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

TL;DR

This study compares data assimilation methods for differentiable hydrologic models, demonstrating that variational DA can significantly improve streamflow forecasts, matching or surpassing LSTM-based approaches across various US regions.

Contribution

Developed variational data assimilation methods tailored for physics-informed differentiable hydrologic models, showing their effectiveness in improving forecast accuracy without systematic training data.

Findings

Variational DA improves NSE from 0.75 to 0.82 for one-day lead forecasts.

Differentiable models benefit equally from variational DA as LSTM models.

Both precipitation and state adjusters are crucial for optimal performance.

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.