Coupling Machine Learning into Hydrodynamic Models to Improve River Modeling with Complex Boundary Conditions

Rivers play an important role in water supply, irrigation, navigation, and ecological maintenance. Forecasting the river hydrodynamic changes is critical for flood management under climate change and intensified human activities. However, efficient and accurate river modeling is challenging, especially with complex lake boundary conditions and uncontrolled downstream boundary conditions. Here, we proposed a coupled framework by taking the advantages of interpretability of physical hydrodynamic modeling and the adaptability of machine learning. Specifically, we coupled the Gated Recurrent Unit (GRU) with a 1-D HydroDynamic model (GRU-HD) and applied it to the middle and lower reaches of the Yangtze River, the longest river in China. We show that the GRU-HD model could quickly and accurately simulate the water levels, streamflow, and water exchange rates between the Yangtze River and two important lakes (Poyang and Dongting), with most of the Kling-Gupta efficiency coefficient (KGE $\mathrm{K}\mathrm{G}\mathrm{E}$) above 0.90. Using machine learning-based predicted water levels, instead of the rating curve approach, as the downstream boundary conditions could improve the accuracy of modeling the downstream water levels of the lake-connected river system. The GRU-HD model is dedicated to the synergy of physical modeling and machine learning, providing a powerful avenue for modeling rivers with complex boundary conditions.