= Radiative equilibrium of a single grey cloud layer
{title2=$T_g^4=Q/[\sigma(1-e/2)]$}
A black surface receiving absorbed stellar <irradiance> $Q$, beneath a single non-solar-absorbing <cloud> with thermal <emissivity> $e>0$, satisfies $T_c^4=T_g^4/2$ when both bodies are in pure <radiative equilibrium>. The surface balance is $\sigma T_g^4=Q+e\sigma T_c^4$, giving the displayed result. If instead <convection> pins $T_c=qT_g$, the whole-column balance gives $T_g^4=Q/[\sigma(1-e+eq^4)]$; the nonradiative energy budget cannot then be discarded.
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