Comparation of different probability distribution functions in order to drought assessment using standardized runoff index (SRI): a case study

This research examines drought behavior in the Lake Urmia basin, Iran, over the years 1994 to 2023 using the SRI and a selection of statistical distribution models to improve drought assessment and monitoring. The suitability of each distribution was tested using standard performance measures such as RMSE, MSE, CC, and R2. Among the tested models, the Weibull distribution consistently gave the most reliable results, while the LogLogistic distribution also performed well across most criteria. In contrast, the Stable distribution showed weaker alignment with observed data. At the Chahrigh-Olia station, the LogLogistic model produced the most accurate SRI predictions, with an RMSE of 0.236, MSE of 0.052, CC of 0.993, and R2 of 0.989. The linear equation Y = –3.242 + 0.011X accounted for nearly 99.1% of the observed variation. To assess spatial drought conditions, a map was created using the IDW method for the year 2005, revealing areas under severe hydrological stress. The study supports the application of appropriate distribution functions to improve drought modeling in semi-arid environments. By comparing several distribution models and evaluating their performance across space and time, the analysis offers practical guidance for selecting reliable approaches to streamflow-based drought monitoring and water management planning.