Stochastic evaluation of the effect of cross-correlation between precipitation and evapotranspiration on SPEI performance

In this study, we conducted an extensive evaluation of how the cross-correlation coefficient between precipitation and evapotranspiration affects the performance of the Standardized Precipitation Evapotranspiration Index (SPEI) in predicting the behavior of agricultural drought characteristics under four different climatic conditions: arid, semi-arid, semi-humid and humid. Its performance was compared with Standardized Precipitation Index (SPI). For each climatic condition, we generated long dependent annual stochastic precipitation (P) and evapotranspiration (ET) time series (10,000 pairs) using the Lag-one Multivariate Autoregressive Model [MAR(1)] for a wide range of correlation coefficients between precipitation and evapotranspiration. We then used these pairs-generated time series to determine different drought characteristics. The results showed systematic and dependent behavior of different drought characteristics based on SPEI with cross-correlation between precipitation and evapotranspiration in arid, semi-arid, and semi-humid climates. However, the performance of SPEI was independent of cross-correlation in the humid climate and was almost close to SPI for high cross-correlation values of precipitation and evapotranspiration (|R|double right arrow 1(. Finally, the study results clarified inconsistencies between different studies comparing the SPEI and SPI indices and provided an extensive guide for accurately and realistically inferring drought characteristics behavior based on SPEI, which can be an effective aid in interpreting drought results by SPEI.