Modelling of bivariate meteorological drought analysis in Lake Urmia Basin using Archimedean copula functions

Abstract

The Urmia Lake Basin as the world's second largest salt lake has experienced severe drought during recent years. The purpose of this study is to analyse the bivariate characteristics of drought (i.e., duration and severity) using two indices including SPI (standard precipitation index) and SPImod (modified SPI) associated with copula functions. For this purpose, rainfall data of six stations were used for the period of 1971–2017. At first, the characteristics of drought were extracted using the two indices. Then, through coding in the MATLAB software environment, eight families of Archimedean copula functions were applied. The simultaneous return period and conditional and Kendall returns were also investigated. The result showed that the Joe copula function was the best predictor for the analysis of both intensity and duration of drought for the study area. The correlation coefficients of Spearman, linear correlation and Tau Kendall computed for the SPI of stations were >0.65, >0.72 and >0.48, respectively, while all of them were significant. At a given critical probability level, t, the value of the Kendall return period was much greater than the standard return period, so that this difference increased with increasing t value. The results obtained from the time series of indices indicated that at least 40% of the months were dry, and the severity of droughts in the Urmia station was much higher than other stations during the studied period. Moreover, SPImod to a large extent eliminates the disadvantages of conventional SPI and takes into account seasonal variations of precipitation in the calculation of SPI.