A PROBABILITY-DISTRIBUTION MODEL FOR RAIN RATE

A systematic approach is suggested for modeling the probability distri bution of rain rate. Rain rate, conditional on rain and averaged over a region, is modeled as a temporally homogeneous diffusion process wit h appropriate boundary conditions. The approach requires a drift coeff icient-conditional average instantaneous rate of change of rain intens ity-as well as a diffusion coefficient-the conditional average magnitu de of the rate of growth and decay of rain rate about its drift. Under certain assumptions on the drift and diffusion coefficients compatibl e with rain rate, a new parametric family-containing the lognormal dis tribution-is obtained for the continuous part of the stationary limit probability distribution. The family is fitted to tropical rainfall fr om Darwin and Florida, and it is found that the lognormal distribution provides adequate fits as compared with other members of the family a nd also with the gamma distribution.