A copula-based joint meteorological–hydrological drought index in a humid region (Kasilian basin, North Iran)

Drought is a complex, multi-dimensional, and recurrent natural hazard that impacts on the Earth hydrological and biological systems. The cause–effect relationship of meteorological and hydrological droughts induced the study to aim at evaluating capability of a copula-based joint meteorological–hydrological drought index (MHDI) in identifying overall status of droughts at upstream and downstream of the Kasilian basin. Using three meteorological drought indices (MDIs) including standardized precipitation index (SPI), standardized precipitation evapotranspiration index (SPEI), and reconnaissance drought index (RDI) and one hydrological drought index (i.e., standardized drought index (SDI)), three different combinations of MHDI including SPI–SDI, SPEI–SDI, and RDI–SDI were constructed at the upstream and downstream of the basin. Results of the dependence measures such as Kendall’s τ and chi-plot showed that there were relatively high correlation structure between MDIs and SDI at both upstream and downstream. Evaluation of fitting six popular copula functions on dependence structure of different combinations of meteorological and hydrological drought revealed that the normal, Frank, Gumbel, and Joe copulas were the best-fit functions in most cases, respectively. MHDIs appropriately detected the onset and persisting of historical drought periods at both upstream and downstream of the basin. They satisfactorily responded to joint meteorological and hydrological drought indices. Establishing the normal meteorological (hydrological) condition in the basin could modify the extreme hydrological (meteorological) droughts when employing them in the framework of MHDI.