No abstract

Numerical groundwater flow and solute transport models are usually subject to model structural error due to simplification and/or misrepresentation of the real system, which raises questions regarding the suitability of conventional least squares regression‐based (LSR) calibration. We present a new framework that explicitly describes the model structural error statistically in an inductive, data‐driven way. We adopt a fully Bayesian approach that integrates Gaussian process error models into the calibration, prediction, and uncertainty analysis of groundwater flow models. We test the usefulness of the fully Bayesian approach with a synthetic case study of the impact of pumping on surface‐ground water interaction. We illustrate through this example that the Bayesian parameter posterior distributions differ significantly from parameters estimated by conventional LSR, which does not account for model structural error. For the latter method, parameter compensation for model structural error leads to biased, overconfident prediction under changing pumping condition. In contrast, integrating Gaussian process error models significantly reduces predictive bias and leads to prediction intervals that are more consistent with validation data. Finally, we carry out a generalized LSR recalibration step to assimilate the Bayesian prediction while preserving mass conservation and other physical constraints, using a full error covariance matrix obtained from Bayesian results. It is found that the recalibrated model achieved lower predictive bias compared to the model calibrated using conventional LSR. The results highlight the importance of explicit treatment of model structural error especially in circumstances where subsequent decision‐making and risk analysis require accurate prediction and uncertainty quantification.

Groundwater model structural error is ubiquitous, due to simplification and/or misrepresentation of real aquifer systems. During model calibration, the basic hydrogeological parameters may be adjusted to compensate for structural error. This may result in biased predictions when such calibrated models are used to forecast aquifer responses to new forcing. We investigate the impact of model structural error on calibration and prediction of a real‐world groundwater flow model, using a Bayesian method with a data‐driven error model to explicitly account for model structural error. The error‐explicit Bayesian method jointly infers model parameters and structural error and thereby reduces parameter compensation. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models (based on machine learning techniques) as a substitute for the computationally expensive groundwater model. We demonstrate that with explicit treatment of model structural error, the Bayesian method yields parameter posterior distributions that are substantially different from those derived using classical Bayesian calibration that does not account for model structural error. We also found that the error‐explicit Bayesian method gives significantly more accurate prediction along with reasonable credible intervals. Finally, through variance decomposition, we provide a comprehensive assessment of prediction uncertainty contributed from parameter, model structure, and measurement uncertainty. The results suggest that the error‐explicit Bayesian approach provides a solution to real‐world modeling applications for which data support the presence of model structural error, yet model deficiency cannot be specifically identified or corrected.

Quantitative analyses of groundwater flow and transport typically rely on a physically-based model, which is inherently subject to error. Errors in model structure, parameter and data lead to both random and systematic error even in the output of a calibrated model. We develop complementary data-driven models (DDMs) to reduce the predictive error of physically-based groundwater models. Two machine learning techniques, the instance-based weighting and support vector regression, are used to build the DDMs. This approach is illustrated using two real-world case studies of the Republican River Compact Administration model and the Spokane Valley-Rathdrum Prairie model. The two groundwater models have different hydrogeologic settings, parameterization, and calibration methods. In the first case study, cluster analysis is introduced for data preprocessing to make the DDMs more robust and computationally efficient. The DDMs reduce the root-mean-square error (RMSE) of the temporal, spatial, and spatiotemporal prediction of piezometric head of the groundwater model by 82%, 60%, and 48%, respectively. In the second case study, the DDMs reduce the RMSE of the temporal prediction of piezometric head of the groundwater model by 77%. It is further demonstrated that the effectiveness of the DDMs depends on the existence and extent of the structure in the error of the physically-based model.