Advances in Quantifying Streamflow Variability Across Continental Scales: 2. Improved Model Regionalization and Prediction Uncertainties Using Hierarchical Bayesian Methods

The precise estimation of process effects in hydrological models requires applying models to large scales with extensive spatial variability in controlling factors. Despite progress in large-scale applications of hydrological models in conterminous United States (CONUS) river basins, spatial constraints in model parameters have prevented the interbasin sharing of data, complicating quantification of process effects and limiting the accuracy of model predictions and uncertainties. Hierarchical Bayesian methods enable data sharing between basins and the identification of the causes of model uncertainties, which can improve model accuracy and interpretability; however, computational inefficiencies have been an obstacle to their large-scale application. We used a new generation of Bayesian methods to develop a hierarchical version of a previous hybrid (statistical-mechanistic) SPAtially Referenced Regression On Watershed attributes model of long-term mean annual streamflow in the CONUS. We identified hierarchical (regional) variations in model coefficients and uncertainties and evaluated their effects on model accuracy and interpretability across diverse environments in 16 major CONUS regions. Hierarchical coefficients significantly improved spatial accuracy of model predictions, with the largest improvements in humid eastern regions, where uncertainties were approximately one third of those in arid western regions. Half of the coefficients varied regionally, with the largest variations in coefficients associated with water losses in streams and reservoirs. Our unraveling of the causes of model uncertainties identified a small latent process component of runoff that varies inversely with river size in most CONUS regions. Our study advances the use of hierarchical Bayesian methods to improve the predictive capabilities of hydrological models.