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.

27 pages, 16 figures, submitted to Journal of Computational Physics

Cited by in corpus (4)

• On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation
• Stochastic Discontinuous Galerkin Methods for Robust Deterministic Control of Convection Diffusion Equations with Uncertain Coefficients
• Stein-based preconditioners for weak-constraint 4D-var
• Stochastic Discontinuous Galerkin Methods with Low--Rank Solvers for Convection Diffusion Equations