An Alternative Approach for Computing the Standardized Precipitation-Evapotranspiration Index (SPEI)

This study presents an alternative approach for computing the Standardized Precipitation Evapotranspiration Index (SPEI). The proposed approach, called the Simplified Standardized Precipitation-Evapotranspiration Index (SSPEI), uses the Box-Cox transformation to normalize water balance anomalies (WBA) and subsequently convert the transformed series into the standard normal distribution (SND) using the Z-score formula. This approach is tested in 45 synoptic stations with varied climates across Iran. The stations' monthly total precipitation and average minimum and maximum air temperatures for 1971-2017 were used to compute the potential evapotranspiration and eventually WBA series needed for SPEI/SSPEI computation. According to the findings, the skewness of the Box-Cox transformed series of almost all the time scales and stations are close to zero. Therefore, the transformed WBA series can be confidentially used for computing SSPEI. The normality of the computed SSPEI series and the SPEI time series computed with the Log-logistics (LLG) and Generalized Extreme Value (GEV) distributions for the studied stations were examined using different normality assessment measures. The computed SSPEI for all the time scales and stations was found to be normally distributed, and the percentage of the SSPEI series with SND was comparable to those of the SPEILLG and SPEIGEV time series. However, SSPEI was superior to SPEILLG and SPEIGEV as it is simple in computation, requires no distribution fitting, and never results in null values due to computation failure, as is common with SPEI.