As a genre of physics-informed machine learning, differentiable process-based hydrologic models (abbreviated as δ or delta models) with regionalized deep-network-based parameterization pipelines were recently shown to provide daily streamflow prediction performance closely approaching that of state-of-the-art long short-term memory (LSTM) deep networks. Meanwhile, δ models provide a full suite of diagnostic physical variables and guaranteed mass conservation. Here, we ran experiments to test (1) their ability to extrapolate to regions far from streamflow gauges and (2) their ability to make credible predictions of long-term (decadal-scale) change trends. We evaluated the models based on daily hydrograph metrics (Nash–Sutcliffe model efficiency coefficient, etc.) and predicted decadal streamflow trends. For prediction in ungauged basins (PUB; randomly sampled ungauged basins representing spatial interpolation), δ models either approached or surpassed the performance of LSTM in daily hydrograph metrics, depending on the meteorological forcing data used. They presented a comparable trend performance to LSTM for annual mean flow and high flow but worse trends for low flow. For prediction in ungauged regions (PUR; regional holdout test representing spatial extrapolation in a highly data-sparse scenario), δ models surpassed LSTM in daily hydrograph metrics, and their advantages in mean and high flow trends became prominent. In addition, an untrained variable, evapotranspiration, retained good seasonality even for extrapolated cases. The δ models' deep-network-based parameterization pipeline produced parameter fields that maintain remarkably stable spatial patterns even in highly data-scarce scenarios, which explains their robustness. Combined with their interpretability and ability to assimilate multi-source observations, the δ models are strong candidates for regional and global-scale hydrologic simulations and climate change impact assessment.
Bibliographical noteKAUST Repository Item: Exported on 2023-07-19
Acknowledgements: Dapeng Feng has been supported by the Office of Biological and Environmental Research of the U.S. Department of Energy (contract no. DESC0016605) and U.S. National Science Foundation (NSF; grant nos. EAR-1832294 and EAR-2221880). Chaopeng Shen has been funded by the National Oceanic and Atmospheric Administration (NOAA), which was awarded to the Cooperative Institute for Research to Operations in Hydrology (CIROH) through the NOAA Cooperative Agreement with the University of Alabama (grant no. NA22NWS4320003). Computational resources have been partially provided by the NSF (grant no. OAC 1940190). The differentiable hydrologic models were implemented on the PyTorch platform (Paszke et al., 2017) that supports automatic differentiation. We thank the two anonymous referees for their helpful comments to improve the quality of this paper.