The time for radiative cooling to occur following the imposition of a small temperature gradient. From Holton (1979), the change in energy flux as a function of height z in an atmosphere is given by
where is the density, is the heat capacity at constant pressure in J K-1 kg-1, and T is the temperature. Rearranging and integrating gives
If and are constant with z, then
where is the column density. Energy balance requires that
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