Joint probability distribution of annual maximum storm peaks and amounts as represented by daily rainfalls

Abstract

A procedure is presented for using the bivariate normal distribution to describe the joint distribution of storm peaks (maximum rainfall intensities) and amounts which are mutually correlated. The Box-Cox transformation method is used to normalize original marginal distributions of storm peaks and amounts regardless of the original forms of these distributions. The transformation parameter is estimated using the maximum likelihood method. The joint cumulative distribution function, the conditional cumulative distribution function, and the associated return periods can be readily obtained based on the bivariate normal distribution. The method is tested and validated using two rainfall data sets from two meteorological stations that are located in different climatic regions of Japan. The theoretical distributions show a good fit to observed ones.