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Abstract 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 betweenwandMis robustly linear, with the slope of the linear fit being primarily a function of temperature and secondarily a function of supersaturation. TheR²of 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 betweenwandMis substituted into the condensate tendency equation and rearranged to form a diagnostic equation forw. 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⁻¹throughout the upper half of the clouds. Potential applications of the linear relationship betweenwandMand the diagnosticwequation are discussed. 

Abstract Precipitation estimation based on passive microwave (MW) observations from low-Earth-orbiting satellites is one of the essential variables for understanding the global climate. However, almost all validation studies for such precipitation estimation have focused only on the surface precipitation rate. This study investigates the vertical precipitation profiles estimated by two passive MW-based retrieval algorithms, i.e., the emissivity principal components (EPC) algorithm and the Goddard profiling algorithm (GPROF). The passive MW-based condensed water content profiles estimated from the Global Precipitation Measurement Microwave Imager (GMI) are validated using the GMI + Dual-Frequency Precipitation Radar combined algorithm as the reference product. It is shown that the EPC generally underestimates the magnitude of the condensed water content profiles, described by the mean condensed water content, by about 20%–50% in the middle-to-high latitudes, while GPROF overestimates it by about 20%–50% in the middle-to-high latitudes and more than 50% in the tropics. Part of the EPC magnitude biases is associated with the representation of the precipitation type (i.e., convective and stratiform) in the retrieval algorithm. This suggests that a separate technique for precipitation type identification would aid in mitigating these biases. In contrast to the magnitude of the profile, the profile shapes are relatively well represented by these two passive MW-based retrievals. The joint analysis between the estimation performances of the vertical profiles and surface precipitation rate shows that the physically reasonable connections between the surface precipitation rate and the associated vertical profiles are achieved to some extent by the passive MW-based algorithms.