Monday, May 04, 2015

Quadratic Coke

Eli has been spending some time over at Bishop Hill's talking the Salby.  To be honest Frederick Engelbeen has been carrying the load, but Eli has been ducking in now and again.  The issue, of course is whether pCO2, the pressure of CO2 above the oceans follows the temperature (Salby) or drives it (Everybunny sensible).

There are lots of reasons to hold that the Murray is wrong, not only the old standbys, but some new ones, which will be discussed in a following post, but something interesting (to Eli, but Eli is easily amused) about the fizzy coke effect came up, how useful is Henry's law for describing the equilibrium concentration of CO2 above the ocean given the complex equilibrium between CO2 in the gas phase and in the ocean, and the carbonic acid, H2CO3, the hydrogen carbonate ion, HCO3-, and the carbonate ions CO32-.

Henry's law states that the pressure of CO2 in the gas phase is related to the amount of CO2 dissolved in the liquid,

pCO2 = k[CO2(aq)]

For most purposes, e.g. physical chemistry classes, k is treated as a constant.  Not a bad approximation, but really is a function of temperature, T, and in the oceans, the salinity, S

k= exp [-60.2409 + 9345/T + 23.3585 log(T/100)]
 + S [0.023517 - 0.00023656 T + 0.0047036 (T/100)2]
Fortunately, there is an app for that, which includes the nice figure to the right, the R code for the calculation and the applet, and a discussion of the chemistry involved with pointers to the original articles.

For this Eli has to thank Scott Denning at Colorado State and his group.

Runing the calculation at fixed alkalinity and dissolved inorganic carbon over a range of temperature more or less representative of what is found in the oceans shows that pCO2 varies pretty close to quadratically with temperature

Both the Henry's law constant, k, and the  [CO2(aq)]/[HCO3-(aq)] equilibrium ratio change quadratically with temperature over the same range.  As a practical matter, 
pCO2(T) = k(T)[CO2(aq)](T) 
where all three terms are quadratic functions of temperature (ok, well approximated as quadratic functions, but R2  >  .9997 for all three)

The oceans are non-linear fizzy coke.


JohnMashey said...

I still am eager to see Murry Salby give a public talk in the US. Colorado would be nice, I might even fly over for the entertainment.

John said...

The topic of CO2 in seawater is complicated enough that it is the subject of a massive (356 page) monograph.
CO2 in Seawater: Equilibrium, Kinetics, Isotopes, by Richard E. Zeebe and Dieter Wolf-Gladrow (Elsevier, 2001).

Gentle Readers of Rabett Run (are there any other types of readers?) will of course immediately recognize that I cited this book back in 2008 when I published The Scientific Case for Modern Anthropogenic Global Warming. where it is footnote #22.

WHAT?? you forgot footnote 22? I'm shocked.

I confess that I didn't read the whole book. But I read enough about CO2 in the oceans that I realized I was out of my depth (Ha!)


John, what's your take on the degree to which reducing SST locally would shift local surface ocean pH?

Fernando Leanme said...

Russel, as they say in Nepal, it depends on the wind speed. The better you mix the two the faster the liquid absorbs gas. If you get lots of waves and the water overturns then it works pretty good.

If you build a cylinder and bubble air from the bottom and pour water from above its better. And if you introduce perforated plates perpendicular to the cylinder axis this forces the rising air to contact the water that falls through the perforations. .

I wonder, why have a debate over something like this? If we add CO2 to the air the water absorbs it. As long as we keep adding it keeps absorbing, until the water gets so hot it reaches equilibrium. Then it starts spitting CO2 back into the air. It's fairly straightforward.

What complicates the process is the details, I suppose

Anonymous said...

Eli, maybe you can answer this question. What is the net effect of a 1C rise in globally averaged temperature on non-dissolved carbon - on both ocean and land? CO2 (and methane) release from land is frequently cited as a positive 'feedback' to anthropogenic warming.

The permafrost has significant stores of carbon, which means, at an earlier point when it was biologically active it participated heavily in the carbon cycle (again, seems intuitive, as land capable of cycling carbon which is dormant due to temperature would have a relative higher capacity from a baseline zero than tropical zones which remain carbon-rich to begin with).

Increase in temperature would drive would drive out dissolved CO2, yes. Increase in temperature would also increase the band of latitude that supports organisms, which would draw down carbon. But this effect cannot be the end of the story. As ecosystems increase in complexity they activate more soil carbon which then enters the cycle?

As a net result, how much of a net atmospheric CO2 increase can be expected with 1C global rise?

I have tried to find answers but it does not seem easy to find.

Barton Paul Levenson said...

Eli-san, what units are T and S in in the equation you cite? Is T in C or in K? Is S in % or ppt? You really should define all the terms you use, and give units.

EliRabett said...

S is salinity in gm/kg

T, well Tin the formula for K is Kelvin, but T in the graph is C just so that the extrapolation is not so large. You can do it for Kelvin, but the abc esp the a and c reflect the distant extrapolation.

Eli first looked at this as a phenominological thing, so C or K was not an issue.

Barton Paul Levenson said...

The formula is useless if I don't know whether to plug in Tc or Tk.