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    Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms

    Source: Monthly Weather Review:;2013:;volume( 142 ):;issue: 002::page 755
    Author:
    Janjić, Tijana
    ,
    McLaughlin, Dennis
    ,
    Cohn, Stephen E.
    ,
    Verlaan, Martin
    DOI: 10.1175/MWR-D-13-00056.1
    Publisher: American Meteorological Society
    Abstract: his paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate nonnegativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a nonnegativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.
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      Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4230161
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    contributor authorJanjić, Tijana
    contributor authorMcLaughlin, Dennis
    contributor authorCohn, Stephen E.
    contributor authorVerlaan, Martin
    date accessioned2017-06-09T17:31:04Z
    date available2017-06-09T17:31:04Z
    date copyright2014/02/01
    date issued2013
    identifier issn0027-0644
    identifier otherams-86587.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4230161
    description abstracthis paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate nonnegativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a nonnegativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.
    publisherAmerican Meteorological Society
    titleConservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms
    typeJournal Paper
    journal volume142
    journal issue2
    journal titleMonthly Weather Review
    identifier doi10.1175/MWR-D-13-00056.1
    journal fristpage755
    journal lastpage773
    treeMonthly Weather Review:;2013:;volume( 142 ):;issue: 002
    contenttypeFulltext
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