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Derivative‐free optimization for large‐scale nonlinear data assimilation problems
Author(s) -
Gratton S.,
Laloyaux P.,
Sartenaer A.
Publication year - 2014
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.2169
Subject(s) - data assimilation , computer science , kalman filter , krylov subspace , mathematical optimization , linear subspace , ensemble kalman filter , subspace topology , computation , algorithm , extended kalman filter , mathematics , iterative method , artificial intelligence , physics , geometry , meteorology
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.