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    The Shape–Slope Relation in Observed Gamma Raindrop Size Distributions: Statistical Error or Useful Information?

    Source: Journal of Atmospheric and Oceanic Technology:;2003:;volume( 020 ):;issue: 008::page 1106
    Author:
    Zhang, Guifu
    ,
    Vivekanandan, J.
    ,
    Brandes, Edward A.
    ,
    Meneghini, Robert
    ,
    Kozu, Toshiaki
    DOI: 10.1175/1520-0426(2003)020<1106:TSRIOG>2.0.CO;2
    Publisher: American Meteorological Society
    Abstract: The three-parameter gamma distribution n(D) = N0Dµ exp(??D) is often used to characterize a raindrop size distribution (DSD). The parameters µ and ? correspond to the shape and slope of the DSD. If µ and ? are related to one another, as recent disdrometer measurements suggest, the gamma DSD model is simplified, which facilitates retrieval of rain parameters from remote measurements. It is important to determine whether the µ?? relation arises from errors in estimated DSD moments, or from natural rain processes, or from a combination of both statistical error and rain physics. In this paper, the error propagation from moment estimators to rain DSD parameter estimators is studied. The standard errors and correlation coefficient are derived through systematic error analysis. Using numerical simulations, errors in estimated DSD parameters are quantified. The analysis shows that errors in moment estimators do cause correlations among the estimated DSD parameters and cause a linear relation between estimators ?? and ??. However, the slope and intercept of the error-induced relation depend on the expected values µ and ?, and it differs from the µ?? relation derived from disdrometer measurements. Further, the mean values of the DSD parameter estimators are unbiased. Consequently, the derived µ?? relation is believed to contain useful information in that it describes the mean behavior of the DSD parameters and reflects a characteristic of actual raindrop size distributions. The µ?? relation improves retrievals of rain parameters from a pair of remote measurements such as reflectivity and differential reflectivity or attenuation, and it reduces the bias and standard error in retrieved rain parameters.
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      The Shape–Slope Relation in Observed Gamma Raindrop Size Distributions: Statistical Error or Useful Information?

    URI
    http://yetl.yabesh.ir/yetl1/handle/yetl/4157868
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    • Journal of Atmospheric and Oceanic Technology

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    contributor authorZhang, Guifu
    contributor authorVivekanandan, J.
    contributor authorBrandes, Edward A.
    contributor authorMeneghini, Robert
    contributor authorKozu, Toshiaki
    date accessioned2017-06-09T14:33:13Z
    date available2017-06-09T14:33:13Z
    date copyright2003/08/01
    date issued2003
    identifier issn0739-0572
    identifier otherams-2152.pdf
    identifier urihttp://onlinelibrary.yabesh.ir/handle/yetl/4157868
    description abstractThe three-parameter gamma distribution n(D) = N0Dµ exp(??D) is often used to characterize a raindrop size distribution (DSD). The parameters µ and ? correspond to the shape and slope of the DSD. If µ and ? are related to one another, as recent disdrometer measurements suggest, the gamma DSD model is simplified, which facilitates retrieval of rain parameters from remote measurements. It is important to determine whether the µ?? relation arises from errors in estimated DSD moments, or from natural rain processes, or from a combination of both statistical error and rain physics. In this paper, the error propagation from moment estimators to rain DSD parameter estimators is studied. The standard errors and correlation coefficient are derived through systematic error analysis. Using numerical simulations, errors in estimated DSD parameters are quantified. The analysis shows that errors in moment estimators do cause correlations among the estimated DSD parameters and cause a linear relation between estimators ?? and ??. However, the slope and intercept of the error-induced relation depend on the expected values µ and ?, and it differs from the µ?? relation derived from disdrometer measurements. Further, the mean values of the DSD parameter estimators are unbiased. Consequently, the derived µ?? relation is believed to contain useful information in that it describes the mean behavior of the DSD parameters and reflects a characteristic of actual raindrop size distributions. The µ?? relation improves retrievals of rain parameters from a pair of remote measurements such as reflectivity and differential reflectivity or attenuation, and it reduces the bias and standard error in retrieved rain parameters.
    publisherAmerican Meteorological Society
    titleThe Shape–Slope Relation in Observed Gamma Raindrop Size Distributions: Statistical Error or Useful Information?
    typeJournal Paper
    journal volume20
    journal issue8
    journal titleJournal of Atmospheric and Oceanic Technology
    identifier doi10.1175/1520-0426(2003)020<1106:TSRIOG>2.0.CO;2
    journal fristpage1106
    journal lastpage1119
    treeJournal of Atmospheric and Oceanic Technology:;2003:;volume( 020 ):;issue: 008
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
    yabeshDSpacePersian