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

Melina Freitag, Daniel Green

Research output: Contribution to journalArticle

2 Citations (Scopus)
30 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)263–281
Number of pages19
JournalJournal of Computational Physics
Early online date2 Jan 2018
Publication statusPublished - 15 Mar 2018



  • Data assimilation
  • Iterative methods
  • Low-rank methods
  • Matrix equations
  • Preconditioning
  • Weak constraint 4D-Var

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

Cite this