A differentiable ecosystem modeling framework for large-scale inverse problems: demonstration with photosynthesis simulations

Photosynthesis plays an important role in carbon, nitrogen, and water cycles. Ecosystem models for photosynthesis are characterized by many parameters that are obtained from limited in-situ measurements and applied to the same plant types. Previous site-by-site calibration approaches could not leverage big data and faced issues like overfitting or parameter non-uniqueness. Here we developed a programmatically differentiable (meaning gradients of outputs to variables used in the model can be obtained efficiently and accurately) version of the photosynthesis process representation within the Functionally Assembled Terrestrial Ecosystem Simulator (FATES) model. This model is coupled to neural networks that learn parameterization from observations of photosynthesis rates. We first demonstrated that the framework was able to recover multiple assumed parameter values concurrently using synthetic training data. Then, using a real-world dataset consisting of many different plant functional types, we learned parameters that performed substantially better and dramatically reduced biases compared to literature values. Further, the framework allowed us to gain insights at a large scale. Our results showed that the carboxylation rate at 25°C (Vc,max25), was more impactful than a factor representing water limitation, although tuning both was helpful in addressing biases with the default values. This framework could potentially enable a substantial improvement in our capability to learn parameters and reduce biases for ecosystem modeling at large scales.