Negative Outflows from Muskingum Flood Routing

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Abstract
The Muskingum flood routing method was developed in studies made for the Muskingum Conservancy District Flood-Control Project during the mid-1930s. Since its development, investigations into the nature of the method have experienced surges of activity. Application of linear system theory led to one form of interpretation. Development of the routing equation from kinematic wave theory provided an additional interpretation. Many investigators have transformed the Muskingum hypothesis into a continuous equivalent. The resulting differential equation was then investigated. The inevitability of negative discharges in the routed outflow using the continuous equivalent has drawn comment from these investigators and is a cause for concern among practicing engineers. A definitive solution to this anomalous result is still unavailable. In practice, however, the continuous approach is seldom practical. The inflow is given as discrete values occurring at discrete times. The result of the routing is a table of discrete outflows at discrete times. For this reason, discrete system methods are used in this study and it is shown that the classical limits on routing parameters ensure nonnegative outflows.

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