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Ocean carbon sink & Henry's law

David Archer at is promoting a new kind of climate catastrophe. The ocean is already getting "fed up" with absorbing man-made carbon dioxide, he says. The ocean will get so upset that it may start to emit CO2 instead, we learn. A usual discussion about positive feedbacks and tipping points follows.

Archer is an atmospheric chemist and when you read his text, it is very clear that he has been taught certain basic laws of chemistry, including Henry's law. Henry's law exactly says that it is impossible for the ocean to get "fed up" with a gas. More quantitatively, the principle states that

at constant temperature, the amount of gas dissolved in a liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.
It means that if you add 7 units of CO2 into the atmosphere and give the system time to reach equilibrium, the amount of CO2 in the ocean increases by 7 (other) units. If you add 19 more units into the atmosphere, the amount of CO2 in the ocean increases by 19 more (other) units. Oceans can't get fed up with a gas. It is not hard to understand why the law is true.

Think about a Maxwell-Boltzmann distribution for CO2 molecules. They can occupy different regions and states with different potential and kinetic energy. However, until quantum statistical mechanics kicks in, which is very far for these low concentrations, classical physics makes the concentrations extensive. If you double the concentration in the air, the concentration in the water doubles, too. If you subtract some short-term fluctuations, the oceans always absorb the same fraction of new CO2. This fraction doesn't change: that's what we call Henry's law. Archer seems to know the law but he denies it in 80 percent of his article.

Moreover, we will see that at fixed temperature, the ocean uptake was always small in comparison with the CO2 in the atmosphere because a majority of CO2 (we will calculate 3/4) is stored in the atmosphere. Don't forget that there are other sinks that can absorb increasing amounts of CO2, especially vegetation: we will neglect this part of CO2 in this article.


We may be somewhat more quantitative. Henry's formula reads:
p = kc
Here, "p" is the partial pressure of CO2 in the atmosphere (in units called atmospheres), "c" is the concentration of CO2 in the ocean (in moles per liter), and "k" is Henry's universal constant (29.4 atmospheres per (mole per liter) for CO2).

Numerically, CO2 is 385 ppm of the volume of our atmosphere, so the partial pressure "p" is clearly 0.000385 atmospheres. The concentration increases approximately by 1.8 ppm a year. In the law above, "p/k=c", we may calculate "p/k". It is equal to 13 micromoles per liter and the law says that it is equal to the concentration in the ocean.
See Al Gore's explanation of outgassing
Let's now take the total water volume on Earth (over 95% is in the ocean). It is 1.36 x 10^{21} liters. If you multiply it by 13.6 micromoles per liter, you obtain about 1.8 x 10^{16} moles of CO2 in the ocean.

How does it compare with CO2 in the atmosphere? The total mass of the atmosphere is about 5.14 x 10^{21} grams and it has 28.8 grams per mole in average. Divide them to get 1.8 x 10^{20} moles - the total amount of gas in the atmosphere. Multiply it by 385 ppm (dimensionless) and you obtain 7 x 10^{16} moles of CO2 in the atmosphere.

The result? Even if you allow CO2 to dissolve in the whole deep ocean - which may normally take some time (deep ocean circulation takes 2000 years, if you wanted to wait for it) - you see that a small fraction of CO2 is in the ocean, about 1/4. At fixed temperature, the ocean only absorbs a small portion of the man-made CO2 and it never absorbed much more. Henry's law says that in the long run, the ratio is fixed. An article that something is changing about the ratio right now inevitably violates this law of Nature.

Observations show a lot of other short-term effects because we are not at equilibrium. But these effects certainly can't be extrapolated into the future.

Temperature dependence

Henry's law assumes that the temperature is fixed. Of course, when temperature changes, the corresponding constant "k" and consequently the fraction of CO2 held in the oceans changes, too. This is nothing else than the reason behind outgassing - the mechanism that determines the relationship between CO2 and temperature during the ice ages and interglacials. When oceans get warmer, they become less able to store gases (think of an exploding Coke can in a heated car in the summer) which means that they release them to the atmosphere: the constant "k" explained above increases, too. When temperature is higher, the atmospheric concentrations and partial pressures "p" of all gases - not just carbon dioxide - increase.

So we encounter an effect that can transform changes of temperature into changes of CO2 concentrations. But how much does it actually change the concentrations? During the glaciation cycles in the last half a million years, the CO2 concentration was changing from 180 to 280 ppm while the closely correlated temperature was changing between a minimum and a maximum that was about 8 Celsius degrees warmer. The correlation used to be nearly perfect but you see that the increase by 8 Celsius degrees leads to the increase of atmospheric CO2 by 100 ppm.

Incidentally, that allows you to see another trivial argument why the correlation can't be evidence of the greenhouse effect. If the CO2 were the cause, if the temperature were its consequence, and if the greenhouse effect were able to transform a 100 ppm increase of CO2 into 8 degrees of warming as suggested by Al Gore, something like that would have happened since 1850, too: since 1850, we have increased CO2 by additional 100 ppm. But the temperatures clearly didn't increase by 8 Celsius degrees since 1850. That's why we see that the prediction for the recent temperature change by the hypothesis that CO2 was a major climate driver during the glaciation periods is brutally falsified. The observed warming is 13 times smaller than the prediction.

Quite clearly, the correlation shows the effect of temperature on concentrations of gases - as can be determined by many other methods, including the universal influence on all gases as well as the famous lag. The correlation is very strong but you must be very careful when you calculate the coefficients: "k" and "1/k" are not the same thing. The correlation shows that pretty high temperature changes (8 Celsius degrees) are needed for relatively decent CO2 changes (100 ppm). The ratio of these two numbers can also be used to deduce how much CO2 increase may be induced by the warming oceans by 2100. Even if you imagine that the 2007-2100 warming will be 2 Celsius degrees (and I surely think that we have strong evidence that it will be less than 1 Celsius degree), such 2 degrees will only add 25 ppm of CO2 or so - the equivalent of 15 years of direct production by business-as-usual. Such additional 25 ppm might lead to 0.15 Celsius degrees per century. It's a correction but the corresponding geometric series is clearly convergent.

Incidentally, a more realistic greenhouse warming by 2100, 0.8 Celsius degrees, will lead to the equivalent of 7 years of CO2 production which is about 13 times shorter than the actual period 2007-2100. It is no coincidence that the number 13 appeared again: in both cases, the number says that the present direct production of CO2 is 13 times more important than the concentration change induced by outgassing.

Again, we see that the temperature-dependence of outgassing is relatively a very small effect. The correlation between temperature and CO2 during the ice ages was only good because only linear mechanisms transforming temperature into CO2 were important - and outgassing was quite certainly the crucial one. Today, we change the concentration of CO2 much more rapidly by other means which means that the old relationships no longer hold and the natural contributions to the changing CO2 concentrations become less important, much like their possible secondary effects on the temperature.


The fixed-temperature fraction of the new CO2 that is absorbed by the oceans is a universal constant because of basic laws of chemistry: it is a very small fraction. The changes of CO2 concentrations induced by warming are negligible in comparison with the direct production of CO2. Moreover, neither of these effects can lead to any kind of exponential escalation.

These effects don't deserve to be discussed by anyone except for people who are scientifically interested in them and it is very irresponsible and dishonest to emit these statements - inpenetrable for most people - combined with irrational gloomy sentiments because such an explosive combination almost certainly leads laymen to completely incorrect conclusions as the discussion beneath Archer's text clearly shows.

And that's the memo.

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reader GeorgeL said...

Lubos, your memo not only ignores the fact that, due to the operation of several other carbon sources and sinks, the Co2 partial pressure between ocean and atmosphere is always in disequilibrium, but you also apparently commit the error of assuming that the carbon content of ocean waters is well-mixed throughout. You latch onto one phrase which was only meant to translate for the layman the notion of "variations in carbon flux at the ocean - atmosphere interface" and from there you imply that the conclusions of the RC post were all wrong, when in fact most of the interesting effects on oceanic carbon fluxes are the result of disequilibrium processes determining the behaviour of different layers and columns of water, processes which are always perturbed by an array of interacting drivers (salinity, heat transport, winds, biology, etc.) thus forever preventing the global climate system from reaching the equilibrium that you referred to in your memo.

It is precisely these disequilibrium dynamics that you so cavalierly bypassed, which are responsible for the shifting flux of carbon at the ocean - atmosphere interface. Who really cares for the tautology that, at a theoretical equilibrium which shall never be reached in practice, the partial pressures of Co2 in ocean and air must necessarily be equal? What really matters is the disequlibrium path taken in the next decades, and whether this implies a net increase or decrease in the oceanic carbon flux.

It seems to me that you are a very smart physicist. A scientist who is this smart, should probably be a little more circumspect about speaking in such absolute tones on subjects, such as climate science, in which he seems to have little or no formal education....

reader Luboš Motl said...

The simplest reason why out-of-equilibrium contributions are not that interesting is simply that they are, by definition, temporary.

They are analogous to weather patterns and any extrapolation of such oscillations is scientifically unjustifiable. Also, much like in the case of weather, their precise reasons are not understood.

The text at RealClimate.ORG talked about a systematic process whose outcome is that these ratios start to be completely different than in equilibrium and running. Indeed, I wrote that it is wrong and I insist that it is wrong.

Of course that local dynamics is responsible for out-of-equilibrium processes and detailed fluctuations. What do you want to deduce out of this tautology? What's important is that these fluctuations are not understood. What is understood are equilibrium calculations that are the best predictions for the long-term behavior we can have.

reader GeorgeL said...

Well, there are several good reasons why disequilibrium dynamics are far more interesting and relevant, but if I were to sum them up, I would say: system dynamics, positive feedbacks, nonlinearities, transition to new "potential equilibrium" end-states.

As an example, consider this. Assume ocean lags behind in keeping up with fossil-fuel based "fast" carbon growth in atmosphere. The greenhouse effect increases temperature directly and also melts ice sheets decreasing planetary albedo and thus increasing temperature indirectly. Rising temperatures cause the melting of permafrost and the release, over some decades, of carbon equivalent to another 200 ppm. Temperatures keep rising, feedbacks keep getting stronger. All of the above are examples of the disequilibrium dynamics that are menacing our planet. I agree that in a theoretical equilibrium state, with constant temperatures, you are correct in your analysis of partial pressure physics. However, that fact is simply not interesting in comparison to the disequilibrium dynamical path our planetary system is now embarked on.

reader Luboš Motl said...

Dear george, without a proper calculation, the words "system dynamics, positive feedbacks, nonlinearities, transition to new potential equilibrium end-states" are just empty ideological cliches used to fool naive laymen which usually includes the ideologues themselves.

Unlike in your world view, in proper science, these terms have no emotional or moral content, most of them are rare in reality, and besides positive feedbacks, there are also (and mostly) negative feedbacks. The very fact that you are forgetting about them shows your breathtaking bias.

The items in your list are types of phenomena that can occur in some hypothetical systems but what is much more important is that they do not occur in particular situations describing the real climate where we live. Moreover, the usual hysterical fairy-tale you wrote here is not really about disequilibrium. It is about a hypothetical instability.

If you're not able to participate in a meaningful scientific - and quantitative, if possible - debate, I strongly urge you to stop posting this stinky garbage about menacing our planet here. You have hundreds of other websites that can be freely spammed by this trash but TRF is not one of them.

reader Steel Rat said...

Sorry, GeorgeL but the scientific community has not yet validated a CO2-driven atmospheric hypothesis, therefore the burden is on you to prove than anything out of the ordinary is happening.

reader Luboš Motl said...

Dear revenant, I apologize for having deleted George's original comment that was inappropriate for this forum.

I won't allow Stalinist "arguments", blackmailing, and intimidation with extremely stupid concepts such as "scientific consensus" to be promoted on my blog. If this is the kind of discourse that George believes in, he is not welcome on this blog.

Here we try to exchange information and rational arguments in a balanced fashion instead of blackmailing each other with asymmetric burdens justified by muscles of 2500 disciples of a new savior of the world.

reader Anonymous said...

Thanks for a brilliant analysis. Clear, rational, quantitative.

Is the calculation of amount of CO2 in the ocean in agreement with others, like Real Climate folks? I thought the amount was higher?
As for:
"Dear george, without a proper calculation, the words "system dynamics, positive feedbacks, nonlinearities, transition to new potential equilibrium end-states" are just empty ideological cliches used to fool naive laymen which usually includes the ideologues themselves."

Hey, that's what I was thinking.
Any 'disequilibrium' is indeed 'interesting' from the perspective that there will be a chaotic process driven by the underlying processes, but the 'feedbacks' are precisely the forces (eg diffusion) that drive it back to equilibrium. That's why it is the equilibirum! To dismiss the equilibrium as unimportant is bizarre. Much of economics is built on such concepts, and they work in predicting known effects.

It's as if he is saying that you can violate entropy/diffusion laws if you make a complex enough scenario. opposite of Occam's razor.

reader Unknown said...

Unfortunately you have strayed beyond your expertise and by your simple application of Henry's Law got it almost completely wrong!
Henry's Law can't be applied the way you have when the gas reacts with the solvent as CO2 does with water. When CO2 dissolves in water it forms carbonic acid which dissociates into bicarbonate ion, carbonate ion and hydrogen ions. Analysis of the resulting chemical equilibria and buffers gives an expression called the Revelle factor. Typical values for sea water range between 9 and 14, a value of 10 means that a change of 10% in atmospheric pCO2 is needed to change the total CO2 content of sea water by 1% at equilibrium.

reader Anonymous said...

Consider the biological fertilization factor as well when considering ocean uptake of CO2:

Enhanced biological carbon consumption in a high CO2 ocean.

And this:

A four-box model of ocean and atmosphere is used to estimate the effects of various changes in the ocean, including CO2 variations. Parameters considered include the ratios of carbon, alkalinity, and phosphorous carried by biogenic particles. The effects of different processes (e.g., atmospheric CO2 transport) on the atmospheric equilibrium partial pressure of CO2 and it isotopic composition were tested, and an increase in upwelling circulation (a deep-water formation) from 15 to 30 sverdrup was found to produce a 25 ppm decrease in atmospheric CO2. It is proposed that surface ocean circulation changes caused the rapid atmospheric CO2 variations during and at the end of the last Ice Age, and that the Atlantic Ocean has significant influence over the level of atmospheric CO2.

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