A doubling is Carbon Dioxide is estimated to increase atmospheric absorption of outgoing long wave radiation by 3.7Wm-2. Based on Earth Energy Budgets compiled by NASA, that same atmosphere absorbed approximately 26 PW of out going radiation and 33 PW of solar radiation. PW is Peta Watts of 10 raised to the 15th power Watts per second. 3.7Wm-2 per second with a total surface area of the Earth of 5.1 times 10 raised to the 14th power would be 0.51 PW.
That would be a 1.9PW increase in the outgoing long wave radiation absorbed by the atmosphere increasing the total OLR absorbed to 27.9PW assuming a doubling from the CO2 concentration at the time the Energy Budget chart was created. That extra 1.9PW would be a 7.3 percent increase in the OLR absorbed which would increase the total radiant energy absorbed by the atmosphere by 3.2 percent. Conduction, convection and latent energy is also transferred to the atmosphere. Then total shown on the chart is 111PW, that is all the energy that the atmosphere radiates to space. The doubling of CO2 would initially change that value by 1.7 percent. there is also 10 PW shown of the chart radiated from the surface directly to space, so the total energy radiated to space would be 121PW, so the doubling would initially change that value by one percent.
How much will the solar absorbed by the atmosphere change? How much will the conductive, convective, latent and direct to space energy transfer change?
Of the incoming solar, 33PW is absorbed in the atmosphere and 89PW absorbed by the surface. So of the total 122PW absorbed by the surface and atmosphere, 27% is absorbed by the atmosphere. Of the total 121PW leaving the surface and atmosphere headed to space, 26PW or 21% is from OLR absorbed in the atmosphere. That is a difference of approximately six percent or 7.3PW.
Interestingly, water vapor, which many say absorbs almost no solar radiation, absorbs approximately six percent of the incoming solar absorbed by the surface and atmosphere. That is about 7.3PW versus the 1.9PW of additional absorption expected by a doubling of CO2. That almost negligible absorption by water vapor is nearly four times the expected change from Green House Gas (GHG) Effect change.
With warmer surface temperatures, there will be more moisture in the atmosphere. That increased moisture, water vapor, will absorb more incoming solar. Depending on the altitude of the absorption, the additional energy absorbed will increase convection cooling the surface or block solar absorption at the surface if the additional moisture is near or above the tropopause. Additionally, that increase in water vapor will also absorb more of the returned CO2 radiation, further increasing the rate of convection which is a cooling effect. Water in liquid and gas phase will also absorb more of the incoming solar and the return CO2 return radiation, increasing the rate of convection,m a cooling effect. The water and liquid and ice, is also likely to undergo phase changes in the troposphere, a cooling effect. Lat but not least, in order for there to be more water vapor in the atmosphere, there has to be more surface evaporation, also a cooling effect. The increased surface evaporation would also increase conductive/convective heat transfer from the surface, a cooling effect.
For something that absorbs almost no solar radiation, it sure has a great potential for absorbing solar radiation and changing the impact of returned long wave radiation.