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    A Solution to Small Sample Bias in Flood Estimation

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    Author
    Metler, William
    Affiliation
    Systems & Industrial Engineering, University of Arizona, Tucson, Arizona 85721
    Issue Date
    1972-05-06
    Keywords
    Hydrology -- Arizona.
    Water resources development -- Arizona.
    Hydrology -- Southwestern states.
    Water resources development -- Southwestern states.
    Flood forecasting
    Sampling
    Algorithms
    Design criteria
    Statistical models
    Culverts
    Bridges
    Regression analysis
    Equations
    History
    Stream gages
    Average flow
    Peak discharge
    Regional flood
    Regional development
    Missouri
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    Copyright ©, where appropriate, is held by the author.
    Collection Information
    This article is part of the Hydrology and Water Resources in Arizona and the Southwest collections. Digital access to this material is made possible by the Arizona-Nevada Academy of Science and the University of Arizona Libraries. For more information about items in this collection, contact anashydrology@gmail.com.
    Publisher
    Arizona-Nevada Academy of Science
    Journal
    Hydrology and Water Resources in Arizona and the Southwest
    Abstract
    In order to design culverts and bridges, it is necessary to compute an estimate of the design flood. Regionalization of flows by regression analysis is currently the method advocated by the U.S. Geological Survey to provide an estimate of the culvert and bridge design floods. In the regression analysis a set of simultaneous equations is solved for the regression coefficients which will be used to compute a design flood prediction for a construction site. The dependent variables in the set of simultaneous equations are the historical estimates of the design flood computed from the historical records of gaged sites in a region. If a log normal distribution of the annual peak flows is assumed, then the historical estimate of the design flood for site i may be computed by the normal as log Q(d,i) = x(i) + k(d)s(i). However because of the relatively small samples of peak flows commonly used in this problem, this paper shows that the historical estimate should be computed by to log Q(d,i) = X(i) + t(d,n-1) √((n+1)/n) s(i) where t(d,n-1) is obtained from tables of the Student's t. This t-estimate when used as input to the regression analysis provides a more realistic prediction in light of the small sample size, than the estimate yielded by the normal.
    ISSN
    0272-6106
    Collections
    Hydrology and Water Resources in Arizona and the Southwest, Volume 02 (1972)

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