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    On the Evaluation of Boundary Errors in the Barnes Objective Analysis Scheme

    Source: Monthly Weather Review:;1990:;volume( 118 ):;issue: 005::page 1203
    Author:
    Pauley, Patricia M.
    DOI: 10.1175/1520-0493(1990)118<1203:OTEOBE>2.0.CO;2
    Publisher: American Meteorological Society
    Abstract: The spectral response of the Barnes objective analysis scheme near data boundaries is the focus of this note. First of all, a modification of the results presented by Achtemeier is described. In order for the weighted sum (or integral) defining the Barnes scheme to provide an unbiased estimate of the field at grid points, the sum (or integral) of the normalized weights must equal one. The normalizing factor is therefore written as an integral whose limits of integration are kept identical to those for the weighted integral of observations defining the scheme, even as the integral is truncated near a boundary. This modification serves to phrase the theoretical form of the Barnes scheme in a manner that is more consistent with the commonly used discrete form of the scheme. The amplitude and phase-shifted responses using the proposed normalization at an interpolation point on a boundary differ from Achtemeier's results by a factor of two. The amplitude and phase-shifted responses for a discrete application of the scheme are also examined using the Barnes scheme cast in rectangular coordinates. The amplitude and phase-shifted responses are integrated both using a small sampling interval to approximate the continuous case and using larger sampling intervals representative of typical observation spacings. These discrete results show that the phase shift near boundaries can be reduced by using a larger nondimensional sampling interval (or equivalently, a smaller smoothing scale length). However, this is at the expense of increasing the amplitude response of aliased unresolvable wavelengths. An estimate of the response at the boundary made from gridded values at the boundary confirms the discrete estimate of the response and the proposed modification of Achtemeier's results.
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      On the Evaluation of Boundary Errors in the Barnes Objective Analysis Scheme

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    http://yetl.yabesh.ir/yetl1/handle/yetl/4202415
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    contributor authorPauley, Patricia M.
    date accessioned2017-06-09T16:07:51Z
    date available2017-06-09T16:07:51Z
    date copyright1990/05/01
    date issued1990
    identifier issn0027-0644
    identifier otherams-61614.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4202415
    description abstractThe spectral response of the Barnes objective analysis scheme near data boundaries is the focus of this note. First of all, a modification of the results presented by Achtemeier is described. In order for the weighted sum (or integral) defining the Barnes scheme to provide an unbiased estimate of the field at grid points, the sum (or integral) of the normalized weights must equal one. The normalizing factor is therefore written as an integral whose limits of integration are kept identical to those for the weighted integral of observations defining the scheme, even as the integral is truncated near a boundary. This modification serves to phrase the theoretical form of the Barnes scheme in a manner that is more consistent with the commonly used discrete form of the scheme. The amplitude and phase-shifted responses using the proposed normalization at an interpolation point on a boundary differ from Achtemeier's results by a factor of two. The amplitude and phase-shifted responses for a discrete application of the scheme are also examined using the Barnes scheme cast in rectangular coordinates. The amplitude and phase-shifted responses are integrated both using a small sampling interval to approximate the continuous case and using larger sampling intervals representative of typical observation spacings. These discrete results show that the phase shift near boundaries can be reduced by using a larger nondimensional sampling interval (or equivalently, a smaller smoothing scale length). However, this is at the expense of increasing the amplitude response of aliased unresolvable wavelengths. An estimate of the response at the boundary made from gridded values at the boundary confirms the discrete estimate of the response and the proposed modification of Achtemeier's results.
    publisherAmerican Meteorological Society
    titleOn the Evaluation of Boundary Errors in the Barnes Objective Analysis Scheme
    typeJournal Paper
    journal volume118
    journal issue5
    journal titleMonthly Weather Review
    identifier doi10.1175/1520-0493(1990)118<1203:OTEOBE>2.0.CO;2
    journal fristpage1203
    journal lastpage1210
    treeMonthly Weather Review:;1990:;volume( 118 ):;issue: 005
    contenttypeFulltext
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