Chapter 24 - Parameter estimation of a new four-parameter Muskingum flood routing model

Abstract

Floods are natural hazards that threaten hydraulic structures, infrastructures, and even human lives. Flood routing is a key process in flood management projects. In the present chapter, a new Muskingum model with four parameters, which is a hydrological flood routing method, is proposed. The parameter estimation of this new model is carried out using three optimization algorithms including Modified Honey Bee Mating Optimization (MHBMO) algorithm and the Generalized Reduced Gradient (GRG) algorithm, and the hybrid MHBMO-GRG. Three flood hydrographs and two types of simulation processes were used not only to assess the applicability of the new flood routing model but also to compare the performances of different algorithms in routing floods and predicting the maximum outflow. Although the outflow estimates of a single peak data using the new four-parameter Muskingum model yielded a higher sum of the square of deviation in outflows (SSQ) than the common three-parameter Muskingum model, it reduced the SSQ of double peak data by 28.63% using the MHBMO algorithm. Moreover, the comparison indicates that applying the second simulation process, which implements average inflows instead of inflow at each time interval, improves the SSQ between 43.51% and 91.35% for the three datasets using the new version of the Muskingum model. Finally, the new Muskingum model may have a more reliable structure than the common three-parameter nonlinear version because any type of optimization technique used in this study could reach the optimum values in its parameter estimation.