Regional Flow‐Duration Curves for Ungauged Sites in Massachusetts
Publication: Journal of Water Resources Planning and Management
Volume 116, Issue 4
Abstract
A regional hydrologic model is developed for estimating flow‐duration curves at ungauged and unregulated basins in Massachusetts. Flow‐duration curves often exhibit complex shapes, requiring probability density functions with three or more parameters. This study approximates the lower half of daily flow‐duration curves using a two‐parameter lognormal probability density function. A conjugate gradient algorithm is employed to fit lognormal density functions to the lower half of observed flow‐duration curves at 23 basins. Regional regression equations are developed to describe the lognormal model parameters in terms of easily measured basin characteristics. The resulting regional flow‐duration model only requires estimates of the watershed area, and a basin relief parameter, both of which are easily obtained from U.S. Geological Survey 7.5‐min quadrangle maps. In addition, confidence intervals are derived for flow‐duration curves estimated at ungauged sites. A validation experiment reveals that the resulting regional hydro‐logic model can provide remarkably precise estimates of a flow‐duration curve at an ungauged site, considering the simplicity of the model and its ease of application.
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References
1.
Abramowitz, M., and Stegun, I. A. (1964). The handbook of mathematical functions. Dover Press, New York, N.Y.
2.
Beard, L. R. (1943), “Statistical analysis in hydrology.Trans., ASCE, 108, 1110–1160.
3.
Brutsaert, W., and Nieber, J. L. (1977). “Regionalized drought flow hydrographs from a mature glaciated plateau.” Water Resour. Res., 13(3), 637–643.
4.
Chow, V. T. (1964). Handbook of applied hydrology. McGraw Hill Book Co., New York, N.Y.
5.
Cunnane, C. (1978). “Unbiased plotting positions—a review.” J. Hydrol., 37, 205–222.
6.
Dingman, S. L. (1978). “Synthesis of flow‐duration curves for unregulated streams in New Hampshire.” Water Resour. Bull, 14(6), 1481–1502.
7.
Entekhabi, D., Rodriguez‐Iturbe, I., and Eagleson, P. S. (1989). “Probabilistic representation of the temporal rainfall process by a modified Neyman‐Scott rectangular pulses model: Parameter estimation and validation.” Water Resour. Res., 25(2), 295–302.
8.
Foster, H. A. (1934). “Duration curves.” Trans., ASCE, 99, 1213–1267.
9.
Gupta, R. S. (1989). Hydrology and hydraulic systems. Prentice‐Hall, Inc., N.J., 363–367.
10.
Johnson, C. G. (1970). A proposed streamflow data program for central New England. U.S. Geological Survey, Boston, Mass.
11.
Linsley, R. K., and Franzini, J. B. (1979). Water‐resources engineering. McGraw Hill Book Co., New York, N.Y., 127–129.
12.
Loaiciga, H. A. (1989). “Variability of empirical flow quantiles.” J. Hydr. Engrg., ASCE, 115(1), 82–100.
13.
Male, J. W., and Ogawa, H. (1982). “Low flows of Massachusetts streams.” Publication No. 125, Water Resour. Res. Center, Univ. of Massachusetts, Amherst, Mass.
14.
Male, J. W., and Ogawa, H. (1984). “Tradeoffs in water quality management.” J. Water Resour. Plng. and Mgmt., ASCE, 110(4), 434–444.
15.
Mimikou, M., and Kaemaki, S. (1985). “Regionalization of flow duration characteristics.” J. Hydrol., 82, 77–91.
16.
Quimpo, R. G., Alejandrino, A. A., and McNally, T. A. (1983). “Regionalized flow duration curves for Philippines.” J. Water Res. Plng. and Mgmt., ASCE, 109(4), 320–330.
17.
Riggs, H. C. (1972). “Low‐flow investigations.” U.S. Geological Survey Techniques of Water Resources Investigations, Book 4, U.S. Geological Survey, Washington, D.C.
18.
Riggs, H. C., et al. (1980). “Characteristics of low flows.” J. Hydr. Engrg., ASCE, 106(5), 717–731.
19.
Searcy, J. K. (1959). “Flow‐duration curves.” Paper 1542‐A, U.S. Geological Survey Water‐Supply, U.S. Government Printing Office, Washington, D.C.
20.
Singh, K. P. (1971). “Model flow duration and streamflow variability.” Water Resour. Res., 7(4), 1031–1036.
21.
Stedinger, J. R. (1980). “Fitting log normal distributions.” Water Resour. Res., 16(3), 481–490.
22.
Stedinger, J. R., and Tasker, G. D. (1985). “Regional hydrologic analysis 1. ordinary, weighted, and generalized least squares compared.” Water Resour. Res., 21(9), 1421–1432.
23.
Strahler, A. N. (1950). “Equilibrium theory of erosional slopes approached by frequency distribution analysis.” Am. J. Sci., 248, 673–696, 800–814.
24.
Tasker, G. D. (1972). “Estimating low‐flow characteristics of streams in southeastern Massachusetts from maps of groundwater availability.” Professional Paper 800‐D, U.S. Geological Survey, Washington, D.C., D217‐D220.
25.
Tasker, G. D. (1983). “Effective record length for the T‐year event.” J. Hydrol., 64, 39–47.
26.
Tukey, J. W. (1960). “The practical relationship between the common transformation of percentages or fractions and of amounts.” Technical Report No. 36, Statistical Res. Group, Princeton, N.J.
27.
“Users manual—math/library.” (1987). Version 1.0, Int. Mathematical Subroutine Library, Houston, Tex.
28.
Vogel, R. M., and Kroll, C. N. (1989). “Low‐flow frequency analysis using probability‐plot correlation coefficients.” J. Water Res. Plng. and Mgmt., ASCE, 115(3), 338–357.
29.
Vogel, R. M., and Kroll, C. N. (1990). “Generalized low‐flow frequency relationships for ungaged sites.” Water Resour. Bull.
30.
Vogel, R. M., Kroll, C. N., and Driscoll, K. (1989). “Regional geohydrologic‐geomorphic relationships for the estimation of low‐flows.” Proc. Int. Conf. on Channel Flow and Catchment Runoff, Univ. of Virginia, 267–277.
31.
Warnick, C. C. (1984). Hydropower engineering. Prentice‐Hall, Inc., N.J., 59–73.
32.
Zecharias, Y. B., and Brutsaert, W. (1985). “Ground surface slope as a basin scale parameter.” Water Resour. Res., 21(12), 1895–1902.
33.
Zecharias, Y. B., and Brutsaert, W. (1988). “Recession characteristics of groundwater outflow and baseflow from mountainous watersheds.” Water Resour. Res., 24(10), 1651–1658.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 116 • Issue 4 • July 1990
Pages: 530 - 549
Copyright
Copyright © 1990 ASCE.
History
Published online: Jul 1, 1990
Published in print: Jul 1990
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