Flow‐Duration Curves. I: New Interpretation and Confidence Intervals
Publication: Journal of Water Resources Planning and Management
Volume 120, Issue 4
Abstract
A flow‐duration curve (FDC) is simply the complement of the cumulative distribution function of daily, weekly, monthly (or some other time interval of) streamflow. Applications of FDCs include, but are not limited to, hydropower planning, water‐quality management, river and reservoir sedimentation studies, habitat suitability, and low‐flow augmentation. Although FDCs have a long and rich history in the field of hydrology, they are sometimes criticized because, traditionally, their interpretation depends on the particular period of record on which they are based. If one considers individual FDCs, each corresponding to one of the individual years of record, then one may treat those annual FDCs in much the same way one treats a sequence of annual maximum or annual minimum streamflows. This new annual‐based interpretation enables confidence intervals and recurrence intervals to be associated with FDCs in a nonparametric framework.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abramowitz, M., and Stegun, I. A. (1972). Handbook of mathematical functions, Dover Publications, Inc., New York, N.Y., 945.
2.
Adamowski, K. (1985). “Nonparametric kernel estimation of flood frequencies.” Water Resour. Res., 21(11), 1585–1590.
3.
Alaouze, C. M. (1989). “Reservoir releases to uses with different reliability requirements.” Water Resour. Bull., 25(6), 1163–1168.
4.
Anderson, P. K., and Vaeth, M. (1988). “Survival Analysis.” Encyclopedia of statistical sciences—Vol. 8, John Wiley & Sons, New York, N.Y., 119–129.
5.
Beard, L. R. (1943). “Statistical analysis in hydrology.” ASCE Trans., 108, 1110–1160.
6.
Chow, V. T. (1964). Handbook of applied hydrology, Mc‐Graw Hill Book Co., New York, N.Y.
7.
Cross, W. P., and Bernhagen, R. J. (1949). “Flow duration.” Ohio streamflow characteristics, Bull. 10, part 1, Ohio Dept. of Natural Resour., Div. of Water.
8.
Dingman, S. L. (1978). “Synthesis of flow‐duration curves for unregulated streams in New Hampshire.” Water Resour. Bull., 14(6), 1481–1502.
9.
Efron, B. (1982). The jackknife, the bootstrap and other resampling plans. Society for Industrial and Applied Mathematics, Philadelphia, Pa.
10.
Fennessey, N. M., and Vogel, R. M. (1990). Regional flow duration curves for ungaged sites in Massachusetts. J. Water Resour. Plng. and Mgmt., ASCE, 116(4), 530–549.
11.
Fienberg, S. E. (1979). “Graphical methods in statistics.” The Am. Statistician, 33(4), 165–178.
12.
Foster, H. A. (1934). “Duration curves.” ASCE Trans., 99, 1213–1267.
13.
Gordon, N. D., McMahon, T. A., and Finlayson, B. L. (1992). Stream hydrology—an introduction for ecologists. John Wiley & Sons, New York, N.Y., 373–377.
14.
“Guidelines for determining flood flow frequency.” (1982). Bull. 17B, Interagency Advisory Committee on Water Data (IACWD), Hydrology Subcommittee, Office of Water Data Collection, U.S. Geological Survey, Reston, Va.
15.
Guo, S. L. (1991). Nonparametric variable kernel estimation with historical floods and paleoflood information. Water Resour. Res., 27(1), 91–98.
16.
Harrell, F. E., and Davis, D. E. (1982). A new distribution‐free quantile estimator. Biometrika, 69(3), 635–640.
17.
Hosking, J. R. M. (1990). L‐Moments: analysis and estimation of distributions using linear combinations of order statistics. J. Royal Statistical Soc., B, 52(2), 105–124.
18.
Kaigh, W. D., and Driscoll, M. F. (1987). Numerical and graphical data summary using O‐statistics. The Am. Statistician, 41(1), 25–32.
19.
Kaigh, W. D., and Lachenbruch, P. A. (1982). “A generalized quantile estimator.” Communications in Statistics—Series A—Theory and Methods, 11(19), 2217–2238.
20.
Loucks, D. P., Stedinger, J. R., and Haith, D. A. (1981). Water resource systems planning and analysis, Prentice‐Hall, Inc., Englewood Cliffs, N.J., 109.
21.
“Low flow studies.” (1980). Rep. No. 2.1, Flow duration curve estimation manual, Institute of Hydrology, Wallingford, Oxon.
22.
Majumdar, K. L., and Bhattacharjee, G. P. (1973). “The incomplete beta integral (algorithm AS63).” Appl. Statistics, 22, 409–411.
23.
Male, J. W., and Ogawa, H. (1984). “Tradeoffs in water quality management.” J. Water Resour. Plng. and Mgmt., 110(4), 434–444.
24.
Mitchell, W. D. (1957). “Flow duration curves of Illinois streams.” Illinois Dept. of Public Works and Buildings, Division of Waterways.
25.
Parrish, R. S. (1990). “Comparison of quantile estimators in normal sampling.” Biometrics, 46, 247–257.
26.
Parzen, E. (1979). “Nonparametric statistical data modeling.” J. Am. Statistical Assoc., 74(365), 105–122.
27.
Saville, Thorndike, and Watson, J. D. (1933). “An investigation of the flow‐duration characteristics of North Carolina streams. Trans., Am. Geophys. Union, 406–525.
28.
Searcy, J. K. (1959). “Flow‐duration curves.” Water Supply Paper 1542‐A, U.S. Geological Survey, Reston, Virginia.
29.
Sheather, S. J., and Marron, J. S. (1990). Kernel quantile estimators. J. Am. Statistical Assoc., 85(410), 410–416.
30.
Singh, K. P. (1971). “Model flow duration and streamflow variability.” Water Resour. Res., 7(4), 1031–1036.
31.
Stedinger, J. R., Vogel, R. M., and Foufoula‐Georgiou, E. F. (1993). “Chapter 18: frequency analysis of extreme events.” Handbook of Hydrology, D. R. Maidment, ed., Mc‐Graw Hill Book Company, New York, N.Y.
32.
Strand, R. I., and Pemberton, E. L. (1982). “Reservoir sedimentation.” Tech. Guideline for Bureau of Reclamation, U.S. Bureau of Reclamation, Denver, Colo.
33.
Vogel, R. M., and Fennessey, N. M. (1993). “L‐moment diagrams should replace product‐moment diagrams.” Water Resour. Res., 29(6), 1745–1752.
34.
Vogel, R. M., and Kroll, C. N. (1989). “Low‐flow frequency analysis using probability plot correlation coefficients.” J. Water Resour. Plng. and Mgmt., ASCE, 115(3), 338–357.
35.
Vogel, R. M., and McMartin, D. E. (1991). “Probability plot goodness‐of‐fit and skewness estimation procedures for the Pearson type 3 distribution.” Water Resour. Res., 27(12), 3149–3158:
Correction in Water Resour. Res., (1992), 28(6), 1757.
36.
Warnick, C. C. (1984). Hydropower engineering. Prentice‐Hall, Inc., Englewood Cliffs, New Jersey, 59–73.
37.
Yang, S. S. (1985). A smooth nonparametric estimator of a quantile function. J. Am. Statistical Assoc., 80(392), 1004–1011.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 120 • Issue 4 • July 1994
Pages: 485 - 504
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Jan 28, 1993
Published online: Jul 1, 1994
Published in print: Jul 1994
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.