Water Science and Engineering 2008, 1(3) 16-23  DOI:   10.3882/j.issn.1674-2370.2008.03.002   ISSN: 1674-2370 CN: 32-1785/TV

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Muskingum method parameter X
physical meaning
numerical analysis
stability condition
parameter calibration
Xiao-fang RUI
Fang-gui LIU
Mei YU
Article by
Article by
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Discussion of Muskingum method parameter X

Xiao-fang RUI*1,2, Fang-gui LIU1,2, Mei YU1,2

1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Nanjing 210098, P. R. China
2. College of Hydrology and Water Resources, Hohai University, Nanjing 210098, P. R. China


The parameter X of the Muskingum method is a physical parameter that reflects the flood peak attenuation and hydrograph shape flattening of a diffusion wave in motion. In this paper, the historic process that hydrologists have undergone to find a physical explanation of this parameter is briefly discussed. Based on the fact that the Muskingum method is the second-order accuracy difference solution to the diffusion wave equation, its numerical stability condition is analyzed, and a conclusion is drawn: X<=0.5 is the uniform condition satisfying the demands for its physical meaning and numerical stability. It is also pointed out that the methods that regard the sum of squares of differences between the calculated and observed discharges or stages as the objective function and the routing coefficients C0 , C1 and C2 of the Muskingum method as the optimization parameters cannot guarantee the physical meaning of X.

Keywords Muskingum method parameter X   physical meaning   numerical analysis   stability condition   parameter calibration  
Received 2008-07-28 Revised 2008-08-15 Online:  
DOI: 10.3882/j.issn.1674-2370.2008.03.002
Corresponding Authors: Xiao-fang RUI
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