The lumped Muskingum flood routing model revisited: the storage relationship

Abstract

Muskingum models are hydrological flood routing approach and vary only in the form of the storage relationship. The storage relationship was first established based on the weighted arithmetic mean. The weighted arithmetic averaging used in the classical linear Muskingum models is not the only way for expressing the storage in the river reach. This study proposes a generalized Muskingum model by establishing the storage using the weighted power mean between the storage volumes due to the inflow and outflow. All traditional models are special cases of the proposed model. The proposed model reduces to four novel storage equations which have not been reported before. The results showed that the proposed models (a) effectively capture the characteristics of the flood wave (b) lead to results with higher efficiency compared to the traditional Muskingum models and (c) make possible to select the most efficient model for a given river.