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Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. In this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs. 

This dataset includes model configurations, scripts and outputs to process and recreate the outputs from Ladwig et al. (2021): Long-term Change in Metabolism Phenology across North-Temperate Lakes. The provided scripts will process the input data from various sources, as well as recreate the figures from the manuscript. Further, all output data from the metabolism models of Allequash, Big Muskellunge, Crystal, Fish, Mendota, Monona, Sparkling and Trout are included. 

This dataset includes model configurations, scripts and outputs to process and recreate the outputs from Ladwig et al. (2021): Long-term Change in Metabolism Phenology across North-Temperate Lakes. The provided scripts will process the input data from various sources, as well as recreate the figures from the manuscript. Further, all output data from the metabolism models of Allequash, Big Muskellunge, Crystal, Fish, Mendota, Monona, Sparkling and Trout are included. 

Mean annual temperature and mean annual precipitation drive much of the variation in productivity across Earth's terrestrial ecosystems but do not explain variation in gross primary productivity (GPP) or ecosystem respiration (ER) in flowing waters. We document substantial variation in the magnitude and seasonality of GPP and ER across 222 US rivers. In contrast to their terrestrial counterparts, most river ecosystems respire far more carbon than they fix and have less pronounced and consistent seasonality in their metabolic rates. We find that variation in annual solar energy inputs and stability of flows are the primary drivers of GPP and ER across rivers. A classification schema based on these drivers advances river science and informs management. 

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.