Improving the normalization procedure of the simplified standardized precipitation index (SSPI) using Box–Cox transformation

摘要

Abstract This study uses the Box–Cox transformation to improve the normalization procedure of the simplified standardized precipitation index (SSPI), utilizing the monthly precipitation of 45 stations distributed across Iran spanning from 1971 to 2017. The results showed that the Box–Cox transformation can reduce the skewness of the monthly precipitation aggregated at 1-, 3-, 6-, 9-, 12, and 24-month time scales to as close as zero, and successfully transforms them into an approximately normally distributed series. The normally distributed Box–Cox transformed precipitation series of the studied stations was then used to compute SSPI (SSPIBox–Cox) for the considered stations and time scales. For almost all the stations and time scales, the computed Shapiro and Wilk (S-W) test and the associated p value of the SSPIBox–Cox time series were found to be larger than the critical values of 0.96 and 0.1, respectively. For the majority of the stations, the mean and standard deviation of the SSPIBox–Cox computed for all the time scales were also close to 0.0 and unity, respectively. The mentioned statistics values suggest that the SSPIBox–Cox time series of almost all of the stations follow the standard normal distribution for all the time scales, except for 1- and 3-month time scales corresponding to the warm season calendar months of the stations located in the arid and hyper-arid areas. The results also show that the association between SSPIBox–Cox and the standardized precipitation index was considerably improved for all the stations and time scales when compared to the SSPI time series computed with the original SSPI procedure that uses a reformulation of the rainfall anomaly index for normalizing the data.