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Erschienen in: Water Resources Management 10/2017

26.04.2017

Kinematic Wave Theory of Overland Flow

verfasst von: Vijay P. Singh

Erschienen in: Water Resources Management | Ausgabe 10/2017

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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.

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Literatur
Zurück zum Zitat De Lima JLMP, Singh VP (2002) The influence of pattern of moving rainstorms on overland flow. Adv Water Resour 25(7):817–828CrossRef De Lima JLMP, Singh VP (2002) The influence of pattern of moving rainstorms on overland flow. Adv Water Resour 25(7):817–828CrossRef
Zurück zum Zitat 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):39–56CrossRef 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):39–56CrossRef
Zurück zum Zitat Lighthill MJ, Whitham GB (1955) On kinematic waves: 1. Flood movement in long rivers. Proc R Soc London, Ser A 229:281–3156CrossRef Lighthill MJ, Whitham GB (1955) On kinematic waves: 1. Flood movement in long rivers. Proc R Soc London, Ser A 229:281–3156CrossRef
Zurück zum Zitat Singh VP (1994a) Accuracy of kinematic wave and diffusion wave approximations for space independent flows. Hydrol Process 8:45–62CrossRef Singh VP (1994a) Accuracy of kinematic wave and diffusion wave approximations for space independent flows. Hydrol Process 8:45–62CrossRef
Zurück zum Zitat Singh VP (1994b) Derivation of errors of kinematic-wave and diffusion-wave approximations for space-independent flows. Water Resour Manag 8:57–82CrossRef Singh VP (1994b) Derivation of errors of kinematic-wave and diffusion-wave approximations for space-independent flows. Water Resour Manag 8:57–82CrossRef
Zurück zum Zitat Singh VP (1996) Kinematic wave modeling in water resources: surface water hydrology. Wiley, New York Singh VP (1996) Kinematic wave modeling in water resources: surface water hydrology. Wiley, New York
Zurück zum Zitat Singh VP, Aravamuthan V (1995a) Accuracy of kinematic wave and diffusion wave approximations for time-independent flows. Hydrol Process 9:755–782CrossRef Singh VP, Aravamuthan V (1995a) Accuracy of kinematic wave and diffusion wave approximations for time-independent flows. Hydrol Process 9:755–782CrossRef
Zurück zum Zitat Singh VP, Aravamuthan V (1995b) Errors of kinematic-wave and diffusion-wave approximations for time-independent flows. Water Resour Manag 9:175–202CrossRef Singh VP, Aravamuthan V (1995b) Errors of kinematic-wave and diffusion-wave approximations for time-independent flows. Water Resour Manag 9:175–202CrossRef
Zurück zum Zitat Woolhiser DA, Liggett JA (1967) Unsteady one-dimensional flow over a plane-the rising hydrograph. Water Resour Res 3:753–771CrossRef Woolhiser DA, Liggett JA (1967) Unsteady one-dimensional flow over a plane-the rising hydrograph. Water Resour Res 3:753–771CrossRef
Metadaten
Titel
Kinematic Wave Theory of Overland Flow
verfasst von
Vijay P. Singh
Publikationsdatum
26.04.2017
Verlag
Springer Netherlands
Erschienen in
Water Resources Management / Ausgabe 10/2017
Print ISSN: 0920-4741
Elektronische ISSN: 1573-1650
DOI
https://doi.org/10.1007/s11269-017-1654-1

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