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Publication Date
1 October 2022

Differentiable, Learnable, Regionalized Process‐Based Models With Multiphysical Outputs can Approach State‐Of‐The‐Art Hydrologic Prediction Accuracy

Subtitle
Introducing a genre of physics-informed machine learning: embedded neural networks parameterize, enhance, and/or replace modules in a process-based model. 
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Science

We use a simple hydrologic model as the backbone and use embedded neural networks, which can only be trained in a differentiable programming framework, to parameterize, enhance, or replace the process-based model's modules. The general framework can work with models with various process complexity and opens up the path for learning physics from big data. 

Impact

Differentiable, learnable process-based models can output a full set of untrained variables (including those that cannot be easily or continuously monitored), which can be used to improve predictions. The models tested matched the performance of pure deep learning models, which had been thought impossible. 

Summary

Predictions of hydrologic variables across the entire water cycle have significant value for water resources 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 untrained physical variables and remain challenging to interpret. Here, we show that differentiable, learnable, process-based models (called δ 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, enhance, or replace the process-based model's modules. Without using an ensemble or post-processor, δ models can obtain a median Nash-Sutcliffe efficiency of 0.732 for 671 basins across the USA for the Daymet forcing data set, compared to 0.748 from a state-of-the-art LSTM model with the same setup. For another forcing data set, the difference is even smaller: 0.715 versus 0.722. Meanwhile, the resulting learnable process-based models can output a full set of untrained variables, for example, soil and groundwater storage, snowpack, evapotranspiration, and baseflow, and can later be constrained by their observations. 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. 

Point of Contact
Renu Joseph, Renu.Joseph@science.doe.gov
Institution(s)
Civil and Environmental Engineering Pennsylvania State University University Park PA USA
Funding Program Area(s)