The way you hold steady the energy content of any volume in space is to ensure that any energy gained is matched by energy lost. In the context of Earth, and Earth's climate, it means that the sun is busy heating up Earth during the day, and at night, largely, Earth is busy getting rid of all that heat. But this interest with differences in heat is only with differences of heat at the surface of Earth; what happens in the molten core is of no interest. And, as for the surface, the interest is only with air temperature. Air temperature is what gives rise to the Annual Global Mean Surface Air Temperature, and that is the variable that we seem to care about, and track.
In the "climate change" scenario, when you add CO2 to the atmosphere, it upsets this balance between energy gained and energy lost, by reducing Earth's ability to cool down. But as Earth gets hotter, its ability to radiate heat away is increased [that's just Stephan-Boltzmann], so that a balance can again be restored, although now at a higher temperature.
But this way of looking at the mechanics of climate change is incomplete. It is true enough that the change in energy is equal to energy gained minus energy lost, for Earth, as a unit of analysis, or for the atmosphere, as a unit of analysis. And it is true enough that when the atmosphere loses heat to outer space, heat is lost from both the atmosphere and from Earth. What is not mentioned is that when the atmosphere loses heat to the ocean, that heat is not lost to Earth. This upsets the equilibrium of Earth, even if the Annual Global Mean Surface Air Temperature does not reflect it.
For the atmosphere over the ocean, the problem with the equilibrium of Earth, as measured by Annual Global Mean Surface Air Temperature, is even clearer. Some solar radiation over the ocean is reflected and not absorbed, so that has no effect on the energy content of the ocean, or of the air, or of Earth. But solar radiation that penetrates into the ocean and is absorbed, loses heat by conduction, not initially by infrared radiation, so that this solar radiation tends to warm the ocean. That warming has been reported, and measured, and that warming causes expansion of water, leading to mild sea level rise. But that is not the point. The point is that the heat is retained, not radiated away into space. It is upsetting the equilibrium of Earth; Earth has gained energy, and this will, at some point, change the Annual Global Mean Surface Air Temperature.
The claim that increases in CO2 levels have a long term pressure on temperature implies that some mechanism exists to delay Earth coming to equilibrium, and this stashing of energy in the ocean, temporarily, might be that mechanism. Also a warmer ocean can hold less CO2, so it may become a CO2 source.
Of course, a warmer ocean melts ice. This is another place Earth can dump energy for a while, because melting ice is a state change, not a temperature change. So the ice caps, and the melting of the ice caps, hide the full warming effect of the increase in CO2.
We do have a way to see delayed effect on air temperature that will be caused by our stashing energy into the ocean as opposed to radiating it into space. That way is during an el Nino event. It becomes harder to dump energy into a warmer ocean, and in that case the Annual Global Mean Surface Air Temperature departs from baseline by an additional 50%. Instead of a .4 degree rise, one sees a .6 degree rise. This allows us to begin to estimate the delayed warming effect of CO2 when the entire ocean, in its normal state, is warmer.
This graphic, while specific, is incorrect. It says heat into Earth equals heat out. Don't we wish this were true. Some of that heat lost is "lost" into the ocean. Not lost from Earth into space, sadly.
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