• Journal of Korea Water Resources Association
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• v.36 no.5
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• pp.751-760
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• 2003

Error analysis of finite difference equation on the Muskingum-Cunge flood routing method with free time and space weighting factor was carried out. The error analysis shows that the numerical solution of the Muskingum-Cunge method becomes diverged with time when the sum of time weighting factor and space weighting factor is greater than 1.0. Numerical diffusion increases when the sum of time weighting factor and space weighting factor decreases. Numerical diffusion and numerical oscillation increase when the grid resolution is coarse. Numerical experiments and field applications show that the Muskingum-Cunge method with free space weighting factor is more effective for simulating the flood routing with great peak diminution than conventional Muskingum-Cunge method with fixed space weighting factor, 0.5.

• Journal of Korea Water Resources Association
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• v.43 no.2
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• pp.233-243
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• 2010

A method is proposed of estimating Muskingum-Cunge parameters for natural streams using cross-sectional and longitudinal channel geometry and roughness coefficient data. Firstly, for various water-surface levels at a cross section cross-sectional areas and hydraulic radii are calculated. Corresponding discharges are then calculated using Manning's equation. This procedure is repeated for all cross-sections in the reach. Finally, routing parameters are estimated from the calculated cross-sectional area and discharge value pairs by regression analysis. The procedures for estimating Muskingum-Cunge parameters are applied to the South Han River. Flows calculated by Muskingum-Cunge model with estimated parameters showed much better agreement with those by dynamic wave model in peak discharge, time to peak discharge, and normalized RMS errors than those calculated by the HEC-1 Muskingum-Cunge model.

• Journal of Korea Water Resources Association
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• v.32 no.4
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• pp.417-426
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• 1999

A series of numerical experiments is performed to compare the characteristics of outflow hydrograph using linear and nonlinear Muskingum-Cunge methods for two cases: (a) sinusoidal inflow hydrographs and (b) rainfall inputs. The nonlinear method shows the steepening of the rising limb, coupled with a corresponding flattening of the receding limb. The linear method conserves mass exactly. In contrast, the nonlinear method is subject to a gain and a loss of mass. The loss of mass and the subsidence of peak outflow increases with a mild slope, a small baseflow $q_b$ and a large peak inflow to baseflow ratio $q_p/q_b$. A shock wave and associated numerical instability results in the increase of mass for a steep slope and a large $q_p/q_b$ ratio. While the linear method depends on the reference flow per unit-width, the nonlinear method depends on a baseflow and the $q_p/q_b$ ratio. It is found that, unlike for the sinusoidal inflow, the outflow for the rainfall inputs conserves mass fairly exactly in the nonlinear method.

• Water for future
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• v.29 no.5
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• pp.139-150
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• 1996

This paper presents the effect of numerical parameters, such as grid size and grid ratio, on the outflow hydrograph of a unit-width plane in the linear Muskingum-Cunge method. The numerical results depend on Courant number C and cell Reynolds number D, two physically and numerically meaningful parameters. As C approache 1 and D increases, the numerical dispersion-relating oscillations are difficult to occur. The numerical oscillations occur in the front of a propagating wave for C < 1, while smaller oscillations occur behind the wave for C > 1 due to the numerical diffusion effect. For a plane with a small value of characteristic reach length L (e.g., a steep plane), the numerical solution of the Muskingum-Cunge method is similar to that of the kinematic wave method, which shows no wave attenuation. However, for a plane with a large value of L (e.g., a mild plane), the Muskingum-Cunge method leads to the diffusion waves which are essentially independent of the Courant number. Accordingly, the Muskingum-Cunge method will be suited for the routing of the catchment with relatively mild slopes.

• Proceedings of the Korea Water Resources Association Conference
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• 1996.05a
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• pp.375-380
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• 1996

• Proceedings of the Korea Water Resources Association Conference
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• 1995.05a
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• pp.355-360
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• 1995

• Magazine of the Korean Society of Agricultural Engineers
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• v.21 no.1
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• pp.13-23
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• 1979

The predictien of a design flood hydrograph at a particular site on a river may be based on the derivation of a discharge or stage hydrograph at an upstream section, together with a method to route this hydrograph along the rest of the river. In order to limit this investigation to cases where the assumption like uniform rainfall may be reasonably valid, the derivation of unit hydrographs has been limited to catchment with an area less than 500 km2. Consequently, flood routing methods provide a useful tool for the analysis of flooding in all but the smaller catchment, particularly where the shape of the hydrograph as well as the peak value is required. The author, therefore, will introduce here a flood routing method on the open channel with a peak discharge of the catchment area concerned. The importance of being able to route floods accurately is also reflected in the large number of flood routing method which have been developed since the year 1900. There are the modified puls method, Steinberg method, Goodrich method, Ekdahl method, Tatum's mean continuously Equation, wisler-Brater method, Muskingum, chung, and Muskingum-cunge (M-C) method and so on. The author will try to introduce a flood routing method which is revised Muskingum-cunge method. In calculating flood routing by the M-C method, whole variable parameters on the river were assumed to almost uniform values from the upstream to the downstream. In the results, the controlled flood rates at the 40km downstream on the river is appeared to decrease 22m$^3$/sec or 12 percent of the peak flood 170m$^3$/sec.

• Korean Journal of Hydrosciences
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• v.8
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• pp.41-56
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• 1997

A new routing computer model for the symmetric compound channel called the ASRMCS(Apparent Shear Force Muskingum-Cunge Method in Symmetry) has been developed. The Muskingum-Cunge routing method is adapted. The Apparent Shear Force (ASF) between the deep main channel and the shallow floodplan flow is introduced while the flow is routed. The nonlinear parameter method is applied. The temporal and spatial increments are varied according to the flow rate. The adaptation of above schemes is tested against the routed hydrographs using the DAMBRK model. The results of general routing practice of Muskingum-Cunge Method(GPMC) are also compared with those of above two models. The results of the new model match remarkably well with those of DAMBRK. The routed hydrographs show a smooth variation from the inflow boundary condition without any distortions caused by the difference of cross-section shape. However, the results of GPMC, showing early rise and fall of routed hydrograph, have considerable differences from those of the ASFMCS and DAMBRK.

• Water for future
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• v.18 no.3
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• pp.265-270
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• 1985

The prediction of a design-flood hydrograph at a particular site on a river may be based on the derivation of discharge or stage hydrograph at an upstream section, togeater with a method to route this hydrograph along the rest of river. On the other hand, flood routing methods provide a useful tool for the analysis of flooding in all but the smaller catchment, and these methods are largely stored into hydrological method and hydraulic method. Although the Muskingum Method as a hydrological method ignores dynamic effects on the flood wave, Muskingum-Cunge Method based on hydraulic method is possible to improve the method so that it gives a good approximation to the solution of the linear convective-diffusion equation. This is made on the basis of the finite diffeience equation for the Muskingum Method. In the study, the outflows predicted by Muskingum-Cunge Method are campared with the observed outflows of the Pyung Chang River.

• Water for future
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• v.29 no.3
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• pp.217-228
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• 1996

A new routing computer model for the symmetric compound channel called the ASFMCS (Apparent Shear Force Muskingum-Cung Method in Symmetry) is developed. The Muskingum-Cunge routing method is adapted. The Apparent Shear Force(ASF) between the deep main channel and shallow floodplain flow is introduced while the flow is routed. The nonlinear parameter method is applied. The temporal and spatial increments are varied according to the flow rate. The adaptation of above schemes is tested against the routed hydrographs using the DAMBRK model. The results of general routing practice of Muskingum-Cunge Method (GFMC) are also compared with those of the above two models. The results of the new model match remarkably well with those of DAMBRK. The routed hydrographs show smooth variation from the inflow boundary condition without any distortions caused by the difference of cross-section shape. However, the results of GPMC, showing earlier rising and falling of routed hydrograph, have considerable differences from those of the ASFMCS and DAMBRK.