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.

This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physicsbased models to leverage their complementary strengths and improve the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physical models, while generating outputs consistent with physical laws, and achieving good generalizability. Standard RNNs, even when producing superior prediction accuracy, often produce physically inconsistent results and lack generalizability. We further enhance this approach by using a pre-training method that leverages the simulated data from a physics-based model to address the scarcity of observed data. Although we present and evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where mechanistic (also known as process-based) models are used, e.g., power engineering, climate science, materials science, computational chemistry, and biomedicine.

Metabolism is a fundamental process in ecosystems that crosses multiple scales of organization from individual organisms to whole ecosystems. To improve sharing and reuse of published metabolism models, we developed LakeMetabolizer, an R package for estimating lake metabolism from in situ time series of dissolved oxygen, water temperature, and, optionally, additional environmental variables. LakeMetabolizer implements 5 different metabolism models with diverse statistical underpinnings: bookkeeping, ordinary least squares, maximum likelihood, Kalman filter, and Bayesian. Each of these 5 metabolism models can be combined with 1 of 7 models for computing the coefficient of gas exchange across the air-water interface (k). LakeMetabolizer also features a variety of supporting functions that compute conversions and implement calculations commonly applied to raw data prior to estimating metabolism (e.g., oxygen saturation and optical conversion models). These tools have been organized into an R package that contains example data, example use-cases, and function documentation. The release package version is available on the Comprehensive R Archive Network (CRAN), and the full open-source GPL-licensed code is freely available for examination and extension online. With this unified, open-source, and freely available package, we hope to improve access and facilitate the application of metabolism in studies and management of lentic ecosystems.

An experiment in >1000 river and riparian sites found spatial patterns and controls of carbon processing at the global scale.

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