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

Document Type


Publication Date



Negative-exponential distributions have been used to characterize raindrop size spectra since the earliest experiments in the 1940s and it is by now well established that they emerge in a limit as progressively more space and/or time averaging is performed. A simple probability factorization argument is used to discuss a statistical interpretation of the ubiquity of the exponential size spectra and its emergence in the limit of extensive averaging. The authors employ the "patchy" rain approach and the associated non-Poissonian counting statistics, developed in the previous two papers of this sequence, to elucidate the "asymptotic" conditions required for the emergence of the limit distribution and to explain such observations as the "Waldvogel N0 jumps," relatively rapid emergence of the exponential spectra in exceptionally steady rain, strong deviations of the "instantaneous" distributions from the average shape, and the fact that exponential spectra are seldom seen in individual rain events. Computer simulations and data analyses are also presented to support our interpretation of these phenomena.

Publication Title

Journal of the Atmospheric Sciences