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

Abstract

AbstractThe 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.