A data-driven method coupling multiple physical constraints for correcting structural errors in groundwater contaminant transport models

Abstract. Model structural errors are pervasive in groundwater contaminant transport modeling under complex environmental conditions, hindering accurate prediction of contamination transport. Data-driven methods (DDMs) coupled with physical constraints provide an effective approach for correcting structural errors and improving prediction. However, in multicomponent reactive transport systems, multiple physical mechanisms must be satisfied simultaneously, whereas existing DDMs have limited capacity to effectively couple multiple physical constraints. To address this challenge, this study proposes a general method for correcting structural errors in groundwater models. A combined likelihood function is constructed and sub-likelihood weights are dynamically updated to effectively couple multiple physical constraints. The method is evaluated using a synthetic three-dimensional tetrachloroethylene reactive transport simulation and a cadmium-phosphate cotransport sand column experiment. These tests systematically assess the effects of coupling single versus multiple physical constraints on structural error correction and predictive performance. The results show that coupling multiple constraints can constrain parameter identification, reduce predictive uncertainty, and more comprehensively improve model predictions. Appropriate physical constraints function analogously to incorporating additional observations. Moreover, coupling multiple physical constraints results in a simpler form of structural error in the calibrated groundwater model, making it easier to characterize, thereby enhancing prediction accuracy and physical consistency. The proposed dynamic updating and stopping criterion of sub-likelihood weights maintains a balance between multiple physical constraints and observations, improving the robustness of parameter identification and constraint enforcement. Overall, the proposed DDM coupled with multiple physical constraints provides a general framework for correcting structural errors in complex groundwater contaminant transport models.