Flood Coincidence Risk Analysis Using Multivariate Copula Functions

Abstract

The coincidence of flood flows of the mainstream and its tributaries may determine flood peaks. This study analyzed the risk of flooding as a result of such flood coincidences by considering flood magnitudes and time (dates) of occurrence. The Pearson Type III (P3) and log-Pearson Type III (LP3) distributions were selected as the marginal distribution of flood magnitude for annual maximum flood series; the mixed von Mises distribution was selected as the marginal distribution of flood occurrence dates. Two four-dimensional (4D) copula functions were developed for the joint distribution of flood magnitudes and occurrence dates. The upper Yangtze River in China and the Colorado River in the United States were selected to evaluate the method of computing risk. The coincidence probabilities of flood magnitudes and dates were calculated, and the conditional probabilities for the Three Gorges Reservoir (TGR) were analyzed. Results show that the von Mises distribution can fit the observed flood dates data well. The X-Gumbel copula was selected for risk analysis. On the basis of the proposed model, the coincidence and conditional probabilities for any return period were obtained.