The processes and biomass that characterize any ecosystem are fundamentally constrained by the total amount of energy that is either fixed within or delivered across its boundaries. Ultimately, ecosystems may be understood and classified by their rates of total and net productivity and by the seasonal patterns of photosynthesis and respiration. Such understanding is well developed for terrestrial and lentic ecosystems but our understanding of ecosystem phenology has lagged well behind for rivers. The proliferation of reliable and inexpensive sensors for monitoring dissolved oxygen and carbon dioxide is underpinning a revolution in our understanding of the ecosystem energetics of rivers. Here, we synthesize our current understanding of the drivers and constraints on river metabolism, and set out a research agenda aimed at characterizing, classifying and modeling the current and future metabolic regimes of flowing waters.The fuel that powers almost all of Earth's ecosystems is created by organisms capable of the alchemy of photosynthesis, in which solar energy, water, and carbon dioxide are converted into reduced carbon compounds that are then used to sustain life. We measure this conversion of solar energy into organic energy as the gross primary productivity (GPP) of ecosystems. The collective dissipation of this organic energy through organismal metabolism (of both autotrophs and heterotrophs) is measured as ecosystem respiration (ER). Together, GPP and ER are the fundamental metabolic rates of ecosystems that constrain the energy supply and energy dissipation through food chains, and the balance of these two fluxes, measured as net ecosystem production (NEP), determines whether carbon accumulates or is depleted within an ecosystem. Terrestrial ecosystems often have predictable annual cycles, with both GPP and NEP typically peaking during warmer and wetter months of the year. In many well-studied lakes productivity peaks when warming temperatures, lengthening days, and high nutrient concentrations occur in concert. The life cycles of many consumers are likely synchronized to these seasonal oscillations such that periods of peak energetic demand by consumers coincide with or follow the peak productivity of their preferred plant or prey (e.g., Lampert et al. 1986;Berger et al. 2010). As a result, ecosystem respiration tends to

The foundational ecosystem processes of gross primary production (GPP) and ecosystem respiration (ER) cannot be measured directly but can be modeled in aquatic ecosystems from subdaily patterns of oxygen (O2) concentrations. Because rivers and streams constantly exchange O2 with the atmosphere, models must either use empirical estimates of the gas exchange rate coefficient (K600) or solve for all three parameters (GPP, ER, and K600) simultaneously. Empirical measurements of K600 require substantial field work and can still be inaccurate. Three‐parameter models have suffered from equifinality, where good fits to O2 data are achieved by many different parameter values, some unrealistic. We developed a new three‐parameter, multiday model that ensures similar values for K600 among days with similar physical conditions (e.g., discharge). Our new model overcomes the equifinality problem by (1) flexibly relating K600 to discharge while permitting moderate daily deviations and (2) avoiding the oft‐violated assumption that residuals in O2 predictions are uncorrelated. We implemented this hierarchical state‐space model and several competitor models in an open‐source R package, streamMetabolizer. We then tested the models against both simulated and field data. Our new model reduces error by as much as 70% in daily estimates of K600, GPP, and ER. Further, accuracy benefits of multiday data sets require as few as 3 days of data. This approach facilitates more accurate metabolism estimates for more streams and days, enabling researchers to better quantify carbon fluxes, compare streams by their metabolic regimes, and investigate controls on aquatic activity.

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.

A national-scale quantification of metabolic energy flow in streams and rivers can improve understanding of the temporal dynamics of in-stream activity, links between energy cycling and ecosystem services, and the effects of human activities on aquatic metabolism. The two dominant terms in aquatic metabolism, gross primary production (GPP) and aerobic respiration (ER), have recently become practical to estimate for many sites due to improved modeling approaches and the availability of requisite model inputs in public datasets. We assembled inputs from the U.S. Geological Survey and National Aeronautics and Space Administration for October 2007 to January 2017. We then ran models to estimate daily GPP, ER, and the gas exchange rate coefficient for 356 streams and rivers across the continental United States. We also gathered potential explanatory variables and spatial information for cross-referencing this dataset with other datasets of watershed characteristics. This dataset offers a first national assessment of many-day time series of metabolic rates for up to 9 years per site, with a total of 490,907 site-days of estimates.

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.