Toward a Simultaneous Scaling for Mean and Extreme Precipitation Rates

Established theories exist for the responses of both mean and extreme tropical precipitation to warming. In the mean, boundary layer moisture increases faster with warming than surface precipitation, and convective mass fluxes are expected to decrease. Extreme precipitation rates, on the other hand, are expected to scale approximately with near-surface specific humidity, with changes in dynamics playing a secondary role. However, a connection between means and extremes-- that is, a theory for the entire distribution of precipitation rates-- has yet to be formulated. As a first step toward this goal, we modify a condensation-based scaling for precipitation extremes to incorporate information about the distribution of column saturated air mass. When applied to output from a set of cloud-resolving model simulations of radiative-convective equilibrium (RCE), the modified scaling reproduces many of the features of the precipitation rate distribution, including sub-exponential decay at low rates and a roll-off into an exponential tail, and it successfully diagnoses changes in both mean and extreme precipitation rates with warming. Decomposing the scaling allows us to examine the roles played by specific humidity, convective mass fluxes, and cloudy air mass in setting the shape of the precipitation rate distribution. In the tail of the distribution, air is saturated throughout almost the whole depth of the troposphere, and the shape of the precipitation distribution is set by mass fluxes. The transition at lower rain rates to a sub-exponential decay occurs where variability in the distribution of cloudy air mass begins to play an important role. The effects of specific humidity are quantile-independent, and changing the surface temperature stretches or compresses the entire distribution by an amount approximately proportional to the change in near-surface specific humidity. Overall, condensation-based scalings appear to provide a promising step towards understanding the distribution of modeled precipitation rates in RCE.