There is a growing consensus that solutions to complex science and engineering problems require novel methodologies that are able to integrate traditional physics-based modeling approaches with state-of-the-art machine learning (ML) techniques. This article provides a structured overview of such techniques. Application-centric objective areas for which these approaches have been applied are summarized, and then classes of methodologies used to construct physics-guided ML models and hybrid physics-ML frameworks are described. We then provide a taxonomy of these existing techniques, which uncovers knowledge gaps and potential crossovers of methods between disciplines that can serve as ideas for future research.

Most environmental data come from a minority of well‐monitored sites. An ongoing challenge in the environmental sciences is transferring knowledge from monitored sites to unmonitored sites. Here, we demonstrate a novel transfer‐learning framework that accurately predicts depth‐specific temperature in unmonitored lakes (targets) by borrowing models from well‐monitored lakes (sources). This method, meta‐transfer learning (MTL), builds a meta‐learning model to predict transfer performance from candidate source models to targets using lake attributes and candidates' past performance. We constructed source models at 145 well‐monitored lakes using calibrated process‐based (PB) modeling and a recently developed approach called process‐guided deep learning (PGDL). We applied MTL to either PB or PGDL source models (PB‐MTL or PGDL‐MTL, respectively) to predict temperatures in 305 target lakes treated as unmonitored in the Upper Midwestern United States. We show significantly improved performance relative to the uncalibrated PB General Lake Model, where the median root mean squared error (RMSE) for the target lakes is 2.52°C. PB‐MTL yielded a median RMSE of 2.43°C; PGDL‐MTL yielded 2.16°C; and a PGDL‐MTL ensemble of nine sources per target yielded 1.88°C. For sparsely monitored target lakes, PGDL‐MTL often outperformed PGDL models trained on the target lakes themselves. Differences in maximum depth between the source and target were consistently the most important predictors. Our approach readily scales to thousands of lakes in the Midwestern United States, demonstrating that MTL with meaningful predictor variables and high‐quality source models is a promising approach for many kinds of unmonitored systems and environmental variables.

The global decline of water quality in rivers and streams has resulted in a pressing need to design new watershed management strategies. Water quality can be affected by multiple stressors including population growth, land use change, global warming, and extreme events, with repercussions on human and ecosystem health. A scientific understanding of factors affecting riverine water quality and predictions at local to regional scales, and at sub‐daily to decadal timescales are needed for optimal management of watersheds and river basins. Here, we discuss how machine learning (ML) can enable development of more accurate, computationally tractable, and scalable models for analysis and predictions of river water quality. We review relevant state‐of‐the art applications of ML for water quality models and discuss opportunities to improve the use of ML with emerging computational and mathematical methods for model selection, hyperparameter optimization, incorporating process knowledge into ML models, improving explainablity, uncertainty quantification, and model‐data integration. We then present considerations for using ML to address water quality problems given their scale and complexity, available data and computational resources, and stakeholder needs. When combined with decades of process understanding, interdisciplinary advances in knowledge‐guided ML, information theory, data integration, and analytics can help address fundamental science questions and enable decision‐relevant predictions of riverine water quality.

The dataset described here includes estimates of historical (1980–2020) daily surface water temperature, lake metadata, and daily weather conditions for lakes bigger than 4 ha in the conterminous United States (n = 185,549), and also in situ temperature observations for a subset of lakes (n = 12,227). Estimates were generated using a long short‐term memory deep learning model and compared to existing process‐based and linear regression models. Model training was optimized for prediction on unmonitored lakes through cross‐validation that held out lakes to assess generalizability and estimate error. On the held‐out lakes with in situ observations, median lake‐specific error was 1.24°C, and the overall root mean squared error was 1.61°C. This dataset increases the number of lakes with daily temperature predictions when compared to existing datasets, as well as substantially improves predictive accuracy compared to a prior empirical model and a debiased process‐based approach (2.01°C and 1.79°C median error, respectively).

Prediction of dynamic environmental variables in unmonitored sites remains a long-standing challenge for water resources science. The majority of the world’s freshwater resources have inadequate monitoring of critical environmental variables needed for management. Yet, the need to have widespread predictions of hydrological variables such as river flow and water quality has become increasingly urgent due to climate and land use change over the past decades, and their associated impacts on water resources. Modern machine learning methods increasingly outperform their process-based and empirical model counterparts for hydrologic time series prediction with their ability to extract information from large, diverse data sets. We review relevant state-of-the art applications of machine learning for streamflow, water quality, and other water resources prediction and discuss opportunities to improve the use of machine learning with emerging methods for incorporating watershed characteristics and process knowledge into classical, deep learning, and transfer learning methodologies. The analysis here suggests most prior efforts have been focused on deep learning frameworks built on many sites for predictions at daily time scales in the United States, but that comparisons between different classes of machine learning methods are few and inadequate. We identify several open questions for time series predictions in unmonitored sites that include incorporating dynamic inputs and site characteristics, mechanistic understanding and spatial context, and explainable AI techniques in modern machine learning frameworks.

The rapid rise of deep learning (DL) in numerical weather prediction (NWP) has led to a proliferation of models which forecast atmospheric variables with comparable or superior skill than traditional physics-based NWP. However, among these leading DL models, there is a wide variance in both the training settings and architecture used. Further, the lack of thorough ablation studies makes it hard to discern which components are most critical to success. In this work, we show that it is possible to attain high forecast skill even with relatively off-the-shelf architectures, simple training procedures, and moderate compute budgets. Specifically, we train a minimally modified Swin Transformer V2 (SwinV2) on ERA5 data and find that it attains superior skill in terms of mean-square errors of deterministic forecasts when compared against the European Centre for Medium-Range Weather Forecasts’ Integrated Forecasting System (IFS). Almost all DL–NWP systems share a core set of hyperparameters and design decisions. To aid and expedite future DL–NWP research, we present an in-depth, systematic exploration of different loss functions, model sizes and depths, patch sizes, and multistep training objectives. We also examine the model performance with metrics beyond the typical accuracy (ACC) and RMSE and investigate how the performance scales with model size. Through our open-source code, scoring pipelines, and models, we share our findings on key aspects of the training pipeline. These ablations reduce the necessity for expensive hyperparameter tuning and lower the barrier to entry for future DL–NWP research. Significance Statement: This study investigates the potential of using large-scale transformer-based models for weather prediction, showing that it is possible to achieve high forecast accuracy with simpler, off-the-shelf architectures. By training a minimally modified SwinV2 transformer on ERA5 data, we show that the model achieves competitive forecast skill in terms of mean-square error for key variables, outperforming the European Centre for Medium-Range Weather Forecasts’ Integrated Forecasting System (IFS) at all lead times. Our findings suggest that effective training strategies, such as multistep fine-tuning and channel-weighted losses, significantly enhance the model’s performance. However, we also highlight that these improvements come with trade-offs in other areas, such as ensemble spread and high-frequency spatial detail. This work highlights the promise of deep learning in improving weather forecasts, which could lead to better preparedness and response to weather events, ultimately benefiting society by providing more reliable weather predictions.