A Numerical Model of a Hail-Bearing Cloud

Abstract

A numerical model of a hail-bearing cumulus cloud is presented. The model is one-dimensional and time-dependent, and it employs extensive parameterization of the microphysical processes. The raindrop and hailstone size distributions are assumed to be exponential at all times. Cloud droplets are converted to raindrops according to Berry's parameterization of the autoconversion process and are accreted by the raindrops according to Kessler's formulation. Raindrops are frozen at a rate consistent with Bigg's freezing equation, and the hailstones so formed then accrete raindrops and cloud droplets. Ice crystals are not allowed by the model, and for consistency, then, it is assumed that the cloud droplets do not freeze except when accreted by hailstones at temperatures less than0C. The melting and evaporation processes are modeled, and their impact on the results is explored. The results of five test cases are presented. The sequence of cases is designed to illustrate the effects of the presence of hail, the melting process, and the evaporation of rain on the model by eliminating them, one at a time, from the complete model. In addition, we examine briefly the effect of a lower limit on the cloud radius as it pertains to the entrainment process. The conclusions of this study are that 1) hail is a critical component of the precipitation process, 2) a steady-state assumption is appropriate until the formation of hail in the cloud, and 3) the downdraft begins at the melting level and propagates downward.