# Jeevanjee and Romps, Mean precipitation change from a deepening troposphere, PNAS, 2018

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Why does the equilibrated global precipitation rate increase at roughly 2% per K in all global climate models? The reason stems from the fact that water vapor is the dominant greenhouse gas (as well as the dominant shortwave absorber) and that its density is a fixed function of temperature. As a result, the atmospheric profile of net upwelling radiative flux F is very well approximated by a fixed function of temperature, F = F_{t} - k (T - T_{t})^{n}, where k and n are positive constants and F_{t} is the net flux at the tropopause. Therefore, the net radiative cooling of the troposphere, F_{t} - F_{s}, is equal to k (T_{s} - T_{t})^{n}, where s denotes the surface. Since the radiative cooling of the troposphere is largely balanced by the release of latent heat, the precipitation rate P, measured in W m^{-2}, is also equal to k (T_{s} - T_{t})^{n}. Therefore, since T_{t} is invariant (think FAT, or see our upcoming paper on FiTT), the fractional change in precipitation per change in surface temperature is n/(T_{s} - T_{t}). For Earth, n = 2 and the depth of the troposphere is 100 K, so precipitation increases at 2% / K.