Degree Name

Master of Engineering (Hons.)


Department of Civil and Mining Engineering


Flood routing is commonly used to calculate the shape of the flood hydrograph at the downstream end of a reservoir or a river reach, if the flood hydrograph at the upstream end of the reach is known. The flood routing procedure also enables prediction of the time at which the flood will occur at the downstream station. One of the methods of flood routing which has been widely applied in engineering practice because of its simplicity and accuracy is the Muskingum method. This method is based on the assumption of a linear algebraic relationship between inflow I, outflow Q and storage S in a reach. The equation used is basically and numerically derived from the differential equation of continuity or conservation of mass. As mentioned above, flood routing normally involves the use of an upstream hydrograph to estimate a downstream hydrograph, an example is estimating the flood hydrograph at the downstream end of a river reach. An estimate of the upstream hydrograph from the recorded flood hydrograph at the downstream end is sometimes required. This case is less common, but still significant. For example, it can be needed to fill in missing records using those at a downstream station. This reverse routing equation, mathematically, can be deduced easily from the conventional Muskingum equation, i.e.: re-arranging the Muskingum equation to solve for inflow I given outflow Q. Difficulties often arise, since the process is numerically unstable. This numerical instability can cause the process to diverge from the true solution or oscillations to occur in the calculated upstream hydrograph. In practice, satisfactory upstream hydrographs cannot be obtained. This project is intended to investigate that problem, to determine the cause of the numerical instability and to develop some alternative approaches which can overcome the problem. Several methods of solution were investigated, including an iterative approach combined with a smoothing and averaging algorithms. Results using this method show that the numerical instability can be overcome by selecting an appropriate time step (routing period), which has been shown to depend on the values of the Muskingum model parameters. The solution converges rapidly because of the use of the averaging algorithm, and accurate estimates of the upstream hydrograph are obtained. It can be said that this method has the same order of accuracy as the conventional downstream routing using the Muskingum method.