The cause of negative initial outflow with the Muskingum method

Abstract

The cause of negative or reduced outflow formation at the beginning of a Muskingum solution is examined in two steps. The first step involves a physical interpretation of the Muskingum weighted discharge and the storage equation, using theory based on an extension of the Kalinin-Milyukov method. The second step involves the derivation of an analytical solution for the weighted discharge based on linear systems analysis theory, and then subsequently the Muskingum solution from that analytical solution using the assumption of linear variation of discharge within the reach. It is proved that this assumption causes the formation of negative or reduced outflow at the beginning of a Muskingum solution.