Revisiting the Rainfall Anomaly Index to serve as a Simplified Standardized Precipitation Index

The Rainfall Anomaly Index (RAI) is revisited herein as an alternative to the Standardized Precipitation Index (SPI), taking into account different time scales and the probability of zero precipitation as in the SPI procedure. To evaluate the performance of the modified RAI that stands as a Simplified Standardized Precipitation Index (SSPI), both indices were computed for 45 stations distributed across diverse climates of Iran. The resulted time series and frequency distribution of the indices values between different dry/wet classes were statistically compared. The results show a very strong association between the two indices at all stations and time scales, particularly at longer time scales. The spatial distribution of the correlation coefficient (R) computed between the two indices depicts large R values across Iran, particularly over northern and western Iran where precipitation is distributed more regularly throughout the year. The spatial distribution of the Shapiro-Wilks (S-W) normality test computed for all studied stations and time scales show values larger than 0.96 in northern and western Iran and lower values ranging from 0.82 to 0.96 for a few stations scattered in eastern, central, and southern Iran. This indicated that both indices have a closer distribution to the standard normal distribution in northern and western Iran where precipitation is less skewed. However, SSPI shows a lower S-W test than the SPI for some stations scattered over central-eastern Iran, which is an indication of its higher deviation from the normal distribution. The comparison of the frequency distribution of the indices values between different dry/wet classes also reveals a very strong association between the two indices, as indicated by very high values of contingency coefficient and Cramer's V statistic for all time scales at the studied stations. SSPI is simpler in calculation than the SPI and permits for missing data and large numbers of zero values in the data records, which is very common in arid and hyper-arid climates. Thus, SSPI is preferred over SPI when the length of data records is short or contains a large number of zero values for which SPI is incomputable or unreliable.