Céline Robert

Reduced-order 4D-Var: a preconditioner for the Incremental 4D-Var data assimilation method

This study demonstrates how the incremental 4D-Var data assimilation method can be applied efficiently preconditione d in an application to an oceanographic problem. The approach consists in performing a few iterations of the reduced-order 4D-Var prior to the incremental 4D-Var in the full space in order to achieve faster convergence. An application performed in the tropical Pacific Ocean, with assimilation of TAO temperature data, shows the method to be both feasible and efficient. It allows the global cost of the assimilation to be reduced by a factor of 2 without affecting the quality of the solution.

A reduced-order strategy for 4D-Var data assimilation

This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EOF analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a multivariate background error covariance matrix Br, and an important decrease of the computational burden of the method, due to the drastic reduction of the dimension of the control space. An illustration of the feasibility and the effectiveness of this method are given in the academic framework of twin experiments for a model of the equatorial Pacific Ocean. It is shown that the multivariate aspect of Br brings additional information which substantially improves the identification procedure. Moreover the computational cost can be decreased by one order of magnitude with regard to the full-space 4D-Var method.

Comparison of reduced-order, sequential and variational data assimilation methods in the tropical Pacific Ocean

This paper presents a comparison of two reduced-order, sequential, and variational data assimilation methods: the singular evolutive extended Kalman filter (SEEK) and the reduced 4D-Var (R-4D-Var). A hybridization of the two, combining the variational framework and the sequential evolution of covariance matrices, is also preliminarily investigated and assessed in the same experimental conditions. The comparison is performed using the twin-experiment approach on a model of the tropical Pacific domain. The assimilated data are simulated temperature profiles at the locations of the TAO/TRITON array moorings. It is shown that, in a quasilinear regime, both methods produce similarly good results. However, the hybrid approach provides slightly better results and thus appears as potentially fruitful. In a more nonlinear regime, when tropical instability waves develop, the global nature of the variational approach helps control model dynamics better than the sequential approach of the SEEK filter. This aspect is probably enhanced by the context of the experiments in that there is a limited amount of assimilated data and no model error.