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Abstract In lakes, the rates of gross primary production (GPP), ecosystem respiration (R), and net ecosystem production (NEP) are often controlled by resource availability. Herein, we explore how catchment vs. within lake predictors of metabolism compare using data from 16 lakes spanning 39°N to 64°N, a range of inflowing streams, and trophic status. For each lake, we combined stream loads of dissolved organic carbon (DOC), total nitrogen (TN), and total phosphorus (TP) with lake DOC, TN, and TP concentrations and high frequencyin situmonitoring of dissolved oxygen. We found that stream load stoichiometry indicated lake stoichiometry for C : N and C : P (r² = 0.74 andr² = 0.84, respectively), but not for N : P (r² = 0.04). As we found a strong positive correlation between TN and TP, we only used TP in our statistical models. For the catchment model, GPP and R were best predicted by DOC load, TP load, and load N : P (R² = 0.85 andR² = 0.82, respectively). For the lake model, GPP and R were best predicted by TP concentrations (R² = 0.86 andR² = 0.67, respectively). The inclusion of N : P in the catchment model, but not the lake model, suggests that both N and P regulate metabolism and that organisms may be responding more strongly to catchment inputs than lake resources. Our models predicted NEP poorly, though it is unclear why. Overall, our work stresses the importance of characterizing lake catchment loads to predict metabolic rates, a result that may be particularly important in catchments experiencing changing hydrologic regimes related to global environmental change. 

Physics-based models are often used to study engineering and environmental systems. The ability to model these systems is the key to achieving our future environmental sustainability and improving the quality of human life. This article focuses on simulating lake water temperature, which is critical for understanding the impact of changing climate on aquatic ecosystems and assisting in aquatic resource management decisions. General Lake Model (GLM) is a state-of-the-art physics-based model used for addressing such problems. However, like other physics-based models used for studying scientific and engineering systems, it has several well-known limitations due to simplified representations of the physical processes being modeled or challenges in selecting appropriate parameters. While state-of-the-art machine learning models can sometimes outperform physics-based models given ample amount of training data, they can produce results that are physically inconsistent. This article proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improves the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physics-based models (by over 20% even with very little training data), while generating outputs consistent with physical laws. An important aspect of our PGRNN approach lies in its ability to incorporate the knowledge encoded in physics-based models. This allows training the PGRNN model using very few true observed data while also ensuring high prediction accuracy. 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 physics-based (also known as mechanistic) models are used.