Effective Dynamics of Warm-Rain Production

Microphysical parameterizations continue to advance in realism and performance, in accordance with their critical role in today's weather and climate models. But, simplified descriptions of microphysical dynamics which isolate key parameters while also emulating more comprehensive calculations remain elusive. Here we develop such a description for the processes of gravitational coagulation as well as sedimentation. We simulate these processes with a bin microphysics scheme, and use these simulations to construct dynamical equations for bulk cloud and rain water which evolve via accretion and sedimentation. By separating the bulk dynamics into a a mass-conserving and sedimentation-dominated regime, we find that the overall dynamics are governed by a single non-dimensional parameter $\mu$, the ratio of accretion and sedimentation time scales. This leads to a collapse of cloud observables such as precipitation efficiency as a function of $\mu$, and to an unexpected relationship between cloud water and accumulated rain. We also find that sedimentation can be accurately modeled with a constant bulk fall speed, despite an evolving raindrop distribution.