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Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system

Chaos 18, 023112 (2008); doi:10.1063/1.2909862

Published 7 May 2008

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Alberto Carrassi,1 Michael Ghil,2,3 Anna Trevisan,4 and Francesco Uboldi5
1Institut Royal Météorologique de Belgique, 1180 Bruxelles, Belgium
2École Normale Supérieure, F-75231 Paris Cedex 05, France
3University of California, Los Angeles, California 90095-1567, USA
4ISAC-CNR, 40129 Bologna, Italy
5Consultant, 20026 Novate Milanese, Italy
We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method. ©2008 American Institute of Physics
History: Received 13 November 2007; accepted 26 March 2008; published 7 May 2008
Permalink: http://link.aip.org/link/?CHAOEH/18/023112/1
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KEYWORDS and PACS

Keywords
PACS
  • 93.85.Bc
    Computational methods and data processing in geophysics, data acquisition and storage
  • 05.45.Pq
    Numerical simulations of chaotic systems
  • YEAR: 2008

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PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
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