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

机译：质量守恒和储水一致的可变参数Muskingum-Cunge方法

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摘要

The variable parameter Muskingum-Cunge (MC) flood routing approach, togetherwith several variants proposed in the literature, does not fully preservethe mass balance, particularly when dealing with very mild slopes (<10−3). This paper revisits the derivation of theMC and demonstrates (i) that the loss of mass balance in MC is caused by theuse of time variant parameters which violate the implicit assumptionembedded in the original derivation of the Muskingum scheme, which impliesconstant parameters and at the same time (ii) that the parameters estimatedby means of the Cunge approach violate the two basic equations of theMuskingum formulation. The paper also derives the modifications needed toallow the MC to fully preserve the mass balance and, at the same time, tocomply with the original Muskingum formulation in terms of water storage.The properties of the proposed algorithm have been assessed by varying thecross section, the slope, the roughness, the space and the time integrationsteps. The results of all the tests also show that the new algorithm isalways mass conservative. Finally, it is also shown that the proposedapproach closely approaches the full de Saint Venant equation solution, bothin terms of water levels and discharge, when the parabolic approximationholds.
机译：可变参数Muskingum-Cunge（MC）洪水路由方法以及文献中提出的几种变型方法不能完全保持质量平衡，尤其是在处理非常缓和的坡度（<10 -3 ）时。本文回顾了MC的推导，并证明（i）MC中的质量平衡损失是由使用时变参数引起的，该参数违反了Muskingum方案原始推导中包含的隐含假设，该隐含假设同时暗示了恒定参数（ii）通过Cunge方法估算的参数违反了Muskingum公式的两个基本方程式。本文还得出了需要修改的条件，以允许MC完全保持质量平衡，同时在储水方面与原始Muskingum配方相符。通过改变横截面，坡度，粗糙度，空间和时间积分步骤。所有测试的结果还表明，新算法始终是质量保守的。最后，还表明，当抛物线近似成立时，无论是在水位还是流量方面，所提出的方法都非常接近完整的de Saint Venant方程解。

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