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

Dapeng Feng, Jiangtao Liu+2 more|arXiv (Cornell University)|Mar 28, 2022

Hydrological Forecasting Using AI19 citations

TL;DR

This paper introduces differentiable, learnable, regionalized process-based hydrologic models (called δ models) that combine physical process understanding with neural network optimization. By embedding neural networks into the HBV hydrologic model to parameterize key modules, δ models achieve near-state-of-the-art streamflow prediction accuracy (median NSE of 0.732 across 671 U.S. basins) while producing physically consistent outputs like soil moisture, evapotranspiration, and baseflow.

ABSTRACT

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 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 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 dataset, compared to 0.748 from a state-of-the-art LSTM model with the same setup. For another forcing dataset, the difference is even smaller: 0.715 vs. 0.722. Meanwhile, the resulting learnable process-based models can output a full set of untrained variables, e.g., soil and groundwater storage, snowpack, evapotranspiration, and baseflow, and 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.

Motivation & Objective

• Address the limitations of purely data-driven deep learning models in hydrology, such as lack of interpretability and inability to predict untrained physical variables.
• Develop a hybrid modeling framework that retains physical process representation while enabling end-to-end differentiable learning.
• Enable regionalized parameterization of process-based models using neural networks to improve generalization across diverse hydroclimatic conditions.
• Ensure model outputs remain physically consistent and can be constrained by observations of untrained variables like evapotranspiration and baseflow.
• Demonstrate that physics-informed, learnable models can rival the predictive accuracy of state-of-the-art LSTM models without ensembles or post-processing.

Proposed method

• Use the HBV (Hydrologiska Byrån model) as a physical backbone for simulating the water cycle with process-based modules.
• Replace or enhance key HBV modules (e.g., snowmelt, soil moisture, routing) with differentiable neural networks trained via backpropagation.
• Apply regionalized parameterization by training models on basin-specific data, allowing transfer learning across hydroclimatically similar regions.
• Train the entire model end-to-end using a differentiable programming framework, enabling gradient-based optimization of both physical parameters and neural network weights.
• Use the Daymet meteorological forcing dataset and a second alternative dataset to evaluate model performance under different climatic conditions.
• Ensure physical consistency by allowing model outputs (e.g., evapotranspiration, baseflow) to be compared and constrained by independent observations.

Experimental results

Research questions

• RQ1 Can differentiable, learnable, process-based models achieve streamflow prediction accuracy comparable to state-of-the-art deep learning models like LSTM?
• RQ2 To what extent can neural networks enhance or replace process-based modules while preserving physical consistency and interpretability?
• RQ3 Can the proposed framework predict untrained physical variables (e.g., soil moisture, evapotranspiration, baseflow) with reasonable accuracy?
• RQ4 How does regionalized parameterization affect model generalization and performance across diverse U.S. basins?
• RQ5 Can the model’s outputs be meaningfully constrained by independent observations of physical variables beyond streamflow?

Key findings

• The δ model achieved a median Nash-Sutcliffe efficiency (NSE) of 0.732 across 671 U.S. basins using the Daymet forcing dataset, closely approaching the LSTM model’s performance of 0.748 under identical conditions.
• For a second forcing dataset, the δ model achieved an NSE of 0.715 compared to the LSTM’s 0.722, indicating near-parity in predictive accuracy.
• The model successfully generated physically consistent outputs for untrained variables, including evapotranspiration and baseflow, which showed decent agreement with alternative estimates.
• The framework enables end-to-end training of process-based models with differentiable neural networks, allowing gradient-based optimization of both physical and learned components.
• Regionalized parameterization significantly improved model generalization, enabling robust performance across diverse hydroclimatic regimes.
• The approach maintains physical interpretability while achieving performance levels previously attainable only by purely data-driven models.