TR-1 : Cause of negative outflow in muskingum method

Abstract

The Muskingum method is a widely used method for routing floods in rivers and channels. The applicability of the method has increased after Cunge related the parameters of the method, based on the conventional difference scheme, with the channel and flow characteristics using the principle of diffusion analogy. Since Cunge's study a number of papers and reports have been added to the literature of Muskingum method. However, one of the disturbing fact of the Muskingum method is the formation of negative or reduced outflow in the beginning of the solution. Various remedial measures like skipping the negative or reduced outflow zone, finding lower bound of reach length so that the magnitude of the defect is reduced, accepting this defect considering that it is small enough and short lived etc. have been suggested in the literature. Some researchers have even suggested not to use Muskingum method for field applications due to the presence of this defect. Another researcher's suggestion for the amendment of the method, through initial conditions, in order to correct this defect was met with severe criticisms and it led to many controversies. Inspite of nearly fifty years of widespread usage, the potential for controversy regarding Muskingum method has not been fully explored. Until the reason for this anomaly is identified, the Muskingum method will suffer from a lack of credibility. This can only hamper its wide acceptance for practical channel routing applications. Taking this into consideration, it is attempted in this note to explore the theoretical basis for the formation of negative or reduced outflow in the. beginning of the Muskingum solution.