Bivariate design flood quantile selection using copulas

Abstract

Flood event consists of peak discharge and flood volume that are mutually correlated and can be described by a copula function. For a given bivariate joint distribution, a choice of design return period will lead to infinite combinations of peak discharge and flood volume. A boundary identification method is developed to define the feasible ranges of flood peak and volume suitable for combination, and two combination methods, i.e., equivalent frequency combination (EFC) method and conditional expectation combination method for estimating unique bivariate flood quantiles are also proposed. Monte Carlo simulation method is used to evaluate the performance of these combination methods. The Geheyan reservoir in China was selected as case study. It is shown that the joint design values estimated by the two proposed combination methods are both within the feasible range, which means that the methods could be selected for designing unique flood quantiles. The proposed bivariate combination methods are also compared with univariate method, and the reservoir water level estimated by EFC method is higher than the other methods, which means the EFC method is safer for reservoir design. The developed approach provides an applicable way for the identification of feasible range and flood quantile estimation.