Evaluating the Selection of the Most Suitable Probability Distribution Function for Using the RDI and SPI Drought Indices

The purpose of this paper is the selection of the most suitable probability distribution function to calculate and compare the RDI and SPI drought indices. Accordingly, using the meteorological data of thirty synoptic stations in Iran, annual rainfall data series and the ratio of precipitation to potential evapotranspiration were obtained. At first, Normal or Gamma distributions and Log-normal or Gamma distributions were used to determine the SPI and RDI annual values, respectively. Then using Kolmogorov-Smirnov index, the best distribution function was obtained to fit with the data series in the studied stations. After determining the index values based on the superior distribution function and also the mentioned distribution functions, replacement of different drought classes was evaluated. The results showed that in the most stations, the mentioned distribution functions could not be selected as the most appropriate distribution function and using them in determination of the indices could change the drought classes. The results of the statistical indices (RMSER2>0.819) showed that the annual time series of the SPI and RDI indices (calculated on the basis of the most suitable probability distribution function) were approximately similar and their difference was not significant in none of the stations. Also the results showed that the RDI index was more sensitive than the SPI index to the selection of the distribution function, so the selection of the most suitable distribution function for determination of this index was more important.