Suitability of distributions for standard precipitation and evapotranspiration index over meteorologically homogeneous zones of India

Abstract

The Standardised Precipitation and Evapotranspiration Index (SPEI) became one of the popular drought indices in the context of increasing temperatures under global warming in recent periods. The SPEI is estimated by fitting a probability distribution for the difference between precipitation (P) and potential evapotranspiration (PET), which represents the climatic water balance. The choice of an inappropriate probability distribution may lead to bias in the index values leading to distorted drought severity. Till date, none of the studies have focused on the suitability of the probability distribution for SPEI over India. The objective of the present study is to compare and evaluate the performance of a group of candidate probability distributions over seven meteorologically homogeneous zones and all over India using high resolution (0.25°) gridded daily precipitation data from India Meteorological Department (IMD). The Kolmogorov–Smirnov (K–S) test was used to test the goodness-of-fit for (P–PET) and Akaike Information Criterion (AIC) was used to obtain the relative distribution rankings for each grid point. The results of the study suggest that Pearson type III distribution has performed better than other distributions, significantly for shorter time scales and slightly for longer time scales, for each meteorological homogeneous zone based on K–S test. Also, for shorter time scales, Pearson type III distribution has been observed to be significantly better based on AIC with 82.89% and 71.91% grid points for 3 and 6 months, respectively. However, the relative ranking by AIC revealed GEV distribution as the best fit for SPEI values all over India for longer time scales with total grid points as 50.26%, and 58.81% for 12- and 24-month time scales respectively. Pearson type III distribution for shorter time scales (3 and 6 months) and GEV distribution for longer time scales (12 and 24 months) have been identified as the best distributions for fitting SPEI for Indian case study. Comparison of GEV based SPEI with remote sensing-based drought severity index (DSI) for drought events indicated concordance for most of regions in India. Also, SPEI is evaluated to test its capability to represent seasonality and its performance has been compared with Standardised Precipitation Anomaly Index (SPAI) which is known to represent seasonality well.