Anthropogenic CO2 is emitted to the atmosphere first, then a good part of it is absorbed by the ocean. An estimate of the oceanic anthropogenic sink for the period 1800-1994 shows that 48% of anthropogenic carbon emitted during this period is in the ocean (Sabine et al., 2004). In terms of warming, atmosphere warms first as an effect of the increased trapping of longwave radiation. Again, the ocean comes to the rescue absorbing part of the anthropogenic heat (I don't have a number for this, I'll look into it). After this initial atmosphere-to-ocean flux, both carbon and heat become part of complex and dynamic feedback cycles between atmosphere and ocean. One of them is what you mention, the effect of warming on the CO2 solubility in sea water.

Are there ocean temperature variabilities independently of atmosphere behaviour? If the ocean will be warmed indepedently of atmosphere interaction, the old CO2 which is included in the ocean will be released.

The source of heat for the ocean are the atmosphere and the sea-floor. I don't think the second one is big enough to cause significant reductions in CO2 solubility in sea water. Maybe locally, around hot-spots of geothermal activity but I don't think it has a global impact on the carbon cycle, at the timescsales relevant for human-induced climate change, at least. At geological timescales, to be honest, I have no idea.

There is a great mismatch in timescales here.

Human activities are adding energy to the ocean-atmospheric interface. Some of thta extra energy immediately goes into the atmosphere where it quickly mixes away (i.e. build a fire, local heating only, 10 feet away, air is mixed).

What goes into the ocean works much more slowly because of the gigantic heat capacity of water.

As a result of this, changes in the surface temperature and/or temperature profile of the ocean take 100-1000 years to occur in a significant way. So yes, continued heating of the oceans lessen the ability for CO2 to get mixed into the surface ocean waters (the solubility effect) - the other effect which is a warming ocean exudes more CO2 from its various storage reservoirs occurs over much longer timescales.

The 2012 paper by Leavitus etall is a very good quantitative study of ocean heating

http://onlinelibrary.wiley.com/doi/10.1029/2012GL051106/abstract

Yes the CO2 is emitted to the atmosphere and is later a part of it is sequestered to ocean warmer ocean will lower the CO2 uptake. The release of CO2 from ocean is not a very likely scenario in normal circumstances.

This is mentioned in this report...

http://www.lloyds.com/~/media/lloyds/reports/emerging%20risk%20reports/cc%20and%20modelling%20template%20v6.pdf

Heating starts in the atmosphere and is then transferred to the ocean. Heat enters the ocean by diffusion and mixing at the surface, and by thermohaline circulation for deep water. Recent evidence suggest that Antarctic Bottom Waters are already showing signs of warming. http://onlinelibrary.wiley.com/doi/10.1002/2014GL059923/abstract

If Bottom Waters are already showing signs of warming, what is the feedback of the ocean heating in the future? Will we observe increased heat exchange between ocean and atmosphere with a probably possitive heat forcing to the first meters of atmosphere and intensification of global warming effect? Because according to this assumption we will have a significant increase of total energy budget in the system of Air-Sea.

the heat stored in Antarctic Bottom Waters is likely to stay there for thousands of years, while the heat stored in the main thermocline is the fraction that will play a role in ocean-atmospheric feedbacks. That fraction will stay there (and increase) as long as the radiative forcing increases as a result of increasing atmospheric CO2. What happens if we stop CO2 emissions? An interesting paper about this, by Frolicher et al., 2013:

http://www.nature.com/nclimate/journal/v4/n1/full/nclimate2060.html

@ Raffaele: Great paper and I salute the expert :-) I have a question. I understand that AADW is slightly fresher than intermediate water but is more dense because it is so cold. How much does it have to warm before the buoyancy of deep and intermediate waters converge. And what happens?

David, I don't have an answer to neither of your two questions. However, AABW is formed mostly on the continental shelf where it starts sinking and mixing with other water masses and finally it reaches the bottom because it has a higher density than the rest of water masses, among them AAIW. The observed warming in AABW reflects changes occurring in its formation on the Antarctic shelf and during the complex mixing once it has left the surface. This changes are not enough to stop their formation, I guess. If and when these changes were to become strong enough to give AABW a density similar to AAIW, I guess there won't be any more formation of AABW, shutting the abyssal ocean off from any direct contact to the atmosphere.

Just my point... Please ask around. There must be someone there who knows, you are at a great institution (I am a Brit so biased :-)

This is absolute that oceans warmed first and influence to weather because water has a higher specific heat value and influences on the air above the water surface. So weather cant influence on the ocean water temperature. Factors due to global warming first increase ocean water temp.

I agree with David that the warming starts in the air from the extra greenhouse CO2 gas and is transferred to the oceans. The oceans evaporate more, so we see an unprecedented increase in humidity worldwide that leads to health problems such as colds, asthma, blocked air pipe - this winter the demand for oxygen to help mostly old people to breath exceeded all records.

From the earth's history, the release of abundant CO2 from volcanoes contributed to the fatal Global Warming 250 million years ago - The Great Dying or the Permian Mass Extinction that killed over 90 % of all species (NOT the death of dinosaurs, that was mush later). Apparently, it triggered the release of methane from the ocean floor - it is happening in the Atlantic already as a result of our own Global Warming event - and the two gases together (CO2 and methane, both are "greenhouse" gases) raised the temperature some 10 degrees higher - that passed the Death sentence.

Today, we all know where this extra CO2 gas comes from - burning the dirty fossil fuels -, so if we don't want serious changes in the air, change into other forms of energy before it gets too late...

This is simple answer

The oceans are about 850 times more dense than the atmosphere and both are fluids. About 97% of the excess heat produced by surface activities ends up in the oceans.

The oceans transfers this excess heat into the atmosphere through various processes on various timescales..  For the most part, the oceans have served as a giant buffer but buffer space is running out.

Nice answer... The oceans are directly heated by the sun, and by IR radiation from GHG the atmosphere. On average more energy enters the ocean surface (e.g. at night) from the atmosphere than directly from the sun. The buffer analogy is spot on. Great summary here. 

http://www.skepticalscience.com/How-Increasing-Carbon-Dioxide-Heats-The-Ocean.html

One of the mechanisms that caused the Permian/Triassic extinction was increased acidification of the oceans which itself was caused by increased CO2 in the atmosphere. The marine animals most affected by the extinction were those with calcium carbonate shells. Increased ocean acidification is detrimental to the animals ability to produce shells and they are at the most risk.

Since the beginning of the Industrial Revolution, the pH of surface ocean waters has fallen by 0.1 pH units. The pH scale is logarithmic so this apparent tiny change is in fact much more significant than it seems.

The threat to marine life is a far more serious ecological threat than atmospheric warming. As the oceans absorb more CO2 they will become more acidic killing vast quantities of biomass. This will have devastating effects on the marine food chain since much of the non shelled marine animals rely on this food source.

The events of the Permian/Triassic mass extinction were largely influenced by plate tectonics, in particular the existence of the huge supercontinent Gondwanaland. The distribution of the land mass today is very different

Permian Gondwanaland paleoenvironment inferred from carbon and oxygen isotope records of brachiopod fossils from Sydney Basin, southeast Australia

Horng-sheng Mii , , G.R. Shi, Chih-jen Cheng, Yun-yung Chen Chemical Geology Volume 291, 6 January 2012, Pages 87–103