SPI-3 Analysis of Medjerda River Basin and Gamma Model Limits in Semi-Arid and Arid Contexts

The Standardized Precipitation Index SPI-3, associated with three months of rainfall accumulation, is a drought index for detecting immediate drought impacts. The two-parameter gamma distribution, recommended by the World Meteorological Organization as the underlying distribution for estimating SPI, has shown limits in semi-arid and arid conditions with respect to the normality test for the resulting SPI series. Our purpose was to evaluate its relevance for the Medjerda River Basin (Tunisia), a transboundary basin where the climate classes are temperate, dry, and hot summer, as well as arid hot desert and arid hot steppe. When analyzing the time series of 144 stations from 1950 to 2018, we found that the normality Shapiro–Wilk test was rejected in 17% of the cases, which agreed with the literature review results. The transition season (August, September, and October) had the highest rejection percentage. Three factors were identified to explain the deviation from normality. We first identified the rate of occurrence of completely dry (zero rain) three-month periods. The higher the rate of occurrence was, the higher that the probability was of its rejecting the normality test. High sample skewness was the second influencing factor. Finally, a series where the Grubbs’ test of identifying outliers was rejected was more likely to show the SPI-3 series deviating from normality.