Uncertainty analysis of SPI and SRI calculation using bootstrap in the Mediterranean regions of Algeria

The standardized precipitation index (SPI) and the standardized runoff index (SRI) are widely used in drought monitoring. In the calculation of these indices, the time scale and distribution functions are especially significant. In the current study, the uncertainty in the estimation of the two indices, in terms of time scale and distribution functions, was investigated in the wadi Mina basin (Algeria) using monthly precipitation and runoff values based on the gamma-II (GAM-II), extreme value-III (EVD-III), Pierson-III (PEI-III) and Weibull-II (WEI-II) distribution functions. With this aim, precipitation and runoff amounts were calculated considering 12- and a 24-month time scales; then, using the bootstrap method, 1000 random sample were generated for each precipitation and runoff event and for each time scale, and the confidence interval of the two indices was calculated at around 95%. The size of the confidence interval was considered as uncertainty and the error rate between the estimated and observed data was calculated. The results showed that all the considered distributions fit the time series acceptably, and that the time scale of the data is not significantly correlated with the goodness of fit. Moreover, there is no apparent relationship between the rejection cases and the scale and position of the regional stations or the investigated variables. The lack of significant differences between the observed and estimated time series for a specific distribution caused the averages estimated in SPI to fall within the same descriptive class. Based on the results, WEI-II and EVD-III showed the lowest estimation error and uncertainty in meteorological and hydrological drought, respectively, at both 12- and 24-month time scales, thus suggesting the use of these two functions for drought monitoring at medium-term and long-term time scales.