A linear relationship between vertical velocity and condensation processes in deep convection

Vertical velocities and microphysical processes within deep convection are intricately linked, having wide-ranging impacts on water and mass vertical transport, severe weather, extreme precipitation, and the global circulation. The goal of this research is to investigate the functional form of the relationship between vertical velocity, w, and microphysical processes that convert water vapor into condensed water, M, in deep convection. We examine an ensemble of high-resolution simulations spanning a range of tropical and midlatitude environments, a variety of convective organizational modes, and different model platforms and microphysics schemes. The results demonstrate that the relationship between w and M is robustly linear, with the slope of the linear fit being primarily a function of temperature and secondarily a function of supersaturation. The R2 of the linear fit is generally above 0.6 except near the freezing and homogeneous freezing levels. The linear fit is examined both as a function of local in-cloud temperature and environmental temperature. The results for in-cloud temperature are more consistent across the simulation suite, although environmental temperatures are more useful when considering potential observational applications. The linear relationship between w and M is substituted into the condensate tendency equation and rearranged to form a diagnostic equation for w. The performance of the diagnostic equation is tested in several simulations, and it is found to diagnose the storm-scale updraft speeds to within 1 m s-1 throughout the upper half of the clouds. Potential applications of the linear relationship between w and M and the diagnostic w equation are discussed.