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    Analysis Scheme in the Ensemble Kalman Filter

    Source: Monthly Weather Review:;1998:;volume( 126 ):;issue: 006::page 1719
    Author:
    Burgers, Gerrit
    ,
    Jan van Leeuwen, Peter
    ,
    Evensen, Geir
    DOI: 10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2
    Publisher: American Meteorological Society
    Abstract: This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low. This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach.
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      Analysis Scheme in the Ensemble Kalman Filter

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4204108
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    contributor authorBurgers, Gerrit
    contributor authorJan van Leeuwen, Peter
    contributor authorEvensen, Geir
    date accessioned2017-06-09T16:11:59Z
    date available2017-06-09T16:11:59Z
    date copyright1998/06/01
    date issued1998
    identifier issn0027-0644
    identifier otherams-63138.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4204108
    description abstractThis paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low. This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach.
    publisherAmerican Meteorological Society
    titleAnalysis Scheme in the Ensemble Kalman Filter
    typeJournal Paper
    journal volume126
    journal issue6
    journal titleMonthly Weather Review
    identifier doi10.1175/1520-0493(1998)126<1719:ASITEK>2.0.CO;2
    journal fristpage1719
    journal lastpage1724
    treeMonthly Weather Review:;1998:;volume( 126 ):;issue: 006
    contenttypeFulltext
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