Overland Flow Times of Concentration for Hillslopes of Complex Topography
Publication: Journal of Irrigation and Drainage Engineering
Volume 142, Issue 3
Abstract
The time of concentration is an important parameter for predicting peak discharge at the basin outlet and for designing urban infrastructure facilities. In studying the hillslope response, employing hydraulic equations of flow, the shape of the hillslope geometry has often been assumed as rectangular and planar. However, natural hillslopes have complex topographies whose shapes are characterized by irregularly spaced contour lines. Recently, kinematic wave time of concentration has been derived for rectangular and curved parallel hillslopes. This paper extends this work to hillslopes of complex planform geometry, considering the degree of divergence or convergence of the hillslope. The extended formulation consists of only one equation that is valid for both divergent/convergent surfaces and for concave/convex hillslope profile, and is compared with the formulations for plane convergent and plane divergent surfaces previously introduced. Results are compared with those already available in the literature, which were obtained by using the nonlinear storage model applied to the same complex hillslopes.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Research was co-financed by Università degli Studi di Palermo (FFR 2012–2013) and by Ministero dell’Istruzione, dell’Università e della Ricerca (FIRB 2012–2015). The contribution to the manuscript has to be shared between authors as follows: derivations and applications of the proposed procedure were carried out by the first author; both authors analyzed results and wrote the text. The authors wish to thank the anonymous reviewers for the helpful comments and suggestions made during the revision stage.
References
Agiralioglu, N. (1988). “Estimation of the time of concentration for diverging surface.” J. Hydrol. Sci., 33(2), 173–179.
Agiralioglu, N., and Singh, V. P. (1981). “Overland flow on a diverging surface.” Hydrol. Sci. Bull., 26(2), 137–147.
Agnese, C., Bagarello, V., Baiamonte, G., and Iovino, M. (2011). “Comparing physical quality of forest and pasture soils in a sicilian watershed.” Soil Sci. Soc. Am. J., 75(5), 1958–1970.
Agnese, C., Baiamonte, G., and Cammalleri, C. (2014). “Modelling the occurrence of rainy days under a typical Mediterranean climate.” Adv. Water Resour., 64, 62–76.
Agnese, C., Baiamonte, G., and Corrao, C. (2001). “A simple model of hillslope response for overland flow generation.” Hydrol. Process., 15(17), 3225–3238.
Agnese, C., Baiamonte, G., and Corrao, C. (2007). “Overland flow generation on hillslopes of complex topography: Analytical solutions.” Hydrol. Process., 21(10), 1308–1317.
Agnese, C., Baiamonte, G., D’Asaro, F., Grillone, G. (2015) “Probability distribution of peak discharge at the hillslope scale generated by Hortonian runoff.” J. Irrig. Drain. Eng., 04015052.
Akan, O. (1985). “Similarity solution of overland flow on pervious surface.” J. Hydrol. Eng., 1057–1067.
Akan, O. (1986). “Time of concentration of overland flow.” J. Irrig. Drain. Eng., 283–292.
Baiamonte, G., and Agnese, C. (2010). “An analytical solution of kinematic wave equations for overland flow under Green-Ampt infiltration.” J. Agric. Eng., 41(1), 41–49.
Baiamonte, G., D’Asaro, F., and Grillone, G. (2015a). “Simplified probabilistic-topologic model for reproducing hillslope rill network surface runoff.” J. Irrig. Drain. Eng., 04014080.
Baiamonte, G., De Pasquale, C., Marsala, V., Conte, P., Alonzo, G., and Crescimanno, G. (2015b). “Structure alteration of a sandy-clay soil by biochar amendments.” J. Soils Sediments, 15(4), 816–824.
Baiamonte, G., and Singh, V. P. (2015). “Analytical solution of kinematic wave time of concentration for overland flow under Green-Ampt infiltration.” J. Hydrol. Eng., in press.
Brutsaert, W. (2005). Hydrology: An introduction, Cambridge.
Campbell, S. Y., Parlange, J. Y., and Rose, C. W. (1984). “Overland flow on converging and diverging surfaces—Kinematic model and similarity solutions.” J. Hydrol., 67, 1–4, 367–374.
Carson, M. A., andKirkby, M. J. (1972). Hillslope form and processes, Cambridge University Press, Cambridge, U.K.
Evans, I. S. (1980). “An integrated system of terrain analysis and slope mapping.” Zeitschrift fur Geomorphologie, 36, 274–295.
Guo, J., and Hsu, E. (2015). “Converging kinematic wave flow.” J. Irrig. Drain. Eng., 04015006.
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.
Horton, R. E. (1938). “The interpretation ad application of runoff plane experiments with reference to soil erosion problems.” Soil Sci. Soc. Am. Proc., 1, 401–437.
Lighthill, M. J., and Whitham, G. B. (1955) “On kinematic waves. I. Flood movement in long rivers.” Proc. R. Soc. London, Ser. A, 229, 281–316.
Moore, I. D. (1985). “Kinematic overland flow: Generalization of Rose’s approximate solution.” J. Hydrol., 82(3–4), 233–245.
Noroozpour, S., Saghafian, B., Akhondali, A. M., and Radmanesh, F. (2014). “Travel time of curved parallel hillslopes.” Hydrol. Res., 45(2), 190–199.
Paniconi, C., Troch, P. A., van Loon, E. E., and Hilberts, A. G. J. (2003). “Hillslope-storage Boussinesq model for subsurface flow and variable source areas along complex hillslopes: 2. Intercomparison with a three-dimensional Richards equation model.” Water Resour. Res., 39, 1317, 11.
Philip, J. R. (1991). “Hillslope infiltration: Divergent and convergent slopes.” Water Resour. Res., 27(6), 1035–1040.
Reggiani, P., Todini, E., and Meißner, D. (2014). “Analytical solution of a kinematic wave approximation for channel routing.” Hydrol. Res., 45(1), 43–57.
Robinson, J. S., and Sivapalan, M. (1996). “Instantaneous response functions of overland flow and subsurface stormflow for catchment models.” Hydrol. Process., 10(6), 845–862.
Rose, C. W., Parlange, J. Y., Sander, G. C, Campbell, S. Y., and Barry, D. A. (1983). “Kinematic flow approximation to runoff on a plane: An approximate analytical solution.” J. Hydrol., 62(1–4), 363–369.
Sabzevari, T., Talebi, A., Ardakanian, R., and Shamsai, A. (2010). “A steady-state saturation model to determine the subsurface travel time (STT) in complex hillslopes.” Hydrol. Earth Syst. Sci., 14(6), 891–900.
Saghafian, B., and Julien, P. Y. (1995). “Time to equilibrium for spatially variable watersheds.” J. Hydrol., 172(1–4), 231–245.
Sherman, B. and Singh, V. P. (1976a). “A distributed converging overland flow model: 2. Effect of infiltration.” Water Resour. Res., 12(5), 898–901.
Sherman, B., and Singh, V. P. (1976b). “A distributed converging overland flow model: l. Mathematical solutions.” Water Resour. Res., 12(5), 889–896.
Singh, V. P. (1975). “A laboratory investigation of surface runoff.” J. Hydrol., 25(3–4), 187–200.
Singh, V. P. (1976a). “A distributed converging overland flow model: 3. Application to natural watersheds.” Water Resour. Res., 12(5), 902–908.
Singh, V. P. (1976b). “Derivation of time of concentration.” J. Hydrol., 30(1–2), 147–165.
Singh, V. P. (1996). Kinematic-wave modeling in water resources: Surface-water hydrology, Wiley, New York.
Singh, V. P. (1997). Kinematic-wave modeling in water resources: Environmental hydrology, Wiley, New York.
Singh, V. P., and Agiralioglu, N. (1981a). “Diverging overland flow.” Adv. Water Resour., 4(3), 117–124.
Singh, V. P., and Agiralioglu, N. (1981b). “Diverging overland flow: 2. Application to natural watersheds.” Nordic Hydrol., 12(2), 99–110.
Singh, V. P., and Agiralioglu, N. (1981c). “Diverging overland flow: l. Analytical solution with rainfall-excess.” Nordic Hydrol., 12(2), 81–98.
Singh, V. P., and Woolhiser, D. A. (1976). “A non-linear kinematic wave model for watershed surface runoff.” J. Hydrol., 31(3–4), 221–243.
Talebi, A., Troch, P. A., and Uijlenhoet, R. (2008). “A steady-state analytical hillslope stability model for complex hillslopes.” Hydrol. Process., 22, 546–553.
Troch, P. A., Paniconi, C., and van Loon, E. E. (2003). “Hillslope-storage Boussinesq model for subsurface flow and variable source areas along complex hillslopes: 1. Formulation and characteristic response.” Water Resour. Res., 39(1).
Wolfram, S. (1999). The mathematica book, 4th Ed., Cambridge University Press, Cambridge, U.K.
Woolhiser, D. A. (1969). “Overland flow on a converging surface.” Trans. ASABE, 12(4), 0460–0462.
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.
Information & Authors
Information
Published In
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Feb 7, 2015
Accepted: Sep 23, 2015
Published online: Dec 10, 2015
Published in print: Mar 1, 2016
Discussion open until: May 10, 2016
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.