Improved Time of Concentration Estimation on Overland Flow Surfaces Including Low-Sloped Planes
Publication: Journal of Hydrologic Engineering
Volume 19, Issue 3
Abstract
Time of concentration () is one of the most used time parameters in hydrologic analyses. As topographic slope () approaches zero, traditional estimation formulas predict large . Based on numerical modeling and a review of relevant literature, a lower bound for slope () of 0.1% was identified as a threshold below which traditional estimation formulas become unreliable and alternate methods should be considered. In this study, slopes less than are defined as low slopes. Slopes equal to or exceeding are defined as standard slopes where traditional estimation formulas are appropriate. A field study was conducted on a concrete plot with a topographic slope of 0.25% to collect rainfall and runoff data between April 2009 and March 2010 to support numerical modeling of overland flows on low-sloped planes. A quasi-two-dimensional dynamic wave model (Q2DWM) was developed for overland flow simulation and validated using published and observed data. The validated Q2DWM was used in a parametric study to generate data for a range of slopes that were used to develop regression formulas for standard slopes () and low slopes ().
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors wish to express their thanks to Texas Department of Transportation (TxDOT) and its members for their guidance and support for the study. This study was partially supported by TxDOT Research Project 0–6382. The authors thank the three reviewers for their valuable comments.
References
Abbott, M., Bathurst, J., Cunge, J., O’connell, P., and Rasmussen, J. (1986). “An introduction to the European hydrological system—Systeme hydrologique Europeen, ‘SHE’, 2: Structure of a physically-based, distributed modelling system.” J. Hydrol., 87(1–2), 61–77.
Akan, A. O., and Yen, B. C. (1981). “Diffusion-wave flood routing in channel networks.” J. Hydraul. Div., 107(6), 719–732.
Bennis, S., and Crobeddu, E. (2007). “New runoff simulation model for small urban catchments.” J. Hydrol. Eng., 540–544.
Capece, J. C., Campbell, K. L., and Baldwin, L. B. (1988). “Estimating runoff peak rates from flat, high-water-table watersheds.” Trans. ASAE, 31(1), 74–81.
Chen, C. N., and Wong, T. S. W. (1993). “Critical rainfall duration for maximum discharge from overland plane.” J. Hydraul. Eng., 1040–1045.
Cleveland, T. G., Thompson, D. B., Fang, X., and He, X. (2008). “Synthesis of unit hydrographs from a digital elevation model.” J. Irrig. Drain. Eng., 212–221.
Cleveland, T. G., Thompson, D. B., Fang, X., and Li, M.-H. (2011). “Establish effective lower bounds of watershed slope for traditional hydrologic methods – Final report.”, Dept. of Civil and Environmental Engineering, Texas Tech Univ., Lubbock, TX.
Courant, R., Friedrichs, K., and Lewy, H. (1967). “On the partial difference equations of mathematical physics.” IBM J. Res. Dev., 11(2), 215–234.
De Lima, J. L. M. P., and Torfs, P. J. J. F. (1990). “Upper boundary conditions for overland flow.” J. Hydraul. Eng., 951–957.
Dhakal, N., Fang, X., Cleveland, G. T., Thompson, D., Asquith, W. H., and Marzen, L. J. (2012). “Estimation of volumetric runoff coefficients for Texas watersheds using land use and rainfall runoff data.” J. Irrig. Drain. Eng., 43–54.
Habib, E., Krajewski, W. F., and Kruger, A. (2001). “Sampling errors of tipping-bucket rain gauge measurements.” J. Hydrol. Eng., 159–166.
Henderson, F. M., and Wooding, R. A. (1964). “Overland flow and groundwater flow from a steady rainfall of finite duration.” J. Geophys. Res., 69(8), 1531–1540.
Hicks, W. I. (1942). “Discussion of ‘Surface runoff determination from rainfall without using coefficients’ by W. W. Horner and S. W. Jens.” Trans. ASCE, 107(1), 1097–1102.
Hromadka, T. V., II, and Yen, C. C. (1986). “A diffusion hydrodynamic model (DHM).” Adv. Water Resour., 9(3), 118–170.
Ivanov, V. Y., Vivoni, E. R., Bras, R. L., and Entekhabi, D. (2004). “Preserving high-resolution surface and rainfall data in operational-scale basin hydrology: A fully-distributed physically-based approach.” J. Hydrol., 298(1), 80–111.
Izzard, C. F. (1946). “Hydraulics of runoff from developed surfaces.” Proc. Highw. Res. Board, 26, 129–150.
Izzard, C. F., and Augustine, M. T. (1943). “Preliminary report on analysis of runoff resulting from simulated rainfall on a paved plot.” Trans., Am. Geophys. Union, 24(2), 500–509.
Jia, Y., Ni, G., Kawahara, Y., and Suetsugi, T. (2001). “Development of WEP model and its application to an urban watershed.” Hydrol. Processes, 15(11), 2175–2194.
Johnstone, D., and Cross, W. P. (1949). Elements of applied hydrology, Ronald Press, New York.
Kazezyılmaz-Alhan, C. M., and Medina, M. A., Jr. (2007). “Kinematic and diffusion waves: Analytical and numerical solutions to overland and channel flow.” J. Hydraul. Eng., 217–228.
Kibler, D. F., and Aron, G. (1983). “Evaluation of tc methods for urban watersheds.” Frontiers in Hydraulic Engineering: Proc., Cambridge Conf., H. T. Shen, ed., ASCE, New York, 553–558.
Kirpich, Z. P. (1940). “Time of concentration of small agricultural watersheds.” Civ. Eng., 10(6), 362.
Kuichling, E. (1889). “The relation between the rainfall and the discharge of sewers in populous areas.” Trans. ASCE, 20(1), 1–56.
Legates, D. R., and McCabe, G. J. (1999). “Evaluating the use of ‘goodness-of-fit’ measures in hydrologic and hydroclimatic model validation.” Water Resour. Res., 35(1), 233–241.
Li, M.-H., and Chibber, P. (2008). “Overland flow time of concentration on very flat terrains.”, Transportation Research Board, Washington, DC, 133–140.
Li, M.-H., Chibber, P., and Cahill, A. T. (2005). “Estimating time of concentration of overland flow on very flat terrains.” 2005 ASAE Annual Int. Meeting, American Society of Agricultural Engineers, St. Joseph, MI.
Linsley, R. K., Kohler, M. A., and Paulhus, J. L. H. (1958). Hydrology for engineers, McGraw- Hill, New York.
López-Barrera, D., García-Navarro, P., and Brufau, P., and Burguete, J. (2012). “Diffusive-wave based hydrologic-hydraulic model with sediment transport. I: Model development.” J. Hydrol. Eng., 1093–1104.
McCuen, R. H. (1998). Hydrologic analysis and design, 2nd Ed., Prentice-Hall, Upper Saddle River, NJ, 814.
McCuen, R. H. (2009). “Uncertainty analyses of watershed time parameters.” J. Hydrol. Eng., 490–498.
McCuen, R. H., and Spiess, J. M. (1995). “Assessment of kinematic wave time of concentration.” J. Hydraul. Eng., 256–266.
McCuen, R. H., Wong, S. L., and Rawls, W. J. (1984). “Estimating urban time of concentration.” J. Hydraul. Eng., 887–904.
Moramarco, T., and Singh, V. P. (2002). “Accuracy of kinematic wave and diffusion wave for spatial-varying rainfall excess over a plane.” Hydrol. Process., 16(17), 3419–3435.
Morgali, J. R., and Linsley, R. K. (1965). “Computer analysis of overland flow.” J. Hydraul. Div., 91(3), 81–100.
Mulvany, T. J. (1851). “On the use of self-registering rain and flood gauges in making observations of the relations of rainfall and flood discharges in a given catchment.” Proc., Institution of Civil Engineers of Ireland, 4(2), 18–33.
Muzik, I. (1974). “Laboratory experiments with surface runoff.” J. Hydraul. Div., 100(4), 501–516.
Natural Resources Censervation Service (NRCS). (1986). “Urban hydrology for small watersheds.”, Washington, DC.
Pilgrim, D. H. (1966). “Radioactive tracing of storm runoff on a small catchment II. Discussion of results.” J. Hydrol., 4, 306–326.
Richardson, J. R., and Julien, P. Y. (1994). “Suitability of simplified overland flow equations.” Water Resour. Res., 30(3), 665–671.
Riggs, H. C. (1976). “A simplified slope-area method for estimating flood discharges in natural channels.” J. Res. U.S. Geol. Surv., 4(3), 285–291.
Sheridan, J. M. (1994). “Hydrograph time parameters for flatland watersheds.” Trans. Am. Soc. Agric. Eng., 37(1), 103–113.
Sheridan, J. M., Merkel, W. H., and Bosch, D. D. (2002). “Peak rate factors for flatland watersheds.” Appl. Eng. Agric., 18(1), 65–69.
Singh, V. (1976). “Derivation of time of concentration.” J. Hydrol., 30(1–2), 147–165.
Singh, V. P., and Aravamuthan, V. (1995). “Accuracy of kinematic wave and diffusion wave approximations for time-independent flows.” Hydrol. Process., 9(7), 755–782.
Singh, V. P., Jain, S. K., and Sherif, M. M. (2005). “Errors of kinematic wave and diffusion wave approximations for time-independent flows with infiltration and momentum exchange included.” Hydrol. Process., 19(9), 1771–1790.
Su, D. H., and Fang, X. (2004). “Estimating traveling time of flat terrain by 2-dimensional overland flow model.” Shallow flows, G. Jirka and W. Uijttewaal, eds., Balkema, Roterdam, The Netherlands, 623–625.
Thompson, D. B., Cleveland, T. G., Copula, D. B., and Fang, X. (2008). “Loss-rate functions for selected Texas watersheds.”, Dept. of Transportation, TX.
Van der Molen, W. H., Torfs, P. J. J. F., and de Lima, J. L. M. P. (1995). “Water depths at the upper boundary for overland flow on small gradients.” J. Hydrol., 171(1–2), 93–102.
Wong, T. S. W. (1996). “Time of concentration and peak discharge formulas for planes in series.” J. Irrig. Drain. Eng., 256–258.
Wong, T. S. W. (2005). “Assessment of time of concentration formulas for overland flow.” J. Irrig. Drain. Eng., 383–387.
Woolhiser, D. A., and Liggett, J. A. (1967). “Unsteady one-dimensional flow over a plane-the rising hydrograph.” Water Resour. Res., 3(3), 753–771.
Yates, P., and Sheridan, J. M. (1973). “Flow measurement of low-gradient streams in sandy soils.” Proc., Int. Symp. on Hydrometry, Koblez, Germany, Vol. 1, United Nations Education Scientific and Cultural Organization–World Meteorological Organization–International Association of Hydrological Sciences, 345–352.
Yeh, G. T., Cheng, H. P., Cheng, J. R., Lin, H. C. J., and Martin, W. D. (1998). “A numerical model simulating water flow and contaminant and sediment transport in watershed systems of 1-D stream-river network, 2-D overland regime, and 3-D subsurface media (WASH123D: Version 1.0).”, U.S. Army Corps of Engineers.
Yen, B. C., ed. (1982). “Some measures for evaluation and comparison of simulated models.” Proc., 2nd Int. Conf. on Urban Storm Drainage, Water Resources, Littleton, CO, 341–349.
Yen, B. C., and Chow, V. T. (1983). “Local design storms: Vol. III.”, U.S. Dept. of Transportation, Federal Highway Administration, Washington, DC.
Yu, Y. S., and McNown, J. S. (1963). “Runoff from impervious surfaces.” 2-66, Univ. of Kansas, Lawrence, KS, 30.
Yu, Y. S., and McNown, J. S. (1964). “Runoff from impervious surfaces.” J. Hydraul. Res., 2(1), 3–24.
Information & Authors
Information
Published In
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Apr 26, 2012
Accepted: Apr 10, 2013
Published online: Apr 12, 2013
Discussion open until: Sep 12, 2013
Published in print: Mar 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.