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Flood stage analysis considering the uncertainty of roughness coefficients and discharge for Cheongmicheon watershed

조도계수와 유량의 불확실성을 고려한 청미천 유역의 홍수위 해석

  • Shin, Sat-Byeol (Department of Rural Systems Engineering, Seoul National University) ;
  • Park, Jihoon (Climate Application Department, APEC Climate Center) ;
  • Song, Jung-Hun (Research Institute for Agriculture and Life Sciences, Seoul National University) ;
  • Kang, Moon Seong (Research Institute for Agriculture and Life Sciences, Seoul National University)
  • 신샛별 (서울대학교 생태조경.지역시스템공학부) ;
  • 박지훈 (APEC 기후센터 응용사업본부) ;
  • 송정헌 (서울대학교 농업생명과학연구원) ;
  • 강문성 (서울대학교 농업생명과학연구원)
  • Received : 2017.03.20
  • Accepted : 2017.08.14
  • Published : 2017.10.31

Abstract

The objective of this study was to analyze the flood stage considering the uncertainty caused by the river roughness coefficients and discharge. The methodology of this study involved the GLUE (Generalized Likelihood Uncertainty Estimation) to quantify the uncertainty bounds applying three different storm events. The uncertainty range of the roughness was 0.025~0.040. In case of discharge, the uncertainty stemmed from parameters in stage-discharge rating curve, if h represents stage for discharge Q, which can be written as $Q=A(h-B)^C$. Parameters in rating curve (A, B and C) were estimated by non-linear regression model and assumed by t distribution. The range of parameters in rating curve was 5.138~18.442 for A, -0.524~0.104 for B and 2.427~2.924 for C. By sampling 10,000 parameter sets, Monte Carlo simulations were performed. The simulated stage value was represented by 95% confidence interval. In storm event 1~3, the average bound was 0.39 m, 0.83 m and 0.96 m, respectively. The peak bound was 0.52 m, 1.36 m and 1.75 m, respectively. The recurrence year of each storm event applying the frequency analysis was 1-year, 10-year and 25-year, respectively.

본 연구의 목적은 하천의 조도계수와 유량의 불확실성을 고려하여, 부정류 흐름에서 홍수위 해석에 미치는 영향을 정량적으로 분석하는 데 있다. 본 연구에서는 GLUE (Generalized Likelihood Uncertainty Estimation) 기법을 적용하여 조도계수와 유량의 불확실성이 홍수위 해석에 미치는 영향을 분석하고, 강우사상의 크기와 불확실성과의 관계를 분석하였다. 조도계수의 불확실성은 하천기본계획을 참고하여 0.025~0.040의 범위에서 분석하였다. 유량의 불확실성은 수위 h일 때의 유량을 Q라고 할 때, $Q=A(h-B)^C$로 표현되는 수위-유량관계식의 회귀계수 A, B, C를 통해 분석하였다. 수위-유량관계식의 회귀계수를 비선형 회귀분석을 통해 추정하였으며, 회귀계수는 t 분포를 가정하여 95% 신뢰도로 상한과 하한의 범위를 산정하였다. 산정된 회귀계수의 범위는 A는 5.138~18.442, B는 -0.524~0.104, C는 2.427~2.924로 산정되었다. 범위 내에서 10,000개의 매개변수 세트를 추출하여 HEC-RAS (Hydrologic Engineering Center's River Analysis System)에 적용하여 Monte Carlo 모의를 수행하였다. 강우사상 1~3에서 모의된 홍수위의 95% 신뢰구간의 평균적인 범위는 각각 0.39 m, 0.83 m, 0.96 m이며, 첨두 홍수위가 발생했을 때의 범위는 각각 0.52 m, 1.36 m, 1.75 m로 산정되었다. 또한 이천관측소의 1986~2015년의 일 강우에 대한 빈도해석을 수행하였으며, 수행 결과 GEV (Generalized Extreme Vlaue) 분포일 때 강우사상 1~3의 재현기간은 각각 1년, 10년, 25년 빈도에 해당되었다. 본 연구를 통해 강우사상의 크기와 불확실성의 관계를 분석하였으며, 향후 다양한 강우사상에 적용하여 검증한다면 홍수위의 불확실성을 예측하여, 하천관리 등을 위한 구조물의 계획 및 설계 시 의사 결정에 실질적인 도움이 될 수 있을 것으로 사료된다.

Keywords

References

  1. Abbaspour, K. C., Johnson, C. A., and Van Genuchten, M. T. (2004). "Estimating uncertain flow and transport parameters using a sequential uncertainty fitting procedure." Vadose Zone Journal, Vol. 3, No. 4, pp. 1340-1352. https://doi.org/10.2136/vzj2004.1340
  2. Beven, K. (2006). "A manifesto for the equifinality thesis." Journal of Hydrology, Vol. 320, No. 1, pp. 18-36. https://doi.org/10.1016/j.jhydrol.2005.07.007
  3. Beven, K., and Binley, A. (1992). "The future of distributed models: model calibration and uncertainty prediction." Hydrological Processes, Vol. 6, No. 3, pp. 279-298. https://doi.org/10.1002/hyp.3360060305
  4. Chang, K. H., and Lee, J. H. (2005). "Stage-discharge rating curve model development and modification." Journal of Korea Water Resources Association, Vol. 38, No. 4, pp. 271-280. https://doi.org/10.3741/JKWRA.2005.38.4.271
  5. Cho, J., and Mostaghimi, S. (2009). "Dynamic agricultural non-point source assessment tool (DANSAT): model application." Biosystems Engineering, Vol. 102, No. 4, pp. 500-515. https://doi.org/10.1016/j.biosystemseng.2009.01.012
  6. Cho, M. S., Kim, S. H., Choi, H. S., and Park, J. S. (2004). "Uncertainty analysis of flow measurement data in sum river experimental watershed." Conference of Korean Society of Civil Engineers, KSCE, pp. 4114-4119.
  7. Chow, V. T. (1959). Open channel hydraulics. McGraw-Hill Book Company, New York, USA.
  8. Freer, J., Beven, K., and Ambroise, B. (1996). "Bayesian estimation of uncertainty in runoff prediction and the value of data: an application of the GLUE approach." Water Resources Research, Vol. 32, No. 7, pp. 2161-2173. https://doi.org/10.1029/95WR03723
  9. James, L. D., and Burges, S. J. (1982). "Selection, calibration and testing of hydrologic models." Hydrologic Modeling of Small Watersheds, ASAE, St. Joseph, MI, Vol. 5, pp. 435-472.
  10. Jung, Y. H., Yeo, K. D., Kim, S. Y., and Lee, S. O. (2013). "The effect of uncertainty in roughness and discharge on flood inundation mapping." Journal of the Korean Society of Civil Engineers, Vol. 33, No. 3, pp. 937-945. https://doi.org/10.12652/Ksce.2013.33.3.937
  11. Kang, M. S., and Park, S. W. (2003). "Short-term food forecasting using artificial neural networks." Journal of the Korean Society of Agricultural Engineers, Vol. 45, No. 2, pp. 45-57.
  12. Kim, N. S., Kim, J. S., Jang, H. W. and Lee, J. H. (2015). "Hydrologic risk analysis based on extremer drought over the Korean peninsula unter climate change." Journal of Korean Society of Hazard Mitigation, Vol. 15, No. 4, pp. 45-52. https://doi.org/10.9798/KOSHAM.2015.15.4.45
  13. Kim, S. U., and Lee, G. S. (2008a). "Uncertainty, where ignorance is bliss, is it folly to be wise?" Water for Future, Vol. 41, No. 9, pp. 35-40.
  14. Kim, S. U., and Lee, G. S. (2008b). "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
  15. Kim, W. (2005). "Uncertainty and improvement in the calculation of flood stage." Conference of Korean Society of Civil Engineers, KSCE, Vol. 10, pp. 2942-2949.
  16. Kim, Y. S., Kim, J. Y., An, H. U., and Jung, K. S. (2015). "Improvement of the method using the coefficient of variation for Automatic Multi-segmentation method of a rating curve." Journal of Korea Water Resources Association, Vol. 48, No. 10, pp. 807-816. https://doi.org/10.3741/JKWRA.2015.48.10.807
  17. Korea Water Resources Association (2009). River design standard and explanation, KWRA, pp. 93-100.
  18. Lambie, J. C. (1978). Measurement of flow-velocity-area methods. Hydrometry: Principles and Practices, first edition, edited by Herschy R.W., Wiley, Chichester, UK.
  19. Lee, W. S., Kim, S. U., Chung, E. S., and Lee, K. S. (2008). "Improvement of rating curve fitting considering variance function with Pseudo-likelihood estimation." Journal of Korea Water Resources Association, Vol. 41, No. 8, pp. 807-823. https://doi.org/10.3741/JKWRA.2008.41.8.807
  20. Li, L., Xia, J., Xu, C. Y., and Singh, V. P. (2010). "Evaluation of the subjective factors of the GLUE method and comparison with the formal Bayesian method in uncertainty assessment of hydrological models." Journal of Hydrology, Vol. 390, No. 3, pp. 210-221. https://doi.org/10.1016/j.jhydrol.2010.06.044
  21. Matott, L. S., Babendreier, J. E., and Purucker, S. T. (2009). "Evaluating uncertainty in integrated environmental models: a review of concepts and tools." Water Resources Research, Vol. 45, No. 6, W06421. https://doi.org/10.1029/2008WR007301
  22. Ministry of Land, Transport and Maritime Affairs (2011). Report of master plan (alteration) for Cheongmicheon river. pp. 4-126-4-136.
  23. Moriasi, D. N., Gitau, M. W., Pai, N., and Daggupati, P. (2015). "Hydrologic and water quality models: performance measures and evaluation criteria." Transactions of the ASABE, Vol. 58, No. 6, pp. 1763-1785. https://doi.org/10.13031/trans.58.10715
  24. Nash J. E., and Sutcliffe, J. V. (1970). "River flow forecasting through conceptual models part I - a discussion of principles." Journal of Hydrology, Vol. 10, No. 3, pp. 282-290. https://doi.org/10.1016/0022-1694(70)90255-6
  25. Pappenberger, F., Beven, K., Horritt, M., and Blazkova, S. (2004). "Uncertainty in the calibration of effective roughness parameters in HEC-RAS using inundation and downstream level observations." Journal of Hydrology, Vol. 302, No. 1, pp. 46-69. https://doi.org/10.1016/j.jhydrol.2004.06.036
  26. Pappenberger, F., Matgen, P., Beven, K., Henry, J. B., Pfister, L., and Fraipont, P. (2006). "Influence of uncertain boundary conditions and model structure on flood inundation predictions." Advances in Water Resources, Vol. 29, No. 10, pp. 1430-1449. https://doi.org/10.1016/j.advwatres.2005.11.012
  27. Park, J. E., and Kim, S. H. (2013). "Application of Levenberg Marquardt method for calibration of unsteady friction model for a pipeline system." Journal of Korea Water Resources Association, Vol. 46, No. 4, pp. 389-400. https://doi.org/10.3741/JKWRA.2013.46.4.389
  28. Retian, T., and Petersen-Overleir, A. (2008). "Baysian 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
  29. Song, J. H., and Kang, M. S. (2016). "Performance measures and valibration methods for hydrologic and water quality models." Rural Resources, Vol. 58, No. 2, pp. 11-22.
  30. Song, J. H., Kang, M. S., Song, I. H., and Jun, S. M. (2016). "Water balance in irrigation reservoirs considering flood control and irrigation efficiency variation." Journal of Irrigation and Drainage Engineering, Vol. 142, No. 4, 04016003. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000989
  31. United States Army Corps of Engineers (2010). HEC-RAS river analysis system: User's Manual 4.1. Institute for Water Resources, Hydrologic Engineering Center, USA.
  32. Van Griensven, A., and Bauwens, W. (2003). "Multiobjective autocalibration for semidistributed water quality models." Water Resources Research, Vol. 39, No. 12, pp. SWC 9-1.
  33. Yevjevich, V. (1972). Probability and statistics in hydrology. Water Resources publications, Fort Collins, Colorado, USA.