한국수자원학회논문집 (Journal of Korea Water Resources Association)

  • 제50권3호
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  • Pages.211-221
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  • 2017
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  • 2799-8746(pISSN)
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  • 2799-8754(eISSN)
한국수자원학회 (Korea Water Resources Association)
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우리나라 강우자료의 무차원 L-moment ratio를 통한 Burr XII 분포의 수문학적 적용성 검토

Applicability of the Burr XII distribution through dimensionless L-moment ratio of rainfall data in South Korea

  • 서정호 (연세대학교 토목환경공학과) ;
  • 신홍준 (연세대학교 토목환경공학과) ;
  • 안현준 (연세대학교 토목환경공학과) ;
  • 허준행 (연세대학교 토목환경공학과)
  • Seo, Jungho (School of Civil and Environmental Engineering, Yonsei University) ;
  • Shin, Hongjoon (School of Civil and Environmental Engineering, Yonsei University) ;
  • Ahn, Hyunjun (School of Civil and Environmental Engineering, Yonsei University) ;
  • Heo, Jun-Haeng (School of Civil and Environmental Engineering, Yonsei University)
  • 투고 : 2017.02.13
  • 심사 : 2017.03.06
  • 발행 : 2017.03.31
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초록

수문통계분야에서는 극치 사상을 해석하기 위해 generalized extreme value (GEV), generalized logistic (GLO), Gumbel (GUM) 모형과 같은 다양한 극치분포들을 사용하여 왔다. 특히 우리나라 강우 사상의 경우 다양한 극치분포 모형 중 GEV 분포와 Gumbel 분포가 비교적 적합한 것으로 알려져 있지만 하나의 형상매개변수를 가지고 있어 각 분포 모형이 나타낼 수 있는 통계적 특성에 한계를 가지고 있다. 이러한 점에서 두 개의 형상매개변수를 가지고 있어 분포 모형이 나타낼 수 있는 통계적 특성의 범위가 넓은 분포의 적용이 필요하다. 이에 본 연구에서는 두 개의 형상매개변수를 가지고 있어 다양한 통계적 특성을 표현할 수 있는 Burr XII 분포와 우리나라 620개 지점의 강우자료의 무차원 L-moment 비를 이용하여 우리나라 강우자료의 수문학적 적용성을 검토하였다. 이를 위해 Burr XII 분포의 L-moment ratio인 L-skewness와 L-kurtosis를 유도하고 그 관계식을 이용하여 L-moment diagram을 작성하고 620개 지점이 해당 영역에 포함되는 정도를 검토하여 그 적용성을 살펴보았다. 그 결과 L-skewness가 L-kurtosis보다 상대적으로 큰 한강 유역에 해당하는 지점들에 대한 Burr XII 분포의 적용성이 우수한 것으로 나타났으며, 이는 일반적으로 많이 사용되는 GEV 또는 Gumbel 분포를 대체할 수 있는 분포가 될 가능성을 보였다고 할 수 있다.

In statistical hydrology, various extreme distributions such as the generalized extreme value (GEV), generalized logistic (GLO) and Gumbel (GUM) models have been widely used to analyze the extreme events. In the case of rainfall events in South Korea, the GEV and Gumbel distributions are known to be appropriate among various extreme distribution models. However, the proper probability distribution model may be different depending on the type of extreme events, rainfall duration, region, and statistical characteristics of extreme events. In this regard, it is necessary to apply a wide range of statistical properties that can be represented by the distribution model because it has two shape parameters. In this study, the statistical applicability of rainfall data is analyzed using the Burr XII distribution and the dimensionless L-moment ratio for 620 stations in South Korea. For this purpose, L-skewness and L-kurtosis of the Burr XII distribution are derived and L-moment ratio diagram is drawn and then the applicability of 620 stations was analyzed. As a result, it is found that the Burr XII distribution for the stations of the Han River basin in which L-skewness is relatively larger than L-kurtosis is appropriate, It is possibility of replacing the distribution of commonly used Gumbel or GEV distributions. Therefore, the Burr XII model can be replaced as an appropriate probability model in this basin.

키워드

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