Bypassing Determination of Time of Concentration
Publication: Journal of Hydrologic Engineering
Volume 18, Issue 12
Abstract
Reanalysis of the records, upon which the 120-year-old Rational Formula is based, reveals that the published linear relationship between rainfall duration and the ratio of peak discharge to the product of rainfall intensity and watershed area can also be replaced by a logarithmic regression. Such a regression is found, with reasonable correlation, suitable for two-dimensional laboratory watersheds, for four experimental urban watersheds, and for five small watersheds in Israel. Combining this regression with a power-law regression between rainfall intensity and duration, associated with any given recurrence interval, yields a general relationship between the variables. From this and through simple mathematical operations, the maximum discharge associated with that recurrence interval is determined. The variables in the new equation are watershed area and the empirical parameters of the regressions. Application of this equation bypasses determination of the highly influential time of concentration, which is an immeasurable variable and for which varied surrogates are used. It also saves determination of the coefficient of the Rational Formula. Yet, it requires preparation of regional models for estimation parameter values of the logarithmic regression. Application of the proposed method on the outdoor watersheds, with intensity-duration-frequency curves for representative meteorological stations, yields realistic results. The application for one of those watersheds, with an observational period of 40 years, reveals a wide difference between the prediction through the proposed method and that through statistics of recorded peak discharges. The difference is attributable to association of recurrence intervals of rainfall intensities with peak runoff discharges. The difference is reduced by use of statistics for rainfall intensities during the subseason of high discharges rather than during the entire rainy season.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
A. Ben-Zvi was supported by the NSF Grants GP-1464 and GK-1155. Rita Chudinov of the Israel Hydrological Service prepared the map of the hydrometric and meteorological stations. Ayal Siegel of the Israel Hydrological Service provided the data of his thesis. Benjamin Azmon of the Israel Hydrological service provided helpful information on K. Eliezer hydrometric station. Two reviewers contributed to the quality of the paper.
References
ASCE. (1949). Hydrology handbook, ASCE Manuals of Engineering Practice No. 28, ASCE, Reston, VA.
Ben-Zvi, A. (1970). “On the relationship between rainfall and surface runoff on laboratory watersheds.” Ph.D. thesis, CE Dept., Univ. Of Illinois, Urbana, IL.
Ben-Zvi, A. (1984). “Runoff peaks from two-dimensional laboratory watersheds.” J. Hydrol., 68, 115–139.
Ben-Zvi, A. (1989). “Toward a new rational method.” J. Hydraul. Eng., 115(9), 1241–1255.
Ben-Zvi, A. (2009). “Rainfall intensity-duration-frequency relationships derived from large partial duration series.” J. Hydrol., 367(1–2), 104–114.
Biswas, A. K. (1970). History of hydrology, North-Holland Publishing Company, Amsterdam, The Netherlands.
Chen, C. N., and Wong, T. S. W. (1993). “Critical rainfall duration for maximum discharge from overland plane.” J. Hydraul. Eng., 119(9), 1040–1045.
Chow, V. T. (1964). Handbook of applied hydrology, McGraw-Hill, New York.
Chow, V. T., Maidment, D. R., and Mays, L. W. (1988). Applied hydrology, McGraw-Hill, New York.
Gregory, R. L., and Arnold, C. B. (1932). “Run-off–rational runoff formulas.” Trans. ASCE, 96(1), 1038–1099.
Guo, J. C. Y. (2001). “Rational hydrograph method for small urban watersheds.” J. Hydrol. Eng., 6(4), 352–356.
Guo, Y., and Adams, B. J. (1998a). “Hydrologic analysis of urban catchments with event-based probabilistic models: 1. Runoff volumes.” Water Resour. Res., 34(12), 3421–3431.
Guo, Y., and Adams, B. J. (1998b). “Hydrologic analysis of urban catchments with event-based probabilistic models: 2. Peak discharge rate.” Water Resour. Res., 34(12), 3433–3443.
Krimgold, D. B. (1946). “On the hydrology of culverts.” Proc. Highway Res. Board, National Res. Council, Vol. 26, Highway Research Board, Washington, DC, 214–226.
Kuichling, E. (1889). “The relation between the rainfall and the discharge of sewers in populous districts.” Trans. ASCE, 20(1), 1–60.
Linsley, Ray K. (1970). “Discussion of ‘Urban runoff by road research laboratory method’ by M. L. Terstriep and J. B. Stall.” J. Hydraul. Div., 97(HY4), 1100–1102.
Mulvaney, T. J. (1851). “On the use of self-registering rain and flood gauges in making observations of the relations of rainfall and of flood discharges in a given catchment.” Proc., Institute of Civil Engineers, Vol. 4, North-Holland Publishing Company, Amsterdam, The Netherlands, 18–31.
Sharifi, S., and Hosseini, S. M. (2011). “Methodology for identifying the best equations for estimating the time of concentration of watersheds in a particular region.” J. Irrig. Drain. Eng., 137(11), 712–719.
Siegel, A. (2009). “Finding the runoff coefficient in urban area.” Ph.D. thesis, Haifa Univ., Israel (in Hebrew).
Snyder, F. F. (1970). “Discussion of ‘Urban runoff by road research laboratory method’ by M. L. Terstriep and J. B. Stall.” J. Hydraul. Div., 97(HY7), 1626–1629.
Terstriep, M. L., and Stall, J. B. (1969). “Urban runoff by road research laboratory method.” J. Hydraul. Div., 96(HY6), 1809–1834.
Terstriep, M. L., and Stall, J. B. (1971). “Closure to ‘Urban runoff by road research laboratory method’ by M. L. Terstriep and J. B. Stall.” J. Hydraul. Div., 98(HY4), 574–579.
Watkins, L. H. (1962). “The design of urban sewer systems.”, Dept. of Scientific and Industrial research, Road Research Laboratory, London, England.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 18 • Issue 12 • December 2013
Pages: 1674 - 1683
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Feb 9, 2012
Accepted: Nov 7, 2012
Published online: Nov 9, 2012
Discussion open until: Apr 9, 2013
Published in print: Dec 1, 2013
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.