A Model for Atmospheric Carbon Dioxide: Abstract

by Edwin Berry, PhD, CCM (Certified Consulting Meteorologist)

Below is the Abstract for my forthcoming professional paper.

Yesterday, I submitted this Abstract to the American Meteorological Society for presentation at its “31st Conference on Climate Variability and Change.”

I hope to have my complete paper ready for publication in a few more weeks. My thanks to all who have helped me in this endeavor by reviewing my drafts.

After debating climate alarmists for many years, I have concluded the only way to win a climate debate (note I did not say “convert the believer”) is to clearly negate the alarmist hypothesis. Otherwise, a climate debate can go on for years and accomplish nothing.

I think the focus of this Abstract on its point #1, may be the simplest and best way to negate the alarmist hypothesis. While this Abstract is necessarily in scientific language, this argument can easily be put into layman’s language.


The critical questions about climate change are not about whether climate has changed or the impacts of climate change. The critical questions about climate change are about cause-and-effect:

  1. How much does human-emitted carbon dioxide increase atmospheric carbon dioxide?
  2. How much does increased atmospheric carbon dioxide change climate?

This paper focuses on the first question.

This paper derives, possibly for the first time from fundamental principles, a simple model, with a rate equation and its analytic solution, which accurately describes how the level of carbon dioxide in the atmosphere adjusts the carbon dioxide outflow to balance carbon dioxide inflow. The two universally-accepted, fundamental principles are the continuity equation and the gas version of Torricelli’s Law.

This paper will call the model described in this paper, “the Model.”

The Model follows the proper design for such models as described by Forrester of MIT. Models should include defined levels (of carbon dioxide in this instance) and rate equations that describe the flow of carbon dioxide or carbon between the levels.

The Model’s conclusions support the conclusions of other papers regarding carbon dioxide residence time and the effect of human emissions on atmospheric carbon dioxide levels.

The Model shows how the flow of carbon dioxide into the atmosphere sets the equilibrium level of atmospheric carbon dioxide. This equilibrium level equals the total inflow multiplied by the residence time. The Model shows the level will always move toward its equilibrium level.

Because of Raoult’s Law and Dalton’s Law, the Model applies to the total atmospheric carbon dioxide as well as to its individual parts, such as 14CO2, natural 12CO2, and human-produced CO2.

The Model shows that human-produced carbon dioxide and nature-produced carbon dioxide independently set their equilibrium levels based upon their respective inflows, and the sum of these independent equilibrium levels equals the total equilibrium level of atmospheric carbon dioxide.

The Model is meant to replace the Bern model used by the Intergovernmental Panel on Climate Change (IPCC) because the Bern model is not based on fundamental physics.

The Model shows that nature treats human-produced carbon dioxide exactly like nature-produced carbon dioxide because, once in the atmosphere, nature cannot tell the difference between human-produced and nature-produced carbon dioxide.

IPCC’s Bern model treats human-produced and nature-produced carbon dioxide differently, which defies physical laws and is therefore impossible. The emissions term in the Bern equation is for human emissions and not for natural emissions. If natural emissions were inserted into the Bern-model emissions term, the Model would compute an ever-increasing, irreversible, unstoppable level of atmospheric carbon dioxide – even with no human emissions and even if nature’s emissions continued constant as they were in 1750.

The Bern model is a seven-parameter curve-fit to the output of IPCC’s climate models, which include the same assumptions as the Bern model. By contrast, the Model is derived from fundamental physics and it requires data to fit only one parameter, the residence time.

In sharp contrast to the Bern model, the Model accurately reproduces how the level of atmospheric 14CO2 decreased after the end of the above-ground atomic-bomb tests in 1963. The creators of the original Bern model, Siegenthaler and Joos (1992), understood that their model should reproduce the 14CO2 data and were disappointed that it did not do so.

Siegenthaler and Joos designed their original Bern model with separate levels for the atmosphere and different parts of the ocean. However, the IPCC’s version of the Bern model omits the separate levels and incorrectly attaches the slow time-constant between the upper ocean and the deep ocean, directly to the atmosphere. This unrealistic connection causes IPCC’s Bern model to vastly over-estimate the residence time of carbon dioxide in the atmosphere.

The proper way to include the deep ocean is to expand the Model to include explicit levels for the upper ocean and the deep ocean, as originally planned by the creators of the Bern model. Then one would add to the expanded Model, rate equations that describe the slow flows between the upper ocean and the deep ocean. It is incorrect to connect the rate equations for the deep ocean directly to the atmosphere level, as the present Bern model does.

The IPCC is the only group that claims carbon dioxide residence time is hundreds of years to infinity. Siegenthaler (1989), and more than thirty other scientific papers, conclude carbon dioxide residence time is between 3 and 15 years.

This present paper uses 14CO2 data to conclude that the residence time of 14CO2 is 14.4 years. The Model shows that residence time equals the level of atmospheric carbon dioxide at equilibrium divided by the total inflow; this computes the 12CO2 residence time to be ~4 years.

Some authors have tried to defend the IPCC’s extremely long, unrealistic, and irreversible residence time by claiming the Bern model uses a “different kind” of residence time than that which the 14CO2 data describes. The present paper concludes the Bern model, the 14CO2 data, and all other definitions of 1/e residence time are the same – because they all use the same parameter to measure residence time, i.e., the level (or concentration) of atmospheric carbon dioxide.

The Model shows that the ratio of human to natural carbon dioxide in the atmosphere at equilibrium, equals the ratio of their inflows; this ratio equality is independent of residence time.

The Model computes the human-caused equilibrium level to be ~18 ppm and the nature-caused equilibrium level to be ~382 ppm. The total of each part adds up to the ~400 ppm of today.

The Model shows if ALL human carbon dioxide emissions were terminated today and nature stayed constant, the total carbon dioxide level would fall to ~390 ppm in 4 years, to ~387 ppm in 8 years, and would never fall below 382 ppm because the constant inflow of natural carbon dioxide would always maintain that level.

To answer the first question above: human emissions are insignificant to climate change.

Note to authors of other websites: You are welcome to copy and cross-post my post above on your website, provided you include a link to this original post. Please encourage those who wish to comment to do so on this site. Otherwise, I will never be able to read and reply to their comments. Thanks. – Ed

20 thoughts on “A Model for Atmospheric Carbon Dioxide: Abstract”

    1. Robin, it looks like not just that page but your whole website is blocked in Australia. It comes up as a blank page. So much for freedom of expression.

  1. Thanks for your work, Ed. I look forward to reading your full paper. I hope it will be as clear and easy to understand (for us laymen) as this abstract.

    1. Sorry, Ed, but I'm a little confused by your last sentence: "To answer the first question above: human emissions are insignificant to climate change."

      Shouldn't that be, "To answer the SECOND question above"?

      1. Hi Chris, well, I might have improved my last sentence to read,

        "To answer the first question above (because that is the only point we address in this paper), human emissions are insignificant to the increase and amount of carbon dioxide in the atmosphere. Therefore, human emissions are insignificant to climate change."

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  3. Frederick Colbourne

    I am curious about something. Diffusion of CO2 into surface water does not seem sufficient to achieve short residence time for CO2 in the atmosphere.

    I have never read of the potential impact of rainfall upon atmospheric CO2 as having a role in transferring CO2 from the atmosphere into the oceans.

    At altitude, upon condensation, water is cold and therefore able to dissolve CO2 as it falls. The total surface area of so many droplets would facilitate this process. The disolved CO2 would then enter the oceans either directly or indirectly. On land the fate of the CO2 would depend on season, latitude, soil, and vegetation and drainage.

    I would expect that rainfall could partially strip the atmosphere of CO2 for variable periods of time at the location and elevation of Mauna Loa. Summer is the dry season there, when we might expect more CO2 in the atmosphere for more days per month.

    In my opinion, there is enough data at the Mauna Loa observatory to test the hypothesis that rainfall affects the amount of CO2 in the atmosphere on a daily basis.

    I don't know how to test the hypothesis that the short residence time of CO2 in the atmosphere is driven by rainfall rather than diffusion.

    We could think too about the quantum of CO2 in firn. Would precipitation falling on a glacier be deficient in CO2 compared to precipitation falling upon the tropical oceans?

    Put another way, would ice crystals (snow) contain more or less CO2 than liquid water?

    1. Hi Frederick,

      Truth is in the data. Data show the residence time of CO2 is about 4 years.

      You bring up an interesting idea about the effect of rain. I don’t know that anyone has considered this effect. In its simplest form, you are suggesting that cloud droplets contain a surface area that is not insignificant compared to the surface of the oceans, or at least to a local area of an ocean. That idea can be addressed in a theoretical calculation and with analysis of data.

      There are many sites that measure CO2 daily. As you suggest, someone could try to find a correlation between daily rainfall and CO2 at any of these sites.

      To respond to your other questions, precipitation falling on glaciers would likely be colder than precipitation falling on tropical oceans. However, the number of small cloud droplets at any given time is much larger over tropical oceans than over cold land areas.

      Snow crystals form directly from water vapor, not from water droplets. Therefore, if your idea is correct, we would expect snow crystals to have less CO2 than water droplets.

      1. Frederick Colbourne

        Dr Ed

        Many thanks for this reply. Encouragement to follow up. I am wondering if there is a PhD dissertation in this?

  4. Michelle Montgomery

    Welcome back, Ed! Was a bit worried. … I'm an interested non-scientist and have followed you for a couple of years. I really encourage more of this type of work and the hard work of getting it out in the mainstream. Marketing is my area, and I cannot over-emphasize its' importance. Also, more scientists such as yourself doing same.

    Yours has been a great site for me, but my leftist family will not budge. It's been an eye-opener about the mind-set people have. I can see from a marketing angle that the IPCC has the optics advantage (a large world group). More scientists like you need to "team up" in an organized way. Not sure what you might have going on in that regard, or if anything like this is already stirring.

    Thanks for your work.

    1. Hi Michelle, sorry it took me so long to send another email to my subscribers. I was too involved in writing my scientific paper to attend to doing emails.

      But notice to the right of this comment that I am still alive. On the same day (August 9) that I sent emails regarding this post, I also set a personal record on my Concept 2 rower that put me in world first place in my age group for the 500 meters race.

  5. Richard Petschauer

    Ed, very interesting work!

    I know most projections of CO2 atmospheric increases (and temperature increases) assume about 1% per year because of human emissions, but the actual increase of CO2 is closer to about 1/2 of that.

    So what do you think is causing the increase in CO2 if not from humans? Could it be from warming including the ocean?

    1. Hi Richard, you are correct. The rise in the temperature of the ocean surface is the primary cause of the rise in atmospheric carbon dioxide. As Salby shows, the rate of change of carbon dioxide in the atmosphere is proportional to temperature.

      To quote my previous post,

      Salby (2015) shows, directly from data and with no hypotheses, that Temperature sets the rate at which Atmosphere CO2 increases or decreases.

      My new paper, not yet posted, is a significant improvement on my previous post on this subject. It is simpler and it derives more powerful conclusions.

      1. Frederick Colbourne

        Dr Ed, I read that the annual volume of upwelling cold water is about 1,000,000 cubic kilometers. About the area of California to a depth of about 3 km below the thermocline.

        Since below 1,000 meters seawater is very cold and the pressure is very great, would not the volume of CO2 emitted quite substantial when the water warms and the pressure falls to one Atmosphere.

        How many parts per million by volume would upwelling alone contribute to atmospheric CO2?

        Since we know that oceanic oscillations affect upwelling, would not the PDO, ENSO, AMO etc modulate the volume of CO2 release by upwelling?

  6. How does your model explain the relatively constrained CO2 in 100,000 before present and the 43% increase since 1750? The rate of increase in CO2 has increased in the last 60 years as fossil fuel emissions have increased. Does your model predict that atmospheric CO2 will stop increasing? I am interested in global carbon budgets, such as the publication by Quere et al. 2016. Is your model consistent with the published carbon budgets that show oceans and land as significant sinks?

    1. Hi BillD, No. The history of CO2 is outside the scope of the Model. The Model allows any inputs for human and natural emissions. The Model uses IPCC data, so there will be no dispute over the data.

      Then the Model makes it very clear that, even with IPCC data and no matter what the history of atmospheric CO2, the final result is indisputable: the ratio of human to natural CO2 in the atmosphere will be the same as the ratio of human to natural CO2 emissions.

      IPCC data show this ratio is less than 5 percent. Therefore, at equilibrium, the amount of human CO2 in the atmosphere is less than 5 percent of nature's contribution. The Model also shows, using IPCC data, that the 1/e residence time is 4 years. So, atmospheric CO2 is always near equilibrium to the total inflow of CO2. This means human CO2 emissions are insignificant to climate change.

      The Model puts the IPCC claims about the effect of human CO2 on the atmosphere and on climate in checkmate.

    2. BillD

      You asked "How does your model explain the relatively constrained CO2 in 100,000 before present and the 43% increase since 1750? The rate of increase in CO2 has increased in the last 60 years as fossil fuel emissions have increased"

      An explanation of the relatively constrained CO2 is that the CO2 record prior to Mauna Loa is incorrect as accepted by the IPCC. They have accepted the Antarctic ice core record as definitive but rejected much work that disputes that. Stomatta evidence shows periods of 450 PPM in the early Holocene (see papers by Wagner). Chemical analysis from the mid 1800 to after Mauna Loa was set up show several periods of over 400 PPM including in the 1940s but Calander rejected any that disagreed with the ice cores (see work by Beck). Several papers discount the accuracy of the ice cores for CO2 and age analysis (see Jaworoski and Segalstad) .

      Having studied these and other works I have concluded the acceptance of the Antarctic ice cores, which disagree with the Greenland cores, is based on circular reasoning and poor analysis of the records.

      Professor Salby's explanation of thermally generated atmospheric CO2 is a much more believable route to the present CO2 content and a better estimate of the past changes of CO2.

      1. Frederick Colbourne

        Actually, the CO2 in ice cores could be correct. But the CO2 in ice cores may not representative of global atmospheric CO2 at the time the ice formed.

        On a glacier, snowflakes become firn, and firn becomes ice. But snowflakes are solid crystals. So the question we should ask is: how much CO2 can ice crystals entrain? Note, the word "entrain" implies that CO2 molecules inhabit the interstices of the snow crystals. But it also implies that CO2 is not dissolved in snow crystals, nor in firn. Is

        How about experiments to determine how much CO2 is entrained in modern snow and how much there is in modern firn?

        Does anyone know of such measurements?

        There are many forms of ice, including both crystalline and amorphous (non-crystalline).

        "Pressure is another important factor in the formation of amorphous ice, and changes in pressure may cause one form to convert into another."

        Does anyone know of measurements of the CO2 in crystalline versus amorphous ice?

        (There are over 10,000 research papers on the subject of the structure of ice. The problem is to find papers relevant to CO2 entrainment / solution.)

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