Application of the Nested Copula Functions for Analysis of Four variate of Meteorological Droughts (Case Study: West of Iran)

Drought is a natural disaster and inevitable phenomenon, which should be considered preventable, but can be managed and organized. The main purpose of this study is to show how copula functions are used in the four-variable analysis of drought in the west of Iran. For this purpose, the drought characteristics, including severity, duration, inter arrival time and peak were extracted using modified Standardized Precipitation Index (SPImod). Then the frequency distributions were fitted to the mentioned drought characteristics and the best fitted marginal distribution were specified for every drought characteristics. The results showed that the gamma and exponential distributions had the best fitness on the drought severity and duration, respectively. Also, for drought peak and inter arrival time variables, the GEV function was known as the best fitted marginal distribution. In order to four variate analysis of drought characteristics, these variables were paired two by two using nested copula method. For this purpose, the fitness of nine copula functions, including Clayton, Ali-Mikhail- Haq, Farlie- Gamble- Morgenstern, Frank, Gamble, Gamble- Hougaard, Plackett, Philip Gamble and Joe were examined using Akaike Information Criterion (AIC), Maximum Likelihood (ML), and Nash-Sutcliffe Efficiency (NSE) criteria. The results showed that Joe copula is the best function for constructing the multivariate distribution in the study area. Also, this study showed that a four-variate analysis of drought provide useful information for planners and managers for drought prediction and planning to cope with drought consequences.