Frequency Analysis of Trivariate Drought characteristics Properties Using Nested Copula Functions (Case Study: Eastern Iran)

Drought as a long-term water scarcity situation is a challenging issue in water resources management. This phenomenon is one of the less expensive and less known natural disasters. Until now, most drought studies have been either univariate or bivariate. In this study, trivariate of drought analysis in eastern Iran for 13 meteorological stations in the period 1971- 2017 were investigated. SPImod index was used to extract the intensity, duration and peak drought parameters. In this regard, the ability of twelve copula functions of Clayton, Frank, Galambos, Platelet, Gumble-Hoggard, Ali-Mikhail-Hagg, Farley-Gumble-Morgenstern, HRT, Filip-Gumble, Joey, Gumble-Barnett and Sarmonov to create a joint -distribution of trivariate were tested. For this purpose, the nested method was used to connect two-dimensional joint functions and create a three-dimensional joint distribution function. To determine the best copula function at each station, RMSE, NSE-NSE, and maximum likelihood (ML) statistics were used. The results showed that the HRT copula function has the best performance in generating bivariate and trivial distribution functions. The results also showed that the use of SPImod greatly eliminates the disadvantages of general SPI and takes into account seasonal variations in precipitation in the calculation of SPI. The results of SPImod indicated that the highest percentage of dry months were observed in the Sabzevar station with 52% and the lowest in Torbat- Heydariyeh station with 35%, which were identified as the areas have experienced the highest and lowest dry months, respectively.