Recent research has discovered that a warmer climate corresponds to a higher atmospheric concentration of carbon dioxide. Two explanations have been presented: Either the carbon dioxide may warm the earth because of the greenhouse effect, or the carbon dioxide concentration may increase due to decreased solubility in the oceans by a temperature increase forced by something else than carbon dioxide. The second explanation can be tested by equilibrium calculations. In this report a general simulation program for chemical equilibrium calculations created by Westerlund (1990) is utilized. Here I will give only a short description of some of the equations involved, and a few results of the calculations with the simulation program.

  Chemical reactions

The dissolution of carbon dioxide in the ocean water is defined by the following chemical reactions:

MgCO₃(s) = Mg²⁺ + CO₃^2-                                                                             (1)

CaCO₃(s) = Ca²⁺ + CO₃^2-                                                                              (2)

H₃O⁺ + CO₃^2- = HCO₃^- + H₂O                                                                       (3)

H₃O⁺ + HCO₃^- = CO₂(aq) + 2 H₂O                                                               (4)

CO₂(aq) = CO₂(g)                                                                                            (5)

where CO₂(aq) denotes both aqueous carbon dioxide and H₂CO₃,

2H₂O = H₃O⁺ + OH^-                                                                                         (6)

The first two reactions are slow, the others are fast.

The dynamics of the system is of general interest. As the bulk of the ocean still has a carbon content that is in equilibrium with pre-industrial atmospheric concentration of carbon dioxide (abt. 280 ppm), an increase of atmospheric concentration to a value of X due to anthropogenic emissions will increase the absorption rate proportional to the difference X - 280 ppm (Fick's first law of diffusion). It does not matter where the diffusion resistances are located, are they in the boundary layer between the atmosphere and the ocean, or somewhere within the water, or in both places, the proportionality is still valid. This is a good explanation of the findings that such global carbon cycle models which imply an almost constant value of the "airborne fraction" cannot explain the slow increase of the atmospheric carbon dioxide concentration during recent decades.

But here we look at the system statically and without anthropogenic emissions, assuming that there is enough time for equilibrium.

   Equilibrium equations

At a pre-industrial reference state and reference temperature, the equilibrium concentration should be 280 ppm. The equilbrium constants and their temperature dependence are well known. If we want to calculate how a temperature increase of the ocean water influences the atmospheric concentration we must however know the water volume that is assumed to be in equilibrium with the atmosphere during the temperature change. This is, of course, difficult. We know that it will take thousands of years for an equilibrium between the atmosphere and the total global water volume. But we can use an equivalent part of this volume as a parameter and calculate the temperature senistivity for different values of this parameter. As a measure of this part, the equivalent "back-mixed ocean layer" can be used. From the equilibrium reactions (1) - (6) the following expressions are obtained:

k₁ = (Mg²⁺)(CO₃^2-)                                                                                      (7)

k₂ = (Ca²⁺)(CO₃^2-)                                                                                       (8)

k₃ = (HCO₃^-) / (CO₃^2-) / (H₃O⁺)                                                                  (9)

k₄ = (CO₂(aq)) / (HCO₃^-) / (H₃O⁺)                                                            (10)

k₅ = X / (CO₂(aq))                                                                                       (11)

where the notation (A) means the concentration of (A) in moles/liter. If now the total mass of carbon as carbon dioxide in the atmosphere and as carbon dioxide, bicarbonate and carbonate in the equivalent water volume, V_w, (liter), that is assumed to be in equilibrium with the atmosphere, is denoted m_C ,we obtain from a carbon balance:

(Ca²⁺)=[1+k₃(H₃O⁺)[1+k₄(H₃O⁺)[1+k₅n_air /V_w]]]M_C V_wk₂/m_C           (12)

where n_air= 0.177e21 moles is the total amount of air in the atmosphere. M_C  is the molar mass of carbon. The calcium ione concentration, (Ca²⁺), of the bulk of the ocean water is about 0.01024 mol/l. Neither pH nor (Ca²⁺) will remain constant if the temperature changes because all the equilibrium constants will change. But the same equations also give:

X = k₂k₃k₄k₅(H₃O⁺)² / (Ca²⁺)                                                                 (13)

The calculation of the temperature dependence of X will therefore be as follows.

   Calculation of the reference state

- First we define the water temperature for the reference state

- Then we assume that X = 280 ppm for the reference state

- Finally we assume that (Ca²⁺) = 10.24 mmol/l for the reference state

- We calculate (H₃O⁺) and pH = -log(H3O+) from equation (13). We obtain pH = 8.2 which is close to the global mean value of 8.1 that has been reported by many sources.

For (Mg²⁺) we get 53.6 mmol/l which is close to the measured value. The ocean water seems to obey normal chemical laws. Finally we calculate the concentrations of all the other species for the reference state.

- We use a value of V_w corresponding to, for example, 150 m surface layer of the ocean for the reference state and calculate m_C from equation (12).

   Calculation of X for a new temperature

If the temperature changes and no (antropogenic) carbon is put into the system, the value of m_C will remain constant. Only the portitioning between the atmosphere and the water will change.

For a new temperature, we cannot use the old values of (Ca²⁺) or (H₃O⁺), and we do not know the value of X . Equation (13) thus contains two unknown parameters. This unpleasent problem can be solved by introducing one more equation, the charge balance according to:

(H₃O⁺) = 2(CO₃^2-) + (HCO₃^-) +2 (SO₄^2-) + k_w / (H₃O⁺) -2(Ca²⁺) -2(Mg²⁺) + (diff)          (14)

where k_w is the ion product of water and (diff) is the difference between the concentrations of other positive and negative charges. (SO₄^2-) is assumed to remain constant, 28.2 mmol/l.

Now the whole set of eqations can be solved in the computer simulation program to calculate not only new values of Ca²⁺ , pH, and X , but also the concentrations of all the other species in the equivalent ocean layer.

   Equilibrium constants

The following constants were used in the calculation:

Constants for temperatures between are obtained by quadratic interpolation.

   Results

The results are shown in the figure. As one could expect, a temperature increase of one degree celsius will increase the atmospheric concentration of carbon dioxide in the range of 8 ppm (150 m layer) to 18 ppm (600 m layer). The influence of the assumed layer thickness is great in the beginning, but for thicker layers the influence will level out. If we assume that the whole ocean (mean depth 3795 m) is in equilibrium with the atmosphere, a one degree celsius global warming will increase the atmospheric carbon dioxide concentration by 28 ppm. For a very long time scale (ice ages and interglacials) the whole water volume may be in equilibrium with the atmosphere.

   Discussion

The calculations show that the atmosphere connected to a warm ocean contains more carbon dioxide than if connected to a cold ocean. This fundamental mechanism drives the absorption close to the poles and the desorption in the tropics. The concentrations of both Ca²⁺ and Mg²⁺ will decrease somewhat when the temperature increases. The concentrations of both CO₃^2- and HCO₃^- decrease to a great extent if the temperature increases. Because this calculation is performed with global mean values, the calculation of absolute concentrations is rough because these concentrations are different in different regions and for different times of the year.

The sensitivity calculation, however, may be very reliable. It shows that natural temperature increase cannot be the whole reason for the increase of atmospheric carbon dioxide concentration of about 80 ppm during this century. But the question of the `Chicken and the Egg' for the ice core measurements seems quite clear: First comes the warming, then comes the CO₂.

   Reference

Westerlund, Tapio: On Modeling of the Atmospheric Carbon Dioxide Change, Internal report 90-111-A, Abo Akademi University, dep. of Chemical Engineering, Finland, 1990.

Comments and/or discussion on the above paper are invited on an `Open Review' basis. Contributions should be emailed to daly@microtech.com.au with "CO2 and Ocean Warming" in the subject line.

Subject: CO2 and Ocean Warming
Date: Mon, 12 Apr 1999 23:38:51 -0300
From: "Dr. Theodor Landscheidt" <theodor.landscheidt@ns.sympatico.ca>

Dear Dr. Ahlbeck,

The model you used is rather rough. Yet rough models often prove more reliable than very sophisticated ones. So we have to accept all your results including the sensitivity calculation as long as no one shows that they are flawed.

Cordially,

Theodor Landscheidt

Subject: CO2 and Ocean Warming
Date: Sat, 17 Apr 1999 22:04:27 +0300
From: "Jarl Ahlbeck" <jarl.ahlbeck@abo.fi>
To: Theodor Landscheidt

Dear Theodor,

Yes, the model is rough, but still the calculation is far from trivial. As a matter of fact, I have not seen any competiting calculations. If anybody has seen, please let me know !

Analytical chemists often utilize different kinds of diagrams to solve the pH problem for complicated mixtures. The program by Westerlund uses a numerical algorithm that is more stringent. The equilibrium constants corrected for ocean salinity, 5 degrees Celsius, and reference state (pre-industrial) are in the program approximated to values about:

The temperature- salinity- and ionic strength- dependences of the constants are obtained by multiple regression analysis from a database containing information from many different sources, mainly from the fundamental experimental works by Sille'n, Martell and Kramer during the period 1958 - 1964. Recent measurements have proved that these old values are still valid today.

If you look at the ice-core CO2 - temperature picture on the main Daly page, a sensitivity of about 30 ppm for every degree Celsius seems very reasonable. The ice-core analysis gives about the same sensitivity as the equilibrium calculation when the whole ocean water volume and the whole atmosphere are set into equilibrium with each other.

I did not first believe that the Chicken-Egg problem was that trivial, but now I believe. Reserachers do have a dangerously strong believe in their own calculations....

As Tapio Westerlund however is my boss, I know that he has great skill and experience in solving chemical equilibrium problems on the computer. He usually gets the same results theoretically as we researchers get experimentally in the laboratory. This time we do not have direct experimental proof from the laboratory, but we have the ice-core data.

Cordially

Jarl Ahlbeck

Subject: Dr. Landscheidt's comment
Date: Mon, 24 May 1999 09:41:14 +0200
From: 091335371-0001@t-online.de (P. Dietze) Reply-To: 091335371@t-online.de
To: jarl.ahlbeck@abo.fi

Dear Jarl,

Dr. Landscheidt wrote about your ocean chemistry at http://www.john-daly.com/oceanco2/oceanco2.htm

> The model you used is rather rough. Yet rough models often prove more
> reliable than very sophisticated ones. So we have to accept all your
> results including the sensitivity calculation as long as no one shows
> that they are flawed

Sigh, the "solar and CO2 thermometer coalition", so far ever assuming that the CO2 level is not caused by human emissions, but stems from integration of solar-caused variations of biomass and ocean degassing, has slowly to "accept" what they have kept debating and insisting against. But I feel, still there is a bit of hope, somebody would turn up, saying your ocean chemistry is flawed...

I would like to know your opinion re Dr. Kasting's assumed (incredible low) ocean absorption capacity of 1300 GtC. Thanks for your excellent paper at Daly's! It may help some more people to agree to our former statements about the iceage sensitivity - and last not least help to stop absurding my emission/absorption-based carbon cycle model (now being discussed at john-daly.com/co2debat.htm).

Best regards, Peter

Subject: CO2 and Ocean Warming
Date: Fri, 4 Jun 1999 23:20:16 +0300
From: "Jarl Ahlbeck" <jarl.ahlbeck@abo.fi>
To: Peter Dietze
CC: <daly@vision.net.au>

Dear Peter,

The equilibrium calculation program can give many interesting results. For example, if we should stop all emissions today, the atmospheric carbon dioxide will fall quite rapidly in the beginning. But the resulting atmospheric concentration would not (after some hundreds of years) be 280 ppm as calculated by my statistical mass-transfer model, but about 290 ppm due to the change of the composition of the ocean bulk as carbon from the fossil reserves has been transported to the air-ocean system. The change of the ocean bulk is not accounted for in our diffusion models, but the error is small for a limited time into the future and for moderate emission scenarios.

When we have emitted 1300 GtC more into an ocean-water system (without biosphere !!), the resulting equilibrium concentration in the atmosphere will be about 365 ppm or the same as today's concentration which is, of course, not equilibrium. As we use in our models 280 ppm as a constant value of the "resisting" partial pressure, we therefore make a considerable error if we go too far into the future with very high emission scenarios. For an atm. concentration of say 500 ppm we use a driving difference of 500-280 = 220 ppm for the net sink flow rate. I think the correct number would be something about 500-325 = 175 ppm, but I don't know for sure and it depends strongly on the time scale. But still, we beat the IPCC model that implies a constant "airborne fraction" which is fundamentally wrong. Another fact in favour of our models is that a great part of the anthropogenic carbon goes into the biosphere as increase of the biomass. We cannot possibly assume that everything goes into the ocean. The net sink rate to the biosphere is forced by the partial pressure too.

Because our models are verified by data and statistical calculations (the IPCC model is not) they are the best models until now. But they are not necessarily completely correct for future predictions althogh I think that your model was the first step in the right direction (followed by my model as the second step).

Every model development I get paid for from the process industry is based on observations and stiffness of the model. The model structure must have good agreement with basical physical laws such as heat- and mass transfer, diffusion, chemical equilibrium a.s.o. Nobody would pay me for making anything like the IPCC carbon models or GCM:s with hundreds of unknown or adapted parameters, and nobody will pay anything for "predictions" made with such flexible models that can predict almost anything you feel is going to happen.

It is useless to develop our models for taking into account the change of the ocean bulk composition as long as anybody cannot quantify the biospheric net sink rate. If we try, we will slowly transform ourself into junk scientists (as many "climate change" scientists are today). It is better to be a honest technocrate and keep the feet steadily on the ground.

As an answer to your question, the ocean can take at least ten times more than 1300 GtC. It will only rise the equilibrium concentration in the atmosphere over 365 ppm and decrease the pH of the ocean bulk. If also very slow silicate equilibrium is taken into account (silicates take thousands of years, my equilibrium calculation takes only solid carbonates into account) the oceans can absorb hundred times more.

regards, Jarl