Incorporating non-stationarity in normalized meteorological drought indices with Bayesian splines

Abstract:

Under non-stationary climate conditions, normalized meteorological drought indices like the Standardized Precipitation Index (SPI) can be sensitive to the normalization reference period. Existing solutions either adopt a quasi-stationary reference period, typically fitting a 30 year subset, or ignore non-stationarity to fit the entire available record. This study proposes an alternative Bayesian approach for the SPI using penalized tensor product splines to simultaneously account for seasonality and multi-decadal non-stationarity for gamma-distributed precipitation. Using this approach, information from the entire instrumental record is retained, while allowing a post-hoc reference period to be chosen, mimicking a typical 30-year climate normal. To test model effectiveness, existing frequentist approaches are contrasted with the proposed spline model using pre-defined synthetic precipitation time series and 6 instrumental precipitation records across a range of hydroclimates. The proposed model more closely matches known probability distributions, decreases parameter uncertainty for the instrumental data, and better captures uncertainty around periods with zero precipitation.