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Advanced data assimilation in strongly nonlinear dynamical systemsAdvanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.
Document ID
19950031207
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Miller, Robert N.
(Oregon State Univ. Corvallis, OR, United States)
Ghil, Michael
(Univ. of California, Los Angeles, Los Angeles, CA United States)
Gauthiez, Francois
(Ecole Polytechnique Palaiseau, France)
Date Acquired
August 16, 2013
Publication Date
April 15, 1994
Publication Information
Publication: Journal of the Atmospheric Sciences
Volume: 51
Issue: 8
ISSN: 0022-4928
Subject Category
Meteorology And Climatology
Accession Number
95A62806
Funding Number(s)
CONTRACT_GRANT: NSF OCE-88-00004
CONTRACT_GRANT: N00014-90-J-1125
CONTRACT_GRANT: NSF OCE-89-19439
CONTRACT_GRANT: N00014-90-J-1481
Distribution Limits
Public
Copyright
Other

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