Using the normality assumption to calculate probability-based standardized drought indices: selection criteria with emphases on typical events

Enhancing the capability of both standardized precipitation index (SPI) and standardized precipitation evapotranspiration index (SPEI) for quantifying wet and dry events under distinct climate conditions is of paramount importance. The different recommendations of recent studies regarding the best distribution to calculate the SPEI and the lack of studies addressing the effect of different parameters estimation methods on the SPI motivated us to apply and adapt distinct testing methodologies to select candidate models for calculating these standardized drought indices (SDI). The study is based on two data sets. The first represents a tropical-subtropical region of Brazil. The second comprises the same weather stations that were used for developing the original version of the SPEI. The study also emphasized the performance of the models within the range of typical SDI values [-2.0 : 2.0]. Along with goodness-of-fit tests, we calculated the mean absolute errors between the indices values estimated from the candidate distributions, and their corresponding theoretical values derived from the standard normal distribution. The two-parameter gamma and the generalized extreme value distributions are, respectively, recommended for general use in SPI and SPEI algorithms (1-12-month timescales). The unbiased probability weighted moments are recommended to estimate the distributions parameters. The study also described a trade-off between choosing the best model for the central part and for the tails of the distributions. This trade-off suggests that the methodologies used to select models for the SDI algorithms may have to decide which part of the distribution (central or tails) should be emphasized. The behaviour of the errors among different wet/dry categories showed that both indices were only capable of representing drought and floods in a similar probabilistic way within the range [-2.0 : 2.0]. This feature supports our decision to emphasize model performances within such range.