A universal Standardized Precipitation Index candidate distribution function for observations and simulations

The Standardized Precipitation Index (SPI) is awidely accepted drought index. Its calculation algorithm nor-malizes the index via a distribution function. Which distribu-tion function to use is still disputed within the literature. Thisstudy illuminates that long-standing dispute and proposes asolution that ensures the normality of the index for all com-mon accumulation periods in observations and simulations.We compare the normality of SPI time series derived withthe gamma, Weibull, generalized gamma, and the exponenti-ated Weibull distribution. Our normality comparison is basedon a complementary evaluation. Actual compared to theo-retical occurrence probabilities of SPI categories evaluatethe absolute performance of candidate distribution functions.Complementary, the Akaike information criterion evaluatescandidate distribution functions relative to each other whileanalytically punishing complexity. SPI time series, span-ning 1983–2013, are calculated from the Global PrecipitationClimatology Project’s monthly precipitation dataset, and sea-sonal precipitation hindcasts are from the Max Planck Insti-tute Earth System Model. We evaluate these SPI time seriesover the global land area and for each continent individuallyduring winter and summer. While focusing on regional per-formance disparities between observations and simulationsthat manifest in an accumulation period of 3 months, we ad-ditionally test the drawn conclusions for other common ac-cumulation periods (1, 6, 9, and 12 months).Our results suggest that calculating SPI with the com-monly used gamma distribution leads to deficiencies in theevaluation of ensemble simulations. Replacing it with theexponentiated Weibull distribution reduces the area of thoseregions where the index does not have any skill for precip-itation obtained from ensemble simulations by more than one magnitude. The exponentiated Weibull distribution max-imizes also the normality of SPI obtained from observationaldata and a single ensemble simulation. We demonstrate thatcalculating SPI with the exponentiated Weibull distributiondelivers better results for each continent and every investi-gated accumulation period, irrespective of the heritage of theprecipitation data. Therefore, we advocate the employmentof the exponentiated Weibull distribution as the basis for SPI