A low-rank approach to the solution of weak constraint variational data assimilation problems
For researchers in data assimilation, this work offers a memory-efficient solution to a known bottleneck in saddle point systems.
The paper presents a low-rank approach to solve weak constraint variational data assimilation problems, reducing storage requirements. Numerical experiments show the low-rank Krylov subspace solver is more effective than traditional solvers for the linear advection-diffusion equation and the non-linear Lorenz-95 model.
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.