A Two‐Stage Bayesian Data‐Driven Method to Improve Model Prediction

Abstract

AbstractBecause of the earth system complexity, groundwater/hydrology models are always built with structural errors, which may lead to systematic errors in model predictions. Bayesian data‐driven methods (DDMs) provide a feasible way to correct systematic model errors statistically. Generally, the physical and statistical model parameters, namely physical parameters and hyperparameters, are assumed to be independent and jointly calibrated. However, this assumption may be unreasonable and lead to over‐adjusted parameter estimation and biased model prediction. This study proposes a two‐stage DDM to calibrate physical parameters and hyperparameters separately, which does not make the independence assumption. Three case studies, including a groundwater solute transport analytical model, a three‐dimensional groundwater flow model, and a real‐world snowmelt runoff model, were used to evaluate the predictive performance of this two‐stage DDM. Based on the three case studies, we found that the independence assumption of physical parameters and hyperparameters could lead to the over‐fitting of parameter estimation and deviations in model predictions. Two‐stage DDM can constrain the systematic error model calibration; that is, physical parameters are first calibrated in the entire hyperparameter prior probability space, and then hyperparameters are calibrated in the posterior probability space of physical parameters obtained previously. As a result, compared with traditional joint calibration‐based DDM, two‐stage DDM can alleviate parameter over‐fitting and improve model predictive performance.