Muskingum-Cunge

Muskingum-Cunge routing differs from Storage routing in that it considers a linear change in depth along the reach length. This method is more accurate because unlike the Storage Routing method, it does not assume that the flow depth is the same throughout the reach length. In fact the inflow rate is not the same as the outflow rate.

Consider the case when flow is in the rising stage of the inflow hydrograph. Under such a condition, the inflow rate would exceed the outflow rate. Commensurate with this realization, it is obvious that the depth of flow at the upstream end would be greater than at the outlet end. The Muskingum method accounts for this by making the storage in the reach a linear function of both the inflow and outflow rates.

Where k and x are channel characteristics. The coefficient k is also known as the storage constant and is usually equal to the travel time through the reach. If x is set to zero, the method reduces to reservoir storage routing.

Outflow can be expressed as:

Where

In 1967 Cunge developed an approach for estimating the values of C0, C1, C2 that did not rely on simply setting the k value to the reach travel time and x to some assumed constant. In Cunge’s method,

where is the reach length and c represents a flood wave celerity determined from

The coefficient m can be taken as 5/3 (Viessman, 1989). The velocity, v, can be taken as the average velocity at bank full discharge. The value of x is then

Where q0 is the peak flow rate and S0 is the channel slope.