However perhaps it is a transport issue and not a capacity issue as Willy suggests. If the deep cold water capacity is as Willy suggests then perhaps the slight positive feedback of warming shallow waters is not important. Like I've said many times I make no claims to being a climatologist, I'm picking up all of this as I go along.
That's not climatology, that's basic chemistry. Nearly all gases are more soluble in cooler solvents, and nearly all solids are more soluble in warmer solvents. All gases are more soluble at higher pressure.
If even assuming 25 C as a mean ocean temperature, CO2 is soluble at 1.45 g/L of water at atmospheric pressure. Total ocean volume is ~1.3 billion cubic kilometers, which translates to ~1.3 x 10^21 liters. This in turn can disolve ~1.9 x 10^21 grams, or 1.9 x 10^18 kilograms of CO2. For reference, total CO2 in the atmophere today is about 3.0 x 10^15 kilograms. All numbers courtesy of Wikipedia.
Obviously this is a back of an envelope type calculation. I picked room temperature, rather than the 10-15 C that the actual ocean mean temperature would fall. This would boost solubility 35-60%. I also ignored salinity, which would decrease solubility by a factor I couldn't easily find (there are papers on it, but I'm not a subscriber).
I also ignored pressure. Again, all the papers I've found were inaccessible*. More importantly, it would be a disaster of estimates, as pressure changes vastly over the depth of the water column (every ~34ft of water adds another atmosphere of pressure). Then estimate how much area of the ocean is what particular depth, etc. Better to ignore pressure and actual temp, especially given that the intentionally-lowballed estimate shows the ocean can absorb the entire atmosphere's carbon content nearly 500 times.
*found a reference in a paper to the solubility of CO2 at depth. At 2000 meters, CO2 solubility is in the range of 140 g/L. Of course, that drops pH to below 3.5, but the point is that solubility at depth is 100 times my lowballed assumption of solubility.
That's not to say it will, of course. It's an equilibrium. When you add to one side of it, the other side absorbs it until they reach equilibrium again. To get the oceans to saturation would require the atmosphere to be all CO2. But the point is that there is effectively no upper limit on how much the ocean can absorb, just on how fast it can absorb.
But that 25% you mentioned is troubling me, I will indeed chase that but if you can give me a reference I'd appreciate it.
That came from one of your links in #633. I'll admit I put the numbers together myself, but they list fossil fuel CO2 output at 8.7 +/- 0.5 Pg per year and the uncertainty in the global carbon budget at +/- 2.1 Pg per year. Land use change contributed 1.5 +/- 0.7 Pg which I didn't consider, so it's closer to 20% than 25%
It's not likely there is a huge totally unknown process responsible, just that they haven't measured known processes accurately enough to have their contributions correctly calculated. Check the section listed as "Filling the gaps in the global CO2 budget".
As for references for the total solubility, there are none. That is a complete hypothetical on my part, as no one is seriously looking into the maximum possible solubility of CO2. People are looking into deep ocean solubility as a means of preventing emissions from entering the atmosphere, though. This link is an example, although they calculate how much could be dumped (effectively bypassing the absorbsion-rate issue I pointed out, getting the carbon into the ocean manually) without sinificant disruption of the water chemistry. As they point out, this would be highly dependant on carbonate reactions with the CO2 after it is in the ocean, so this is a minimum, not a maximum.