Reliability Indices for Water Supply Systems
Publication: Journal of Water Resources Planning and Management
Volume 113, Issue 4
Abstract
In the design of hydraulic structures for flood control, it has become standard practice to employ the average return period of a flood as the design event. This study introduces an analogous index for the design of a water supply system: the average return period of a reservoir system failure, defined as the expected number of years until the first reservoir system failure. Here a failure is defined as a year in which the prespecified yield could not be delivered by a water supply system. The mean and variance of the time until the first reservoir system failure are derived, as are the mean and variance of the duration of a reservoir system failure for a simple Markov failure model. Other indices of the reliability of a water supply system are also introduced. The assumption that sequences of reservoir surplus and failures can be represented by a two‐state Markov chain is validated for the Pacific Northwest Hydroelectric Power System.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Barnes, F. B., “Storage Required for a City Water Supply,” Journal of the Institute of Engineers (Australia) Vol. 26, No. 198, 1954.
2.
Chow, V. T., Ed., Handbook of Applied Hydrology, McGraw Hill Book Co. Inc., New York, N.Y., 1964.
3.
Dean, L. A., and Polos, J. A., Frequency of Failures to Meet Firm Loads for the Pacific Northwest Hydroelectric System, Bonneville Power Administration, Division of Power Supply, Portland, Oreg., 1983, (unpublished report).
4.
Fiering, M. B, “Statistical Analysis of the Reservoir Storage‐Yield Relations,” Operations Research in Water Quality Management, H. A. Thomas, Jr., and R. P. Burden, Eds., Harvard Water Resources Group, Cambridge, Mass., 1963.
5.
Fiering, M. B, Streamflow Synthesis, Harvard University Press, Cambridge, Mass., 1967.
6.
Gumbel, E. J., “The Calculated Risk in Flood Control,” Applied Science Research, Vol. 5A, 1955, The Hague, The Netherlands, pp. 272–280.
7.
Gumbel, E. J., “The Return Period of Flood Flows,” Annals of Mathematical Statistics, Vol. 12, No. 2, 1941, pp. 163–190.
8.
Haan, C. T., Statistical Methods in Hydrology, The Iowa State University Press, Ames, Iowa, 1977.
9.
Hashimoto, T., Stedinger, J. R., and Loucks, D. P., “Robustness of Water Resource Systems,” Water Resources Research, Vol. 18, No. 1., Feb., 1982, pp. 21–26.
10.
Hirsch, R. M., “Synthetic Hydrology and Water Supply Reliability,” Water Resources Research, Vol. 15, No. 6, Dec., 1979, pp. 1603–1615.
11.
Jackson, B. B., “Markov Mixture Models for Drought Lengths,” Water Resources Research, Vol. 11, No. 1, Feb., 1975, pp. 64–74.
12.
Klemes, V., “Applied Storage Theory in Evolution,” Advances in Hydroscience, Vol. 12, 1979, pp. 79–141.
13.
Klemes, V., “Reliability Estimates for a Storage Reservoir with Seasonal Input,” Journal of Hydrology, Vol. 7, No. 2, 1969, pp. 198–216.
14.
Klemes, V., “Reliability of a Water Supply Performed by Means of a Storage Reservoir Within a Limited Period of Time,” Journal of Hydrology, Vol. 5, 1967, pp. 70–92.
15.
Klemes, V., “Some Problems in Pure and Applied Stochastic Hydrology,” Miscellaneous Publication No. 1275, Agricultural Research Service, U.S. Dept. of Agriculture, Washington, D.C., 1974.
16.
Klemes, V., Srikanthan, R., and McMahon, T. A. “Long‐Memory Flow Models in Reservoir Analysis: What is their Practical Value?,” Water Resources Research, Vol. 17, No. 3, Jan., 1981, pp. 737–751.
17.
Linsley, R. K., and Franzini, J. B., Water Resources Engineering, McGraw‐Hill Book Co., New York, N.Y., 1979, pp. 157–158.
18.
Linsley, R. K., Kohler, M. A., and Paulhus, J. L. H., Hydrology for Engineers, McGraw‐Hill Book Co., New York, N.Y., 1982.
19.
Maass, A., Hufschmidt, M. M., Dorfman, R., Thomas, H. A., Marglin, A., and Fair, G. M., Design of Water Resource Systems, Harvard University Press, Cambridge, Mass., 1962.
20.
Moran, P. A. P., “Probability Theory of Dams and Storage Systems,” Australian Journal of Applied Science, Vol. 5, 1954.
21.
Palmer, R. N., Smith, J. A., Cohon, J. L., and ReVelle, C. S., “Reservoir Management in Potomic River Basin,” Journal of the Water Resources Planning and Management Division, ASCE, Vol. 108, No. 1, Mar., 1982, pp. 47–66.
22.
Peavy, H. S., Rowe, D. R., and Tchobanoglous, G., Environmental Engineering, McGraw‐Hill Book Co., New York, N.Y., 1985, pp. 329–331.
23.
Rippl, W., “The Capacity of Storage‐Reservoirs for Water‐Supply,” Minutes of the Proceedings of the Institute of Civil Engineers, Vol. LXXI, 1983, pp. 270–278.
24.
Ross, S., A First Course in Probability, Macmillan Publishing Co., Inc., New York, N.Y., 1976.
25.
Sheer, D. P., and Flynn, K., “Water Supply,” Civil Engineering, ASCE, Vol. 53, No. 6, Jun., 1983, pp. 50–53.
26.
Stedinger, J. R., Sule, B. F., and Pei, D., “Multiple Reservoir System Screening Models,” Water Resources Research, Vol. 19, No. 6, Dec., 1983, pp. 1383–1393.
27.
Steel, E. W., and McGhee, T. J., Water Supply and Sewage, McGraw‐Hill Book Co., New York, N.Y., 1979, pp. 44–47.
28.
Sudler, C. E., “Storage Required for the Regulation of Streamflow,” Transactions, ASCE, Vol. 91, 1927, pp. 622–660.
29.
Thomas, H. A., “Frequency of Minor Floods,” Journal of the Boston Society of Civil Engineers, Vol. 35, No. 1, 1948, pp. 425–442.
30.
Vesilind, P. A., and Peirce, J. J., Environmental Engineering, Ann Arbor Science, Ann Arbor, Mich., 1982, pp. 81–86.
31.
Viessman, W., and Hammer, M. J., Water Supply and Pollution Control, 4th ed., Harper and Row, Publishers, Inc., New York, N.Y., 1985, pp. 73–76.
32.
Viessman, W., and Welty, C., Water Management—Technology and Institutions, Harper and Row, Publishers, Inc., New York, N.Y., 1985, pp. 432–433.
33.
Vogel, R. M., “The Variability of Reservoir Storage Estimates,” thesis presented to Cornell University, at Ithaca, N.Y., in 1985, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
34.
Vogel, R. M., and Stedinger, J. R., “Generalized Storage‐Reliability‐Yield Relationships,” Journal of Hydrology, Vol. 89, Jan., 1987, pp. 303–327.
35.
Vogel, R. M., and Stedinger, J. R., “The Value of Stochastic Streamflow Models in Reservoir Design Applications,” Water Resources Research, (manuscript under review).
36.
Water Resources Council, The Nation's Water Resources, 1975–2000, Vol. 1 Summary, Water Resources Council, Washington, D.C., 1978.
37.
Yen, B. C., “Risks in Hydrologic Design of Engineering Projects,” Journal of the Hydraulic Division, ASCE, Vol. 96, No. 4, Apr., 1970, pp. 959–966.
38.
Yevjevich, V., “Fluctuations of Wet and Dry Years, 2, Analysis by Serial Correlation,” Hydrology Paper No. 4, Colorado State University, Fort Collins, Colo., 1964.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 113 • Issue 4 • July 1987
Pages: 563 - 579
Copyright
Copyright © 1987 ASCE.
History
Published online: Jul 1, 1987
Published in print: Jul 1987
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.