The Muskingum method is based on the continuity equation and the storage-discharge relation. Cunge (1969) extended the method into a finite-difference scheme. The Muskingum-Cunge channel routing technique is a non-linear coefficient method that accounts for hydrograph diffusion based on physical channel properties and the inflow hydrograph. The advantages of this method over other hydrologic techniques are:
- it is very simple conceptually, and can be readily applied by desk calculation, and is much cheaper than the other methods when applied by computer,
- it would be advantageous to use the Muskingum-Cunge method for rivers that have major tributaries and are not well gauged,
- this method can include a tributary as a discrete lateral inflow, which the other methods cannot do in a simple way,
- the hydrologic approach greatly improves computational efficiency and speed, and reduces the amount and detail of field data traditionally needed for hydraulic routing,
- the parameters of the model are physical based, the scheme is stable with properly selected coefficients,
- the method has been shown to compare well against the full unsteady flow equations over a wide range of flow situations,
- it produces consistent results in that the results are reproducible with varying grid solution,
- it is comparable to the diffusion wave routing,
- it is largely independent of the time and space intervals when these are selected within the spatial and temporal resolution criteria.
The major limitations are:
- it cannot account for backwater effects,
- the method begins to diverge from the full unsteady flow solution when very rapidly rising hydrographs are routed through flat channel sections,
- a disadvantage with the Muskingum-Cunge method arises when there is a disturbance such as a tide affecting the flow in the river upstream of the downstream boundary,
- it does not accurately predict the shape of the discharge hydrograph at the downstream boundary when there are large variations in the kinematic wave speed, such as due to the inundation of a large flood plain.