Evaluation of the Combined Drought Index MCDI Based on Multivariate Copula Distribution

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.