USE OF THE GAMMA DISTRIBUTION IN SINGLE-CLOUD RAINFALL ANALYSIS

Abstract

This study is based on the radar-evaluated rainfall data from 52 south Florida cumulus clouds, 26 seeded and 26 control clouds, selected by a randomization procedure. The fourth root of the rainfall for both seeded and control populations was well fitted by a gamma distribution for probability density. The gamma distribution is prescribed by two parameters, one for scale and one for shape. Since the coefficient of variation of seeded and control cloud populations was the same, the shape parameters for the two gamma distributions were the same, while the seeded population's scale parameter was such as to shift the distribution to higher rainfall values than the control distribution. The best-fit gamma functions were found by application of the principle of maximum entropy. Specification of tractable distributions for natural and modified rainfall populations provides an important prerequisite for the evaluation of seeding effects by Bayesian statistics, a continuing objective in the Experimental Meteorology Laboratory cumulus seeding programs.