한국수자원학회논문집 (Journal of Korea Water Resources Association)

  • 제48권10호
  • /
  • Pages.807-816
  • /
  • 2015
  • /
  • 2799-8746(pISSN)
  • /
  • 2799-8754(eISSN)
한국수자원학회 (Korea Water Resources Association)
권호 표지
DOI QR코드

DOI QR Code

수위-유량관계곡선의 자동구간분할을 위한 변동계수 활용기법의 개선

Improvement of the Method using the Coefficient of Variation for Automatic Multi-segmentation Method of a Rating Curve

  • 김연수 (충남대학교 국제수자원연구소) ;
  • 김정엽 (국토교통부 금강홍수통제소) ;
  • 안현욱 (충남대학교 농업생명과학대학 지역환경토목과) ;
  • 정관수 (충남대학교 공과대학 토목공학과)
  • Kim, Yeonsu (International Water Resources Research Institute, Chungnam National Univ.) ;
  • Kim, Jeongyup (Geum River Flood Control Office) ;
  • An, Hyunuk (Dept. of Agricultural and Rural Eng., Chungnam National Univ.) ;
  • Jung, Kwansue (Dept. of Civil Engrg., Chungnam National Univ.)
  • 투고 : 2015.07.06
  • 심사 : 2015.08.27
  • 발행 : 2015.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

일반적으로 수위-유량관계 곡선식은 선형성과 등분산성 가정을 기반으로 구축되지만, 측정단면의 형태, 단면 상 하류의 지형요인 등으로 인하여 영향을 받기 때문에 실질적인 수위 및 유량의 관계는 관계식 구축에 이용되는 가정에 위배된다. 이로 인한 오차를 줄이기 위하여 곡선식을 분할하여 이용하고 있으나, 측정단면의 변화를 고려한 관계자의 주관적인 판단이 구간분할의 주요 근거로 이용되고 있다. 따라서 본 연구에서는 이러한 주관성을 배제하고 관측데이터를 기반으로 객관화된 분할근거를 제시하고자 한다. 곡선식의 구간 분할을 위하여 변동계수를 이용한 기존의 연구를 바탕으로 변동계수가 정규분포를 따르는 것으로 가정하여, 계산된 변동계수가 전 단계에서 계산된 95% 신뢰구간 이내에 존재하지 않는 경우 구간을 분할하였다. 즉, 변동계수를 이용하여 집단 간의 특성을 비교하였으며, 변동계수의 분포를 이용하여 분할을 위한 기준 값을 제시하였다. 방법론의 추정능력 검토를 위하여 가상의 곡선으로부터 생성된 데이터에 제안된 방법론을 적용하였고, 실제유역에 적용성 검토를 위하여 금강에 위치한 무주 및 산계교 수위관측소 지점에 적용하였다. 결과적으로 자동으로 분할된 관계곡선식을 사용하여 추정의 정확도를 높일 수 있을 뿐만 아니라 외삽을 하는 경우 역시 그 정확도를 향상할 수 있음을 확인하였다. 마지막으로 실측값을 활용한 수위-유량관계 곡선식의 구축 시 구간 분할 전 후의 잔차 데이터에 대하여 Shapiro-wilk 정규성 검정을 수행하였으며, 구간분할 후 잔차가 정규성을 갖게 되는 것으로 나타났다.

In general, the water stage-discharge relationship curve is established based on the assumptions of linearity and homoscedasticity. However, the relationship between the water stage and discharge is affected from geomorphological factors, which violates the basic assumptions of the water stage-discharge relationship curve. In order to reduce the error due to the violations, the curve is divided into several sections based on the manager's judgement considering change of cross-sectional shape. In this research, the objective-splitting criteria of the curve is proposed based on the measured data without the subjective decision. First, it is assumed that the coefficient of variation follows the normal distribution. Then, if the newly calculated coefficient of variation is outside of the 95% confidential interval, the curve is divided. Namely, the groups is divided by the characteristics of the coefficient of variation and the reasonable criteria is provided for establishing a multi-segmented rating curve. To validate the proposed method, it was applied to the data generated by three artificial power functions. In addition, to confirm the applicability of the proposed method, it is applied to the water stage and discharge data of the Muju water stage gauging station and Sangegyo water stage gauging station. As a result, it is found that the automatically divided rating curve improves the accuracy and extrapolation accuracy of the rating curve. Finally, through the residual analysis using Shapiro-Wilk normality test, it is confirmed that the residual of water stage-discharge relationship curve tends to follow the normal distribution.

키워드

참고문헌

  1. Cho, M., Kim, M.S., Choi, H., and Park, J. (2004). "Uncertainty analysis of flow measurement data in sum river experimental watershed." Conference proceeding of Korean Society of Civil Engineers, pp. 4114-4119.
  2. Cho, Y.D. (2003). The automated program in deriving the stage-discharge curve by applying coefficient of variation, Master thesis, Chungnam national university.
  3. Choi, S., Kwon, B., and Lee, S. (2012). "Accuracy of the annual prediction of the stage-discharge relationship." Conference Proceeding of Korean Water Resources Association, Vol. 5, pp. 516-520.
  4. Di Baldassarre, G., and Montanari, A. (2009). "Uncertainty in river discharge observations: a quantitative analysis." Hydrol. Earth Syst. Sci., Vol. 13, pp. 913-921. https://doi.org/10.5194/hess-13-913-2009
  5. Gergov, G., and Karagiozova, T. (2003). "Unique discharge rating curve based on the morphology parameter Z." International Association of Hydrological Sciences, Publication, Vol. 278, pp. 3-8.
  6. Iglewigz, B., and Raymond, H.M. (1970). "Comparisons of Approximations to the Percentage Points of the Sample Coefficient of Variation." Technometrics, Vol. 12, No. 1, pp. 166-169.
  7. Johnson, L.H. (1952). "Nomography and empirical equation." Johnson Willey, New York, p. 150.
  8. Jung, H.S., and Lee, W.H., and Lee, J.J. (1988). "Analysis on the Stage-Discharge Curve with the Temporal Variation of the River Bed." Journal of the Korean Society of Civil Engineers, Vol. 8, No. 3, pp. 61-71.
  9. Kim, S., and Jung, K. (2005). "Manning's n calibration and sensitivity analysis using unsteady flood routing model." Conference proceeding of Korean Water Resources Association, pp. 324-328.
  10. Kim, W., Kim, Y., and Woo, H. (1995). "Estimation of Channel Roughness Coefficients in the Han River Using Unsteady Flow Model." Magazine of Korea Water Resources Association, Vol. 28, No. 26, pp. 133-146.
  11. Kim, Y., Tachikawa, Y., Kim, S., Shiiba, M., Yorozu, K., and Noh, S.J. (2013). "Simultaneous Estimation of Inflow and Channel Roughness Using 2d Hydraulic Model and Particle Filters." Journal of Flood Risk Management, Vol. 6, No. 2, pp. 112-123. https://doi.org/10.1111/j.1753-318X.2012.01164.x
  12. Kim, S.U., and Lee, K.S. (2008). "Identification of Uncertainty in Fitting Rating Curve with Bayesian Regression." Journal of Korea Water Resources Association, Vol. 41, No. 9, pp. 943-958. https://doi.org/10.3741/JKWRA.2008.41.9.943
  13. Le Coz, J. (2012). "A literature review of methods for estimating the uncertainty associated with stagedischarge relations." WMO initiative on Assessment of the Performance of Flow Measurement Instruments and Techniques-Project output.
  14. Lee, C.H. (2002). "Nonlinear Optimization of Rating Curves with VBA." Journal of the Korean Society of Civil Engineers, Vol. 22, No. 1-B, pp. 43-55.
  15. Lee, J.H., and Kang, C.U. (2008). "CV control chart using CUSUM scheme." Proceedings of Korea industrial systems engineering spring conference, pp. 275-278.
  16. Lee, J.J., and Kwon H.H. (2010). "A Basic Study of Stage-discharge Rating Stabilization at the Ssang-chi Gauging Station." Journal of the Korean Society of Civil Engineers, Vol. 30, No. 1B, pp. 81-87.
  17. Lee, S.H., and Gang, S.U. (2001). "Stream Discharge Estimation by Hydraulic Channel Routing and Stage Measurement." Journal of Korea Water Resources Association, Vol. 34, No. 5, pp. 543-549.
  18. MLIT (2008). Technical report of the Yodo River basin (volume of the Katsura River), Ministry of Land Infrastructure Transport and Tourism, Japan (in Japanese)
  19. MOLIT (2011, 2012). Hydrological survey report: I. the part of discharge investigation, Ministry of Land, Infrastructure and Transport, Republic of Korea (in Korean)
  20. Pelletier, M.P. (1987). "Uncertainties in the determination of river discharge: a literature review." Can. J. Civ. Eng., Vol. 15, p. 834-850.
  21. Tawik, M., Ibrahim, A., and Fahmy, H. (1997). "Hysteresis sensitive neural network for modeling rating curves." Journal of Computing in Civil Engineering, ASCE, Vol. 11, No. 3, pp. 206-211. https://doi.org/10.1061/(ASCE)0887-3801(1997)11:3(206)
  22. Reh, W., and Scheffler, B. (1996). "Significance and tests confidence intervals for tests and coefficient of variation." the statistical software newslettes
  23. Reitan, T., and Petersen-Overleir, A. (2008) "Bayesian power-law regression with a location parameter, with applications for construction of discharge rating curves." Stochastic Environmental Research and Risk Assessment, Vol. 22, No. 3, pp. 351-365. https://doi.org/10.1007/s00477-007-0119-0
  24. Reitan, T., and Petersen-Overleir, A. (2009), "Bayesian Methods for Estimating Multi-segment Discharge Rating Curves." Stochastic Environmental Research and Risk Assessment, Vol. 23, No. 5, pp. 627-642. https://doi.org/10.1007/s00477-008-0248-0
  25. Reitan, T., and Petersen-Overleir, A. (2011). "Dynamic Rating Curve Assessment in Unstable Rivers Using Ornstein-Uhlenbeck processes." Water Resources Research, Vol. 47, W02524, No. 14, doi:10.1029/2010WR009504
  26. USGS (1982). Measurement and computation of streamflow: Vol. 2, Computation of discharge, Water Supply Paper 2175
  27. Westphal, J.A., Stevens, G.T., and Strauser, C.N. (1999) "Stage-Discharge Relations on the Middle Mississippi River." Journal of Water Resources Planning and Management, Vol. 125, No. 1, pp. 48-53. https://doi.org/10.1061/(ASCE)0733-9496(1999)125:1(48)