Bivariate flood frequency analysis using the copula method

Using the copula method, bivariate distributions of flood peak and volume, and flood volume and duration were derived. A major advantage of this method is that marginal distributions of individual variables (i.e., flood peak, volume, and duration) can be of any form and the variables can be correlated. The copula method was applied to obtain the conditional return periods that are needed for hydrologic design. The derived distributions were tested using flood data from Amite River at Denham Springs, La., and the Ashuapmushuan River at Saguenay, Quebec, Canada. The derived distributions were also compared with the Gumbel mixed and the bivariate Box-Cox transformed normal distributions. The copula-based distributions were found to be in better agreement with plotting position-based frequency estimates than were other distributions.