Regional risk analysis and derivation of copula-based drought for severity-duration curve in arid and semi-arid regions

This study investigated droughts in arid and semi-arid regions in Iran using long historical data from 25 stations. These stations were clustered into three homogeneous regions using a fuzzy clustering method. The severity and duration were extracted using the Standardized Precipitation Index-12, and the dependence structure between drought severity and duration was evaluated using Pearson’s, Spearman’s ranked, and Kendal’s tau correlation coefficients. The best marginal distributions of severity and duration were selected using graphical and theoretical goodness-of-fit criteria. Results showed that the generalized logistic (GLO) model satisfactorily fitted drought duration in regions I and III, while the Wakeby distribution fitted better in region II. For drought severity, the best fitted model was the GLO model in region I, the generalized extreme value (GEV) model in region III, and the Wakeby model in region II. Furthermore, the Gumbel copula in region I and the Gaussian copulas in regions II and III were able to model the dependence between drought variables well. Also, stochastic simulation of bivariate drought using selected copulas showed that the behavior of bivariate drought changed when the degree of correlation between variables was considered. The copula method was used to obtain bivariate and conditional return periods. The bivariate analysis of drought risk indicated that coastal and internal regions of Iran were more risky than semi-arid and arid regions. The results of this study would be useful for water resource management and risk analysis at the regional scale.