Derivative-free optimization for large-scale nonlinear data assimilation problems

S. Gratton, P. Laloyaux, A. Sartenaer

Research output: Contribution to journalArticlepeer-review


The computation of derivatives and the development of tangent and adjoint codes represent a challenging issue and a major human time-consuming task when solving operational data assimilation problems. The ensemble Kalman filter provides a suitable derivative-free adaptation for the sequential approach by using an ensemble-based implementation of the Kalman filter equations. This article proposes a derivative-free variant for the variational approach, based on an iterative subspace minimization (ISM) technique. At each iteration, a subspace of low dimension is built from the relevant information contained in the empirical orthogonal functions (EOFs), allowing us to define a reduced 4D-Var subproblem which is then solved using a derivative-free optimization (DFO) algorithm. Strategies to improve the quality of the selected subspaces are presented, together with two numerical illustrations. The ISM technique is first compared with a basic stochastic ensemble Kalman filter on an academic shallow-water problem. The DFO algorithm embedded in the ISM technique is then validated in the NEMO framework, using its GYRE configuration.

Original languageEnglish
JournalQuarterly Journal of the Royal Meteorological Society
Publication statusAccepted/In press - 28 May 2013


  • 4D-Var
  • Derivative-free optimization
  • Empirical orthogonal functions


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