The suitability of differentiable, learnable hydrologic models for ungauged regions and climate change impact assessment

Abstract. Differentiable, learnable process-based hydrologic models (abbreviated as δ or delta models) with regionalized parameterization pipelines were recently shown to provide daily streamflow prediction performance that closely approach 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. Due to their physical constraints, we hypothesize that they are suitable for making extrapolated predictions. Here, we ran experiments to test (1) their ability to extrapolate to regions far from streamflow gauges; and (2) their ability to make credible projections of long-term (decadal-scale) change trends. We evaluate the models based on daily hydrograph metrics (Nash-Sutcliffe model efficiency coefficient, etc.), as well as projected decadal streamflow trends. The results show that, for spatial interpolation (test in randomly sampled ungauged basins, or PUB), δ models have mixed comparisons with LSTM, presenting better trends for annual mean flow and high flow but slightly worse for low flow. For spatial extrapolation (test in regionally held out basins, or PUR, representing a highly data-scarce scenario), δ models’ advantages in mean and high flows are more prominent. In addition, an untrained variable, evapotranspiration, retained good seasonality even for extrapolated cases. δ models’ parameterization pipeline produces 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, δ models are strong candidates for regional and global scale hydrologic simulations for climate change impact assessment.