Since the density of an atmosphere always approaches zero with height, in accordance with the hydrostatic law, one can always define an outer layer of the atmosphere that has so few molecules in it that it will have low infrared emissivity. We will call this the skin layer. What is the temperature of this layer? Suppose for the moment that it is transparent to solar radiation, and that atmospheric motions do not transport any heat into the layer; thus, it is heated only by infrared upwelling from below. Because the emissivity of the skin layer is assumed small, little of the upwelling infrared will be absorbed, and so the upwelling infrared is very nearly the same as the OLR. The energy balance is between absorption and emission of infrared. Since the skin layer radiates from both its top and bottom, the energy balance reads
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