Improving River Routing Using a Differentiable Muskingum-Cunge Model and Physics-Informed Machine Learning
We presented a novel differentiable routing method that mimicked the classical Muskingum-Cunge rainfall-runoff routing model over a river network, but contained an embedded a neural network (NN) to infer parameterizations for Manning's channel roughness (n) and channel geometries from raw river reach-scale attributes like catchment areas and sinuosity. The NN was trained solely on downstream hydrographs. All together, we created a routing model able to learn from data, or, from the perspective of ML, a physics-informed graph NN. With short periods of real training data, we were able to improve streamflow prediction in large rivers compared to models not considering routing. For basins >2,000 km2, our framework outperformed deep learning models that assume homogeneity, despite bias being present in the runoff forcings (and thus making accurate prediction a harder problem for physics-constrained models like ours, whereas pure deep learning models are not limited by physical principles like conservation of mass).
Current physics-informed machine learning streamflow models typically make predictions for an entire basin at a time (with predictions made only for specific stream monitoring stations, often just at a watershed’s outflow point), rather than being able to provide a prediction for any given point along a river network within a basin. This model represents an important step towards this ability, by predicting streamflow in stem rivers and learning river parameters throughout a stream network, which is urgently needed to improve the next-generation large-scale hydrologic models. Because our framework is built on physical principles and estimates widely used Manning’s channel roughness values, it can be easily ported to work with other model - for example, the trained NN and the weights can be used to support traditional hydrologic models or routing schemes.
Recently, rainfall-runoff simulations in small headwater basins have been improved by methodological advances such as deep neural networks (NNs) and hybrid physics-NN models—particularly, a genre called differentiable modeling that intermingles NNs with physics to learn relationships between variables. However, hydrologic routing simulations, necessary for simulating floods in stem rivers downstream of large heterogeneous basins, had not yet benefited from these advances and it was unclear if the routing process could be improved via coupled NNs. We present a novel differentiable routing method (δMC-Juniata-hydroDL2) that mimics the classical Muskingum-Cunge routing model over a river network but embeds an NN to infer parameterizations for Manning's roughness (n) and channel geometries from raw reach-scale attributes like catchment areas and sinuosity. The NN was trained solely on downstream hydrographs. Synthetic experiments show that while the channel geometry parameter was unidentifiable, n can be identified with moderate precision. With real-world data, the trained differentiable routing model produced more accurate long-term routing results for both the training gage and untrained inner gages for larger subbasins (>2,000 km2) than either a machine learning model assuming homogeneity, or simply using the sum of runoff from subbasins. The n parameterization trained on short periods gave high performance in other periods, despite significant errors in runoff inputs. The learned n pattern was consistent with literature expectations, demonstrating the framework's potential for knowledge discovery, but the absolute values can vary depending on training periods. The trained n parameterization can be coupled with traditional models to improve national-scale hydrologic flood simulations.