DOI QR코드

DOI QR Code

Parameters Estimation of Clark Model based on Width Function

폭 함수를 기반으로 한 Clark 모형의 매개변수 추정

  • Park, Sang Hyun (Measurement and Analysis Division, Geum River Basin Environmental Office) ;
  • Kim, Joo-Cheol (International Water Resources Research Institute, Chungnam National University) ;
  • Jung, Kwansue (Dept. of Civil Engrg., Chungnam National University)
  • 박상현 (금강유역환경청 측정분석과) ;
  • 김주철 (충남대학교 국제수자원연구소) ;
  • 정관수 (충남대학교 토목공학과)
  • Received : 2013.01.09
  • Accepted : 2013.03.18
  • Published : 2013.06.30

Abstract

This paper presents the methodology for construction of time-area curve via the width function and thereby rational estimation of time of concentration and storage coefficient of Clark model within the framework of method of moments. To this end time-area curve is built by rescaling the grid-based width function under the assumption of pure translation and then the analytical expressions for two parameters of Clark model are proposed in terms of method of moments. The methodology in this study based on the analytical expressions mentioned before is compared with both (1) the traditional optimization method of Clark model provided by HEC-1 in which the symmetric time-area curve is used and the difference between observed and simulated hydrographs is minimized (2) and the same optimization method but replacing time-area curve with rescaled width function in respect of peak discharge and time to peak of simulated direct runoff hydrographs and their efficiency coefficient relative to the observed ones. The following points are worth of emphasizing: (1) The optimization method by HEC-1 with rescaled width function among others results in the parameters well reflecting the observed runoff hydrograph with respect to peak discharge coordinates and coefficient of efficiency; (2) For the better application of Clark model it is recommended to use the time-area curve capable of accounting for irregular drainage structure of a river basin such as rescaled width function instead of symmetric time-area curve by HEC-1; (3) Moment-based methodology with rescaled width function developed in this study also gives rise to satisfactory simulation results in terms of peak discharge coordinates and coefficient of efficiency. Especially the mean velocities estimated from this method, characterizing the translation effect of time-area curve, are well consistent with the field surveying results for the points of interest in this study; (4) It is confirmed that the moment-based methodology could be an effective tool for quantitative assessment of translation and storage effects of natural river basin; (5) The runoff hydrographs simulated by the moment-based methodology tend to be more right skewed relative to the observed ones and have lower peaks. It is inferred that this is due to consideration of only one mean velocity in the parameter estimation. Further research is required to combine the hydrodynamic heterogeneity between hillslope and channel network into the construction of time-area curve.

본 연구에서는 Clark 모형의 시간-면적곡선의 구성 방법과 적용성을 검토하고 모멘트 원리에 의한 도달시간, 저류상수를 합리적으로 산정하기 위한 방법론을 고찰해 보았다. 격자 기반으로 폭 함수를 구성하고 운동과정을 순수 이류현상으로 가정하여 시간-면적곡선으로 사용하였다. 또한 도달시간과 저류상수는 모멘트 법의 원리에 따라 Clark 모형 구조에 적용하여 해석적으로 산정할 수 있는 방법을 제시하였다. 적용성 검토를 위해 (1) HEC-1에서 기본적으로 제공하는 좌우 대칭형상인 무차원 시간-면적곡선을 적용하고 매개변수 산정은 관측유출수문곡선과 계산된 유출수문곡선의 오차를 최소화하는 HEC-1의 최적화 기법 사용, (2) HEC-1에 폭 함수 기반의 시간-면적곡선을 적용하고 매개변수 산정은 HEC-1의 최적화 기법 사용, (3) 폭 함수 기반의 시간-면적곡선을 이용하여 모멘트 원리에 따라 매개변수를 직접 산정하는 방법을 적용하였다. 방법별로 산정된 Clark 모형의 매개변수들을 HEC-1을 이용하여 직접유출량을 산정하고 관측 직접유출량과 비교하여 얻은 결과는 다음과 같다. (1) 정량적으로 비교하기 위해 산정한 첨두유량과 첨두발생 시간의 상대오차 및 효율계수 E(Efficiency Coefficient)를 비교한 결과, 시간-면적곡선을 폭 함수로 대체하여 HEC-1으로부터 추정된 매개변수가 관측값을 잘 반영하였다. (2) Clark 모형의 올바른 적용을 위해서는 HEC-1에서 기본적으로 제공하는 좌우 대칭형상인 무차원 시간-면적곡선보다는 적용 대상유역의 배수구조가 적절하게 반영된 시간-면적곡선의 사용이 합리적일 것으로 판단된다. (3) 본 연구 방법은 첨두유량과 첨두시간의 상대오차 범위와 재현정도를 나타내는 효율계수를 비교하여 볼 때 대체로 양호하게 모의되었고, 대상유역별 유량측정성과인 하천평균유속과 비교했을 때 본 연구 방법이 다소 실제 유속에 접근하고 있음을 확인하였다. (4) 본 연구에서 모멘트 원리를 기반으로 제안한 매개변수 추정을 위한 방법은 유역의 이류현상과 저류현상을 정량적으로 계량할 수 있는 효율적인 관계식으로 사용할 수 있음을 확인하였다. (5) 본 방법에 의해 계산된 수문곡선이 대부분 관측수문곡선의 우측으로 왜곡되고 첨두유량은 과소평가 되는 것을 보이고 있다. 이것은 평균과 분산만을 고려하여 유역을 하나의 평균이송속도로 모의한 본 연구의 한계점으로 판단된다. 만약 모멘트의 왜곡도를 고려하고 유역을 지표면과 하천으로 나누어 평균이송속도를 모의한다면 물리적인 특성을 충분히 반영하여 매개변수를 추정 할 수 있을 것으로 판단된다.

Keywords

References

  1. Clark, C.O. (1945). "Storage and the unit hydrograph." Transactions of the American Society of Civil Engineers, Vol. 110, pp. 1419-1416.
  2. Di Lazzaro, M. (2009). "Regional analysis of storm hydrographs in the rescaled width function framework." Journal of Hydrology, Vol. 373, pp. 352-365. https://doi.org/10.1016/j.jhydrol.2009.04.027
  3. Diskin, M.H. (1964). A basic study of the linearity of the rainfall-runoff process in watersheds. Ph.D. thesis, University of Illinois, Urbana, Ill.
  4. Dooge, J.C.I. (1959). "A general theory of the unit hydrograph." Journal of Geophysical Research, Vol. 64, pp. 241-256. https://doi.org/10.1029/JZ064i002p00241
  5. Dooge, J.C.I. (1973). Linear theory of hydrologic systems. Technical Bulletin 1468, Agricultural Research Service, U. S. Department of Agriculture, Washington, D.C.
  6. Edson, C.G. (1951). "Parameters for relating unit hydrographs to watershed characteristics." Transactions, American Geophysical Union, Vol. 32, No. 4, pp. 591-596. https://doi.org/10.1029/TR032i004p00591
  7. Jeong, D.M., and Bae, D.H. (2003). "Analysis of Time-Area Curve Effects on Watershed Runoff." Journal of Korea Water Resources Association, Vol. 36, No. 2, pp. 211-221. https://doi.org/10.3741/JKWRA.2003.36.2.211
  8. Kim, J.C., Kang, J.W., Son, M.W., and Jung, K.S. (2012). Response Analysis of Clark Model in accordance with Shape of Time-Area Curve. KSCE Conference and Civil Expo 2012, Korean Society of Civil Engineers.
  9. Kim, J.H. (2005). Mathematical Models for Hydrologic Systems based on the Linear Theory. Saeron, pp. 32-33.
  10. Kim, J.H., and Yoon, S.Y. (1993). "Derivation of the Basin Instantaneous Unit Hydrograph Considering the Network Geometry and Hillslope of Small Basin." Journal of the Korean Society of Civil Engineers, Vol. 13, No. 2, pp. 161-171.
  11. Lee, J.S. (1994). A Comparative Study of Conceptual Models for Rainfall-Runoff Relationship. International Hydrologic Programme (IHP) Research Paper, Ministry of Construction and Transportation, pp. 6.1-6.86.
  12. Lienhard, J.H. (1964). "A statistical mechanical prediction of the dimensionless unit hydrograph." Journal of Geophysical Research, Vol. 69, No. 24, pp. 5231-5238. https://doi.org/10.1029/JZ069i024p05231
  13. Mesa, O.J., and Mifflin, E.R. (1986). On the relative role of hillslope and network geometry in hydrologic response. Scale Problems in Hydrology, Dordrecht, Holland, pp. 181-190.
  14. Minister of Land, Transport and Maritime Affairs (2007, 2009, 2010). Annual Hydrological Report on Korea.
  15. Minister of Land, Transport and Maritime Affairs (2011). Hydrological Survey Report.
  16. Ministry of Construction and Transportation (2001-2005). International Hydrologic Programme (IHP) Research Paper.
  17. Nash, J.E. (1957). "The form of the instantaneous unit hydrograph." Proceedings IASH Assemblee Generale de Toronto, Vol. 3, pp. 114-121.
  18. Nash, J.E. (1960). "A unit hydrograph study, with particular reference to British catchments." Proceedings, Institution of Civil Engineers, Vol. 17, pp. 249-282. https://doi.org/10.1680/iicep.1960.11649
  19. Nash, J.E., and Sutcliffe, J.V. (1970). "River flow forecasting through conceptual models. Part I -A Discussion on principles." Journal of Hydrology, Vol. 10, pp. 282-290. https://doi.org/10.1016/0022-1694(70)90255-6
  20. O'Kelly, J.J. (1955). "The employment of unit hydrographs to determine the flows of Irish arterial drainage channels." Proceedings, Institution of Civil Engineers, Vol. 4, No. 3, pp. 365-412. https://doi.org/10.1680/ipeds.1955.11869
  21. Rinaldo, A., Vogel, G.K., Rigon, R., and Rodriguez-Iturbe, I. (1995). "Can one gauge the shape of basin." Water Resources Research, Vol. 31, No. 4, pp. 1119-1127. https://doi.org/10.1029/94WR03290
  22. Rodrigueze-Iturbe, I., and Valdes, J.B. (1979). "The geomorphologic structure of hydrologic response." Water Resources Research, Vol. 15, No. 6, pp. 1409-1420. https://doi.org/10.1029/WR015i006p01409
  23. Rodriguez-Iturbe, I., and Rinaldo, A. (2003). Fractal river basins, Chance and self-organization. Cambridge.
  24. Seong, K.W. (1999). "Analysis of the Clark Model Using the Similarity Characteristics of the Basin." Journal of Korea Water Resources Association, Vol. 32, No. 4, pp. 427-435.
  25. Seong, K.W. (2003). "An Indirect Approach Determining Parameters of Clark's Model Based on Model Fitting to the Gamma Distribution Function." Journal of Korea Water Resources Association, Vol. 36, No. 2, pp. 223-235. https://doi.org/10.3741/JKWRA.2003.36.2.223
  26. Singh, K.P. (1962). A non-linear approach to the instantaneous unit hydrograph. Ph.D. Thesis, University of Illinois, Urbana, Ill.
  27. Smart, J.S. (1972). "Channel networks." Advanced in Hydroscience, Vol. 8, pp. 305-346. https://doi.org/10.1016/B978-0-12-021808-0.50011-5
  28. Water Management Information System(http://www.wamis.go.kr).
  29. Yoo, C.S. (2009). "A Theoretical Review of Basin Storage Coefficient and Concentration Time Using the Nash Model." Journal of Korea Water Resources Association, Vol. 42, No. 3, pp. 235-246. https://doi.org/10.3741/JKWRA.2009.42.3.235
  30. Yoo, C.S., and Shin, J.W. (2010). "Decision of Storage Coefficient and Concentration Time of Observed Basin Using Nash Model's Structure." Journal of Korea Water Resources Association, Vol. 43, No. 6, pp. 559-569. https://doi.org/10.3741/JKWRA.2010.43.6.559
  31. Yoon, S.Y., and Hong, I.P. (1995). "Improvement of the Parameter Estimation Method for the Clark Model." Journal of the Korean Society of Civil Engineers, Vol. 15, No. 5, pp. 1287-1300.
  32. Yoon, T.H., Kim, S.T., and Park, J.W. (2005). "On Redefining of Parameters of Clark Model." Journal of the Korean Society of Civil Engineers, Vol. 25, No. 3B, pp. 181-187.
  33. Zoch, R.T. (1934), "On the relation between rainfall and stream flow." Monthly Weather Review, Part I (62), 315-322
  34. Zoch, R.T. (1936), "On the relation between rainfall and stream flow." Monthly Weather Review, Part II (64), 105-121
  35. Zoch, R.T. (1937), "On the relation between rainfall and stream flow." Monthly Weather Review, Part III (65), 135-147

Cited by

  1. Re-Analysis of Clark Model Based on Drainage Structure of Basin vol.33, pp.6, 2013, https://doi.org/10.12652/Ksce.2013.33.6.2255