The book examines surface rainfall processes through cloud-resolving modeling and quantitative analysis of surface rainfall budget and summarizes modeling and analysis results in recent seven years. The book shows validation of precipitation modeling against observations and derives a set of diagnostic precipitation equations. The book provides detailed discussions of the applications of precipitation equations to the examination of effects of sea surface temperature, vertical wind shear, radiation, and ice clouds on torrential rainfall processes in the tropics and mid-latitudes, and to the studies of sensitivity of precipitation modeling to uncertainty of the initial conditions and to the estimate of precipitation efficiency. The book can be used as a text book for graduate students and will be beneficial to researchers and forecasters for precipitation process studies and operational forecasts.

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