Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Analysis of extreme wind speed and precipitation using copula

코플라함수를 이용한 극단치 강풍과 강수 분석

  • Kwon, Taeyong (Department of Statistics, Daegu University) ;
  • Yoon, Sanghoo (Department of Statistics and Computer Science, Daegu University & Institute of Basic Science, Deagu University)
  • 권태용 (대구대학교 일반대학원 통계학과) ;
  • 윤상후 (대구대학교 전산통계학과, 대구대학교 기초과학연구소)
  • Received : 2017.05.02
  • Accepted : 2017.06.29
  • Published : 2017.07.31
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Abstract

The Korean peninsula is exposed to typhoons every year. Typhoons cause huge socioeconomic damage because tropical cyclones tend to occur with strong winds and heavy precipitation. In order to understand the complex dependence structure between strong winds and heavy precipitation, the copula links a set of univariate distributions to a multivariate distribution and has been actively studied in the field of hydrology. In this study, we carried out analysis using data of wind speed and precipitation collected from the weather stations in Busan and Jeju. Log-Normal, Gamma, and Weibull distributions were considered to explain marginal distributions of the copula. Kolmogorov-Smirnov, Cramer-von-Mises, and Anderson-Darling test statistics were employed for testing the goodness-of-fit of marginal distribution. Observed pseudo data were calculated through inverse transformation method for establishing the copula. Elliptical, archimedean, and extreme copula were considered to explain the dependence structure between strong winds and heavy precipitation. In selecting the best copula, we employed the Cramer-von-Mises test and cross-validation. In Busan, precipitation according to average wind speed followed t copula and precipitation just as maximum wind speed adopted Clayton copula. In Jeju, precipitation according to maximum wind speed complied Normal copula and average wind speed as stated in precipitation followed Frank copula and maximum wind speed according to precipitation observed Husler-Reiss copula.

한반도는 매년 태풍의 위험에 노출되어 있다. 태풍은 강풍과 강우가 동반되는 열대성 저기압으로 사회 경제적으로 막대한 피해를 유발한다. 현재의 자연재해 경고 시스템은 풍속과 강우를 구분하여 위험을 감지토록 설계되어 강풍과 폭우를 동반한 태풍의 위험을 경고하는데 한계점이 존재한다. 코플라모형은 확률변수들 사이의 복잡한 의존성 구조를 파악하기 위해 단변량분포의 집합을 다변량분포로 연결하는 모형으로 강우, 홍수, 가뭄 등의 분야에서 활발하게 연구되고 있다. 본 연구에서는 한반도에서 태풍에 가장 많이 노출된 도시인 부산과 제주도의 기상 관측소 (ASOS)에서 수집된 1904년 4월 9일부터 2015년 12월 31일까지 일강수량 (precipitation), 일최대풍속 (maximum wind speed) 자료를 이용하였다. 각 변수의 주변부확률을 추정하기 위해 두꺼운 꼬리 분포인 로그정규분포, 감마분포, 와이블분포를 고려하였다. 주변부 확률분포의 적합성검정은 Kolmogorov-Smirnov와 Cramervon-Mises, Anderson-Darling 검정통계량을 이용하였다. 코플라모형을 위해 순위를 기반으로 한 유사자료 (pseudo observation)를 생성하여 두 변수 간 의존성을 추정하였다. 강풍과 폭우의 의존성을 설명하기 위한 코플라모형으로 타원형, 나선형, 극단치 코플라모형이 고려되었다. 코플라모형의 적합성은 Cramer-von-Mises로 검정하였고, 교차검증을 통해 최적모형을 선택하였다. 연구결과 일강우량과 풍속의 주변부 확률분포로 대부분 로그정규분포가 적합하였다. 부산의 일평균풍속에 따른 일강우량은 t 코플라, 일최대풍속에 따른 일강우량은 Clayton 코플라가 최적모형으로 선정되었다. 제주도의 일최대풍속에 따른 일강우량은 정규코플라, 일강우량에 따른 일평균풍속은 Frank 코플라, 일강우량에 따른 일최대풍속은 Husler-Reiss 코플라가 최적모형으로 선택되었다.

Keywords

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