On the negative weighting factors in the Muskingum-Cunge scheme

Szél, Sándor; Gáspár, Csaba

doi:10.1080/00221680009498329

Cited by 10 publications

(9 citation statements)

References 3 publications

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“…(9) could be transformed into a proper diffusion wave model by introducing the appropriate diffusive effect through a particular estimation of the model parameter values. By expanding the kinematic model in Taylor series, Cunge (1969) was in fact able to express its numerical diffusion and to estimate the model parameter values by imposing that the numerical diffusion would equal the physical one (for a very clear derivation see Szél and Gáspár, 2000).…”

Section: The Derivation Of the Muskingum Variable Parameter Equationsmentioning

confidence: 99%

A mass conservative and water storage consistent variable parameter Muskingum-Cunge approach

Todini¹

2007

Preprint

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Abstract. The variable parameter Muskingum-Cunge (MC) flood routing approach, together with several variants proposed in the literature, does not fully preserve the mass balance, particularly when dealing with very mild slopes (<10−3). This paper revisits the derivation of the MC and demonstrates (i) that the loss of mass balance in MC is caused by the use of time variant parameters which violate the implicit assumption embedded in the original derivation of the Muskingum scheme, which implies constant parameters and at the same time (ii) that the parameters estimated by means of the Cunge approach violate the two basic equations of the Muskingum formulation. The paper also derives the modifications needed to allow the MC to fully preserve the mass balance and, at the same time, to comply with the original Muskingum formulation in terms of water storage. The properties of the proposed algorithm have been assessed by varying the cross section, the slope, the roughness, the space and the time integration steps. The results of all the tests also show that the new algorithm is always mass conservative. Finally, it is also shown that the proposed approach closely approaches the full de Saint Venant equation solution, both in terms of water levels and discharge, when the parabolic approximation holds.

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Section: The Derivation Of the Muskingum Variable Parameter Equationsmentioning

confidence: 99%

A mass conservative and water storage consistent variable parameter Muskingum-Cunge approach

Todini¹

2007

Preprint

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show abstract

“…According to Szél and Gáspár (2000), though Eq. (2) contains neither the diffusion coefficient nor the expressions for the second-order derivatives, it is possible to define the coefficients of Eq.…”

Section: Numerical Flood Routing Modelmentioning

confidence: 99%

“…The coefficients , , , and are defined by the well-known Courant number and Péclet number in the following equations (Szél and Gáspár, 2000):…”

Section: Numerical Flood Routing Modelmentioning

confidence: 99%

Transmission losses during two flood events in the Platte River, south-central Nebraska

Huang¹,

Chen²,

Chen³

et al. 2015

Journal of Hydrology

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“…As a final remark, please note that, the parameter ε is allowed to take negative values that are legitimate in the variable parameter approaches such as the MC and the newly proposed one, without inducing neither numerical instability nor inaccuracy in the results, as demonstrated by Szél and Gáspár (2000).…”

Section: Resolving the Steady State Inconsistencymentioning

confidence: 99%

“…with second order rounding error (also known as numerical diffusion), given by : Therefore, by imposing that the numerical diffusion equals the physical one (see also Szél and Gáspár, 2000;Wang et al, 2006), Cunge (1969) derived an expression for ε.…”

Section: The Derivation Of the Muskingum Variable Parameter Equationsmentioning

confidence: 99%

A mass conservative and water storage consistent variable parameter Muskingum-Cunge approach

Todini

2007

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

Abstract. The variable parameter Muskingum-Cunge (MC) flood routing approach, together with several variants proposed in the literature, does not fully preserve the mass balance, particularly when dealing with very mild slopes (<10 −3 ). This paper revisits the derivation of the MC and demonstrates (i) that the loss of mass balance in MC is caused by the use of time variant parameters which violate the implicit assumption embedded in the original derivation of the Muskingum scheme, which implies constant parameters and at the same time (ii) that the parameters estimated by means of the Cunge approach violate the two basic equations of the Muskingum formulation. The paper also derives the modifications needed to allow the MC to fully preserve the mass balance and, at the same time, to comply with the original Muskingum formulation in terms of water storage. The properties of the proposed algorithm have been assessed by varying the cross section, the slope, the roughness, the space and the time integration steps. The results of all the tests also show that the new algorithm is always mass conservative. Finally, it is also shown that the proposed approach closely approaches the full de Saint Venant equation solution, both in terms of water levels and discharge, when the parabolic approximation holds.

show abstract

On the negative weighting factors in the Muskingum-Cunge scheme

Cited by 10 publications

References 3 publications

A mass conservative and water storage consistent variable parameter Muskingum-Cunge approach

A mass conservative and water storage consistent variable parameter Muskingum-Cunge approach

Transmission losses during two flood events in the Platte River, south-central Nebraska

A mass conservative and water storage consistent variable parameter Muskingum-Cunge approach

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