# Historical atmospheric partial pressure & Henry's law constant

The explanation given for the fact that temperature has historically led CO₂ levels is Henry's law.

Figure 1: Vostok ice core records for carbon dioxide concentration (Petit 2000) and temperature change (Barnola 2003), posted on www.skepticalscience.com.

However, no statistical evidence for the other Henry's law variables are ever supplied.

What are the historical Henry's law variables?

• Henry's law is only one of the factors that relate temperature and CO2. In practice, the carbon cycle has many different feedback mechanisms that mean that you can't model this simply using Henry's law. Instead you need to use a climate model with a coupled carbon cycle model. Henry's law is enough to give a qualitative explanation of what it seen in the ice core records for the layman, but I suspect you need much more for a meaningful quantative analysis. Jul 8, 2014 at 18:03
• @DikranMarsupial Thank you again Dikran Marsupial! I'm sure for high resolution, more variables must be inserted, but I'd like to see what the actual Henry's Law variables are relative to the above graph. Are they not observed/available? Thank you so much in advance!
– user641
Jul 8, 2014 at 18:08
• my point is that if you were to estimate the constants etc. from the ice core data, you would get the wrong answer, because there were other confounding factors. I would have thought that the constants for Henry's law for sea water are the same now as they were then (I can't think of a reason for them to differ). Jul 8, 2014 at 18:16
• @DikranMarsupial Thank you again! So, take a constant Henry's law constant across time for the atmosphere and an ugly partial pressure can be extracted?
– user641
Jul 8, 2014 at 18:18

The source you mentioned tries to explain why CO2 lags by about 1000 years in historical records. Henry's law tells you something about the equilibrium between the CO2 level in the surface layer and the atmosphere. However, this is not the reason for the 1000 year time-lag mentioned. There's not enough CO2 in the surface layer to cause these increases in atmospheric concentration. What is important is the exchange of CO2 between the deep sea and the surface layer. This seems to have a typical timespan of 1000 a. Citing from your source:

As the Southern Ocean warms, the solubility of CO2 in water falls (Martin 2005). This causes the oceans to give up more CO2, emitting it into the atmosphere. The exact mechanism of how the deep ocean gives up its CO2 is not fully understood but believed to be related to vertical ocean mixing (Toggweiler 1999). The process takes around 800 to 1000 years, so CO2 levels are observed to rise around 1000 years after the initial warming (Monnin 2001, Mudelsee 2001).

So the initial increase in CO2 levels due to Henry's law trigger via feedback mechanisms changes in the vertical circulation pattern thereby transporting more CO2 from the deep sea to the surface. It's this time constant that is seen in the records.

• Great answer! Is there no way to graphically represent the other Henry's law variables over time? It doesn't appear from those two cites that they are available. Is that true?
– user641
Jul 5, 2014 at 19:35
• What do you mean with other variables? Do you mean whether one can deduce the temperature dependence of the Henry coefficient? Jul 5, 2014 at 19:47
• I mean the partial pressure and Henry's law constant for the given temperature & CO2 concentrations in the question's graph. Can the partial pressure be sampled from the ice core, and can the resulting Henry's law constant be derived?
– user641
Jul 5, 2014 at 19:51
• Well, the ice in ice cores stems from precipitation. The CO2 concentration you can get from tiny gas bubbles enclosed. You do not get measurements of the CO2 concentration in the ocean. I don't think Henry's law is very useful here. You can use it to make conclusions about the amount of CO2 dissolved in the ocean, i.e. about its acidity, but I don't think you can learn anything about Henry's law from ice core measurements. Don't know much about it though. Jul 5, 2014 at 23:51
• Thank you! Is there any historical data for atmospheric partial pressure and Henry's law constant?
– user641
Jul 6, 2014 at 0:40