Derivative‐free optimization for large‐scale nonlinear data assimilation problems. (22nd May 2013)

• Record Type: Journal Article
• Authors: Gratton, S.; Laloyaux, P.; Sartenaer, A.
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 140:Number 680(2014:Apr.)
• Page Start: 943
• Page End: 957
• Publication Date: 2013-05-22
• Subjects: Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.2169
• Languages: English
• ISSNs: 0035-9009

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>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.</p> </abstract>