Abstract
We explore the vertical convective flux F c in a radiative-convective grey atmosphere. An expression of the form F c = F s τ o /( C+ Dτ o ) appears useful, where F s is the shortwave flux absorbed at the base of an atmosphere with longwave optical depth τ o and C and D are constants. We find excellent agreement with an idealized grey radiative-convective model with no shortwave absorption for D=1 and C=1∼2 depending on the surface-atmosphere temperature contrast and on the imposed critical lapse rate. Where shortwave absorption is correlated with longwave opacity, as in the atmospheres of Earth and Titan, C=2, D=2 provides an excellent fit, validated against the present terrestrial situation and the results of a nongrey model of Titan's strongly antigreenhouse atmosphere under a wide range of conditions. The expression may be useful for studying the energetics of planetary climates through time where there is insufficient data to constrain more elaborate models.
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