Relating the Drought Precipitation Percentiles Index to the Standardized Precipitation Index (SPI) under Influence of Aridity and Timescale

The Precipitation Deciles Index (DI) and the Precipitation Percentiles Index (PI) are statistically related to the Standardised Precipitation Index (SPI). However, that relation varies, namely with the dryness of the location. This study, therefore, aims at comparing these indices using monthly precipitation totals from 1971 to 2017 using data of 45 weather stations distributed throughout Iran, so having different climates. Several statistical indicators were used to compare the indices, with the respective results showing good agreement in all climates. The study confirms the adequateness of the PI, which is highly comparable to the SPI despite they were calculated using different probability distribution functions, and consists of a simple and robust alternative approach relative to the SPI. It results in a new drought index called Normalized Percentiles Index (NPI), which is obtained when standardizing/normalizing the PI values. Conversely, it was obtained the Percentiled SPI Index (PSPI), which corresponds to the ranking the SPI values, which have shown a more understandable representation of SPI values for use with stakeholders and the public. These conversions facilitate direct comparisons between SPI and PI using statistical indicators commonly adopted to compare continuous variables. The differences between PI and SPI were negligeable or modest in most of climates of Iran, but quite noticeable in arid climates, and when SPI was calculated at shorter timescales. The observed differences were attributed to incorrect distribution fitting in SPI calculations rather than to inadequacy of PI. The current study recommends using either PI or NPI as an alternative to SPI, namely in arid climates, as PI is easier to calculate, more robust and easier to understand than the SPI.