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A Probability Distribution Model for Rain Rate

Benjamin KedemDepartment of Mathematics and Institute for Systems Research, University of Maryland, College Park, Maryland

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Harry PavlopoulosDepartment of Mathematics, University of the Aegean, Samos, Greece

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Xiaodong GuanDepartment of Mathematics and Institute for Systems Research, University of Maryland, College Park, Maryland

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David A. ShortLaboratory for Atmospheres, NASA/GSFC, Greenbelt, Maryland

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Abstract

A systematic approach is suggested for modeling the probability distribution of rain rate. Rain rate, conditional on rain and averaged over a region, is modeled as a temporally homogeneous diffusion process with appropriate boundary conditions. The approach requires a drift coefficient–conditional average instantaneous rate of change of rain intensity—as well as a diffusion coefficient—the conditional average magnitude of the rate of growth and decay of rain rate about its drift. Under certain assumptions on the drift and diffusion coefficients compatible with rain rate, a new parametric family—containing the lognormal distribution—is obtained for the continuous part of the stationary limit probability distribution. The family is fitted to tropical rainfall from Darwin and Florida, and it is found that the lognormal distribution provides adequate fits as compared with other members of the family and also with the gamma distribution.

Abstract

A systematic approach is suggested for modeling the probability distribution of rain rate. Rain rate, conditional on rain and averaged over a region, is modeled as a temporally homogeneous diffusion process with appropriate boundary conditions. The approach requires a drift coefficient–conditional average instantaneous rate of change of rain intensity—as well as a diffusion coefficient—the conditional average magnitude of the rate of growth and decay of rain rate about its drift. Under certain assumptions on the drift and diffusion coefficients compatible with rain rate, a new parametric family—containing the lognormal distribution—is obtained for the continuous part of the stationary limit probability distribution. The family is fitted to tropical rainfall from Darwin and Florida, and it is found that the lognormal distribution provides adequate fits as compared with other members of the family and also with the gamma distribution.

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