mgh, Not Greenhouse Gases, Provides a Warm Earth

P = 584.8 W/m² = σ T⁴ = (5.6697 x 10^-8 W/m²K⁴) T⁴, 

so T = 318.7 K.

Looking at the NASA Earth Energy Budget, the infrared-active gases emit all but 40.1 W/m² of the 239.9 W/m² of outgoing infrared radiation into space, making this a cooling effect of 199.8 W/m² for the entire Earth system.  But if we look at the effects on the surface temperature, then the 77.1 W/m² of solar radiation absorbed by the atmosphere is a cooling mechanism with respect to the surface.  Much of the 77.0 W/m² due to cloud and atmospheric reflection owes to the so-called greenhouse gas water vapor, which again is a cooling mechanism.  Another important cooling mechanism for the surface is the evaporation of water to produce water vapor which removes 86.4 W/m² of heat.  Adding these three surface cooling effects together gives us a surface cooling effect due to infrared-active or greenhouse gases of 240.5 W/m² , which is much more than the 163.3 W/m² of direct solar radiation absorbed by the surface.

Already, one should be able to see that the only way to support the idea that infrared-active gases are warming the surface is to believe in the reality of the 340.3 W/m² of back radiation shown in the diagram.  This back radiation requires that a black body radiator be at a temperature of 278.34 K, which in the U.S. Standard Atmosphere Table of 1976 occurs at an altitude of 1510 m.  The infrared radiation from such a black body would have to travel 1510 m to reach the surface without any absorption by the infrared-active molecules in that path. In reality, because water vapor and carbon dioxide only emit a portion of the spectrum of a black body radiator, to emit so much radiation they would have to be at a much cooler temperature than 278.34 K, which means that the radiation they emitted exclusively at the wavelengths that they also want to absorb would be emitted at a very much higher altitude than 1510 m.  This would require a much longer mean free path for their emitted radiation than 1510 m.  In reality, the mean free path is very much shorter than 1510 m.  This makes this large back radiation from the atmosphere a fiction.

Note that adding still more CO2 to the atmosphere will actually further reduce the mean free path for infra-red radiation and reduce the temperature differentials that are required to transport much heat between areas at different temperatures by radiation.  Because of the T to the fourth power dependence of radiative emissions, smaller temperature differentials yield rapidly decreasing radiative heat transport back from the atmosphere to the surface. Most of the time, when an infrared-active molecule absorbs a photon, it transfers almost all of that energy to other infrared-inactive molecules such as nitrogen, oxygen, or argon during many collisions with them.

The large back radiation of the NASA Earth Energy Budget is a fiction inserted because they have failed to acknowledge the critical role of gravity in providing us with a warm surface.

Having more infra-red active molecules in the upper portion of the troposphere provides more emitters of radiation into space, which will lower the temperature of the altitude whose temperature is in radiative equilibrium with space, but will do so without moving that equilibrium altitude very much at all.  This is because water vapor already has a very low concentration in the upper troposphere, after decreasing in concentration rapidly at altitudes colder than the condensation temperature of water.  CO2 even doubled does little to shift the equilibrium altitude given water vapor dominance in the emission spectrum and given the temperature uniformity in the tropopause.  The net effect is simply more heat emission to space and little change in the distance to the surface over which the gravity-induced temperature gradient works.  The net effect of adding carbon dioxide is a cooling effect in terms of the atmospheric radiation of infrared to space.

The infrared active molecules speed the upward transport of solar insolation which has warmed the surface by short hop radiation from a warmer layer of air to a cooler layer just above it. The mean free path for the reabsorption of emitted infrared is short, so the amount of energy transported this way is small.  But, this effect is a cooling effect in that the energy transport at the speed of light is much faster than the velocity of air molecules traveling upward in convection currents.

The primary infrared active molecule, water vapor, has a mass to heat capacity ratio less than that of the average air molecule, so it reduces the temperature gradient created by gravity in accordance with the calculation performed above.  Because the water molecule is lighter than the average air molecule, it also has a tendency to increase updrafts of air at higher humidity and thus speed up heat dissipation from the surface by carrying heat to the altitude at which water condenses.  The Earth is also cooled by plant growth and the absorption of water and carbon dioxide by minerals, which increases with more carbon dioxide and water vapor in the atmosphere. 

All of these factors are candidates for being underestimated by the NASA Earth Energy Budget and provide mechanisms in which infrared-active molecules actually cool the surface of the Earth and, ultimately, the atmosphere.

We are very fortunate to have a dense atmosphere in a substantial gravitational field composed mostly of infrared inactive molecules with enough water to dissipate heat adequately by evaporation at the surface and enough infrared active molecules to dissipate heat from the upper troposphere.  It is also critically important that the mean free path length for the absorption of infrared radiation emitted by our infrared-active molecules is short so that heat near the surface is not immediately and directly dissipated to space, but must instead rise slowly through the troposphere to the top portion of the troposphere before it is lost to space.  The infrared-active gases play a critical role, but they do so in conjunction with the powerful effect of our Earth’s gravitational field acting on our air molecules.