Invariant Radiative Cooling and Mean Precipitation Change

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