copula function

Drought is a challenging problem that can be evaluated with multi-variable and combined perspectives. Therefore, the aim of this study is to create a comprehensive index of three indices SPI, PDSI, and SRI, which includes all aspects of meteorology, hydrology, and agriculture. For this purpose, three drought variables (severity, duration, Magnitude) were analyzed for 10 meteorological stations in Iran for the statistical period of 1990-2021, firstly using principal component analysis (PCA) and nonlinear coupling based on copula. were analyzed. The probability distribution model for constructing the MCDI composite index. It was then tested with the ability of the exact functions of Clayton, Frank, and Gamble to generate a trivariate joint distribution. The best copula function for each station was determined through the Kolmograf-Smirnov (K_S) test, and the results showed the superiority of the Gumbel function in most stations. Return period curves were drawn for all stations and for all three joints. The period of returns indicated a long-term frequency of drought with greater intensity for periods of 50 and 100 years. The shortest return period of 50 years with the superiority of Clayton's function related to Tabriz and with the superiority of Gumbel's function related to Tehran was 10 months and the longest period was 30 months related to Mashhad with the superiority of Gumbel's function, respectively with intensity of 6.53 and 8.95 and 26/34 were included. For the 100-year return period, the shortest period with the superiority of Clayton is related to Tabriz with 13 months and intensity of 13.75, and the longest period with the superiority of Gumbel's function belongs to Kerman with a duration of 48 months, and the intensity of 42.56. The results of this research show that the use of a multivariate composite index (MCDI) by using detailed functions provides the possibility of a more comprehensive and accurate assessment of drought on a national scale. This approach, taking into account the meteorological, hydrological, and agricultural aspects of drought, provides an efficient tool for managing water resources and strategic planning in the face of drought in different regions of Iran.

Droughts are extreme phenomena that are described based on the characteristics of continuity in time and according to their spatial effects and can occur in any climatic situation. Recognition and behavior of droughts, which are closely and directly related to water resources management, are of particular importance. The main purpose of this study is to assess the risk of drought using Copula functions in the bivariate analysis of drought in the east of the country. For this purpose, drought characteristics including intensity and duration were extracted using modify standardized precipitation index (SPImod). To assess the risk of drought and analyze its two variables, the performance of nine copula functions of Clayton, Ali-Michael-Haq, Farli-Gumble-Morgenstern, Frank, Gumble, Gumble-Hoggard, Plackett, Filip-Gumble and Joe fits the intensity data and Drought duration was tested. Akaike criteria, maximum likelihood, and Nash-Sutcliffe coefficient were used to identify the superior joint function. The results showed that gamma and exponential distribution functions were identified as superior margin distribution functions for the variables of intensity and duration of drought, respectively, and the Nash-Sutcliffe coefficient ranged from 0.76 to 0.99, and the mean square error ranged from 0.007 to0 034., to determine the superior copula function, it was obtained that the copula function of the superior function was known to create a bivariate distribution in the study area. Also, the results of drought risk assessment using the joint return period showed that the highest risk is related to Bojnourd, Sabzevar, Torbat Heydariyeh, and Mashhad stations, so that Sabzevar station was dry about 53% of the total months during the statistical period and for Bojnourd station is about 55%. The results of risk analysis based on return period and copula functions can provide useful information to planners of water resources, environmental issues, farmers.