한국수자원학회논문집 (Journal of Korea Water Resources Association)

  • 제48권1호
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  • Pages.37-44
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  • 2015
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  • 2799-8746(pISSN)
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  • 2799-8754(eISSN)
한국수자원학회 (Korea Water Resources Association)
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Grid Method 기법을 이용한 베이지안 비정상성 확률강수량 산정

Bayesian Nonstationary Probability Rainfall Estimation using the Grid Method

  • 곽도현 (경북대학교 공과대학 건축.토목공학부) ;
  • 김광섭 (경북대학교 대학원 건축.토목공학부)
  • 투고 : 2014.07.01
  • 심사 : 2014.12.23
  • 발행 : 2015.01.31
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초록

본 연구에서는 Grid method를 사용하여 베이지안 비정상성 확률강우량 산정 모형을 확립하였다. 강우 극치자료의 분포로 Gumbel 분포를 채택하였으며, 분포형의 매개변수에 사전분포를 적용하고, 사전분포에 포함된 매개변수에는 초사전 분포를 적용하여 계층적 베이지안 모형을 구성하였다. Grid method는 매개변수의 발생가능 전 구간에 대하여 확률적으로 더 높은 뒷받침이 있는 하위 구간에서 난수를 직접 생성하여 집합을 구성함으로써 잘못된 결과를 도출할 수 가능성이 높은 상황에서도 보다 정확한 매개변수의 추정을 가능케 하므로 매개변수의 추정과정에서 비표준분포로 나타나는 조건부 확률밀도함수를 통한 난수의 추출은 기존에 사용해 온 Metropolis Hastings 알고리즘이 아닌 Grid method를 사용하였다. 개발된 모형은 서울의 1973년부터 2012년까지의 시강우자료를 이용하여 미래에 대한 재현기간에 따른 확률강수량을 산정하였으며, 그 결과로 기존 정상성 가정에 비해 목표연도에 따라 5%에서 8%정도의 증가율을 나타냈다.

A Bayesian nonstationary probability rainfall estimation model using the Grid method is developed. A hierarchical Bayesian framework is consisted with prior and hyper-prior distributions associated with parameters of the Gumbel distribution which is selected for rainfall extreme data. In this study, the Grid method is adopted instead of the Matropolis Hastings algorithm for random number generation since it has advantage that it can provide a thorough sampling of parameter space. This method is good for situations where the best-fit parameter values are not easily inferred a priori, and where there is a high probability of false minima. The developed model was applied to estimated target year probability rainfall using hourly rainfall data of Seoul station from 1973 to 2012. Results demonstrated that the target year estimate using nonstationary assumption is about 5~8% larger than the estimate using stationary assumption.

키워드

참고문헌

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피인용 문헌

  1. Nonstationary Frequency Analysis Using a Hierarchical Bayesian Model vol.15, pp.5, 2015, https://doi.org/10.9798/KOSHAM.2015.15.5.19