We aim to improve streamflow predictions through combining the theory of river routing with the powerful technologies of deep neural networks (NNs) using differentiable modeling (DM). DM connects (flexible amounts of) prior physical knowledge to NNs and trains them together at the same time, using the NNs to fill knowledge gaps and learn from data, and using the priors to constrain what can be learned so the outputs are physically meaningful. This paradigm pushes 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 and scaling performance and efficiency well with increasing data volumes. This particular work aims to apply a DM framework to a flexible suite of process-based models of varying complexity, build a physics-informed and learnable flow routing scheme for complex river networks and test it in large basins, and prepare infrastructure and seamless datasets for large regions across the entire USA.

Thus far, we have announced the DM paradigm via a comprehensive review paper published in Nature Reviews Earth & Environment. One of the works summarized was our differentiable process-based streamflow model that showcases cutting-edge performance while ensuring robustness for extrapolation in ungauged regions. This model successfully realized parameter regionalization on a continental scale and a paper was published in HESS. 

We created a differentiable explicit river routing model by implementing a common river routing technique known as Muskingum-Cunge in a DM framework (paper in the second round of review).  This lets us learn parameters for specific river reaches like those within the Susquehanna River Basin in Pennsylvania, USA based on both data and physical laws, which has not previously been possible. The trained parameters on our study basin match literature expectations, and our river routing outputs are outperforming the comparable pure NN predictions.

We have also been working on an implicit differentiable streamflow model (paper in preparation) where we introduce a novel method enabling advanced schemes and correcting some parameter distortion caused by explicit schemes. We also enhance the model structure by incorporating insights into hydrological processes and addressing the limitations of the core model.

Work continues towards developing a robust code capable of seamlessly extracting spatial attributes across the entire United States for both basin-scale rainfall-runoff modeling and stream network routing. All of these models and methodologies can be used for regional climate change impact analysis by integrating the next-generation National Water Model with ML capabilities and improved modeling.