대한토목학회논문집 (KSCE Journal of Civil and Environmental Engineering Research)

  • 제38권2호
  • /
  • Pages.249-259
  • /
  • 2018
  • /
  • 1015-6348(pISSN)
  • /
  • 2799-9629(eISSN)
대한토목학회 (Korean Society of Civil Engeneers)
권호 표지
DOI QR코드

DOI QR Code

Bayesian 기법을 이용한 혼합 Gumbel 분포 매개변수 추정 및 강우빈도해석 기법 개발

A Bayesian Approach to Gumbel Mixture Distribution for the Estimation of Parameter and its use to the Rainfall Frequency Analysis

  • 투고 : 2017.11.29
  • 심사 : 2018.01.08
  • 발행 : 2018.04.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

우리나라의 기후 지형적 특성에 따라 연강수량의 50% 이상이 여름철에 내린다. 이러한 짧은 기간에 집중적으로 내리는 강수량 조건하에 수공구조물을 설계할 경우 대부분 극치빈도분석을 활용한다. 특히 우리나라의 경우 Gumbel 분포를 활용한 극치빈도분석을 많이 이용한다. 하지만, 최근 이상기후로 인하여 전세계적으로 강수량의 특징이 급격히 변하고 있으며, 우리나라 연강수량 특징도 바뀌고 있다. 즉, 기존의 단일 분포형으로 재현이 가능했던 수문기상 자료들이 혼합분포형의 특징을 가지게 되었으며 이러한 변화를 고려할 수 있는 극치빈도분석 개발이 요구되고 있는 실정이다. 본 연구에서는 두 개 이상의 첨두를 가지는 형태의 극치강수량 자료에 대해서 기존의 단일 Gumbel 분포형 기반 극치빈도분석과 혼합 Gumbel 분포형 기반의 극치빈도분석 결과를 비교하였다. 확률분포의 매개변수 산정시 우도함수를 Bayesian 기법을 통해 산정하여 각 분포형의 Bayesian information criterion (BIC) 값을 비교하였다. 분석한 결과, 앞서 제안된 혼합 Gumbel 분포형은 하나의 첨두를 가지는 단일 Gumbel 분포형에서 반영되지 못한 꼬리(tail)부분의 이중첨두 부분의 거동을 효과적으로 모의하는 것을 확인할 수 있었다. 결과적으로 설계강수량을 추정할 때 보다 신뢰성있는 접근이 가능하였다. 이러한 점에서 우리나라 극치강우자료 분석시 기존 단일분포기반의 빈도해석기법에 대안으로 적용이 가능할 것으로 판단된다.

More than half of annual rainfall occurs in summer season in Korea due to its climate condition and geographical location. A frequency analysis is mostly adopted for designing hydraulic structure under the such concentrated rainfall condition. Among the various distributions, univariate Gumbel distribution has been routinely used for rainfall frequency analysis in Korea. However, the distributional changes in extreme rainfall have been globally observed including Korea. More specifically, the univariate Gumbel distribution based rainfall frequency analysis is often fail to describe multimodal behaviors which are mainly influenced by distinct climate conditions during the wet season. In this context, we purposed a Gumbel mixture distribution based rainfall frequency analysis with a Bayesian framework, and further the results were compared to that of the univariate. It was found that the proposed model showed better performance in describing underlying distributions, leading to the lower Bayesian information criterion (BIC) values. The mixed Gumbel distribution was more robust for describing the upper tail of the distribution which playes a crucial role in estimating more reliable estimates of design rainfall uncertainty occurred by peak of upper tail than single Gumbel distribution. Therefore, it can be concluded that the mixed Gumbel distribution is more compatible for extreme frequency analysis rainfall data with two or more peaks on its distribution.

키워드

참고문헌

  1. Gelman, A., Chew, G. L. and Shnaidman, M. (2004). "Bayesian analysis of serial dilution assays." Biometrics, Vol. 60, No. 2, pp. 407-417. https://doi.org/10.1111/j.0006-341X.2004.00185.x
  2. George, E. I. and McCulloch, R. E. (1993). "Variable selection via Gibbs sampling." Journal of the American Statistical Association, Vol. 88, No. 423, pp. 881-889. https://doi.org/10.1080/01621459.1993.10476353
  3. Heo, J. H., Kim, G. D. and Han, J. H. (1999). "Derivation of rainfall Intensity-Duration-Frequency equation based on the approproate probability distribution." Journal of Korea Water Resources Association, Vol. 32, No. 3, pp. 247-254 (in Korean).
  4. Ho, C. H., Lee, J. Y., Ahn, M. H. and Lee, H. S. (2003). "A sudden change in summer rainfall characteristics in Korea during the late 1970s." International Journal of Climatology, Vol. 23, No. 1, pp. 117-128. https://doi.org/10.1002/joc.864
  5. Kwon, H. H. and Moon, Y. I. (2006). "Improvement of overtopping risk evaluations using probabilistic concepts for existing dams." Stochastic Environmental Research and Risk Assessment, Vol. 20, No. 4, p. 223. https://doi.org/10.1007/s00477-005-0017-2
  6. Kwon, H. H., Brown, C. and Lall, U. (2008a). "Climate informed flood frequency analysis and prediction in Montana using hierarchical Bayesian modeling." Geophysical Research Letters, Vol. 35, No. 5.
  7. Kwon, H. H., Khalil, A. F. and Siegfried, T. (2008b). "Analysis of extreme summer rainfall using climate teleconnections and typhoon characteristics in South Korea." JAWRA Journal of the American Water Resources Association, Vol. 44, No. 2, pp. 436-448. https://doi.org/10.1111/j.1752-1688.2008.00173.x
  8. Kwon, H. H., Kim, J. G., Lee, J. S. and Na, B. K. (2012). "Uncertainty assessment of single event rainfall-runoff model using bayesian model." Journal of Korea Water Resources Association, Vol. 45, No. 5, pp. 505-516 (in Korean). https://doi.org/10.3741/JKWRA.2012.45.5.505
  9. Kwon, H. H., Moon, Y. I. and Khalil, A. F. (2007). "Nonparametric Monte Carlo simulation for flood frequency curve derivation: an application to a Korean watershed." JAWRA Journal of the American Water Resources Association, Vol. 43, No. 5, pp. 1316-1328. https://doi.org/10.1111/j.1752-1688.2007.00115.x
  10. Lee, J. J., Lee, J. S., Kim, B. I. and Park, J. Y. (2000). "Derivation of probable rainfall intensity formula of individual zone based on the representative probability distribution." Journal of Korea Water Resources Association, Vol. 33, No. S1, pp. 124-129 (in Korean).
  11. Lee, J. J., Lee, S. W. and Kwak, C. J. (2009). "Application of jackknife method for determination of representative probability distribution of annual maximum rainfall." Journal of Korea Water Resources Association, Vol. 42, No. 10, pp. 857-866 (in Korean). https://doi.org/10.3741/JKWRA.2009.42.10.857
  12. Park, C. Y., Moon, J. Y., Cha, E. J., Yun, W. T. and Choi, Y. E. (2008). "Recent changes in summer precipitation characteristics over South Korea." Journal of the Korean Geographical Society, Vol. 43, No. 3, pp. 324-336.
  13. Redner, R. A. and Walker, H. F. (1984). "Mixture densities, maximum likelihood and the EM algorithm." SIAM Review, Vol. 26, No. 2, pp. 195-239. https://doi.org/10.1137/1026034
  14. Shin, J. Y. and Lee, T. (2014). "Parameter estimation of the mixture normal distribution for hydro-meteorological variables using metaheuristic maximum likelihood." Journal of Korean Society of Hazard Mitigation, Vol. 14, No. 4, pp. 93-99 (in Korean). https://doi.org/10.9798/KOSHAM.2014.14.4.93
  15. Yoon, P. Y., Kim, T. W., Yang, J. S. and Lee, S. O. (2012). "Estimating quantiles of extreme rainfall using a mixed Gumbel distribution model." Journal of Korea Water Resources Association, Vol. 45, No. 3, pp. 263-274 (in Korean). https://doi.org/10.3741/JKWRA.2012.45.3.263