Parameterization of Raindrop Size Distributions

Abstract

The processes of condensation, coalescence and drop breakup tend to produce exponential raindrop size spectra. The intercept n0 and slope ? of the exponential distribution are given by differential equations expressing the conservation of raindrop concentration and rainwater content M. The differential equations are solved numerically using published experimental data on coalescence efficiency and spontaneous breakup. The number of fragments resulting from a collisional breakup S0 is taken as a variable parameter. Calculations show that 1) the effects of collisional breakup usually predominate over those of spontaneous breakup, 2) for dM/dt=0, a stationary ? results which is a function of S0, and 3) for dM/dt>0, ? tends to a quasi-static value which depends upon S0 and (1/M2) (dM/dt) but is close to the stationary value for the same S0. In each case n0 is determined by the values of ? and M. Binary interactions, i.e., drop coalescence and collisional breakup, tend to produce raindrop size spectra which have approximately constant ? and an n0 approximately proportional to M. A method of parameterization for cumulus dynamics models is suggested in which both n0 and ? are calculated.