Relativistic Conduction of Heat

If the Earth had no albedo and a constant diurnal average incoming 340Wm-2 solar input, its temperature would be approximately equal to the 278.3K degrees, using the S-B equation assuming it is a perfect black body.

Adding a no GHG atmosphere with a combined surface and and atmospheric albedo of .30, 30% of the incoming solar, 102Wm-2 would be reflected to space with no impact of the effective temperature of the surface. 238Wm-2 would be absorbed by the surface an transmitted to space unaffected by the atmosphere. This is an unrealistic assumption. Conductive and latent heat would still transfer heat through the atmosphere before being radiated to space at the top of the atmosphere. There is no perfect means of transferring energy without a loss to entropy.

The surface temperature would be warmer and the energy converted in transfer through the atmosphere creates potential energy by expanding the atmosphere against gravity.

Latent energy is transferred at a higher efficiency than conductive energy. Latent energy efficiency is related to the pressure decrease with altitude created by the conductive flux efficiency in transferring energy through the mixed gas atmosphere, the dry adiabatic lapse rate. The combined effect is that the surface of the Earth is warmer than the 254.5 degrees indicated by the S-B temperature at 238Wm-2 and less than the 278.3 degrees indicated by the S-B temperature at 340Wm-2 assuming perfect block body at both conditions.

While greenhouse gases amplify, the radiative impacts on the atmosphere, the atmosphere still has an emissivity that changes with the density and optical properties of the molecules in the atmosphere. Emissivity in the atmosphere, decreases as pressure decreases. In space, emissivity has its minimum value where opacity is also at its minimum, space is a very clear optical window, but not perfectly clear. Dark energy in space would not be easily visible, due to the combination of very low emissivity and relative high opacity at it point source.

All the heat fluxes have efficiencies based on dG/dD, dT/dP and dD/dP, where G is gravity, T is temperature in K, D is density and P is pressure in millibar.

Using the Kimoto simplification, dF/dT approximately equal to 4(aFc+bFl+cFr)/T,

Where F is flux in Wm-2, a is a function of dG/dD, b is a function of dT/dP and c is a function of e*dD/dP, where e is a combination of the true emissivity of the surface of the Earth and the initial value of the emissivity of the atmosphere at the surface of the Earth in an upward direction.

Solving for the initial values variables a, b, and c, at surface temperature T=288K, standard average air pressure and gravity, a=0.33, b=1.09 and c=0.825. We should be to determine a reasonable solution for all three Earth conditions in three dimensional space. If all three agree, then time is not a part of the solution. If they do not agree, a fourth dimensional solution would be warranted.

This is where I am at currently. Since I don't latex very well, it is the best description I can give online at the moment.

Dallas

ps https://docs.google.com/spreadsheet/ccc?key=0AqLGErXDPyPFdEotM0RZd1Qzc2N5allBa2s1cWotcGc&rm=full#gid=0

is a link to Google documents spread sheet. The text is not over laying empty cells, which is a pain. Click of each cell to view comments and formula.

Anyone interested can leave their email and I will include access.