Determining the appropriate statistical distribution to calculate RDI in arid regions (Case study: Central Iran)

Drought monitoring using appropriate drought indices is of importance in water resources management, especially in arid and semi-arid regions. Therefore, choosing the suitable drought index and calculating the desired drought index appropriately is of considerable importance in the study of drought. This study is aimed to determine the appropriate statistical distribution to calculate RDI drought index in arid and semi-arid regions of Central Iran. For this purpose, 16 synoptic stations in Central Iran were selected. To calculate RDI, precipitation and potential evapotranspiration values are required. The FAO-Penman-Monteith method was used to calculate potential evapotranspiration. To select the most appropriate statistical distribution, 17 statistical distributions were used. RDI for each synoptic station was calculated annually by fitting to each of the 17 distributions, separately. Then, based on the AIC and BIC criteria, the best statistical distribution was selected to calculate RDI for each station. While based on the literature, it is recommended to calculate RDI by fitting the data to one of the Gamma or log Normal distributions, the results showed that in most of the studied stations, the log Normal and Gamma distributions are not the most appropriate distribution. However, according to the results, Gamma distribution was one of the top 6 distributions in all the studied stations. The results also showed that the difference of RDI values ​​calculated based on different distributions in dry and wet years are relatively significant, which shows the importance of choosing the appropriate statistical distribution. The fit of the studied distributions to the precipitation data at different stations showed that the Nakagami distribution presents the best performance. In case of potential evapotranspiration, different distributions provided the best fit at different stations.