# Background Error Covariance Iterative Updating with Invariant Observation Measures for Data Assimilation

arXiv: https://arxiv.org/abs/1910.09408 · HTML: https://mlsanity.com/paper/1910.09408/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2019.

## Built on by (most cited first, 6 of 6)

- [Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models](https://mlsanity.com/paper/2204.03497/) (2022)
- [Observation Error Covariance Specification in Dynamical Systems for Data assimilation using Recurrent Neural Networks](https://mlsanity.com/paper/2111.06447/) (2021)
- [Multi-fidelity physics constrained neural networks for dynamical systems](https://mlsanity.com/paper/2402.02031/) (2024)
- [Mean flow data assimilation using physics-constrained Graph Neural Networks](https://mlsanity.com/paper/2411.09476/) (2024)
- [Surrogate-based variational data assimilation for tidal modelling](https://mlsanity.com/paper/2106.11926/) (2021)
- [Spatiotemporal System Forecasting with Irregular Time Steps via Masked Autoencoder](https://mlsanity.com/paper/2603.25597/) (2026)

## Abstract (arXiv)

In order to leverage the information embedded in the background state and observations, covariance matrices modelling is a pivotal point in data assimilation algorithms. These matrices are often estimated from an ensemble of observations or forecast differences. Nevertheless, for many industrial applications the modelling still remains empirical based on some form of expertise and physical constraints enforcement in the absence of historical observations or predictions. We have developed two novel robust adaptive assimilation methods named CUTE (Covariance Updating iTerativE) and PUB (Partially Updating BLUE). These two non-parametric methods are based on different optimization objectives, both capable of sequentially adapting background error covariance matrices in order to improve assimilation results under the assumption of a good knowledge of the observation error covariances. We have compared these two methods with the standard approach using a misspecified background matrix in a shallow water twin experiments framework with a linear observation operator. Numerical experiments have shown that the proposed methods bear a real advantage both in terms of posterior error correlation identification and assimilation accuracy.