Investigating regional homogeneity using univariate characteristics is an important step in the regional frequency analysis method; however, some hydrological phenomena have multivariate properties that cannot be studied by univariate methods. Droughts are one of these hazards that their definition as univariate will not be effective for risk assessment, decision making and management. Therefore, in this study, we investigate the regional frequency analysis of severity and duration of drought in a multivariate method using SPI (Standardized Precipitation Index), SEI (Standardized Evapotranspiration Index), SSI (Standardized Soil moisture Index) and SRI (Standardized Runoff Index) in the Karkheh river basin during the 1996-2019. Using multivariate linear moment methods and Copula functions, the severity and duration of drought indices calculated the probabilistic distributions between the rainfall, evapotranspiration, runoff and soil moisture, and considered meteorological, agricultural and hydrological droughts simultaneously. In this study, data from 100 stations in Karkheh river basin were used and the required information was received from the Meteorological Organization, Iran Water Resources Management Company and the European Space Agency site. The basin was clustered into four areas using K-Means clustering method. Regional frequency analysis was performed using the univariate and multivariate frequency analysis methods proposed by Hosking and Wallis. The results in the case of univariate drought study in the basin showed that Pearson type (3) and general Pareto distribution functions are suitable for characterizing the severity and duration of SPI and SEI and the basin is homogeneous in terms of SPI and SEI. Also, the Pearson type (3), general Pareto, general normal and general logistics distribution functions were suitable to eva‎luate the severity and duration of the SRI and SSI; However, the basin in the third and fourth clusters is heterogeneous in terms of SRI and SSI. The results of multivariate drought study in the basin indicate that the Gumbell Copula function is the best fitting copula in the region. Also, the basin was identified as homogeneous in terms of severity of SPI-SSI, SEI-SSI, SPI-SRI, SSI-SRI and SPI-SEI combined drought indices and heterogeneous in terms of SEI-SRI combined drought index. The highest homogeneity with the H1 equal to -3.099 for the combined SPI-SSI shows that the two meteorological-agricultural droughts had the most agreement with each other in the study basin. Also, the calculation of regional τ value of Kendall showed that the correlation between meteorological-agricultural droughts in Karkheh river basin is higher than meteorological-hydrological droughts. In other words, bivariate regional frequency analysis of SEI-SRI drought showed that Karkheh river basin is independent in terms of meteorological and hydrological droughts. Finally, estimates of the magnitude of droughts and their joint probability showed that the northern and southern parts of the basin experience short and consecutive droughts with a return periods of 5 to 20 years, but the northeastern, eastern, southeastern and southwestern areas of the basin will have severe drought with return periods of 20 to 100 years. Droughts in areas without meteorological data can be predicted in terms of joint probability using the method of frequency analysis of drought areas proposed in this study.

سعيد اسلاميان، مهدي قيصري

عليرضا گوهري، سعيد سلطاني كوپائي

جهانگير عابدي كوپائي، شمس الله ايوبي، رسول ميرعباسي