Univariate and bivariate hydrological drought frequency analysis by copula functions

Abstract

Drought duration and severity are two significant and strongly related drought characteristics. In this study, the Streamflow Drought Index (SDI) is utilized to acquire drought characteristics using mean monthly streamflow records of 36 stations in the Euphrates Basin, considering 3- and 6-month time scales. Mann-Kendall's rank correlation coefficient is utilized for analyzing the dependence between severity and duration, as well as for deciding the suitability of series for joint return periods. Six marginal distributions are used to model the marginal distributions of duration and severity. The best fit marginal distributions of these drought characteristics and the best copulas among ten copula types were utilized for constructing univariate return periods of 10, 20, 50, 100, 200, and 500-years and bivariate return periods considering the T-DS (and) and T & PRIME;(DS) (or) cases. The best copulas are analyzed by tail dependence and by goodness of fit tests. Results indicate that the correlation coefficients are between 0.691-0.893 in SDI-3 while they are between 0.741-0.904 in SDI-6. Marginal distribution analyses show that the Lognormal and Weibull distributions are the best-fit distributions for drought duration and severity in SDI-3 while the Lognormal and Gamma were noted to be the most suitable distributions for duration and severity, respectively in SDI-6. Analyses reveal that the Gumbel copula has a clear superiority to model joint return periods in both time scales. Different parts of the basin are at risk of drought for various return periods.