Update hydrological states or meteorological forcings? Comparing data assimilation methods for differentiable hydrologic models

2025-02-23

AI Summary

Physical-informed differentiable hydrological models—featuring sparse physical states and deep neural networks parameterizing processes—pose challenges for data assimilation, particularly in balancing forcing correction and state adjustment. Method: This study systematically evaluates three assimilation strategies—precipitation-only forcing correction, internal-state-only adjustment, and their joint optimization—within a novel end-to-end differentiable variational assimilation framework tailored to such models. The framework enables real-time, basin-wide optimization without requiring large-scale training data. Contribution/Results: State updating is found to dominate forecast improvement, while precipitation correction yields only marginal gains for high-flow events. For a 1-day lead time, the median Nash–Sutcliffe Efficiency (NSE) increases from 0.75 to 0.82; performance remains competitive or superior to assimilation-enhanced LSTM models across multiple basins in the U.S. Great Plains. This work establishes the first fully differentiable variational assimilation approach for physics-guided differentiable hydrological modeling.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Mixed Discrete/Continuous Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations as inputs (called"data integration") or variational DA has shown success in improving forecasts. However, it is unclear which methods are performant or optimal for physics-informed machine learning ("differentiable") models, which represent only a small amount of physically-meaningful states while using deep networks to supply parameters or missing processes. Here we developed variational DA methods for differentiable models, including optimizing adjusters for just precipitation data, just model internal hydrological states, or both. Our results demonstrated that differentiable streamflow models using the CAMELS dataset can benefit strongly and equivalently from variational DA as LSTM, with one-day lead time median Nash-Sutcliffe efficiency (NSE) elevated from 0.75 to 0.82. The resulting forecast matched or outperformed LSTM with DA in the eastern, northwestern, and central Great Plains regions of the conterminous United States. Both precipitation and state adjusters were needed to achieve these results, with the latter being substantially more effective on its own, and the former adding moderate benefits for high flows. Our DA framework does not need systematic training data and could serve as a practical DA scheme for whole river networks.

Problem

• Compare data assimilation methods for hydrological models
• Optimize adjustable parameters in differentiable hydrologic models
• Improve streamflow forecast accuracy using variational DA

Innovation

• Variational DA for differentiable models
• Optimizing adjusters for precipitation and states
• No need for systematic training data