Regional Frequency Analysis of Drought Severity of SEI-SRI and SEI-SSI Indices in Common Duration Using Multivariate L-Moments and Copula Functions (Case Study: Karkheh River Basin)

Investigation of homogeneity regions using univariate characteristics is an important step in the regional frequency analysis method. However, some hydrological phenomena have multivariate characteristics that cannot be studied by univariate methods. Droughts are one of these phenomena their definition as univariate will not be effective for risk assessment, decision-making, and management. Therefore, in this study, the regional frequency analysis of drought was studied in multivariate methods using SEI (Standardized Evapotranspiration Index), SSI (Standardized Soil Moisture Index), and SRI (Standardized Runoff Index) indices in the Karkheh River basin from 1996 to 2019. The indices calculated probabilistic distribution between the variables of evapotranspiration, runoff, and soil moisture using multivariate L-moments method and Copula functions and considered meteorological, agricultural, and hydrological droughts simultaneously. The results of multivariate regional frequency analysis considering the Copula Gumbel as the regional Copula showed that the basin is homogeneous in terms of severity of SEI-SSI combined drought indices and is heterogeneous in terms of severity of SEI-SSI combined drought indices. However, after clustering the basin into four homogeneous areas in terms of characteristics of SPI (Standardized Precipitation Index), the basin is homogeneous in all areas in terms of univariate SEI, SSI, and SRI indices and is heterogeneous in the third and fourth clusters of SRI and SSI drought indices. Pearson Type (III), Pareto, normal, and general logistics distribution functions were found suitable to investigate the characteristics of SEI, SSI, and SRI drought indices in this case. Finally, large estimates of the types of combined droughts and their probability of occurrence showed that the northern and southern parts of the Karkheh River basin will experience short and consecutive droughts in the next years. Droughts in areas without meteorological data can be predicted in terms of joint probability using the multivariate regional frequency analysis method proposed in this study.