Symmetry-preserving nudging: theory and application to a shallow water model

Didier Auroux 1, 2 Silvère Bonnabel 3
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : One of the important topics in oceanography is the prediction of ocean circulation. The goal of data assimilation is to combine the mathematical information provided by the modeling of ocean dynamics with observations of the ocean circulation, e.g. measurements of the sea surface height (SSH). In this paper, we focus on a particular class of extended Kalman filters as a data assimilation method: nudging techniques, in which a corrective feedback term is added to the model equations. We consider here a standard shallow water model, and we define an innovation term that takes into account the measurements and respects the symmetries of the physical model. We prove the convergence of the estimation error to zero on a linear approximation of the system. It boils down to estimating the fluid velocity in a water-tank system using only SSH measurements. The observer is very robust to noise and easy to tune. The general nonlinear case is illustrated by numerical experiments, and the results are compared with the standard nudging techniques.
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Didier Auroux, Silvère Bonnabel. Symmetry-preserving nudging: theory and application to a shallow water model. [Research Report] RR-6677, INRIA. 2008. ⟨inria-00329162⟩

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