Flow Duration Curve Using Entropy Theory
Publication: Journal of Hydrologic Engineering
Volume 19, Issue 7
Abstract
Using the entropy theory, this study derives a function for modeling the flow duration curve (FDC) based on two equations that form simple constraints: (1) the total probability of all flow discharges, and (2) the mean discharge. Parameters of the derived curve are determined from the entropy theory with the use of these two constraints. For deriving the flow duration curve by the entropy theory, a nonlinear cumulative distribution function is assumed, which is tested using observed flow data. The derived flow duration curves are tested using field data and are found to be in agreement with observed curves. With the entropy parameter determined for each station, the flow duration curve can also be forecasted for different recurrence intervals. The main advantage of the use of the entropy theory–based FDCs is that the parameters are based on observations, and hence no fitting is needed. Second, the theory permits a probabilistic characterization of the flow duration curve and hence the probability density function underlying the curve. It also permits a quantitative assessment of the uncertainty of the flow duration curve. Additional work is needed to regionalize the FDC parameters.
Get full access to this article
View all available purchase options and get full access to this article.
References
Al-Hamdan, O. Z., and Cruise, J. F. (2010). “Soil moisture profile development from surface observations by principle of maximum entropy.” J. Hydrol. Eng., 327–337.
Barbe, D. E., Cruise, J. F., and Singh, V. P. (1991). “Solution of 3-constraint entropy-based velocity distribution.” J. Hydraul. Eng., 1389–1396.
Chiu, C. L. (1987). “Entropy and probability concepts in hydraulics.” J. Hydraul. Eng., 583–600.
Cui, H., and Singh, V. P. (2012). “On the cumulative distribution function for entropy-based hydrologic modeling.” Trans. ASABE, 55(2), 429–438.
Foster, H. A. (1934). “Duration curves.” Trans. ASCE, 99, 1213–1267.
Hickox, G. H., and Wessenauer, G. O. (1933). “Application of duration curves to hydroelectric studies.” Trans. ASCE, 98(2), 1276–1308.
Jaynes, E. T. (1957). “Information theory and statistical mechanics, I.” Phys. Rev., 106(4), 620–630.
Jaynes, E. T. (1982). “On the rationale of maximum entropy methods.” Proc. IEEE, 70(9), 939–952.
Miller, C. R. (1951). “Analysis of flow duration, sediment-rating curve method of computing sediment yield.” U.S. Dept. of Interior, Bureau of Reclamation, Sedimentation Section, Hydrology Branch, Denver.
Mitchell, W. D. (1957). “Flow-duration of Illinois streams.” Illinois Dept. of Public Works and Buildings, Division of Waterways, 189.
Searcy, J. K. (1959). “Flow-duration curves.” USGS Water-Supply Paper 1542-A, U.S. Government Printing Office, Washington, DC.
Shannon, C. E. (1948). “A mathematical theory of communications, I and II.” Bell Syst. Tech. J., 27(3), 379–443.
Shannon, C. E., and Weaver, W. (1949). The mathematical theory of communication, Univ. Illinois Press, Urbana, IL.
Singh, V. P. (1998). Entropy-based parameter estimation in hydrology, Kluwer Academic Publishers, Boston.
Singh, V. P. (2010a). “Entropy theory for derivation of infiltration equations.” Water Resour. Res., 46(3), 1–20, W03527.
Singh, V. P. (2010b). “Entropy theory for movement of moisture in soils.” Water Resour. Res., 46(3), 1–12, W03516.
Singh, V. P. (2010c). “Tsallis entropy theory for derivation of infiltration equations.” Trans. ASABE, 53(2), 447–463.
U.S. Environmental Protection Agency (USEPA). (2007). “An approach for using load duration curves in the development of TMDL.”, Watershed Branch, Office of Wetlands, Oceans and Watersheds, USEPA, Washington, DC.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 19 • Issue 7 • July 2014
Pages: 1340 - 1348
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Feb 20, 2013
Accepted: Oct 24, 2013
Published online: Oct 26, 2013
Discussion open until: Mar 26, 2014
Published in print: Jul 1, 2014
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.