Comparison between Parametric and Nonparametric Approaches for the Calculation of Two Drought Indices: SPI and SSI

A comparison is provided between parametric and nonparametric approaches for the calculation of two drought indices: the standardized precipitation index (SPI) and the standardized streamflow index (SSI). The parametric approach has been implemented considering two possibilities: (1) a unique probability distribution for the variable of interest with parameters depending on the month of the year, and (2) the probability distribution depending on the month of the year. The parameters’ estimation is made using the maximum likelihood method, while the distribution selection is operated using the Kolmogorov-Smirnov goodness-of-fit test. For the nonparametric approach, the Weibull plotting position has been used to calculate the cumulative frequency. For both indices, the 1-month, 3-month, and 12-month time scales have been considered. As a case study, two 80-year-long monthly time series in Italy are considered: Roma Collegio Romano for precipitation, and Tevere River Basin at Ripetta for streamflow, both in the period 1921–2000. The analysis of the two time series shows how the differences between parametric and nonparametric approaches are more evident in terms of severity and less in terms of duration, and interarrival time. The mean value of the percentage differences, in absolute value, in terms of severity is $\sim 30–175\%$ for SPI, and $\sim 30–80\%$ for SSI. In terms of duration, it is $\sim 6–13\%$, while in terms of interarrival time it is $\sim 1–3\%$, both for SPI and SSI.