Persistent Link:
http://hdl.handle.net/10150/300257
Title:
A Solution to Small Sample Bias in Flood Estimation
Author:
Metler, William
Affiliation:
Systems & Industrial Engineering, University of Arizona, Tucson, Arizona 85721
Issue Date:
6-May-1972
Rights:
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.
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
ISSN:
0272-6106

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleA Solution to Small Sample Bias in Flood Estimationen_US
dc.contributor.authorMetler, Williamen_US
dc.contributor.departmentSystems & Industrial Engineering, University of Arizona, Tucson, Arizona 85721en_US
dc.date.issued1972-05-06-
dc.rightsCopyright ©, where appropriate, is held by the author.en_US
dc.description.collectioninformationThis 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.en_US
dc.publisherArizona-Nevada Academy of Scienceen_US
dc.identifier.journalHydrology and Water Resources in Arizona and the Southwesten_US
dc.description.abstractIn 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.en_US
dc.subjectHydrology -- Arizona.en_US
dc.subjectWater resources development -- Arizona.en_US
dc.subjectHydrology -- Southwestern states.en_US
dc.subjectWater resources development -- Southwestern states.en_US
dc.subjectFlood forecastingen_US
dc.subjectSamplingen_US
dc.subjectAlgorithmsen_US
dc.subjectDesign criteriaen_US
dc.subjectStatistical modelsen_US
dc.subjectCulvertsen_US
dc.subjectBridgesen_US
dc.subjectRegression analysisen_US
dc.subjectEquationsen_US
dc.subjectHistoryen_US
dc.subjectStream gagesen_US
dc.subjectAverage flowen_US
dc.subjectPeak dischargeen_US
dc.subjectRegional flooden_US
dc.subjectRegional developmenten_US
dc.subjectMissourien_US
dc.identifier.issn0272-6106-
dc.identifier.urihttp://hdl.handle.net/10150/300257-
dc.identifier.journalHydrology and Water Resources in Arizona and the Southwesten_US
dc.typetexten_US
dc.typeProceedingsen_US
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