Journal of Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회논문집)

Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회)
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Analysis of Confidence Interval of Design Wave Height Estimated Using a Finite Number of Data

한정된 자료로 추정한 설계파고의 신뢰구간 분석

  • Jeong, Weon-Mu (Coastal Development & Ocean Energy Research Division, Korea Institute of Ocean Science & Technology) ;
  • Cho, Hong-Yeon (Marine Environments & Conservation Research Division, Korea Institute of Ocean Science & Technology) ;
  • Kim, Gunwoo (Department of Ocean Civil & Plant Construction Engineering, Mokpo National Maritime University)
  • 정원무 (한국해양과학기술원 연안개발.에너지연구부) ;
  • 조홍연 (한국해양과학기술원 해양환경.보전연구부) ;
  • 김건우 (국립목포해양대학교 해양.플랜트건설공학과)
  • Received : 2013.06.26
  • Accepted : 2013.08.13
  • Published : 2013.08.31
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Abstract

It is estimated and analyzed that the design wave height and the confidence interval (hereafter CI) according to the return period using the fourteen-year wave data obtained at Pusan New Port. The functions used in the extreme value analysis are the Gumbel function, the Weibull function, and the Kernel function. The CI of the estimated wave heights was predicted using one of the Monte-Carlo simulation methods, the Bootstrap method. The analysis results of the estimated CI of the design wave height indicate that over 150 years of data is necessary in order to satisfy an approximately ${\pm}$10% CI. Also, estimating the number of practically possible data to be around 25~50, the allowable error was found to be approximately ${\pm}$16~22% for Type I PDF and ${\pm}$18~24% for Type III PDF. Whereas, the Kernel distribution method, a typical non-parametric method, shows that the CI of the method is below 40% in comparison with the CI of the other methods and the estimated design wave height is 1.2~1.6 m lower than that of the other methods.

부산항 신항에서 측정한 14년 동안의 파랑자료를 이용하여 재현기간에 따른 설계파고와 신뢰구간을 추정 분석하였다. 극치분석에 사용한 함수는 Gumbel 함수와 Weibull 함수, Kernel 함수이며, 각각의 방법으로 추정한 설계파고의 신뢰구간을 Monte-Carlo 모의기법 중의 하나인 Bootstrap 방법으로 추정하였다. 설계파고의 추정 신뢰구간을 분석한 결과, 약 ${\pm}$10% 수준의 신뢰구간을 만족하기 위해서는 150년 이상의 자료가 필요한 것으로 파악되었다. 그리고 실질적으로 가능한 자료의 개수를 25~50개 정도(25~50년 동안의 추정자료)로 간주하는 경우, Type I 분포함수의 경우 허용오차가 ${\pm}$16~22% 정도이며, Type III 분포함수의 경우, ${\pm}$18~24% 정도로 파악되었다. 한편 비모수적 방법에 해당하는 Kernel 분포함수를 이용한 방법은 Type I과 III을 사용한 것에 비해 신뢰구간은 40% 이하 수준으로 우수한 결과를 보이는 반면, 설계파고는 1.2~1.6 m 정도 낮게 추정하는 결과를 보여주고 있다.

Keywords

References

  1. Agresti, A. and Franklin, C. (2007). Statistics, The Art and Science of Learning from Data, Sec. 2.5, Pearson Education, Inc.
  2. Barnett, V. and Lewis, T. (1994). Outliers in Statistical Data, Third Edition, John Wiley & Sons.
  3. Chae, J.W. (1980). Estimation of design wave height, Bulletin of KORDI, 2, 9-14.
  4. DiCiccio, T.J. and Efron, B. (1996). Bootstrap confidence intervals, Statistical Science, 11(3), 189-228. https://doi.org/10.1214/ss/1032280214
  5. Goda, Y. (2000). Random Seas and Design of Maritime Structures, Chap. 11, Advanced Series on Ocean Engineering, 15, World Scientific Publishing Co., Singapore.
  6. Grubbs, F.E. (1969). Procedures for detecting outlying observations in samples, Technometrics, 11(1), 1-21. American Statistical Association and American Society for Quality. https://doi.org/10.1080/00401706.1969.10490657
  7. Jeong, S.T., Kim, J.D. and Cho, H.Y. (2004). Characteristics on the extreme value distributions of deepwater design wave heights off the Korean coast. Journal of Korean Society of Coastal and Ocean Engineers, 16(3), 130-141.
  8. Jeong, W.M., Jun, K.C., Kim, G., Oh S.-H. and Ryu K.-H. (2012). Shallow-water design waves at Gangreung beach through the analysis of long-term measured wave data and numerical simulation using deepwater wave conditions. Journal of Korean Society of Coastal and Ocean Engineers, 24(5), 343-351. https://doi.org/10.9765/KSCOE.2012.24.5.343
  9. Komsta, L. (2006). Processing data for outliers, R News, 6/2, 10-13.
  10. Lee, D.-Y. and Jun, K.-C. (2006). Estimation of design wave height for the waters around the Korean peninsula. Ocean Science Journal, 41(4), 245-254. https://doi.org/10.1007/BF03020628
  11. Ministry of Oceans and Fisheries (2005). Design criteria for harbor and fishing port.
  12. Rousseeuw, P.J. and Leroy A.M. (2003). Robust regression and Outlier Detection, Wiley Series in Probability and Statistics, John Wiley & Sons.
  13. Rubinstein, R.Y. and Kroese, D.P. (2008). Simulation and the Monte Carlo Method, Second Edition, Chapter 4, John Wiley & Sons.
  14. Suh, K.-D., Kim, M. and Chun, J. (2011). Estimation of deepwater design wave height on southern coast of Korean peninsula by empirical simulation technique. Journal of Korean Society of Coastal and Ocean Engineers, 23(4), 265-275. https://doi.org/10.9765/KSCOE.2011.23.4.265
  15. Soares, C.G. and Scotto, M.G. (2004). Application of the r largestorder statistics for long-term predictions of significant wave height, Coastal Engineering, 51, 387-394. https://doi.org/10.1016/j.coastaleng.2004.04.003
  16. Stephen, M.A. (1974). EDF statistics for goodness of fit and some comparisons, J. of American Statistical Association, 69(347), 730-737. https://doi.org/10.1080/01621459.1974.10480196
  17. Stephen, M.A. (1986). Tests Based on EDF Statistics, Chapter 4 in Goodness-of-Fit Techniques (Edited by D'Agostino, R.B. and Stephens, M.A.). Marcel Dekker, Inc.
  18. US Army Corps of Engineers (2002). Coastal Engineering Manual, Part II, Chapter 8, EM-1110-2-1100,
  19. US Army Corps of Engineers (2008). Environmental Quality, Environmental Statistics, EM-1110-1-4014, Appendix I, Department of the Army
  20. Wand, M.P. and Jones, M.C. (1995). Kernel Smoothing, Monographs on Statistics and Applied Probability 60, Chapman & Hall /CRC.

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