Bivariate Frequency Analysis of Hydrological Drought Using Copula: A Case Study of Northern Iraq

Abstract

In this research work, copula-based methodology is adopted to analyze the hydrological drought frequency. Standardized Runoff Index SRI was calculated using monthly-streamflow data for 50 years of two gauging stations in the northern region of Iraq. The drought duration and severity were extracted using run theory. Three Archimedean family and Gaussian copulas were used and compared to select the most appropriate copula model for bivariate frequency analysis of hydrological-drought characteristics. The dependence between drought duration and drought severity was estimated by Pearson's, Spearman's rho and Kendall's tau correlations. Various probability distributions were utilized to determine the best fit marginal distributions for drought characteristic variables based on the Kolmogorov-Smirnov and Chi-squared statistics. Uni-variate and joint return periods were estimated and compared. Generally, the results indicate that Archimedean copulas performed better than the Gaussian copulas. Exponential and Weibull distributions are the best fit for drought duration and severity, respectively, except for drought severity in case of the 9-month time scale at Lesser Zab region, where lognormal distribution was chosen. The current study can give helpful information for drought-risk assessment and water-resource management under climate change. KEYWORDS: Hydrological drought, Copula, SRI, Greater Zab river, Lesser Zab river, Bivariate return periods.