Global and regional performances of SPI candidate distribution functions in observations and simulations

The Standardized Precipitation Index (SPI) is a widely accepted drought index. Its calculation algorithm normalizes the index via a distribution function. Which distribution function to use is still disputed within literature. This study illuminates the long-standing dispute and proposes a solution which ensures the normality of the index for all common accumulation periods in observations and simulations.

We compare the normality of SPI time-series derived with the gamma, Weibull, generalized gamma, and the exponentiated Weibull distribution. Our normality comparison evaluates actual against theoretical occurrence probabilities of SPI categories, and the quality of the fit of candidate distribution functions against their complexity with Akaike's Information Criterion. SPI time-series, spanning 1983–2013, are calculated from Global Precipitation Climatology Project's monthly precipitation data-set and seasonal precipitation hindcasts from the Max Planck Institute Earth System Model. We evaluate these SPI time-series over the global land area and for each continent individually during winter and summer. While focusing on an accumulation period of 3-months, we additionally test the drawn conclusions for other common accumulation periods (1-, 6-, 9-, and 12-months).

Our results suggest to exercise caution when using the gamma distribution to calculate SPI; especially in simulations or their evaluation. Further, our analysis shows a distinctly improved normality for SPI time-series derived with the exponentiated Weibull distribution relative to other distributions. The use of the exponentiated Weibull distribution maximizes the normality of SPI time-series in observations and simulations both individual as well as concurrent. Its use further maximizes the normality of SPI time-series over each continent and for every investigated accumulation period. We, therefore, advocate to derive SPI with the exponentiated Weibull distribution, irrespective of the heritage of the precipitation data or the length of analyzed accumulation periods.