## Mean Precipitation Change from a Deepening Troposphere

Romps, D., Lawrence Berkeley National Laboratory

Convective Processes

Jeevanjee N and D Romps. 2018. "Mean precipitation change from a deepening troposphere." Proceedings of the National Academy of Sciences, 115(45), 10.1073/pnas.1720683115.

## Science

Why does the equilibrated global precipitation rate increase at roughly 2% per K in all global climate models?  Despite the ubiquity of this result, we have not yet had an explanation for it.

## Impact

Precipitation rates are important for many obvious reasons, including the role that rain and snowmelt play with regard to our crops.  Regional changes in precipitation rate must be understood in the context of the change in the global rate of precipitation.  And, unless we have a mechanistic understanding of the global precipitation rate, it is hard to know whether the changes in that rate predicted by global climate models are trustworthy.

## Summary

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 = Ft - k (T - Tt)n, where k and n are positive constants and Ft is the net flux at the tropopause. Therefore, the net radiative cooling of the troposphere, Ft - Fs, is equal to k (Ts - Tt)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 (Ts - Tt)n. Therefore, since Tt is invariant (think FAT, or see our upcoming paper on FiTT), the fractional change in precipitation per change in surface temperature is n/(Ts - Tt). For Earth, n = 2 and the depth of the troposphere is 100 K, so precipitation increases at 2% / K.