Fluctuation properties of precipitation. Part III: On the ubiquity and emergence of the exponential drop size spectra

Negative-exponential distributions have been used to characterize raindrop size spectra since the earliest experiments in the 1940s and it is by now w ell established that they emerge in a limit as progressively more space and /or time averaging is performed. A simple probability factorization argumen t is used to discuss a statistical interpretation of the ubiquity of the ex ponential size spectra and its emergence in the limit of extensive averagin g. The authors employ the "patchy" rain approach and the associated non-Poi ssonian counting statistics, developed in the previous two papers of this s equence, to elucidate the "asymptotic" conditions required for the emergenc e of the limit distribution and to explain such observations as the ''Waldv ogel N-0 jumps,'' relatively rapid emergence of the exponential spectra in exceptionally steady rain, strong deviations of the "instantaneous" distrib utions from the average shape, and the fact that exponential spectra are se ldom seen in individual rain events. Computer simulations and data analyses are also presented to support our interpretation of these phenomena.