Many hydraulic engineering problems involve the computation of the propagation of flood waves in open channels. The complexity inherent in the calculations based on the solution of the full Saint-Venant equations has led to the development of approximate methods, which have become especially popular among hydrologists. The Muskingum method has found extensive application in connection with flood routing problems. Cunge showed how the Muskingum method is consistent with the Saint Venant equations. The conventional Muskingum procedure assumes that there is no lateral inflow along the river reach. However, the lateral or tributary flow is seldom negligible. The Muskingum procedure has however been extended to include lateral inflow. The basic flood routing equation is an approximation of the Saint Venant equations and is valid for any typical Froude number. This equation includes the lateral inflow (or outflow). The equation implies that flood wave propagation through an open channel is a function of the discharge (Q) and two key parameters namely kinematic wave speed (c0) and attenuation parameter (a0) that are themselves functions of Q alone. The main objectives of this study were to find optimum parameterised functional forms for the kinematic wave speed and the attenuation parameter using optimisation techniques together with the calculation of a uniformly distributed time dependent lateral inflow along the reach. The functional forms for c0 and a0 were based on a theoretical analysis of the wave speed for small and large values of discharge in a river together with experience of the general forms for particular natural rivers. Care was taken to distinguish between inbank and overbank values of c0 and a0. It was concluded that forms for c0 and a0 required time independent parameters to be determined. The optimisation was done by minimising the cumulative sum of the negative values for a filtered lateral inflow calculated from the basic flood routing equation using GLOBE. This is done in the case of knowing both the downstream as well as the upstream discharges during an extended flood event. The method for determining c0 and a0 was applied to the River Wye (UK) and the River Meuse (Netherlands). In each case the effectiveness of the method was confirmed by using the resulting forms of c0 and a0 with the basic flood routing equation to calculate the downstream discharge.
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