Approximate Methods for the Estimation of Muskingum Flood Routing Parameters

Abstract

There are a variety of techniques for estimating the parameters x and K of the Muskingum method of flood routing. One common difficulty in all the approaches is that different storm sequences along the same river reach would typically yield different parameter estimates. The a statistical analysis of these parameters also shows that they are highly variable. As a result achieving of a high level accuracy may not be the principle issue in describing x and K. This paper presents two approximate methods for estimating these parameters rather easily. The first method requires the computation of the slopes of the inflow and outflow hydrographs at their point of intersection, and the computation of the maximum storage within the reach. The second method requires the computation of the inflow and outflow hydrographs at two specific points. Three case studies investigated show that the first method gives estimates for the Muskingum parameters comparable to those derived by traditional estimation procedures for hydrographs showing linear characteristics.

The Muskingum flood routing model using a neuro-fuzzy approach

“…The data sets including inflow and observed outflow hydrograph in case are from Wilson (1974). The data sets have been extensive used by others (Gill, 1978;Tung, 1985;Yoon and Padmanabhan, 1993;Yang and Chang, 2001;Al-Humoud and Esen, 2006).…”

“…The observed inflow and outflow hydrographs along with the routed flows obtained with the linear Muskingum model and the nonlinear Muskingum model. There Gill, 1978;Al-Humoud and Esen, 2006). The non-linear Muskingum model uses the NONLR (Yoon and Padmanabhan, 1993), the HJ+DFP procedure (as used by Tung, 1985), GA (Mohan, 1997), and FIS in order to estimate the parameters which are then used to determine the routed flows.…”

A modified Muskingum routing approach for floodplain flows: Theory and practice

“…Furthermore, no objective-selection criteria exists for choosing the appropriate value of x and the method therefore, requires a level of subjective interpretation to determine a value that optimises the linear relationship (Gelegenis and Serrano, 2000;Yoon and Padmanabhan, 1993;Chang et al, 1983). Muskingum routing parameters have also been estimated using a least-squares scheme based on minimising the sum of squares of the deviations between observed storage and computed storage for given inflow and outflow hydrographs (Gill, 1978;Birkhead and James, 1997;Al-Humoud and Esen, 2006). The underlying principles of the graphical and the least-square methods are the same and both methods should produce similar parameter values.…”

“…The method therefore, does not accommodate changes in these parameters that would reflect more accurately the routing of storm sequences in the river reach beyond the calibration range (Kundzewicz and Strupczewski, 1982). More recent developments to the method however, do allow for parameter variability with changing characteristics of the inflow hydrograph (see for example Perumal, 1992a;GuangTe and Singh, 1992;Al-Humoud and Esen, 2006). Perumal (1992a) developed a multi-linear Muskingum flood routing method based on a time distribution scheme.…”

“…In these methods, the reach travel time (which depends on the storage, channel characteristics and discharge) is obtained from a simplification of the SaintVenant equations. Al-Humoud and Esen (2006) proposed two approximate methods for the estimation of linear Muskingum flood routing parameters. The first method requires the computation of the slopes of the inflow and outflow hydrographs at their point of intersection, and the computation of the maximum storage within the reach.…”