Analysis of the Effect of Statistical Period Length on Occurrence Probability of Drought Using the Copula Functions Approach (Case Study: Arak Synoptic Station)

In recent years, with the development of statistical methods and the application of advanced mathematics, the structure of dependence on extreme phenomena such as drought has been considered. In the present study, multivariate analysis of droughts using SPEI and copula functions and the effect of statistical period length on the occurrence probability of drought was investigated in Arak synoptic station. For this purpose, precipitation and observational temperature data and global climate database (CRU) networks have been collected for the selected station, and two statistical periods of 100 and 37 years have been selected for this research. Then, the characteristics of duration and severity of drought were extracted and at different time scales (1, 3, 6, 9, and 12), and its dependency structure was calculated by Spearman’s rho and Kendall’s tau correlation coefficients that it shows there is a significant correlation between severity and duration of drought except on one-month scales. After determining the best fitted marginal distributions on the drought characteristics, the fitness of five different copulas for developing the bivariate distribution of severity and duration of drought was examined. The results showed that at Arak station for both statistical periods of 100 and 37 years, Clayton and Gumble-Huggard copula functions, respectively, due to having the highest value NS (0.9, 0.9) and the lowest values of NRMSE (12.9, 7.9). The results also showed that the 37-year statistical period was suitable for the study of droughts with the condition "or" but in the case of "and" and the intensification of droughts, the joint return period reaches nearly 45 years. Therefore, it is recommended that a statistical period of 100 years be used to analyze the droughts in the study area.