A low-rank approach to the solution of weak constraint variational data assimilation problems
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.
Cite
@article{arxiv.1702.07278,
title = {A low-rank approach to the solution of weak constraint variational data assimilation problems},
author = {Melina A. Freitag and Daniel L. H. Green},
journal= {arXiv preprint arXiv:1702.07278},
year = {2018}
}
Comments
27 pages, 16 figures, submitted to Journal of Computational Physics