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Lakes support globally important food webs through algal productivity and contribute significantly to the global carbon cycle. However, predictions of how broad‐scale lake carbon flux and productivity may respond to future climate are extremely limited. Here, we used an integrated modeling framework to project changes in lake‐specific and regional primary productivity and carbon fluxes under 21st century climate for thousands of lakes. We observed high uncertainty in whether lakes collectively were to increase or decrease lake CO₂emissions and carbon burial in our modeled region owing to divergence in projected regional water balance among climate models. Variation in projected air temperature influenced projected changes in lake primary productivity (but not CO₂emissions or carbon burial) as warmer air temperatures decreased productivity through reduced lake water volume. Cross‐scale interactions between regional drivers and local characteristics dictated the magnitude and direction of lake‐specific carbon flux and productivity responses to future climate.

 

Lakes are biogeochemical hotspots on the landscape, contributing significantly to the global carbon cycle despite their small areal coverage. Observations and models of lake carbon pools and fluxes are rarely explicitly combined through data assimilation despite successful use of this technique in other fields. Data assimilation adds value to both observations and models by constraining models with observations of the system and by leveraging knowledge of the system formalized by the model to objectively fill observation gaps. In this article, we highlight the utility of data assimilation in lake carbon cycling research by using the ensemble Kalman filter to combine simple lake carbon models with observations of lake carbon pools and fluxes. We demonstrate that data assimilation helps reduce uncertainty in estimates of lake carbon pools and fluxes and more accurately estimate the true carbon pool size compared to estimates derived from observations alone. Data assimilation techniques should be embraced as valuable tools for lake biogeochemists interested in learning about ecosystem dynamics and forecasting ecosystem states and processes.

 

This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based 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.