# A low-rank approach to the solution of weak constraint variational data assimilation problems

## TL;DR

This paper introduces a low-rank Krylov subspace method for weak constraint 4D-Var data assimilation, reducing storage needs and improving efficiency in solving large saddle point systems.

## Contribution

It presents a novel low-rank approach leveraging matrix equation techniques to efficiently solve weak constraint 4D-Var problems, addressing large storage issues.

## Key findings

- Low-rank solver reduces memory requirements.
- Method outperforms traditional solvers in experiments.
- Effective for both linear and non-linear models.

## Abstract

Weak constraint four-dimensional variational data assimilation is an important method for incorporating data (typically observations) into a model. The linearised system arising within the minimisation process can be formulated as a saddle point problem. A disadvantage of this formulation is the large storage requirements involved in the linear system. In this paper, we present a low-rank approach which exploits the structure of the saddle point system using techniques and theory from solving large scale matrix equations. Numerical experiments with the linear advection-diffusion equation, and the non-linear Lorenz-95 model demonstrate the effectiveness of a low-rank Krylov subspace solver when compared to a traditional solver.

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Source: https://tomesphere.com/paper/1702.07278