A bivariate frequency analysis of extreme rainfall with implications for design

Abstract

Analysis of extreme rainfall events has conventionally been performed by prespecifying rainfall duration as a filter to abstract annual maximum rainfall depths as the only variable for analysis. However, this univariate approach does not account for dependence between rainfall properties. To characterize extreme rainfall events, a bivariate analysis is conducted in this study using hourly precipitation data from Indiana, USA. Samples of extreme rainfall events are chosen on the basis of three different criteria: annual maximum volume (AMV), annual maximum peak intensity (AMI), and annual maximum cumulative probability (AMP) based on empirical copulas. Rainfall characteristics, such as total depth, duration, and peak intensity are analyzed using copulas to describe the dependence structures between rainfall variables and to construct their joint distribution for extreme rainfall events. Results from the derived bivariate models are compared to those from conventional univariate analysis by computing the corresponding conditional distributions. Traditional univariate analysis seems to provide reasonable estimates of rainfall depths for durations greater than 10 hours. For shorter durations, a bivariate analysis with extreme events defined on the basis of AMP is recommended. The univariate analysis combined with Huff curves grossly underestimates peak intensities, and again AMP estimates are recommended. Results of this study have implications for current hydrologic design in that they provide better estimates of design rainfall.