions from the reservoirs without manual splicing in the second compartment contributions. Everyone agrees, except maybe you and Ferdinand, that reservoirs were adding more 14C to the atmosphere than the atmosphere was removing.
5. I reserve a response on the Harde and Salby 14C history until I do a thorough review of the appropriate papers.
Thanks again for your questions.
While tweaking my model to get closer to the Schwartz data, I noticed that changing e-times throws off the C12 and 14C equilibration that was assumed to have been established prior to the perturbations introduced by FF and bomb testing. Some, if not all, of the starting variables are interrelated, such as the equilibrium ratio of 14C/12C, a natural e-time for removal, and the starting CO2 concentration. This is an important point, because everyone assumes it was around 280 ppmv. But nature has been trying to establish an equilibrium much before this millennium. In that case, some initial disequilibrium values should be considered acceptable.
Now let’s consider your point 5. where you accused Dr. Ed of not understanding the difference between DC14, the 14C/12C ratio, and molecular 14C. In Berry 2019, he refers frequently to 14C data and equates it to Hua DC14 data. Therefore, I don’t view that as problematic. His whole point was to illustrate that the IPCC model could not do what his model does, replicate the Hua data. Dr. Ed has already admitted mislabeling the graphs and that should be enough said. Also, similarly, nothing other than poor labeling in the Harde 2019 paper indicates him being confused over absolute 14C versus the 14C/12C ratio.
Back on July 10, 2025 at 6:41 pm (https://edberry.com/co2coalition/comment-page-3/#comment-112521), you postulated, with all other things equal, that a bomb experiment would result in 14C decaying to normal in about a decade. Have you ever tried modeling that?
David Andrews
August 13, 2025 at 9:22 pm
I’m working through your paper and came to the analogy in section 3.5 of the couple putting and taking from an account. I have seen this often and think a better analogy would be a bank with many clients some just deposit others just withdraw many do both. The account at the end is just as definitive as the couples’ account – the net increase is less than the deposit record of one client that took no withdrawals. How can the bank know the increase is due to that client? Just like CO2, without some analysis of flow the only valid statement is “That source likely contributed to the increase.”
Jim,c
What starting CO2 concentration works best for your model? No one knows what the CO2 concentration was in 1750.
Jim,
You ask: “Back on July 10, 2025 at 6:41 pm (https://edberry.com/co2coalition/comment-page-3/#comment-112521), you postulated, with all other things equal, that a bomb experiment would result in 14C decaying to normal in about a decade. Have you ever tried modeling that?”
There is not much to model. By the assumption of the thought experiment, everything is in equilibrium until the abrupt injection of a part per trillion of 14C into the atmosphere. That does not stimulate plant growth. That does not appreciably increase ocean carbon content. But it does create an isotopic disequilibrium since the atmospheric 14C level was doubled. The balanced exchanges which are maintaining the overall carbon equilibrium then move 14C from the atmosphere to the land/sea reservoirs, until the isotopic difference is erased. Think MIXING, not ABSORPTION, with no change in carbon levels or flow rates beyond a part per trillion. (Of course this mixing is our “disequilibrium isoflux”.) That is what happened after the real-world experiment in the 1950’s and 1960’s, though the background processes were not perfectly balanced as in the thought experiment. The data from that period tells us that the mixing time scale is about a decade.
I can tell you are struggling with your model because you are wrongly changing carbon levels on a short time scale. Ferdinand tried to tell you that the mixing time scales and level-changing time scales are different. Perhaps you will learn from your struggles.
DMA,
You ask: “the net increase is less than the deposit record of one client that took no withdrawals. How can the bank know the increase is due to that client?”
My first answer would be that if the client that took no withdrawals had also not made any deposits, then the total bank deposits would have decreased. (I have to be careful how I say this, since to a bank, a deposit is a liability and a loan is an asset.)
For carbon and the carbon CYCLE, I think it is better to think about the history of the carbon in any particular stream and ask yourself where it came from and how stocks are changing. Sure, oceans are mostly outgassing carbon in the tropics, but they are mostly absorbing it nearer the poles. The carbon in that outgassing stream in the tropics was not that long ago in the atmosphere. Unless you had evidence that ocean carbon content was decreasing (of course in fact it is increasing), you cannot sensibly separate the tropical ocean outgassing from the polar absorption and call the oceans a source. The same goes for the growing biomass. Trees don’t make carbon, they just borrow it. If the biomass is bigger now than a century ago, then biological processes must be removing carbon from the fast cycle, not adding it. On the other hand global fossil fuel reserves are DOWN. The decrease in carbon in underground reserves accounts for the increase in carbon in the atmosphere, and in the other reservoirs.
Stephen P. Anderson
August 15, 2025 at 7:20 pm
To a first approximation, it doesn’t matter what the CO2 concentration was in 1750. However, you have to have a model that is consistent with maintaining an equilibrium at some distant past time. Then going forward, that model has to correctly match 14C and Mauna Loa data. What I’m finding is I can start with any e-time within 4 and 10 years (although not necessarily limited to that range) and add an exponential amount of additional emissions that will give me a good match to the Mauna Loa data. I have not extended that to 14C data yet. More on this later. The link below is a modified 1-compartment spreadsheet model that illustrates what I’m finding. You can experiment yourself with alternative e-times and changing the exponential parameters to determine the determine the appropriate amount of additional emissions. Warning: This can be time-consuming, but worth the exercise in seeing how the exponential affects the fit. Hint: one parameter shifts the curve and the other bends it.
https://www.dropbox.com/scl/fi/4idfv1xf7omq02g66pwhl/CO2-model-changeable.xlsx?rlkey=7b3i20ajx076j54yke6r7jpk0&dl=0
As for starting concentrations, the model will move to its balance level depending on the e-time. One can get to the balance level immediately by entering a starting input rate = balance level / Te.
David Andrews
August 15, 2025 at 10:04 pm
Dear David,
While being indebted to you for forcing me to look at the other papers aligned with Dr. Ed, I can assure you I am not learning from your and Ferdinand’s simple math and mixing time scales and level-changing time scales. Your disinterest in modeling is telling and might indicate that you are still struggling with understanding the intricacies introduced by Dr. Ed et alia, if not accepting them.
Getting back to Harde and Salby 2021 (August 13, 2025 at 9:22 pm, point 5.) I was pleasantly surprised to see Harde and Salby 2021 proposing an unconventional explanation of the 14C history requiring additional CO2 from non-FF sources. The authors’ beta coefficient accomplishes the same result as my exponentially increasing additional emissions, although they itemize where the additions come from, namely background, asymmetry, temperature, and re-emission. Those currently amount to 3, 27, 3, and 59 ppmv/year, respectively. In my view, re-emission is a misnomer. It basically accounts for the remaining emissions required to make the evolution curve match the Mauna Loa data. Am I wrong? Furthermore, Harde and Salby claim that Tau_eff for 12C was determined independently of its determination from 14C data. I’m inclined to disagree with that. One can’t extricate a Tau determined from 14C when 14C and 12C are both inherently linked by the equivalence principle. The differences in 14C and 12C dispensation is due to the bomb testing injecting an anomalous amount of 14C into the system. That creates differences in their emission and absorption rates but not a difference in rate constant.
Continuing from what I was explaining to Stephen, I find any removal rate constant between 0.1 and 0.25 will match Mauna Loa data with the appropriate emissions added. Do you agree their re-emission term is simply an additional amount needed to supplement the additions contributed by background, asymmetry, and temperature?
Jim,
I will let you believe that the 14C errors of Berry and of Harde and Salby prior to 2019 were mere clerical errors, but they were not. They were fundamental errors critical to the wrong arguments being made. They were the kind of errors that peer review catches. I have nothing to add to my critique of Harde and Salby’s failed attempt to patch up their theory by inventing an unrealistic background. You are the perfect mark for their scam. They are telling a gullible non-scientist what he wants to hear.
Mainstream atmospheric science has never had a problem understanding and interpreting the 14C data. Ed still scoffs at disequilibrium iso-fluxes (DIF), presumably because they fooled him into thinking that his calculation of the composition of the present atmosphere meant something. His analysis in the paper critiquing the CO2 Coalition at the top of this thread shows he still does not understand the Seuss paper from the 1950’s.
Let’s get back to the main question: why is atmospheric CO2 increasing? I am very skeptical of your hypothesis that natural emissions have had a huge increase since 1750, but it is not really a hypothesis. It is just a parameter in a curve fitting exercise that explains nothing. Your spreadsheet inputs fossil fuel emissions data and Mauna Loa data, and so correctly shows a positive net global uptake. Natural processes are removing more carbon from the atmosphere than they are adding in your world as well. I rest my case that human emissions are the culprit. After all your spreadsheet work, what is your argument that natural processes are responsible?
David,
My hypothesis is that some of the rise in CO2 is due to FF emissions and the rest are natural emissions which to some degree are caused by human activity. My justification for arguing that additional natural emissions are necessary comes from failing to find a match to the Mauna Loa data using only industrial emissions. I found that I can achieve good fits with a range of e-times, but only an e-time of four to five years is consistent with the IPCC report that natural emissions are about twenty times those of the industrial emissions.
I am still working through your critique of Harde and Salby 2021 and I think you have some valid complaints, but I give them major credit for incorporating the seasonal variation of CO2 and the 14C oscillations immediately after the bomb testing peak that reflect annual re-enrichments of tropospheric 14CO2 from the stratosphere. One has to admit how cool those are. Those enhancements are basically superimposed on the general evolution of increasing CO2.
Still the question remains, what else drives the CO2 rise, assuming industrial emissions do not account for all of it? In my mind, it’s obvious. Let me try to explain why you don’t see it. I think you, like Ferdinand, ascribe to the view that mass transfer rates are not entirely proportional to concentration differences. Please correct me if I am wrong. To appreciate where I and others are coming from, one must recognize the concentration-dependent bidirectional relationship between the atmosphere and its adjacent reservoirs. The general relationship is dC/dt = – k1*[A] + k-1*[B] where [A] and [B] represent the concentrations of carbon in the atmosphere and in any given reservoir, respectively. Each reservoir has a unique set of forward and reverse rate constants, but in a simplistic general sense k1 and k-1 comprise an average of all exchanges between the atmosphere and the reservoirs. Without an appreciation of this generally true physical phenomenon, you and I will never come to a meeting of minds.
So, if industrial emissions do not accumulate in the atmosphere as you concede, then what causes the rise? All of the players involved in this discussion agree that temperature is only partially responsible. Harde and Salby appear to suggest the asymmetric seasonal change accounts for another part of the rise. Unless I missed it, that is a result of an unexplained cause, not a cause in itself. I do appreciate the need for additional emissions to get a Mauna Loa data fit. Not having thoroughly understood your critique of their “background” scenario, I will move on to the other possible emission sources that have not been mentioned, one from land and the other from the ocean.
Going back to the dC/dt equation, there must be additional emissions coming from somewhere other than industrial emissions, otherwise a near equilibrium would be hovering just above 300 ppmv according to my spreadsheet model. In other words, [B] has been gradually increasing. One obvious possibility is the increased emissions created by an 8 billion population increase. Land use change has probably been significantly under counted. The other possible source of inflated [B] could be an incorrect interpretation of the ocean concentration making its effect less than recognized. I could break that down further, but I would like your take on my other responses first.
I have still been waiting to see the final version of “CO2 Coalition’s not so Golden Science” so that I can circulate it to a climate discussion group. Did I miss it? Thanks.
Jim,
I have spent little time myself worrying about time constants, as the carbon conservation (mass balance) argument does not require that detail. That is the typical beauty of using conservation laws. Your term (Magic Math!) is appropriate.
Still, I think I know what your main problem is. You have pointed to two things that worry you about your spreadsheet results:
1. If you only consider the industrial emissions, your spreadsheet yields too small a rise.
2. You need to postulate increasingly large natural emissions to keep up with the measured (Mauna Loa) atmospheric accumulation of CO2.
Both of these problems would be solved by the use of a much longer time constant.
Some modelers studying problems such as “what exactly happens after net zero” combine the atmosphere and surface ocean into one reservoir. After all, it takes a year or two for the northern and southern hemisphere atmospheres to mix, almost as long as for the atmosphere to mix with the surface ocean. So if you want to study what happens on decadal time scales, you might as well lump them together. Now the question becomes, “how fast do transfers between the atmosphere/surface ocean and the deep ocean occur?” The answer is, much longer than 4 years (maybe 50 years, maybe a century). But those processes are essential for understanding the growth of atmospheric CO2, as the surface ocean CO2 is growing with it. Information about those slower processes is NOT contained in the 14C bomb pulse data.
The real-world carbon cycle is complicated. You are not the first to try to capture the whole thing with one time constant. You won’t be able to do it and others couldn’t either. You are too optimistic about what you can get out of a one box model. But you still can use Magic Math to figure out what is causing the rise.
David,
You are suffering from Wizard of Oz syndrome. Never mind the time constants behind the green curtain, just click your heals together and Magic Math will get you back to Kansas. In the real world using real physics you will never get a model to fit real data with the much longer time constant you suggest.
I agree that transfers between the atmosphere/surface ocean and the deep ocean are essential for understanding the growth of atmospheric CO2, but no one has demonstrated how longer e-times for the ocean require any longer e-time for the atmosphere. And 14C bomb pulse data Information can only improve our understanding about those slower processes.
I finished your critique of Harde and Salby 2021. Although I am troubled by their conversion of a four-year e-time into a ten-year effective one, I don’t find anything unreasonable about their model. At worst, one might say it is only partially quantitative with qualitative assumptions filling in the gaps. I think it’s not unreasonable to say their analysis is somewhat better than your 100% qualitative isoflux-based analysis. You are quick to point out problems with the models of others without having one of your own. It’s time you converted your qualitative arguments into a dC/dt = something model.
At the top of page 41 of your “Clear Thinking about Atmospheric CO2” paper, you wrote, “To transform the red curve in Figure 2 to the green curve, their solution is to postulate new sources of atmospheric 14C that started after about 1964.” That is confusing because Harde and Salby were not transforming red to green. They showed how their model explains the known red curve data. At first glance, in other words without having run the numbers yourself, why would you deem “new” sources of 14C necessary? After all, the main reason for the red curve differing from the green curve is the additional bomb 14C that tracks the atmosphere’s rise in CO2. The green curve only accounts for the bomb pulse. The red curve accounts for additional 14C coming along with the 100 ppmv increase in CO2 since 1965. The only reason to postulate “new” sources of either 14C or CO2 is, because without it, one cannot formulate a model that includes proper physics and explains all the data.
Jim,
The carbon conservation argument is rock solid. It was cited in the Trump administration’s Climate Assessment Report, where it was about the only thing they got right. You have never said what you don’t understand. Go ahead, ask me a question about it. Ed’s approach over the last several years has been to misrepresent it, then argue against the straw man he created, then block posts that counter his points. (I thank him for not blocking me these last couple of months.)
I reviewed what I wrote about Harde and Salby concocting a new background when they realized the concentration curve was not the same as the Delta14C curve as they had previously thought. I stand by what I wrote. It was them, not me, that postulated the unreasonably large new radiocarbon sources. Perhaps you have to read all the papers to understand the history.
Perhaps I should not be surprised that you are sympathetic to the Harde and Salby curve fitting approach. All that you have done is invent numbers to fit the Mauna Loa rise, as they did to fit the 14C concentration curve. Your increasing natural emission numbers are no more credible than their cosmic ray flux increase, and they are required for similar reasons. Yet you call your approach “proper physics”. Sorry. I think you need to go back to school.
David,
I am not the one being childish. It’s you that defends a simplistic view that cannot explain how only a few percent of the atmosphere containing FF emissions causes all of the rise. And you have the gall to ask me what I don’t understand about it! Boy, that is some kind of hubris.
You scoff at Harde and Salby’s cosmic ray flux increase which is based on real data and fills in a part of their model that didn’t fit all the data. You decry our attempts to use proper physics and yet have no model of your own. You claim carbon conservation which isn’t even applicable since you and the rest of your simple math advocates can’t account for all the carbon you claim to have conserved.
Good grief, Charlie Brown.
Since your attacks on me, Harde/Salby, and Dr. Ed are farcical, would you care to be specific about what else you think the Trump administration’s Climate Assessment Report got wrong?