# Low-rank Approximations for Computing Observation Impact in 4D-Var Data Assimilation

arXiv: https://arxiv.org/abs/1307.5076 · HTML: https://mlsanity.com/paper/1307.5076/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2013.

## Built on by (most cited first, 3 of 3)

- [Efficient deep data assimilation with sparse observations and time-varying sensors](https://mlsanity.com/paper/2310.16187/) (2023)
- [Observation Error Covariance Specification in Dynamical Systems for Data assimilation using Recurrent Neural Networks](https://mlsanity.com/paper/2111.06447/) (2021)
- [TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functions](https://mlsanity.com/paper/2409.00244/) (2024)

## Abstract (arXiv)

We present an efficient computational framework to quantify the impact of individual observations in four dimensional variational data assimilation. The proposed methodology uses first and second order adjoint sensitivity analysis, together with matrix-free algorithms to obtain low-rank approximations of ob- servation impact matrix. We illustrate the application of this methodology to important applications such as data pruning and the identification of faulty sensors for a two dimensional shallow water test system.