Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
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Hydrologic Re-Analysis of Muskingum Channel Routing Method: A Linear Combination of Linear Reservoir and Linear Channel Models

Muskingum 하도추적방법의 수문학적 재해석: 선형저수지모형과 선형하천모형의 선형결합

  • Yoo, Chul-Sang (School of Civil, Environmental and Architectural Engineering, College of Engineering, Korea University) ;
  • Kim, Ha-Young (School of Civil, Environmental and Architectural Engineering, College of Engineering, Korea University)
  • 유철상 (고려대학교 공과대학 건축사회환경공학부) ;
  • 김하영 (고려대학교 건축사회환경공학부)
  • Received : 2010.08.02
  • Accepted : 2010.11.30
  • Published : 2010.12.31
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Abstract

This study hydrologically re-analysed the Muskingum channel routing method to represent it as a linear combination of the linear channel model considering only the translation and the linear reservoir model considering only the storage effect. The resulting model becomes a kind of instantaneous unit hydrograph, whose parameters are identical to those of the Muskingum model. That is, the outflow occurs after the routing interval ${\Delta}t$ or concentration time $T_c$, and among the total amount of inflow, the x portion is translated by the linear channel model and the remaining (1-x) portion is routed by the linear reservoir model with the storage coefficient ��$K_c$. The application result of both the Muskingum channel routing method and its corresponding instantaneous unit hydrograph to an imaginary channel showed that these two models are basically identical. This result was also assured by the application to the channel flood routing to the Kumnam and Gongju Station for the discharge from the Daechung Dam.

본 연구에서는 Muskingum 하도추적모형을 수문학적으로 재해석하여 지체효과만을 고려하는 선형하천모형과 저류효과만을 고려하는 선형저수지모형의 선형결합으로 나타내었다. 유도된 모형은 일종의 순간단위도의 형태가 되며, 그 매개 변수는 Muskingum 모형의 매개변수와 동일하다. 즉, 추적시간간격 ${\Delta}t$ 또는지체시간 $T_c$ 후에 최초의 유출이 발생하게 되고, 총 유입량 중 x 만큼은 선형하천모형에 의해 저류효과 없이 빠져나가고 나머지(1-x) 만큼은 선형저수지모형에 의해 저류상수 $K_c$로 대변되는 저류효과를 나타내며 빠져나가는 형태이다. Muskingum 하도추적 모형과 그에 대응하는 순간단위도를 가상하도에 적용해 본 결과, 두 모형이 근본적으로 하도추적결과가 동일함을 확인하였다. 이러한 결과는 대청댐 방류량에 대한 금남 및 공주지점까지의 하도추적결과에서도 확인할 수 있었다.

Keywords

References

  1. 건설교통부(2006). 한강권역 유역종합치수계획 수립.
  2. 건설교통부(2007). 홍수량 산정기법 가이드라인 보고서.
  3. 윤용남(2008). 수문학, 청문각, pp. 513-523.
  4. 박봉진, 강권수, 정관수(1997). “대청댐 방류에 따른 금강 하류부의 홍수추적.” 한국수자원학회논문집, 한국수자원학회, 제30권, 제2호, pp. 131-141.
  5. 정종호, 윤용남(2003). 수자원설계실무, 구미서관, pp. 200-205.
  6. Agirre, U., Goni, M., Lopez, J.J., and Gimena, F.N. (2005). “Application of a unit hydrograph based on subwatershed division and comparison with Nash's instantaneous unit hydrograph.” Catena, Vol. 64, No. 2-3, pp. 321-332. https://doi.org/10.1016/j.catena.2005.08.013
  7. Barry, D.A., and Bajracharya, K. (1995). “On the Muskingum-Cunge flood routing method.” Environmental International, Vol. 21, No. 5, pp. 485-490. https://doi.org/10.1016/0160-4120(95)00046-N
  8. Chow, V.T., Maidment, D.R., and Mays, L.W. (1988). Applied hydrology. McGraw-Hill, pp. 243-260.
  9. Guang-Te, W., and Chen, S. (1996). “A linear spatially distributed model for a surface rainfall-runoff system.” Journal of Hydrology, Vol. 185, No. 1-4, pp. 183-198. https://doi.org/10.1016/0022-1694(95)03001-8
  10. Heergegen, R.G., and Reich, B.M. (1974). “Unit hydrographs for catchments of different sizes and dissimilar regions.” Journal of Hydrology, Vol. 22, No. 1-2, pp. 143-153. https://doi.org/10.1016/0022-1694(74)90101-2
  11. O'Connor, K.M. (1982). “Derivation of discretely coincident forms of continuous linear time-invariant models using the transfer function approach.” Journal of Hydrology, Vol. 59, No. 1-2, pp. 1-48. https://doi.org/10.1016/0022-1694(82)90002-6
  12. Overton, D.E. (1966). “Muskingum flood routing of upland streamflow.” Journal of Hydrology, Vol. 4, pp. 185-200. https://doi.org/10.1016/0022-1694(66)90079-5
  13. Ponce, V.M., Lohani, A.K., and Scheyhing, C. (1996). “Analytical verification of Muskingum-Cunge routing.” Journal of Hydrology, Vol. 174, No. 3-4, pp. 235-241. https://doi.org/10.1016/0022-1694(95)02765-3
  14. Singh, V.P., and McCann, R.C. (1980). “Some notes on Muskingum method of flood routing.” Journal of Hydrology, Vol. 48, No. 3-4, pp. 343-361. https://doi.org/10.1016/0022-1694(80)90125-0
  15. Szymkiewicz, R. (2002). “An alternative IUH for the hydrological lumped models.” Journal of Hydrology, Vol. 259, No. 1-4, pp. 246-253. https://doi.org/10.1016/S0022-1694(01)00595-9
  16. Venetis, C. (1969). “The IUH of the Muskingum channel reach.” Journal of Hydrology, Vol. 7, No. 4, pp. 444- 447. https://doi.org/10.1016/0022-1694(69)90097-3

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