Flood Coincidence Risk Analysis Using Multivariate Copula Functions

The coincidence of flood flows of the mainstream and its tributaries may determine flood peaks. This study analyzed the risk of flooding caused by such flood coincidences in consideration of flood magnitudes and the time (dates) of occurrence. The Pearson Type III distribution and the Log Pearson Type III are selected as the marginal distributions of flood magnitudes for annual maximum flood series, and the mixed von Mises distribution is selected as the marginal distribution of flood occurrence dates. Two four-dimensional copula functions are developed for the joint distribution of flood magnitudes and occurrence dates. The upper Yangtze River in China and the Colorado River in the U.S. are selected to evaluate the computation method for risk analysis. The coincidence probabilities of flood magnitudes and occurrence dates are calculated, and the conditional probabilities for the Three Gorges Reservoir (TGR) are analyzed. Results show that the von Mises distribution can fit the observed flood dates data well. The X-Gumbel copula is selected for risk analysis. Based on the proposed model, the coincidence and conditional probabilities for any return period can be obtained.