Bivariate Flood Frequency Analysis with Historical Information Based on Copula

Flood events consist of flood peaks and flood volumes that are mutually correlated and need to be described by multivariate analysis methods, of which the copula functions are most desirable. Until now, the multivariate flood frequency analysis methods based on copulas does not consider the historical floods or paleological information. This may underestimate or overestimate the flood quantiles or conditional probabilities corresponding to high return periods, especially when the length of gauged record data series is relatively short. In this paper, a modified inference functions for margins (MIFM) method is proposed and used to estimate the parameters of both marginal distribution and joint distribution with incorporation of historical information. The conditional probabilities of flood volumes given that the peak discharge exceeding various values were derived. The Three Gorges reservoir (TGR) in China was selected as a case study. The bivariate flood quantiles were obtained based on bivariate return period and compared with current univariate design values. It is shown that the proposed method provides an alternative way for multivariate frequency analysis with historical information.