Physics-informed LSTM for streamflow modeling using a dataset of intensively-monitored watersheds in the USA

Long Short-Term Memory (LSTM) networks have shown superior performance in predicting time series data in hydrological studies but often lack interpretability and sometimes are inconsistent with physical laws. In this study, we apply a water balance framework to inductively interpret the LSTM, testing the hypothesis that the network's hidden and cell states are broadly representative of hydrologic stores (e.g., snowpack, soil moisture) and fluxes (e.g., snowmelt), as has been suggested in previous studies. Additionally, we add water balance constraints to the model structure to improve streamflow prediction, particularly in non-stationary conditions where out-of-sample data are more frequent. We apply this analysis to 30 intensively monitored watersheds from the Comprehensive Hydrologic Observatory SEnsor Network (CHOSEN) dataset in order to explore how outcomes vary across watersheds where different physical processes dominate. Preliminary results suggest that embedding physics-based constraints to the LSTM results in a more robust model structure that can be generalized to a multitude of catchments and better conforms with physical laws. The high correlations between cell states and observational time series that were not explicitly seen by the model indicate that the physics-informed LSTM structures can reconstruct physically dominating hydrometeorological time series and facilitate the forecasting of streamflow.