A two-dimensional mesoscale numerical model of the evolution of clouds with a mixed phase composition is formulated. In this model the microphysical processes are taken into account in detail in the calculation of the optical and radiation characteristics. This make it possible to investigate their change and interaction with the meteorological parameters in cloud formation, development, and dispersal. Equations describing the basic physical processes in a cloudy atmosphere and an algorithm for solving these equations numerically based on the method of splitting are presented. The results of application of this model for calculation of the evolution of the optical, radiation, and microphysical characteristics of clouds will be presented in a separate paper.
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