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<br />Where: <br /> <br />S = channel storage <br />K = cell travel time <br />X = weighting factor <br />I = inflow <br />o = outflow <br /> <br />Therefore, the coefficients can be expressed as follows: <br /> <br />(28) <br /> <br />(29) <br /> <br />(30) <br /> <br />(31) <br /> <br />(32) <br /> <br />In the Muskingum equation the amount of diffusion is based on the value <br />of X, which varies between 0.0 and 0.5. The Muskingum X parameter is not directly <br />related to physical channel properties. The diffusion obtained with the Muskingum <br />technique is a function of how the equation, is solved, and is therefore considered <br />numerical diffusion rather than physical. Cunge evaluated the diffusion that is <br />produced in the Muskingum equation and analytically solved for the following diffusion <br />coefficient: <br /> <br />(33) <br /> <br />In the Muskingum-Cunge formulation, the amount of diffusion is <br />controlled by forcing the numerical diffusion to match the physical diffusion <br />represented by the convective diffusion equation (23). this is accomplished by setting <br />equations (25) and (33) equal to each other. the Muskingum-Cunge equation is <br />therefore considered an approximation of the convective diffusion equation (23). As <br /> <br />7-52 <br />