Hail Growth by Stochastic Collection in a Cumulus Model

Abstract

A one-dimensional, time-dependent numerical model of a cumulus cloud is presented that generates hail and radar reflectivities at realistic rates. The distribution of hydrometeors evolves with time as a result of condensation, sublimation, stochastic collection through collision and coalescence, sedimentation, drop freezing, and drop breakup. A total of 40 mass categories, each twice the mass of the former, corresponding to radii from 2.5 μm to 2 cm, are used to determine the ice and hail distribution. The first 31 categories up to a radius of 2.5 mm are used for the water drop distribution. Radar reflectivities are computed from Mie scattering theory for water and ice spheres in each category, then summed to give the reflectivities that can be compared to those observed by radar. Only the updraft radius at the earth's surface, the mixing coefficients, and the initial droplet distribution at cloud base are arbitrarily specified. Four initial droplet distributions are studied separately to determine their effect on hail growth rates and the water drop and hail distributions.