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We show that radiative cooling profiles, when described in temperaturecoordinates, are insensitive to surface temperature $T_s$. We argue thistheoretically as well as confirm it in cloud-resolving simulations of radiativeconvective equilibrium (RCE). This $T_s$-invariance holds for shortwave andlongwave cooling separately, as well as their sum. Furthermore, the$T_s$-invariance of radiative cooling profiles leads to a simple expression forthe $T_s$-dependence of column-integrated cooling and hence precipitation, andgives insight into why mean precipitation increases at a rate of $2 -3\%\\mathrm{K^{-1}}$ in RCE. The relevance of these results to global climatesimulations is assessed, and the $T_s$-invariance is found to hold in the midand upper troposphere. In the lower troposphere, the pressure-invariance ofcloud layers and circulation tends to dominate.

Invariant Radiative Cooling and Mean Precipitation Change