Abstract
A time-dependent Eulerian model of the warm-rain process has been developed to investigate the roles of stochastic coalescence and vertical water transport in the development of convective precipitation. Several model runs were made using experimental values of cloud droplet spectra, liquid water contents, and updraft profiles to simulate typical maritime warm cumuli. Comparative model runs made with and without an updraft illustrate the importance of transitory water accumulations in explaining the coalescence growth of cloud droplets to precipitation sizes within a reasonable time and the sudden onset of large-droplet rain in convective showers. The maritime runs were then repeated, this time seeding just above the level of updraft maximum with spray rates and seeding droplet spectra used in the water-spray field experiments of the University of Chicago Cloud Physics Project. Within the framework of the model, the seeded cases show significantly earlier precipitation onset than their non-seeded counterparts. Shortcomings of the model are discussed and comparisons made between its numerical predictions and the experimental results of the Cloud Physics Project. The consequences of a spatially and temporally localized area of high liquid water content in the cloud leading to an equally localized area of coalescence-induced rain formation seem consistent with observations of natural warm rainfall.

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