Auto-Regressive Standard Precipitation Index: A Bayesian Approach for Drought Characterization

This study proposes Auto-Regressive Standardized Precipitation Index (ARSPI) as a novel alternative to the traditional Standardized Precipitation Index (SPI) for measuring drought by relaxing the assumption of independent and identical rainfall distribution over time. ARSPI utilizes an auto-regressive framework to tackle the auto-correlated characteristics of precipitation, providing a more precise depiction of drought dynamics. The proposed model integrates a spike-and-slab log-normal distribution for zero rainfall seasons. The Bayesian Monte Carlo Markov Chain (MCMC) approach simplifies the SPI computation using the non-parametric predictive density estimation of total rainfall across various time windows from simulated samples. The MCMC simulations further ensure robust estimation of severity, duration, peak and return period with greater precision. This study also provides a comparison between the performances of ARSPI and SPI using the precipitation data from the Colorado River Basin (1893-1991). ARSPI emerges to be more efficient than the benchmark SPI in terms of model fit. ARSPI shows enhanced sensitivity to climatic extremes, making it a valuable tool for hydrological research and water resource management.