The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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A Bayesian Analysis of Return Level for Extreme Precipitation in Korea

한국지역 집중호우에 대한 반환주기의 베이지안 모형 분석

  • Lee, Jeong Jin (Department of Statistics, Kyungpook National University) ;
  • Kim, Nam Hee (Department of Statistics, Kyungpook National University) ;
  • Kwon, Hye Ji (Statistics Korea) ;
  • Kim, Yongku (Department of Statistics, Kyungpook National University)
  • Received : 2014.07.29
  • Accepted : 2014.08.29
  • Published : 2014.12.31
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Abstract

Understanding extreme precipitation events is very important for flood planning purposes. Especially, the r-year return level is a common measure of extreme events. In this paper, we present a spatial analysis of precipitation return level using hierarchical Bayesian modeling. For intensity, we model annual maximum daily precipitations and daily precipitation above a high threshold at 62 stations in Korea with generalized extreme value(GEV) and generalized Pareto distribution(GPD), respectively. The spatial dependence among return levels is incorporated to the model through a latent Gaussian process of the GEV and GPD model parameters. We apply the proposed model to precipitation data collected at 62 stations in Korea from 1973 to 2011.

집중호우의 특성을 이해하는 것은 수문관리 및 재해방재 등에서 매우 중요하다. 특히 반환주기는 이러한 집중호우의 특성을 나타내는 측정치로 자주 사용된다. 본 논문에서는 베이지안 계층적 모형을 이용하여 강우의 반환주기에 대한 공간구조를 분석하였다. 먼저 국내 62개 지점에서 측정한 강우 강도을 기초로 하여 연간 일일 최대강우량과 특정한 수준을 초과하는 강우량에 대해서 generalized extreme value(GEV)와 generalized Pareto distribution(GPD)를 각각 가정하여 추정하였다. 집중호우 반환주기에 대한 공간구조는 이 GEV 분포와 GPD 분포의 모수에 공간구조를 가지는 다변량 정규분포를 이용하여 설명하였다. 제안된 모형을 국내 76개 지역에서 39년간 측정된 일별 강우량 관측자료에 적용하였다.

Keywords

References

  1. Casson, E. and Coles, S. (1999). Spatial Regression Models for Extremes, Extremes, 1, 449-468. https://doi.org/10.1023/A:1009931222386
  2. Coles, S. G. (2001). An Introduction to Statistical Modeling of Extreme Values, London: Springer-Verlag.
  3. Coles, S., Heffernan, J. and Tawn, J. (1999). Dependence measures for extreme value analysis, Extremes, 2, 339-365. https://doi.org/10.1023/A:1009963131610
  4. Cooley, D., Naveau, P., Jomelli, V, Rabatel, A. and Grancher, D. (2006). A Bayesian hierarchical extreme value model for lichenometry, Environmetrics, 17, 555-574. https://doi.org/10.1002/env.764
  5. Cooley, D., Nychka, D. and Naveau, P. (2007). Bayesian spatial modeling of extreme precipitation return levels, Journal of the American Statistical Association, 102, 824-840. https://doi.org/10.1198/016214506000000780
  6. Cunderlik, J. M., Burn, D. H., Posbherg, D., Robinson, B. A. and Zyvoloski, G. A. (2008). Generalized likelihood uncertainty estimation(GLUE) using adaptive Markov Chain, Journal of Hydrology, 276, 210-223.
  7. de Haan, L. (1985). Extremes in Higher Dimensions: The Model and Some Statistics, in proceedings of the 45th session of the International Statistical Institute.
  8. Embrechts, P., Kluppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Fi-nance, Berlin: Springer-Verlag.
  9. Heffernan, J. E. and Tawn, J. A. (2004). A conditional approach for multivariate extreme values, Journal of the Royal Statistical Society, Series B, 66, 497-546. https://doi.org/10.1111/j.1467-9868.2004.02050.x
  10. Lee, J. J. (2010). Assessment of nonstationarity in precipitation and development of nonstationary frequency analysis, Ph.D. Thesis, Chonbuk National University.
  11. Jang, S. W., Seo, L., Kim, T. W. and Ahn, J. H. (2011). Non-stationary rainfall frequency analysis based on residual analysis, Journal of the Korean Society of Civil Engineers, 31, 449-457.
  12. Kwak, M. and Kim, Y. (2014). Multi-site stochastic weather generator for daily rainfall in Korea, The Korean Journal of Applied Statistics, 27, 475-485. https://doi.org/10.5351/KJAS.2014.27.3.475
  13. Matern, B. (1986). Spatial Variation, 2nd edition, Springer-Verlag.
  14. Oliveria, O. A., Gomes, M. I. and Alves, M. I. F.(2006). Improvements in the estimation of a heavy tail, REVSTAT - Statistical Journal, 4, 81-109.
  15. Schlather, M. and Tawn, J. (2003). A dependence measure for multivariate and spatial extreme values: Properties and inference, Biometrika, 90, 139-156. https://doi.org/10.1093/biomet/90.1.139
  16. Strupczewski, W. G., Singh, V. P. and Mitosek, H. T. (2001). Non-stationary approach to at-site flood frequency modeling III : Flood analysis of Polish rivers, Journal of Hydrology, 248, 152-167. https://doi.org/10.1016/S0022-1694(01)00399-7