Numerical Simulation of Graupel Development

Abstract

The variation in time of an ice particle size spectrum resulting from collisions of ice particles with super-cooled drops, and the simultaneous variation in time of a size spectrum of supercooled cloud droplets resulting from collisions and coalescence and from drop depletion caused by riming are described in terms of numerical solutions to the stochastic collection equations. The ice crystals were assumed to have the shape of thin hexagonal plates, and to follow Gaussian mass distributions corresponding to a mean ice crystal radius ranging from 205 to 479 mu;m and corresponding to an initial ice crystal concentration ranging from 2.5 ? 103 to 5.0 ? 104 m?3. The initial mass distribution of the cloud drops was that given by Berry and Reinhardt (1974) corresponding to a mean drop radius of 14 µm and a liquid water content of 1.0 ? 10?3 kg m?3. The efficiency with which ice crystal plates collide with water drops was assumed to be that computed by Pitter and Pruppacher (1974). The collection efficiencies used for the drop-drop interaction process were those given by Scott and Chen (1970). The drop breakup kernels were those of Srivastava (1971). It was found that a graupel size spectrum crucially depends on the initial ice crystal size spectrum and ice crystal concentration, and that the presence of riming ice crystals significantly affects the growth of drops by collision and coalescence.