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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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Nonlin. Processes Geophys., 15, 305-319, 2008
© Author(s) 2008. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.
27 Mar 2008
A nudging-based data assimilation method: the Back and Forth Nudging (BFN) algorithm
D. Auroux1 and J. Blum2 1Institut de Mathématiques de Toulouse, Université Paul Sabatier Toulouse 3, 31062 Toulouse Cedex 9, France
2Laboratoire J. A. Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 2, France
Abstract. This paper deals with a new data assimilation algorithm, called Back and Forth Nudging. The standard nudging technique consists in adding to the equations of the model a relaxation term that is supposed to force the observations to the model. The BFN algorithm consists in repeatedly performing forward and backward integrations of the model with relaxation (or nudging) terms, using opposite signs in the direct and inverse integrations, so as to make the backward evolution numerically stable. This algorithm has first been tested on the standard Lorenz model with discrete observations (perfect or noisy) and compared with the variational assimilation method. The same type of study has then been performed on the viscous Burgers equation, comparing again with the variational method and focusing on the time evolution of the reconstruction error, i.e. the difference between the reference trajectory and the identified one over a time period composed of an assimilation period followed by a prediction period. The possible use of the BFN algorithm as an initialization for the variational method has also been investigated. Finally the algorithm has been tested on a layered quasi-geostrophic model with sea-surface height observations. The behaviours of the two algorithms have been compared in the presence of perfect or noisy observations, and also for imperfect models. This has allowed us to reach a conclusion concerning the relative performances of the two algorithms.

Citation: Auroux, D. and Blum, J.: A nudging-based data assimilation method: the Back and Forth Nudging (BFN) algorithm, Nonlin. Processes Geophys., 15, 305-319,, 2008.
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