• 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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• 1996.05a
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• pp.381-386
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• 1996

• Journal of Korea Water Resources Association
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• v.53 no.8
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• pp.597-604
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• 2020

Muskingum, a hydrologic channel flood routing, is a method of predicting outflow by using the relationship between inflow, outflow, and storage. As many studies for Muskingum model were suggested, parameters were gradually increased and the calculation process was complicated by many parameters. To solve this problem, an optimization algorithm was applied to the parameter estimation of Muskingum model. This study applied the Advanced Nonlinear Muskingum Model considering continuous flow (ANLMM-L) to Wilson flood data and Sutculer flood data and compared results of the Linear Nonsingum Model incorporating Lateral flow (LMM-L), and Kinematic Wave Model (KWM). The Sum of Squares (SSQ) was used as an index for comparing simulated and observed results. Exponential Bandwidth Harmony Search with Centralized Global Search (EBHS-CGS) was applied to the parameter estimation of ANLMM-L. In Wilson flood data, ANLMM-L showed more accurate results than LMM-L. In the Sutculer flood data, ANLMM-L showed better results than KWM, but SSQ was larger than in the case of Wilson flood data because the flow rate of Sutculer flood data is large. EBHS-CGS could be appplied to be appplicable to various water resources engineering problems as well as Muskingum flood routing in this study.

• 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.

• Water for future
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• v.23 no.3
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• pp.385-395
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• 1990

Three-parameter Muskingum flood routing model which incorporated the inflows alongside the river channel is applied for the Waegwan-Jeukpogyo reach of the Nakdong River using the flood data of 12 selected flood events experienced in this reach. The flood routing equations for three-parameter model were expressed as a system of finite difference equations and the routing constants were directly computed by matrix inversion method. Then, the three parameters, which consist of the storage constants(K), weighting fator(x), and lateral inflow parameter(α), were determined from the computed routing constants. The results of the present study showed that the model can predict with a fair accuracy the flood discharges at the downsteam end of the reach. The parameters K and x were seen as channel parameters which have close relations with the flood magnitude, whereas the lateral inflow parameter was shown to be strongly governed by the rainfall characteristics of the tributary watersheds contributing to the lateral inflows.

• Journal of Korea Water Resources Association
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• v.33 no.S1
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• pp.3-10
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• 2000

A newly developed heuristic algorithm, Harmony Search, is applied to the parameter calibration problem of the nonlinear Muskingum model. The Harmony Search could, mimicking the improvisation of music player, find better parameter values for in the nonlinear Muskingum model than five other methods including another heuristic method, genetic algorithm, in the aspect of SSQ(the sum of the square of the deviations between the observed and routed outflows) as well as in the aspects of SAD(the sum of the absolute value of the deviations), DPO(deviations of peak of routed and actual flows) and DPOT(deviatios of peak time of routed and actual outflow). Harmony Search also has the advantage that it does not require the process of asuming the initial values of desing parameters. The sensitivity analysis of Harmony Memory Considering Rate showed that relatively large values of Harmony Memory Considering Rate makes the Harmony Search converge to a better solution.

• 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.

• Proceedings of the Korea Water Resources Association Conference
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• 1990.07a
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• pp.29-39
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• 1990

측방유입수가 고려되는 3변수 Muskingum하도추적모형을 낙동강수계중 왜관에서 적포교구간의 12개 홍수사상에 대하여 적용하였고, 기존방법인 2변수 Muskingum방법의 저류상수 K와 가중계수 x에 추가된 $\alpha$는 측방유입수를 고려해주는 변수이다. 3변수모형의 추적방정식은 유한차분 방정식으로 표현되며, 추적상수 결정은 Matrix Inversion에 의하여 직접 계산가능하며, 이로부터 각홍수사상의 K x $\alpha$값을 구할수 있다. 본 연구를 실유역에 적용하여 실측치와 비교하여본 결과 비교적 잘 맞음을 알 수 있었으며, K와 x값은 하도특성인자로서 홍수규모와 관계되고 측방유입인자 $\alpha$는 항특성에 의하여 지배되는 변수로 측방유입량이 클수록 값이 커지는 성향으로 나타났다.

• Proceedings of the Korea Water Resources Association Conference
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• 2000.05a
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• pp.3-10
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• 2000

A newly developed heuristic algorithm, Harmony Search, is applied to the parameter calibration problem of the nonlinear Muskingum model. The Harmony Search could, mimicking the improvisation of music players, find better parameter values for in the nonlinear Muskingum model than five other methods including another heuristic method, genetic algorithm, in the aspect of SSQ (the sum of the square of the deviations between the observed and routed outflows) as well as in the aspects of SAD (the sum of the absolute value of the deviations), DPO (deviations of peak of routed and actual flows) and DPOT (deviations of peak time of rented and actual outflow). Harmony Search also has the advantage that it does not require the process of assuming the initial values of design parameters. The sensitivity analysis of Harmony Memory Considering Rate showed that relatively large values of Harmony Memory Considering Rate makes the Harmony Search converse to a better solution.