Response of Muskingum Equation to Step Input

Abstract

Solution of the Muskingum equation for a step input function has been developed using the Laplace transform method. The solution is in agreement with a previous results, which was obtained by the author using a different method. The solution is different from the one published in the past by many others. The old solution predicts unrealistic negative outflows for small values of time. In contrast, the proposed solution is free of this or any other defect. The solution can be practically used by method of convolution to route physical floods without encountering negative outflows or violating the continuity of mass conservation. The source of error in the previous solution given by others has been pointed out.