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

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.