Ocean carbon sink & Henry's law
David Archer at RealClimate.org 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.
Numbers
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 outgassingLet'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.
Summary
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.
