Determining the most appropriate probability distribution function for meteorological drought indices in Urmia Lake Basin, Iran

Normalization is believed to be one of the most important parts of numerical computation in discrete mathematics. This process aims to transform a wide numerical range into a narrower one. Hence, in a number of fields of study, numerous distribution functions (DF) have been extended based on their applications, one of which is drought calculation. In this research, annual drought was calculated via standard precipitation index (SPI) and China Z Index (CZI) through seven three-parametric DFs (Pearson 5, Weibull, Pearson 3 (gamma), log Pearson, Frechet, log-logistic, and fatigue life) in order to determine the most appropriate one for each index in Urmia Lake Basin. To this end, the results of both SPI and CZI, with DFs and without them, were compared with statistical analyzers (RMSE, ME, R2, and pearson correlation). The results indicated that Weibull-CZI and Pearson 5-SPI had the highest correlation with the normal ones. Therefore, they could be used as the best DFs for these drought indices in this basin. Moreover, among the studied years, Gelazchay and Daryanchay stations experienced the most severe drought in 2008 and 1999 based on the CZI and SPI, respectively. It should be noted that in another section of the current study, the correlation between the two indices was analyzed and the results showed high correlations between them.