Train, inform, borrow, or combine? Approaches to process-guided deep learning for groundwater-influenced stream temperature prediction

Although groundwater discharge is a critical stream temperature control process, it is not explicitly represented in many stream temperature models, an omission that may reduce predictive accuracy, hinder management of aquatic habitat, and decrease user confidence. We assessed the performance of a previously-described process-guided deep learning model of stream temperature in the Delaware River Basin (USA). We found lower accuracy (root mean square error [RMSE] of 1.71 versus 1.35°C) and stronger seasonal bias (absolute mean monthly bias of 1.06 vs. 0.68°C) for reaches primarily influenced by deep groundwater as compared to atmospheric conditions. We then tested four approaches for improving groundwater process representation: (a) a custom loss function leveraging the unique patterns of air and water temperature coupling characteristic of different temperature drivers, (b) inclusion of additional groundwater-relevant catchment attributes, (c) incorporation of additional process model outputs, and (d) a composite model. The custom loss function and the additional attributes significantly improved the predictive accuracy in groundwater-dominated reaches (RMSE of 1.37 and 1.26°C) and reduced the seasonal bias (absolute mean monthly bias of 0.44 and 0.48°C), but neither approach could identify holdout groundwater reaches. Variable importance analysis indicates the custom loss function nudges the model to use the existing inputs more efficiently, whereas with the added features the model relies on a broader suite of inputs. This analysis is a substantial step toward more accurately representing groundwater discharge processes in stream temperature models and will improve predictive accuracy and inform habitat management.