Semi-Bayesian Space-Time Hierarchical Framework for Modeling and Prediction of Seasonal and Extreme Precipitation in the U.S. Northern Great Plains

Abstract

We adapt a semi‐Bayesian hierarchical modeling framework to jointly characterize the space–time variability of seasonal precipitation totals and precipitation extremes across the Northern Great Plains (NGP). In this framework, seasonal precipitation totals at each station and year are modeled using a Gamma distribution, while seasonal maximum precipitation extremes are modeled with a Generalized Extreme Value distribution. Parameters for both distributions vary spatially and temporally as linear functions of selected covariates, including Pacific and Atlantic sea surface temperature indices and regional precipitation anomalies. Covariate coefficients are estimated using Maximum Likelihood methods. In the process layer, these ML‐estimated coefficients for both precipitation totals and extremes are spatially modeled through Gaussian multivariate processes, capturing spatial dependencies among stations. Appropriate priors on model hyperparameters complete the Bayesian formulation at this hierarchical level, resulting in conditional posterior distributions. We apply the model to precipitation data from 60 NGP stations spanning the period 1951–2019 under contemporaneous (0‐month), 1‐month, and 2‐month lead times, thereby assessing the predictive utility of teleconnection signals at varying lead times. Model evaluation and cross‐validation results highlight strong performance in capturing historical spatial and temporal variability in precipitation across all lead times, with contemporaneous models showing the highest skill, as expected. Conditional posterior distributions derived from this modeling approach provide probabilistic forecasts of seasonal precipitation totals and extremes, offering critical information for agricultural planning, ecosystem conservation, and water resource management decisions under climate variability and change conditions.

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