Analysis of Bivariate Censored Low Flows
Publication: Journal of Hydraulic Engineering
Volume 122, Issue 2
Abstract
In this paper, a bivariate model is established to characterize the seven-day, two-year (Q 7,2 ) and seven-day, 10-year (Q 7,10 ) low flows of streams in West-Central Florida under the restriction of Q 7,10 ≤ Q 7,2 . Analysis of prediction errors showed that our model describes these stream low flows well. The measurements under the detection limit were treated as censored data and a bivariate imputation method was developed to impute them into pseudo-complete samples. All-subsets regression was applied to these imputed data for selecting appropriate models, which link the low flows to their basin characteristics. The parameters are first estimated by the least-squares method in a bivariate normal regression and then adjusted to yield their maximum likelihood estimates. This process of imputation, model selection and parameter estimation is repeated iteratively until convergence of the selected model terms, parameter estimates, and imputed data. With the established model, predictions of low flows can be made at gauged and ungauged sites according to their basin variables for water-resources management.
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References
1.
Alley, W. M., and Burns, A. W.(1983). “Mixed station extension of monthly stream flow records.”J. of Hydr. Engrg., 109(10), 1271–1284.
2.
Collings, M. R. (1971). “A proposed streamflow data program for Washington state.”Open-File Rep., U.S. Geological Survey, Washington, D.C.
3.
Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). “Maximum likelihood from incomplete data via the EM algorithm.”J. R. Statist. Soc., B(39), 1–38.
4.
Draper, N. R., and Smith, H. (1981). Applied regression analysis, 2nd Ed., John Wiley, New York, N.Y.
5.
Hamada, M., and Wu, C. F. J.(1991). “Analysis of censored data from highly fractionated experiments.”Technometrics, 33, 25–38.
6.
Hammett, K. M. (1984). “Low-flow frequency analysis for streams in west-central Florida.”Water Resour. Investigation Rep. 84-4299, U.S. Geological Survey, Washington, D.C.
7.
Hirsch, R. M.(1979). “An evaluation of some record reconstruction techniques.”Water Resour. Res., 15(6), 1781–1790.
8.
Hirsch, R. M.(1982). “A comparison of four stream flow record extension techniques.”Water Resour. Res., 18(4), 1081–1088.
9.
Lawless, J. F. (1982). Statistical models and methods for lifetime data, John Wiley & Sons, Inc., New York.
10.
Liu, S., and Stedinger, J. R. (1991). “Low stream flow frequency analysis with ordinary and Tobit regression.”Water Resour. Plng. and Mgmt. and Urban Water Resour., J. L. Anderson, ed., ASCE, New York, N.Y., 27–31.
11.
Lu, J. C., and Unal, C.(1993). “Process characterization and optimization based on censored data from highly fractionated experiments.”IEEE Trans. on Reliability, 43(1), 145–155.
12.
Rabon, J. W. (1971). “Evaluation of streamflow data program in Florida.”Open-File Rep. F1-7008. U.S. Geological Survey, Washington, D.C.
13.
Riggs, H. G.(1965). “Estimating probability distributions of drought flows.”Water and Sewage Works, 112(5), 153–157.
14.
Riggs, H. G. (1968). Frequency curves: U.S. Geological Survey techniques of water resources investigations . Book 4, Chapter A2, U.S. Geological Survey, Washington, D.C.
15.
Riggs, H. G. (1972). Low-flow investigations, U.S. Geological Survey techniques of water resources investigations, Book 4, Chapter B1, U.S. Geological Survey, Washington, D.C.
16.
SAS Version 6. (1989). SAS Institute Inc., Cary, N.C.
17.
Stedinger, J. R., and Tasker, G. D. (1992). “Generalized least square analyses for hydrologic regionalization.”Envir. Engrg., Saving a Threatened Resour. in Search of Solutions, Proc., Envir. Engrg. Sessions Water Forum '92, ASCE, New York, N.Y.
18.
Stedinger, J. R., and Thomas, W. O. Jr. (1985). “Low-flow frequency estimation using base-flow measurements.”U.S.G.S., Open-File Rep. 89-95. U.S. Geological Survey, Washington, D.C.
19.
Tasker, G. D. (1989). “Regionalization of low flow characteristics using logistic and GLS Regression.”New Directions for Surface Water Modeling—Proceedings of the Baltimore Symposium, IAHS Publication No. 181, 323–331.
20.
Thomas, M. P., and Cervione, M. A. Jr. (1970). “A proposed streamflow data program for Connecticut.”Water Resour. Commission, Bull., 23.
21.
Tobin, J.(1958). “Estimation of relationships for limited dependent var- iables.”Econometrica, 26, 24–36.
22.
Vogel, R. M., and Kroll, C. N.(1990). “Generalized low-flow frequency relationships for ungaged sites in Massachusetts.”Water Resour. Bull., 26(2), 241–253.
23.
Vogel, R. M., and Stedinger, J. R.(1985). “Minimum variance streamflow record augmention procedures.”Water Resour. Res., 21(5), 715–723.
24.
Wu, C. F. J.(1983). “On the convergence properties of the EM algorithm.”Ann. of Statistics, 11(1), 95–103.
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Information
Published In
Journal of Hydraulic Engineering
Volume 122 • Issue 2 • February 1996
Pages: 97 - 103
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Feb 1, 1996
Published in print: Feb 1996
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