A Nonstationary Standardized Precipitation Index (NSPI) Using Bayesian Splines

The standardized precipitation index (SPI) measures meteorological drought relative to historical climatology by normalizing accumulated precipitation. Longer record lengths improve parameter estimates, but these longer records may include signals of anthropogenic climate change and multidecadal natural climate fluctuations. Historically, climate nonstationarity has either been ignored or incorporated into the SPI using a quasi-stationary reference period, such as the WMO 30-yr period. This study introduces and evaluates a novel nonstationary SPI model based on Bayesian splines, designed to both improve parameter estimates for stationary climates and to explicitly incorporate nonstationarity. Using synthetically generated precipitation, this study directly compares the proposed Bayesian SPI model with existing SPI approaches based on maximum likelihood estimation for stationary and nonstationary climates. The proposed model not only reproduced the performance of existing SPI models but improved upon them in several key areas: reducing parameter uncertainty and noise, simultaneously modeling the likelihood of zero and positive precipitation, and capturing nonlinear trends and seasonal shifts across all parameters. Further, the fully Bayesian approach ensures all parameters have uncertainty estimates, including zero precipitation likelihood. The study notes that the zero precipitation parameter is too sensitive and could be improved in future iterations. The study concludes with an application of the proposed Bayesian nonstationary SPI model for nine gauges across a range of hydroclimate zones in the United States. Results of this experiment show that the model is stable and reproduces nonstationary patterns identified in prior studies, while also indicating new findings, particularly for the shape and zero precipitation parameters.