한국수자원학회논문집 (Journal of Korea Water Resources Association)

  • 제42권9호
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  • Pages.725-736
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  • 2009
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  • 2799-8746(pISSN)
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  • 2799-8754(eISSN)
한국수자원학회 (Korea Water Resources Association)
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이변량 Gumbel 혼합모형을 이용한 홍수심도 평가

Evaluation of Flood Severity Using Bivariate Gumbel Mixed Model

  • 이정호 (한양대학교 대학원 건설환경공학과) ;
  • 정건희 (고려대학교 방재과학기술연구센터) ;
  • 김태웅 (한양대학교 건설환경시스템공학)
  • Lee, Jeong-Ho (Dept of Civil and Environmental Eng., Hanyang Univ.) ;
  • Chung, Gun-Hui (Research Center for Disaster Prevention Science and Technology, Korea Univ.) ;
  • Kim, Tae-Woong (Dept. of Civil & Environmental System Eng., Hanyang Univ.)
  • 발행 : 2009.09.30
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초록

홍수사상은 크게 첨두홍수량, 홍수용적, 지속기간 등과 같은 서로 상관된 세 가지의 요소로 정의될 수 있다. 그러나 그동안 수공학적 계획이나 설계, 운영 등을 위한 홍수빈도해석에서는 주로 첨두홍수량 한가지 요소에 초점을 맞추어 홍수빈도해석을 수행해 왔다. 이러한 단변량 홍수빈도해석은 서로 상관된 홍수사상 사이의 복잡한 확률적 거동을 분석하는 데 있어 한계를 가지고 있다. 따라서, 본 연구에서는 Gumbel 혼합모형을 이용한 이변량 홍수빈도해석을 수행하여 홍수심도를 평가하는 방안을 제시하였다. 소양강댐의 35개년 일유입량 자료와 대청댐의 28개년 일유입량자료에 대해 각각의 홍수사상을 분리하고, 분리한 홍수사상에 대해 첨두홍수량과 홍수용적 사이의 결합분포와 결합재현기간 등을 도출하였다. 또한 이러한 이변량 홍수빈도해석에 의해 도출된 홍수 특성을 단변량 홍수빈도해석의 결과와 비교함으로써, 홍수심도 평가에 있어 이변량 홍수빈도 해석기법의 적용성에 관하여 검토하였다.

A flood event can be defined by three characteristics; peak discharge, total flood volume, and flood duration, which are correlated each other. However, a conventional flood frequency analysis for the hydrological plan, design, and operation has focused on evaluating only the amount of peak discharge. The interpretation of this univariate flood frequency analysis has a limitation in describing the complex probability behavior of flood events. This study proposed a bivariate flood frequency analysis using a Gumbel mixed model for the flood evaluation. A time series of annual flood events was extracted from observations of inflow to the Soyang River Dam and the Daechung Dam, respectively. The joint probability distribution and return period were derived from the relationship between the amount of peak discharge and the total volume of flood runoff. The applicability of the Gumbel mixed model was tested by comparing the return periods acquired from the proposed bivariate analysis and the conventional univariate analysis.

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참고문헌

  1. 권영문, 김태웅 (2009). “이변량 강우 빈도해석을 이용한 서울지역 I-D-F 곡선 유도.” 대한토목학회논문집, 대한토목학회, 제29권, 제2B호, pp. 155-162
  2. 김병식, 김형수 (2008). “유출수문곡선과 돌발홍수지수를 이용한 돌발홍수심도 산정.” 한국수자원학회논문집, 한국수자원학회, 제41권, 제2호, pp. 185-196 https://doi.org/10.3741/JKWRA.2008.41.2.185
  3. 위성욱, 정건희, 김태웅 (2008). “유출특성 분포함수의 표준화를 통한 종합홍수지수의 개발.” 한국수자원학회논문집, 한국수자원학회, 제41권, 제6호, pp. 605-617 https://doi.org/10.3741/JKWRA.2008.41.6.605
  4. Ashkar, F., El Jabi, N., and Issa, M. (1998). “A bivariate analysis of the volume and duration of low-flow events.” Stochastic Hydrology and Hydraulics, Vol. 12, pp. 97-116 https://doi.org/10.1007/s004770050012
  5. Carlos, E. (2007). “Application of bivariate extreme value distribution to flood frequency analysis: a case study of Northwestern Mexico.” Natural Hazards, Vol. 42, pp. 37-46 https://doi.org/10.1007/s11069-006-9044-7
  6. Gumbel, E.J. (1960). “Multivariate extremal distributions.” Bull. Inst. Internat, De Statistique, Vol. 37, No. 2, pp. 471-475
  7. Gumbel, E.J., and Mustafi, C.K. (1967). “Some analytical properties of bivariate extreme distributions.” J. Am. Stat. Assoc, Vol. 62, pp. 569 -588 https://doi.org/10.2307/2283984
  8. Kao, S. (2007). “A bivariate frequency analysis of extreme rainfall with implications for design.” Journal of Geophysical Research, Vol. 112, pp. 1-15 https://doi.org/10.1029/2007JD008522
  9. Kelly, K.S. and Krzysztofowicz, R. (1997). “A bivariate meta-Gaussian density for use in hydrology.” Stochastic Hydrology and Hydraulics, Vol. 11, pp. 17-31 https://doi.org/10.1007/BF02428423
  10. Lee, C., Kim, T.W., Chung, G., Choi, M., and Yoo, C. (2009). “Application of bivariate frequency analysis to the derivation of rainfall-frequency curves.” Stochastic Environmental Research and Risk Assessment, DOI 10.1007/s00477-009-0328- 0
  11. Oliveria, J.T.D. (1975). “Bivariate extremes: Extensions.” Bull. of the Inter. Statistical Inst, Vol. 46, No. 2, pp. 241-251
  12. Oliveria, J.T.D. (1982). Bivariate Extremes: Models and Statistical Decision. Tech. Report no. 14, Center for Stochastic Processes, Dept. of Statistics, University of North Carolina, Chapel Hill ,North Carolina, U.S.A
  13. Shiau, J.T. (2003). “Return period of bivariate distributed extreme hydrological events.” Stochastic Environmental Research and Risk Assessment, Vol. 17, pp. 42-57 https://doi.org/10.1007/s00477-003-0125-9
  14. Yue, S., Ouarda, T.B.M.J., Bobee, B., Legendre, P. and Bruneau, P. (1999). “The Gumbel mixed model for flood frequency analysis.” Journal of Hydrology, Vol. 226, No. 1–2, pp. 88-100 https://doi.org/10.1016/S0022-1694(99)00168-7
  15. Yue, S. (2000a). “The Gumbel mixed model applied to storm frequency analysis.” Water Resource Management, Vol. 14, pp. 377-389 https://doi.org/10.1023/A:1011124423923
  16. Yue, S. (2000b). “Joint probability distribution of annual maximum storm peaks and amounts as represented by daily rainfalls.” Hydrological Science Journal, Vol. 45, No. 2, pp. 315-326 https://doi.org/10.1080/02626660009492327
  17. Yue, S. (2001a). “A bivariate gamma distribution for use in multivariate flood frequency analysis.” Hydrol Processes, Vol. 15, pp. 1033-1045 https://doi.org/10.1002/hyp.259
  18. Yue, S. (2001b). “A review of bivariate gamma distributions for hydrological application.” Journal of Hydrology, Vol. 246, pp. 1-18 https://doi.org/10.1016/S0022-1694(01)00374-2
  19. Yue, S. (2001c). “The Gumbel logistic model for representing a mutivariate storm event.” Advances in Water Resources, Vol. 24, pp. 179-185 https://doi.org/10.1016/S0309-1708(00)00039-7
  20. Yue, S., and Rasmussen, P. (2002). “Bivariate frequency analysis: discussion of some useful concepts in hydrological application.” Hydrol Process, Vol. 16, pp. 2881–2898 https://doi.org/10.1002/hyp.1185
  21. Zhang, L., and Singh, V.P. (2006). “Bivariate Flood Frequency Analysis Using the Copula Method.” J. Hydrologic Engrg, ASCE, Vol. 11, No. 2, pp. 150-164 https://doi.org/10.1061/(ASCE)1084-0699(2006)11:2(150)

피인용 문헌

  1. Drought Frequency Analysis Using Hidden Markov Chain Model and Bivariate Copula Function vol.48, pp.12, 2015, https://doi.org/10.3741/JKWRA.2015.48.12.969
  2. Bivariate Frequency Analysis of Rainfall using Copula Model vol.45, pp.8, 2012, https://doi.org/10.3741/JKWRA.2012.45.8.827