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A simplified flood routing model: variable prameter muskingum (VPM)

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Sommario

I metodi di ≪flood routing≫ studiano la propagazione di un'onda di piena lungo un tratto di un corso d'acqua, assegnato l'andamento temporale della portata nella sezione di monte e le caratteristiche dell'alveo, e usualmente nell'ipotesi di assenza di perturbazioni provenienti da valle (≪condizione di valle passiva≫). Viene qui proposto un procedimento di ≪flood routing≫, formalmente simile ad un ≪Muskingum≫ ma con i parametri variabili e calcolati per via idraulica; idoneo a stimare anche i livelli idrici; valido anche se i termini cinetici non sono del tutto trascurabili; che sfrutta l'irrilevanza della condizione di valle procedendo a cascata da monte a valle; che sfrutta, a vantaggio della semplicità, il fatto che per le normali onde di piena dei corsi d'acqua il cappio di portata è di dimensioni modeste. I risultati ottenuti sono molto migliori di quelli ottenibili con metodi a parametri costanti e, almeno per i casi in cui il cappio relativo è inferiore al 10%, paragonabili a quelli ottenuti con metodi molto più complessi ed onerosi.

Summary

Flood routing methods are numerical methods for estimating the movement of a flood wave along a channel reach, on the basis of the knowledge of the discharge hydrograph at the upstream end and of the hydraulic characteristics of the reach and, usually, in the hypothesis that no perturbation is coming from downstream (≪free boundary condition≫). The flood routing method wich is proposed is similar to the ≪Muskingum≫ one, but with variable and ≪hydraulic≫ parameters; it is able to estimate water levels too; is effective even if kinetic terms are not completely negligible; take advantage of the insignificance of the downstream condition and make it possible to obtain results starting upstream and proceeding downstream; for simplicity's sake, take advantage of the fact that the discharge loop of normal flood waves is quite small. Obtained results are much better that those obtainable from constant parameters methods and indeed, if the flood loop is less that 10%, very similar to those obtainable from more complex and time consuming models.

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Abbreviations

x, t :

channel distance, starting upstream; time

z :

water surface height above datum

Q :

volumetric rate of discharge

P(x, z) :

steady rating curve

q=Q−P :

flood loop

g :

acceleration of gravity

A, B :

cross section wetted area and free surface width

I, S :

water surface slope and friction slope

c :

kinematic wave velocity

F :

Froude number

L,L 0,L 1,L 2,L 3 :

characteristic lengths of the channel

T=L/c :

characteristic time of the channel

D :

diffusion

p, l :

time and space steps

K, X :

Muskingum parameters

C 1,C 2,C 3,C 4 :

Muskingum coefficients

f x=δf/δx,f t=δf/δt etc.:

for the partial derivatives

References

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Authors and Affiliations

  1. Istituto di Costruzioni Idrauliche, Facoltà di Ingegneria, Università di Bologna, Italia

    Paolo Lamberti & Stefano Pilati

Authors
  1. Paolo Lamberti
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  2. Stefano Pilati
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Lamberti, P., Pilati, S. A simplified flood routing model: variable prameter muskingum (VPM). Meccanica 23, 81–87 (1988). https://doi.org/10.1007/BF01556705

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  • DOI: https://doi.org/10.1007/BF01556705

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