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Proceedings of the International Conference on Hydrology and Water Resources, New Delhi, India, December 1993 pp 261–295Cite as

Physically Based Linear Flood Routing Modeling

  • Conference paper

Part of the book series: Water Science and Technology Library ((WSTL,volume 16))

Abstract

The papers starts from recalling the St. Venant equation, its assumptions and problems of numerical solution of differential equations. Then outline of work on linearization of the St.Venant equation and on its application is given. The reasons why the linearized St. Venant model has not driven out the conceptual flood routing linear models are discussed.

In order to get the linearized equation valid for a large number of choices for the dependent variable, the perturbation potential is introduced. Problems in the linear theory of open channel flow are listed and their solutions either are presented or references to literature are given. Those of them still waiting for solution are also included.

The major part of the paper is given to search for a physical reason to a great practical popularity of the linear conceptual flood routing model in the form of a series of linear reservoirs with pure delay, known as Lag Kalinin-Miliukov model (LKM). It is used as an opportunity to presentation of solutions of some upstream control problems. Impulse response of the LKM model was compared with that of the linearized St. Venant model with upstream input (LCR) together with its limiting case of Froude number equal to one (RF). A comparison of LKM and RF models has shown that in spite of a certain structural similarity, the LKM model is not suitable for a steep river channel. However for certain flow conditions, frequently met during floods, the LKM model shows amazingly good agreement with the LCR measured by the differences of higher order cumulants and a satisfactory one for differences of lags. That is why, taking additionally into account the poor observability of a river system, the model is suggested to be accepted as a third, besides RF and Lag Diffusion Analogy (LDA) models, particular case of LCR.

The introduced coefficient αR (R=4,5,6,..) being a R function of three cumulants has served to find a useful property of LCR and to classify the particular cases solutions. Regions of applicability of the particular cases models were defined by the criterion of an error of fourth cumulant simulation.

In view of presented results LKM model may have been derived by theoreticians working working on fluid mechanics and then recommended for practice. However it has happened contrariwise.

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Author information

Authors and Affiliations

  1. Institute of Geophysics, Polish Academy of Sciences, 64 Ksiecia Janusza, 01-452, Warsaw, Poland

    Witold G. Strupczewski

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  1. Witold G. Strupczewski
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Editors and Affiliations

  1. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, USA

    Vijay P. Singh

  2. National Institute of Hydrology, Roorkee, India

    Bhishm Kumar

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© 1996 Springer Science+Business Media Dordrecht

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Strupczewski, W.G. (1996). Physically Based Linear Flood Routing Modeling. In: Singh, V.P., Kumar, B. (eds) Proceedings of the International Conference on Hydrology and Water Resources, New Delhi, India, December 1993. Water Science and Technology Library, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0389-3_18

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  • DOI: https://doi.org/10.1007/978-94-011-0389-3_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4174-4

  • Online ISBN: 978-94-011-0389-3

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