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<br />Generally the method is not readily compared with the Muskingum <br />method in terms of X, K, and .l.t. It is equivalent to the successive average-lag <br />method, and therefore to X=O and K=.l.t/2 of the Muskingum method, in the single <br />case wherein the number of inflow values being averaged is two and the outflow thus <br />obtained occurs at the time of the second inflow value. <br /> <br />There are several advantages to using the progressive average-lag <br />method. The work necessary to develop storage curves for some alternate methods <br />of routing is not necessary for this method. The principal advantage is the speed with <br />which it can be used. It is useful to obtain hasty or preliminary estimates of flood- <br />control benefits on large watersheds for which a relatively small amount of <br />hydrographic and hydraulic information is available. Modifying conditions, such as <br />reservoir operation for the control of floods, can readily be studied, and results from <br />several proposed storage capacities or from different systems of reservoirs or from <br />individual reservoirs of a system can be found conveniently. <br /> <br />6. MUSKINGUM-CUNGE CHANNEL ROUTING. The Muskingum-Cunge channel <br />routing technique is a non-linear coefficient method that accounts for hydrograph <br />diffusion based on physical channel properties and the inflowing hydrograph. The' <br />advantages of this method over other hydrologic techniques are: (1) the parameters <br />of the model are physically based; (2) the method has been shown to compare well <br />against the full unsteady flow equations over a wide range of flow situations; and (3) <br />the solution is independent of the user specified computation interval. The major <br />limitations of the Muskingum-Cunge technique are that: (1) it cannot account for <br />backwater effects; and (2) the method begins to diverge from the fuU unsteady flow <br />solution when very rapidly rising hydrographs are routed through flat channel sections. <br /> <br />6.1. DEVELOPMENT OF EQUATIONS. The basic formulation of the <br />equations is derived from the continuity equation (21) and the diffusion form of the <br />momentum equation (22): <br /> <br />~+~=q <br />1 <br />at ax <br /> <br />(21) <br /> <br />(22) <br /> <br />By combining equations (21) and (22) and linearizing, the following <br />convective diffusion equation is formulated: <br /> <br />(23) <br /> <br />7-49 <br />