Hierarchical Bayesian Model for Streamflow Estimation at Ungauged Sites via Spatial Scaling in the Great Lakes Basin

Abstract

This study presents a regional, probabilistic framework for estimating streamflow via spatial scaling for the purposes of informing water balance estimates in the Great Lakes basin. The framework follows a twofold strategy, including a quadratic programming–based optimization model to explore model structure, and several variants of a hierarchical Bayesian model based on insights found in the optimization model. The Bayesian model is developed to explore three innovations in hierarchical modeling for reconstructing historical streamflow at ungauged sites: (1) the combination of spatial proximity and physical basin characteristics for streamflow scaling, (2) the use of time-varying weights in the spatial scaling based on climate information, and (3) the consideration of residual heteroscedasticity to improve estimates of uncertainty. The proposed model variants are validated in a cross-validation framework to confirm specific hypotheses embedded in the model structure. Results suggest that each of the three innovations improve historical out-of-sample streamflow reconstructions and estimates of uncertainty around the reconstructed values, with the greatest improvements coming from the combined use of spatial proximity and physical similarity in estimating scaling weights at multiple donor sites.