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

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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.
LanguageEnglish
Pages263–281
JournalJournal of Computational Physics
Volume357
Early online date2 Jan 2018
DOIs
StatusPublished - 15 Mar 2018

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assimilation
saddle points
Advection
linear systems
advection
Linear systems
formulations
requirements
optimization
Experiments

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title = "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.",
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