Process‐Guided Deep Learning Predictions of Lake Water Temperature

TLDR

The rapid growth of water‑resource data enables advanced deep learning, and hybrid models that combine theory with empirical techniques can improve predictions while respecting physical laws. The study evaluates the Process‑Guided Deep Learning framework for predicting depth‑specific lake water temperatures. The PGDL model comprises a temporally aware LSTM core, theory‑based energy‑conservation penalties, and pretraining with synthetic process‑model outputs; it was trained on in‑situ temperatures and compared to standalone DL and process‑based models under sparse data and extrapolation scenarios. PGDL achieved lower RMSE than DL and PB on two lakes when pretraining data had greater variability, and across 68 lakes it yielded a median RMSE of 1.65 °C versus 1.78 °C (DL) and 2.03 °C (PB), demonstrating that embedding scientific knowledge can improve environmental predictions.

Abstract

Abstract The rapid growth of data in water resources has created new opportunities to accelerate knowledge discovery with the use of advanced deep learning tools. Hybrid models that integrate theory with state‐of‐the art empirical techniques have the potential to improve predictions while remaining true to physical laws. This paper evaluates the Process‐Guided Deep Learning (PGDL) hybrid modeling framework with a use‐case of predicting depth‐specific lake water temperatures. The PGDL model has three primary components: a deep learning model with temporal awareness (long short‐term memory recurrence), theory‐based feedback (model penalties for violating conversation of energy), and model pretraining to initialize the network with synthetic data (water temperature predictions from a process‐based model). In situ water temperatures were used to train the PGDL model, a deep learning (DL) model, and a process‐based (PB) model. Model performance was evaluated in various conditions, including when training data were sparse and when predictions were made outside of the range in the training data set. The PGDL model performance (as measured by root‐mean‐square error (RMSE)) was superior to DL and PB for two detailed study lakes, but only when pretraining data included greater variability than the training period. The PGDL model also performed well when extended to 68 lakes, with a median RMSE of 1.65 °C during the test period (DL: 1.78 °C, PB: 2.03 °C; in a small number of lakes PB or DL models were more accurate). This case‐study demonstrates that integrating scientific knowledge into deep learning tools shows promise for improving predictions of many important environmental variables.