Enhancing Water Temperature Prediction in Stratified Reservoirs: A Process-Guided Deep Learning Approach

Abstract

Data-driven models (DDMs) are extensively used in environmental modeling yet encounter obstacles stemming from limited training data and potential discrepancies with physical laws. To address this challenge, this study developed a process-guided deep learning (PGDL) model, integrating a long short-term memory (LSTM) neural network and a process-based model (PBM), CE-QUAL-W2 (W2), to predict water temperature in a stratified reservoir. The PGDL model incorporates an energy constraint term derived from W2′s thermal energy equilibrium into the LSTM’s cost function, alongside the mean square error term. Through this mechanism, PGDL optimizes parameters while penalizing deviations from the energy law, thereby ensuring adherence to crucial physical constraints. In comparison to LSTM’s root mean square error (RMSE) of 0.062 °C, PGDL exhibits a noteworthy 1.5-fold enhancement in water temperature prediction (RMSE of 0.042 °C), coupled with improved satisfaction in maintaining energy balance. Intriguingly, even with training on just 20% of field data, PGDL (RMSE of 0.078 °C) outperforms both LSTM (RMSE of 0.131 °C) and calibrated W2 (RMSE of 1.781 °C) following pre-training with 80% of the data generated by the uncalibrated W2 model. The successful integration of the PBM and DDM in the PGDL validates a novel technique that capitalizes on the strengths of multidimensional mathematical models and data-based deep learning models. Furthermore, the pre-training of PGDL with PBM data demonstrates a highly effective strategy for mitigating bias and variance arising from insufficient field measurement data.