Trivariate Gaussian copula and Student t copula in multivariate hydrological drought frequency analysis

The common copulas modelling dependence structures of higher dimensional variables may be misunderstood. In this paper, based on probability theory, a Gaussian copula and Student t copula were applied to model the multivariate drought joint probability distribution. Monthly average streamflow from Zhuangtou gauging station in Weihe Basin, China, was used to illustrate these methods. Chi-square test, Kolmogorov-Smirnov test, Cramer-von Mises statistic, Anderson-Darling statistic, modified weighted Watson statistic, and Liao and Shimokawa statistic were employed to test goodness-of-fit of these univariate marginal distributions. Pearson's classical correlation coefficient r(n), Spearman's rho(n), and Kendall's tau under different truncation levels indicated that these three possible bivariate dependence structures are different. Based on the AIC, BIC and RMSE, they showed that the Gaussian copula has the better fit for drought joint probability distribution. A bootstrap version based on Rosenblatt's transformation was employed to test the goodness-of-fit for Gaussian copula. The results show that applying Gaussian copula to model multivariate hydrological drought joint distribution is a feasible method.