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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:357

Article

Freitag, Melina A.¹  Green, Daniel L. H.¹ 

[1] Univ Bath, Dept Math Sci, Claverton Down BA2 7AY, England

关键词: Data assimilation;    Weak constraint 4D-Var;    Iterative methods;    Matrix equations;    Low-rank methods;    Preconditioning;   

DOI  :  10.1016/j.jcp.2017.12.039

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free