Abstract
Kinematic wave (KW) theory is widely applied for modeling overland flow. The theory is comprised of (1) continuous waves, (2) formation of shocks, and (3) propagation of shocks. This paper revisits the KW concept for overland flow from fluid mechanical and mathematical points of view. Then, it develops mathematical formulations of overland flow, based on the classification of overland flow problems and the influence of storm movement and areal coverage. Depending on the class of overland flow problems, the mathematical formulation involves free boundary problems that are not known beforehand and must be solved for along with the solution of the problem. Finally, the validity of the KW concept is revisited and the accuracy of the KW approximation can be expressed by Riccati equation that describes the error for the whole hydrograph.
Similar content being viewed by others
References
De Lima JLMP, Singh VP (2002) The influence of pattern of moving rainstorms on overland flow. Adv Water Resour 25(7):817–828
De Lima JLMP, Singh VP, de Lima MIP (2003) The influence of storm movement on water erosion: storm direction and velocity effects. Catena 52(1):39–56
Lighthill MJ, Whitham GB (1955) On kinematic waves: 1. Flood movement in long rivers. Proc R Soc London, Ser A 229:281–3156
Singh VP (1994a) Accuracy of kinematic wave and diffusion wave approximations for space independent flows. Hydrol Process 8:45–62
Singh VP (1994b) Derivation of errors of kinematic-wave and diffusion-wave approximations for space-independent flows. Water Resour Manag 8:57–82
Singh VP (1996) Kinematic wave modeling in water resources: surface water hydrology. Wiley, New York
Singh VP, Aravamuthan V (1995a) Accuracy of kinematic wave and diffusion wave approximations for time-independent flows. Hydrol Process 9:755–782
Singh VP, Aravamuthan V (1995b) Errors of kinematic-wave and diffusion-wave approximations for time-independent flows. Water Resour Manag 9:175–202
Woolhiser DA, Liggett JA (1967) Unsteady one-dimensional flow over a plane-the rising hydrograph. Water Resour Res 3:753–771
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Singh, V.P. Kinematic Wave Theory of Overland Flow. Water Resour Manage 31, 3147–3160 (2017). https://doi.org/10.1007/s11269-017-1654-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-017-1654-1