On the use of the Muskingum method for the simulation of flood wave movements

Abstract

Muskingum method, • transformation of a flood wave, • calibration of parameters, • genetic algorithm. ABSTRACTThe Muskingum method is a hydrological flow routing model with lumped parameters, which describes the transformation of discharge waves in a river bed using two equations. The first one is the continuity equation (conservation of mass) and the second equation is the relationship between the storage, inflow, and outflow of the reach (the discharge storage equation). These equations are applied within a river reach between two cross sections of a river. The parameters of the model can be estimated by several methods. Here the classical graphic method is compared with two new methods where a genetic algorithm and harmony search was used for optimization. The discrete state space formulation of the Muskingum method was applied on the lower Morava reach between Moravský Svätý Ján and Záhorská Ves. The results showed a good degree of accuracy of all three methods, which were assessed by the Nash-Sutcliffe efficiency coefficient.

Variable Parameter Multilinear Muskingum Method: Case Study on the Danube River

“…The discrete state space representation (Szolgay, 1982) is less well known; therefore, for the sake of completeness, we will show (based on Baláž et al, 2010) how to derive the state equations. The Muskingum equation is adopted as:…”

“…3 The histograms show the absolute frequency of the peak discharge and travel time in the river reach for all the discharge waves (period 1992-2014) Fig. 4 Empirical peak travel-time and input peak discharge in the Devín-Bratislava -Medveďov river reach (period 1992-2014), and box plot of the data for the categories selected (1 st and 3 rd quartiles, minimum, median and maximum travel times) et al, 2007;Baláž et al, 2010;Danáčová et al, 2015) that we can try to adopt a similar methodology of introducing multilinearity for the Muskingum model on this river with anthropogenically modified flood regime, namely, by also using the relationship between the travel time parameter K of the model and the peak flow of the input hydrographs as the parametrization for the multilinear Muskingum model in this river reach with an anthropogenically altered flow regime.…”

“…The following two variable parammetrisation approaches were then attempted (similarly as in Baláž et al, 2010): First, several alternative piecewise linear relationships of the K = f (inflow) relationship were tested. These were composed from a preset number of non-overlapping linear segments of equal lengths.…”

“…In several previous studies we have shown that the relationship between the travel-time of flood peaks and peak discharges can be used to parameterize multilinear flood routing models based on the state space representation of the classical Kalinin -Miljukov cascade (see, e.g., Szolgay et al, 2007;Danáčová et al, 2015). A similarly structured multilinear version of the Muskingum routing model was proposed in our previous paper (Baláž et al, 2010). It is based on the discrete state space equations for the Muskingum equation, which enables us to more flexibly reflect the changes of parameters governing the system's dynamics (Szolgay, 1982) through a discharge variable parametrisation.…”

“…In a pilot study by Baláž et al (2010), the Muskingum model was tested in a river reach on the Morava River. In this study the same multilinear version of the Muskingum model was used on a reach of the Danube that contains the Gabčíkovo hydropower utilisation scheme.…”