Two nonlinear versions of the Muskingum equation are considered. The difference between both equations relates to the exponent parameter. In the first version, commonly used in hydrology, this parameter is considered as free, while in the second version, it takes a value resulting from the kinematic wave theory. Consequently, the first version of the equation is dimensionally inconsistent, whereas the proposed second one is consistent. It is shown that the difference between the results provided by both versions of the nonlinear Muskingum equation depends on the longitudinal bed slope of a channel. For an increasing slope, when a propagating wave becomes more kinematic, the value of the exponent considered as the free parameter tends to its value resulting from the kinematic wave theory. Consequently, when the character of an open channel flow tends to a kinematic one, the dimensionally inconsistent version of the nonlinear Muskingum equation becomes a consistent one. The results of the numerical analysis suggest that apart from the parameters involved in the Muskingum equation, usually considered as free, the parameters of the numerical method of the solution (the number of reservoirs and the time step) should be considered also as free parameters. This conclusion results from the fundamental property of the Muskingum equation, relating to the numerical roots of the wave attenuation process. All numerical examples and tests relate to the solutions of the system of Saint Venant equations, considered as the benchmark.

考虑了Muskingum方程的两个非线性版本。两个方程之间的差异与指数参数有关。在第一个版本中（通常用于水文学中），该参数被视为自由参数，而在第二个版本中，该参数采用由运动波理论得出的值。因此，方程的第一个版本在尺寸上不一致，而拟议的第二个版本则是一致的。结果表明，两种形式的非线性Muskingum方程提供的结果之间的差异取决于通道的纵向床坡度。对于增加的斜率，当传播波变得更加运动时，被视为自由参数的指数值趋于趋于其由运动波理论得出的值。所以，当明渠流动的特性趋于运动学特性时，非线性马斯金格方程的尺寸不一致版本变成一致的。数值分析结果表明，除了通常被认为是自由的Muskingum方程所涉及的参数之外，求解数值方法的参数（储层数量和时间步长）也应视为自由参数。该结论来自Muskingum方程的基本性质，与波衰减过程的数值根源有关。所有数值示例和测试均与被视为基准的Saint Venant方程组的解有关。数值分析结果表明，除了通常被认为是自由的Muskingum方程所涉及的参数之外，求解数值方法的参数（储层数量和时间步长）也应视为自由参数。该结论来自Muskingum方程的基本性质，与波衰减过程的数值根源有关。所有数值示例和测试均与被视为基准的圣维南方程组的解有关。数值分析结果表明，除了通常被认为是自由的Muskingum方程所涉及的参数之外，求解数值方法的参数（储层数量和时间步长）也应视为自由参数。该结论来自Muskingum方程的基本性质，与波衰减过程的数值根源有关。所有数值示例和测试均与被视为基准的圣维南方程组的解有关。该结论来自Muskingum方程的基本性质，与波衰减过程的数值根源有关。所有数值示例和测试均与被视为基准的圣维南方程组的解有关。该结论来自Muskingum方程的基本性质，与波衰减过程的数值根源有关。所有数值示例和测试均与被视为基准的Saint Venant方程组的解有关。