Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-13T04:38:29.807Z Has data issue: false hasContentIssue false
  • English
  • Français

Simulating Runoff Using the Method of Characteristics with Unsteady Rainfall Events

Published online by Cambridge University Press:  05 May 2011

C.-M. Wu  and
S.-C. Chen
C.-M. Wu*
Affiliation:
Construction and Disaster Prevention Research Center, Feng Chia University, Taichung, Taiwan 407, R.O.C.
S.-C. Chen*
Affiliation:
Department of Soil and Water Conservation, National Chung Hsing University, Taichung, Taiwan 402, R.O.C.
*
* Research Assistant Professor
** Professor
Get access

Abstract

This investigation presents the solution of kinematic wave equations for overland flow, in which the lateral term is determined from unsteady rainfall and the infiltration φ index model [1], in which the rate of abstractions is constant, yielding an excess rainfall hyetograph with a total depth that equals the depth of direct runoff over the watershed. Lateral inflow is inferred by the unit step function to represent an unsteady rainfall event; the solution uses the method of characteristics. Part of the discharge hydrograph that satisfies the boundary condition is semi-analytically solved, by a reduced, simple procedure, which does not require the use of numerical method such as finite difference. The analysis presented herein this investigation deals with both rising and falling stages. Example calculations, water surface profiles, and discharge hydrographs are also presented.

Keywords

Kinematic waveunit step functionunsteady lateral inflow
Type
Articles
Information
Journal of Mechanics , Volume 21 , Issue 3 , September 2005 , pp. 171 - 178
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Chow, V. T., Maidment, D. R., and Mays, L. W., Applied Hydrology, McGrawHill Book Co., New York pp. 135–139 (1988).Google Scholar
2.Lighthill, M. J. and Whitham, G. B., “On Kinematic Waves: Flow Movement in Long Rivers,” Proc. R. Soc., London, Ser. A, 229, pp. 281–316 (1955).Google Scholar
3.Iwagaki, Y., “Fundamental Studies on the Runoff Analysis by Characteristics.,” Disaster Prevent. Res. Inst. Bull., 10, Kyoto University, Kyoto, Japan (1955).Google Scholar
4.Foster, G. B., Huggins, L. F. and Meyer, L. D., “Simulation of Overland Flow on Short Field Plots,” Water Resources Research, 4(6), pp. 1179–1188 (1968).Google Scholar
5.Smith, R. E. and Woolhiser, D. A., “Overland Flow on an Infiltrating Surface,” Water Resources Research, 7(4), pp. 899–913 (1971).CrossRefGoogle Scholar
6.Woolhiser, D. A. and Liggett, J. A., “Unsteady, One-Dimensional Flow over a Plane - The Rising Hydrograph,” Water Resources Research, 3(3), pp. 753–771 (1967).Google Scholar
7.Henderson, F. M. and Wooding, R. A., “Overland Flow and Groundwater Flow from a Steady Rainfall of Finite Duration,” J. Geophys. Res., 69(8), pp. 1531–1540 (1964).Google Scholar
8.Wooding, R. A., “A Hydraulic Model for the Catchment-Stream Problem - I. Kinematic-Wave Theory,” Journal of Hydrology, 3, pp. 254–267 (1965a).CrossRefGoogle Scholar
9.Wooding, R. A., “A Hydraulic Model for the Catchment-Stream Problem II. Numerical Solutions.” Journal of Hydrology, 3, pp. 268–282 (1965b).Google Scholar
10.Eagleson, P. S., Dynamic Hydrology, McGrawHill Book Co., New York, pp. 325–366 (1970).Google Scholar
11.Giraldez, J. V. and Woolhiser, D. A., “Analytical Integration of the Kinematic Equation for Runoff on a Plane under Constant Rainfall Rate and Smith and Parlange Infiltration,” Water Resources Research, 32(11), pp. 3385–3389 (1996).CrossRefGoogle Scholar
12.Smith, R. E. and Parlange, J. Y., “A Parameter-Efficient Hydrologie Infiltration Model,” Water Resources Research, 14(3), pp. 533–538 (1978).Google Scholar
13.Cundy, T. W., and Tento, S. W., “Solution to the Kinematic Wave Approach to Overland Flow Routing with Rainfall Excess Given by Philip's Equation,” Water Resources Research, 21(8), pp. 1132–1140 (1985).Google Scholar
14.Philip, J. R., ‘Theory of Infiltration,” Advances in Hydroscience, 5, pp. 215–296 (1969).Google Scholar
15.Luce, C. H., and Cundy, T. W., “Modification of the Kinematic Wave-Philip Infiltration Overland Flow Model,” Water Resources Research, 28(4), pp. 1179–1186 (1992).CrossRefGoogle Scholar
16.Chen, S. C., and Wu, C. M., “Kinematic Wave Model of Subsurface Flow under Hillslope,” Proc. Nati. Sci. Counc. ROC(A), 21(5), pp. 437–444 (1997).Google Scholar
17.Chen, S. C., and Wu, C. M., ‘Using Characteristic Wave to Simulate the Runoff Variation under Constant Rainfall of Finite Duration,” The Chinese Journal of Mechanics-Series B, 18(3), pp. 103–116 (2002).Google Scholar