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    Advanced Data Assimilation in Strongly Nonlinear Dynamical Systems

    Source: Journal of the Atmospheric Sciences:;1994:;Volume( 051 ):;issue: 008::page 1037
    Author:
    Miller, Robert N.
    ,
    Ghil, Michael
    ,
    Gauthiez, François
    DOI: 10.1175/1520-0469(1994)051<1037:ADAISN>2.0.CO;2
    Publisher: American Meteorological Society
    Abstract: Advanced 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.
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      Advanced Data Assimilation in Strongly Nonlinear Dynamical Systems

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4157473
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    contributor authorMiller, Robert N.
    contributor authorGhil, Michael
    contributor authorGauthiez, François
    date accessioned2017-06-09T14:32:11Z
    date available2017-06-09T14:32:11Z
    date copyright1994/04/01
    date issued1994
    identifier issn0022-4928
    identifier otherams-21164.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4157473
    description abstractAdvanced 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.
    publisherAmerican Meteorological Society
    titleAdvanced Data Assimilation in Strongly Nonlinear Dynamical Systems
    typeJournal Paper
    journal volume51
    journal issue8
    journal titleJournal of the Atmospheric Sciences
    identifier doi10.1175/1520-0469(1994)051<1037:ADAISN>2.0.CO;2
    journal fristpage1037
    journal lastpage1056
    treeJournal of the Atmospheric Sciences:;1994:;Volume( 051 ):;issue: 008
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
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