Multilevel Model for Gage and Paleoflood Data
Publication: Journal of Water Resources Planning and Management
Volume 120, Issue 4
Abstract
A model is developed to estimate the parameters of a lognormal flow‐frequency distribution, and it can include multiple historical or paleoflood periods in which the largest flow within the period is defined and a current gage record. Asymptotic approximations of the variances and covariances of the distribution parameters are presented and used to compute first‐order approximations of the standard deviations of 100‐year and 500‐year floods. The model is applied to gage paleoflood data for Black Bear Creek at Pawnee, Oklahoma. Distribution parameters, their approximate variances and covariance and , and their standard deviations were computed. A simulation experiment using 300 samples was performed. The and estimated using the multiple‐period model had lower standard errors than those estimated using either a single‐threshold or gage‐record‐only model. First‐order approximations of the standard deviations of and were compared to the simulation results and the largest error was 13%.
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References
1.
Bain, L. J., and Englehardt, M. (1987). Introduction to probability and mathematical statistics. Duxbury Press, Boston, Mass.
2.
Cohn, T. A., and Stedinger, J. R. (1987). “Use of historical information in a maximum likelihood framework.” J. Hydrol., 96, 215–223.
3.
Condie, R. (1986). Flood samples from a three parameter lognormal population with historic information: the asymptotic standard error of estimate of the T‐year flood. J. Hydrol., 85, 139–150.
4.
Condie, R., and Lee, K. A. (1982). “Flood frequency analysis with historic information.” J. Hydrol., 58, 47–61.
5.
Fisher, R. A. (1992). “On the mathematical foundations of theoretical statistics.” Philosophical Trans. of the Royal Soc. of London, Series A, London, England, 222, 323–368.
6.
“Guidelines for determining flood flow frequency.” (1982). Bull. 17B, U.S. Water Resources Council Hydrology Subcommittee, U.S. Geological Survey, Reston, Va.
7.
Haan, C. T. (1977). Statistical methods in hydrology. Iowa State University Press, Ames, Iowa.
8.
McQueen, K. C. (1991). “Late Holocene paleoflood reconstruction of Lower Black Bear Creek in North Central Oklahoma,” PhD thesis, Oklahoma State University, Stillwater, Okla.
9.
Stedinger, J. R., and Cohn, T. A. (1986). “Flood frequency analysis with historical and paleoflood information.” Water Resour. Res., 22(5), 785–793.
10.
Wilkinson, L. (1990). SYSTAT: the system for statistics. SYSTAT, Inc., Evanston, Ill.
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Copyright © 1994 American Society of Civil Engineers.
History
Received: Jun 15, 1992
Published online: Jul 1, 1994
Published in print: Jul 1994
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