Invariant Radiative Cooling and Mean Precipitation Change

TL;DR

This paper demonstrates that radiative cooling profiles are invariant to surface temperature changes in temperature coordinates, providing insights into precipitation response and climate modeling.

Contribution

It introduces the concept of $T_s$-invariance in radiative cooling profiles and explores its implications for precipitation and climate simulations.

Findings

Radiative cooling profiles are insensitive to surface temperature in temperature coordinates.

Column-integrated cooling and precipitation depend simply on surface temperature.

Mean precipitation increases by 2-3% per Kelvin in radiative convective equilibrium.

Abstract

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.