Integrating a calibrated groundwater flow model with error-correcting data-driven models to improve predictions

Physically-based groundwater models (PBMs), such as MODFLOW, contain numerous parameters which are usually estimated using statistically-based methods, which assume that the underlying error is white noise. However, because of the practical difficulties of representing all the natural subsurface complexity, numerical simulations are often prone to large uncertainties that can result in both random and systematic model error. The systematic errors can be attributed to conceptual, parameter, and measurement uncertainty, and most often it can be difficult to determine their physical cause. In this paper, we have developed a framework to handle systematic error in physically-based groundwater flow model applications that uses error-correcting data-driven models (DDMs) in a complementary fashion. The data-driven models are separately developed to predict the MODFLOW head prediction errors, which were subsequently used to update the head predictions at existing and proposed observation wells. The framework is evaluated using a hypothetical case study developed based on a phytoremediation site at the Argonne National Laboratory. This case study includes structural, parameter, and measurement uncertainties. In terms of bias and prediction uncertainty range, the complementary modeling framework has shown substantial improvements (up to 64% reduction in RMSE and prediction error ranges) over the original MODFLOW model, in both the calibration and the verification periods. Moreover, the spatial and temporal correlations of the prediction errors are significantly reduced, thus resulting in reduced local biases and structures in the model prediction errors.