It seems like every time I turn around Trenberth and Kiehl's or Kiehl and Trenberth's energy budget gets brought up. It is still a cartoon, it is still an estimate and it still is based on data not accurate enough to prove or disprove anything.
The latest version, at least to my knowledge, is here, http://www.cgd.ucar.edu/cas/Trenberth/trenberth.papers/BAMSmarTrenberth.pdf
It still shows both the daylight averages and the daily averages, so everyone seem to want to combine the two which is double dipping. Everyone is still saying that the surface absorbs about 240Wm-2 and emits now 396Wm-2. That is not what is happening.
If you look at what the surface is absorbing from the sun, that value is 161Wm-2. Since the surface average temperature is about 289K degrees, it should be emitting 396Wm-2 if it were a true black body. It not a true black body, it is close to a true black body. Since water covers most of the surface, the average emissivity of water is approximately 0.995 or 0.5 percent less than perfect. 0.5 percent of 396Wm-2 is 2Wm-2. So right from the get go, there is 2Wm-2 of error while trying to determine 0.9Wm-2 of radiant imbalance or warming due to CO2. The emissivity of water increase as turbulence increases, more wind more heat loss. Natural variation in circulation of the atmosphere and oceans change the amount of heat loss per unit time.
Would there be missing heat? No way there could not be missing heat! Get over it, it is not easy to measure, and no, the assumption of ideal black body radiation is not valid unless every calculation is based on perfect black body emissivity. Then, the difference be between observation and calculations, i.e. models, gives some indication of what is happening.
So we have an imperfect value for both the average solar absorbed by the surface and the average emission of the surface. Since the surface absorbs about 161Wm-2 and emits about 396Wm-2, 235Wm-2 if that is the true value, has been stored at some time in Earth's history and/or manufactured internally by the Earth.
That, 235Wm-2 is the atmospheric impact on the surface, less whatever energy the Earth generates internally. That internally generated energy is assumed to be negligibly small. That internally generated energy includes, geothermal, biological (people, plants and animals produce heat), combustion of biological and fission of nuclear materials, totaling approximately 0.17Wm-2, or about 20% of the Estimated 0.9Wm-2 radiant imbalance due to CO2.
The atmosphere absorbs solar energy also, 78Wm-2 on average per the Trenberth energy budget. That also has a margin of error greater than the 0.9Wm-2 imbalance the Trenberth is attempting to illustrate in his cartoon.
The global average surface temperature, which is the clue that there is global warming, has a margin of error of optimistically, 0.1 degrees C. That is a +/- 0.54Wm-2 error possibility while attempting to determine 0.9Wm-2 of radiant imbalance.
Is there missing heat? There is heat missing everywhere. Trenberth's travesty is he thinks it is a travesty that there is missing heat.
Now let's think night time. The cartoon shows 17Wm-2 of "thermals" rising dry air due to conductive warming at the surface carried aloft by convection. That value was approximately 24Wm-2 the last time Trenberth drew a cartoon. The latent heat flux is 80Wm-2 on this cartoon where it was 78Wm-2 on the last cartoon. The radiation to free space is 40Wm-2 on this cartoon where it was 40Wm-2 on the last cartoon.
The most referenced estimates of Earth's Energy Budget, the Keihl and Trenberth cartoons, are so bad that they are not even included in Wikipedia!
So can gravity cause a significant impact on climate? Yes, it most certainly can. The question is, how significant may it be? If it can be on the order of 0.2Wm-2, it is significant. 0.2Wm-2 in terms total energy is approximately 1.1 E+8W/sec. About the same amount of energy released to the atmosphere, by geothermal, tidal change and wind friction, all of which are influenced by gravity and orbital forces.
Update: A PhD on one of the blogs mentioned, that K&T is a useful cartoon. If I want to criticize K&T, I should offer a better cartoon. I started one. That was just the NASA energy budget with values based on more current observations. My estimate of down welling longwave radiation wasn't a big hit, though.
My problem it seems, is separating background temperature from DWLR. If the Earth didn't have greenhouse gases, our atmosphere would be nearly isothermal and highly viscous. Standing on what now is the surface with your non-contact thermometer, you would measure the same temperature in all directions. That would not be back radiation, it would be "back ground" radiation. Once the greenhouse effect is turned on, the difference at the surface would be the impact of the down welling long wave radiation, about 160Wm-2. Since the origin of the DWLR would be above the surface, I estimated the the maximum DWLR value, the average radiant layer of GHGs, would be approximately 220Wm-2 near the tropopause with approximately approximately 100% of Eout or 240Wm-2 the absolute maximum value that DWLR could have. If you correct for local temperature when measuring the sky at night, you may come up with about the same estimate.