Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracy

Predictions of hydrologic variables across the entire water cycle have significant value for water resource management as well as downstream applications such as ecosystem and water quality modeling. Recently, purely data-driven deep learning models like long short-term memory (LSTM) showed seemingly-insurmountable performance in modeling rainfall-runoff and other geoscientific variables, yet they cannot predict unobserved physical variables and remain challenging to interpret. Here we show that differentiable, learnable, process-based models (called {\delta} models here) can approach the performance level of LSTM for the intensively-observed variable (streamflow) with regionalized parameterization. We use a simple hydrologic model HBV as the backbone and use embedded neural networks, which can only be trained in a differentiable programming framework, to parameterize, replace, or enhance the process-based model modules. Without using an ensemble or post-processor, {\delta} models can obtain a median Nash Sutcliffe efficiency of 0.715 for 671 basins across the USA for a particular forcing data, compared to 0.72 from a state-of-the-art LSTM model with the same setup. Meanwhile, the resulting learnable process-based models can be evaluated (and later, to be trained) by multiple sources of observations, e.g., groundwater storage, evapotranspiration, surface runoff, and baseflow. Both simulated evapotranspiration and fraction of discharge from baseflow agreed decently with alternative estimates. The general framework can work with models with various process complexity and opens up the path for learning physics from big data.