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

arXiv: https://arxiv.org/abs/2502.16444 · HTML: https://mlsanity.com/paper/2502.16444/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 48 references that are in the map.
- First posted on arXiv 23 Feb 2025.

## Builds on (most cited first, 7 of 7)

- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [Towards Learning Universal, Regional, and Local Hydrological Behaviors via Machine-Learning Applied to Large-Sample Datasets](https://mlsanity.com/paper/1907.08456/) (2019)
- [A trans-disciplinary review of deep learning research for water resources scientists](https://mlsanity.com/paper/1712.02162/) (2017)
- [A Survey on Large-scale Machine Learning](https://mlsanity.com/paper/2008.03911/) (2020)
- [Enhancing streamflow forecast and extracting insights using long-short term memory networks with data integration at continental scales](https://mlsanity.com/paper/1912.08949/) (2019)
- [Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracy](https://mlsanity.com/paper/2203.14827/) (2022)
- [The data synergy effects of time-series deep learning models in hydrology](https://mlsanity.com/paper/2101.01876/) (2021)

## Abstract (arXiv)

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.