Improving differentiable hydrologic modeling with interpretable forcing fusion

Atmospheric forcings for hydrologic models often contain significant errors, but traditional modifications only employ bias correction or distributional transformations based on rainfall measurements. Deep learning could fuse multiple datasets for improved hydrologic modeling, but is difficult to interpret. Here we introduce a “differentiable” data fusion framework where a neural network is pre-trained to provide parameters a process-based hydrologic model while a second network is trained to weigh multiple forcings (Daymet, NLDAS, and Maurer) for a fused precipitation input to the combined model. The fused precipitation data greatly improved streamflow simulation performance (both low flow and high flow, but especially high flow). Applying adaptive weights to a single forcing did not yield improvements. Overall, the fusion placed a higher weight on Daymet, and slightly lower weights on NLDAS and Maurer. NLDAS's weights increased in the humid eastern US while Maurer's increased in mountainous regions. The fused precipitation had similar means and large-magnitude event performance to Daymet. However, it exhibited higher correlation with station-based precipitation than any individual forcing or their simple average, and had close to the smallest bias for large storms. Pre-training the parameterization network based on the best-performing single forcing (Daymet) yielded better results than those based on the average of forcings. Overall, the differentiable hydrologic model offers a generic hydrology-informed fusion method to improve streamflow prediction.