Lubos Motl over at The Reference Frame has an interesting post about CO2 sensitivity. He shows that there is an upper limit to how much we can expect the temperature of a body to increase when it is required to radiate an extra 1 W/m2. So far as we can tell, he implies that this radiation-based limit restricts the amount by which the Earth's surface will warm up if it is required to rid itself of an extra 1 W/m2 of heat.
But the greenhouse effect, so far as we understand it, occurs because the Earth's surface cannot radiate its heat directly into space, but instead must pass its heat to the atmosphere by convection, conduction, and radiation. The heat will be radiated when it reaches an altitude where the atmosphere becomes transparent to long-wave radiation. Black-body radiation arguments apply to the atmosphere at this transparent altitude, but not to the Earth's surface. We have not finished our analysis of the greenhouse effect, but we suspect that this transparent altitude corresponds to the tropopause, at about 12 km, where the temperature of the atmosphere stops decreasing.
In order to force heat up through 12 km of air to the tropopause, the Earth must be warmer than the tropopause. In our previous post, we showed how doubling of the concentration of a black impurity in the atmosphere might raise the altitude of transparency from 12 km to 18 km, thus increasing by 50% the distance that the Earth's heat must pass in order to reach the altitude at which it is radiated. The amount by which the Earth's surface temperature would increase under such circumstances is dominated by convection, and is only weakly dependent upon black-body radiation.
By "CO2 sensitivity", we understand climatologists to mean the amount by which the Earth's surface will warm up if we double the concentration of CO2 in the atmosphere. We don't know of any calculation of CO2 sensitivity that is consistent with our understanding of the greenhouse effect. We have looked at a half-dozen over the years, and all are similar and casual. Implementing such calculations in a computer programs and adjusting them until they fit our climate history is, to us, unconvincing. Our long series of posts on the greenhouse effect is motivated by our desire to produce a calculation for CO2 sensitivity that makes sense to us.