Trivariate frequency analysis of droughts characteristics in Kerman city using asymmetric copula functions

Drought, as a long-term water shortage, is a challenging issue in water resources management. This phenomenon is one of the most costly and less-known natural disasters. Until now, most drought studies have been in the form of univariate and bivariate analyses. The purpose of this research is to analyze the three variables of drought in the city of Kerman, Iran in the statistical period of 1971–2019. For this purpose, the Standardized Precipitation Index (SPI)mod index was used to extract the severity, duration, and peak parameters of drought. In this regard, the ability of the twelve copula functions of Clayton, Frank, Galambos, Plockett, Gamble-Hoggard, Ali-Mikhail-Haq, Farley-Gamble-Morgenstern Heavy Right Tail (HRT), Philip-Gamble, Joy, Gamble-Barnett and Sarmonoff to create a distribution of three variables was tested. For this purpose, the Asymmetric method was used to connect two-dimensional copula functions and create a three-dimensional copula function. To determine the function of the superior copula in the Kerman synoptic station, Root Mean Square Error (RMSE) and Nash Sutcliffe Error (NSE) statistics, as well as Maximum Likelihood (ML) were used. The results showed that the copula HRT function has the best performance in creating bivariate and trivariate distribution functions. Also, the results showed that the use of the SPImod index to a large extent removes the disadvantages of the common SPI and takes into account the seasonal changes of precipitation in the calculation of the SPI index.