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Title

The shape-slope relation in observed gamma raindrop size distributions: Statistical error or useful information?

Abstract

The three-parameter gamma distribution n( D) 5 N0Dmu exp(-LambdaD) is often used to characterize a raindrop size distribution ( DSD). The parameters m and L correspond to the shape and slope of the DSD. If mu and Lambda 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 mu-Lambda 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 (μ) over cap and (&ULambda;) over tilde. However, the slope and intercept of the error-induced relation depend on the expected values mu and Lambda, and it differs from the m - L relation derived from disdrometer measurements. Further, the mean values of the DSD parameter estimators are unbiased. Consequently, the derived mu-Lambda 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 mu-Lambda 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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document

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http://n2t.net/ark:/85065/d73r0tjr

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eng

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geoscientificInformation

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publication

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2016-01-01T00:00:00Z

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publication

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2003-08-01T00:00:00Z

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Copyright 2003 American Meteorological Society (AMS). Permission to use figures, tables, and brief excerpts from this work in scientific and educational works is hereby granted provided that the source is acknowledged. Any use of material in this work that is determined to be "fair use" under Section 107 or that satisfies the conditions specified in Section 108 of the U.S. Copyright Law (17 USC, as revised by P.L. 94-553) does not require the Society's permission. Republication, systematic reproduction, posting in electronic form on servers, or other uses of this material, except as exempted by the above statements, requires written permission or license from the AMS. Additional details are provided in the AMS Copyright Policies, available from the AMS at 617-227-2425 or amspubs@ametsoc.org. Permission to place a copy of this work on this server has been provided by the AMS. The AMS does not guarantee that the copy provided here is an accurate copy of the published work.

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OpenSky Support

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UCAR/NCAR - Library

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PO Box 3000

Boulder

80307-3000

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opensky@ucar.edu

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http://opensky.ucar.edu/

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