Assessing hydrologic drought risk using multi-dimensional copulas: case study in Karkheh River basin

Drought severity, duration and magnitude are important for evaluating the drought condition. This study developed multivariate (Joint Deficit Index) JDI and then used bivariate and trivariate copulas to assess hydrological drought risk in the Karkheh River basin in the west of Iran, since there exists a significant dependency between severity (S), duration (D), and magnitude (M). The JDI was constructed by implementing Kendall’s empirical copula on (SRImod1,…, SRImod12) at 18 stations in the river basin. The generalized gamma (severity), the Pareto (duration), and the log-normal (magnitude) were identified as the best marginal distributions for drought characteristics. The Gaussian, Student’s t, Joe and Clayton were found to be the best bivariate copulas for S and D, S and M, and D and M, respectively. The trivariate Clayton copula was the best copula function of the (S–D–M) variable. Results of fitting were analyzed based on several statistical diagnostic tests and graphs. Further analysis was implemented based on multivariate and conditional return periods. The multivariate return periods of “AND” and “OR” cases were obtained and the spatial graphs of drought risks were constructed. Results showed that the return periods of the “AND” cases were greater than the return periods of the “OR” cases. In the other words, the whole of the sub-basin is in the high risk situation (R > 0.9) when R (OR) S–D, S–M, D–M, S–D–M, in the low risk situation (R = 0.38) when R (AND) S–D, S–M, D–M and in the moderate risk situation (0.48 < R < 0.68) when (OR) S–D–M. This study revealed that separate evaluation of return periods in “OR” and “AND” cases may result in under-dimension or over-dimension. Hence, the return periods of “AND” and “OR” cases should be considered simultaneously. Further investigation showed that multivariate return periods were important in the management of drought condition and decisions.