Applying Bivariate Normal Distribution to Flood Frequency Analysis

Abstract This article provides a procedure for using the bivariate normal distribution to describe the joint distributions of correlated flood peaks and volumes as well as correlated flood volumes and durations. The Box-Cox transformation (power-transformation) method is used to normalize original marginal distributions of flood peaks, volumes, and durations regardless of the original forms of these distributions. The power-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 observed flood data from the Batiscan River basin in the province of Quebec, Canada. The resulting theoretical distributions show a good fit to observed ones. Keywords: Flood frequency analysisbivariate normal distributionBox-Cox transformation