An integrated Bayesian approach to the probabilistic tsunami risk model for the location and magnitude of earthquakes: application to the eastern coast of the Korean Peninsula

  • Kwan-Hyuck Kim
  • Yong-Sik Cho
  • Hyun-Han Kwon
Original Paper


We explored the distributional changes in tsunami height along the eastern coast of the Korean Peninsula resulting from virtual and historical tsunami earthquakes. The results confirm significant distributional changes in tsunami height depending on the location and magnitude of earthquakes. We further developed a statistical model to jointly analyse tsunami heights from multiple events, considering the functional relationships; we estimated parameters conveying earthquake characteristics in a Weibull distribution, all within a Bayesian regression framework. We found the proposed model effective and informative for the estimation of tsunami hazard analysis from an earthquake of a given magnitude at a particular location. Specifically, several applications presented in this study showed that the proposed Bayesian approach has the advantage of conveying the uncertainty of the parameter estimates and its substantial effect on estimating tsunami risk.


Tsunami hazard Bayesian model Regression analysis Risk analysis Uncertainty 



The authors thank the Associate Editor and the two anonymous reviewers for their constructive criticism of the paper. The insightful comments provided by the Associated Editor and reviewers have greatly improved the original manuscript. This research was supported by Korea Institute of Marine Science and Technology promotion. The third author was supported by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2017-2015-0-00378) supervised by the IITP (Institute for Information & communications Technology Promotion). The data used in this study are available upon request from the corresponding author via email (

Supplementary material

477_2017_1488_MOESM1_ESM.docx (22 kb)
Supplementary material 1 (DOCX 22 kb)


  1. Ang AHS, Tang WH (1984) Probability concepts in engineering planning and design, vol 1. Wiley, New YorkGoogle Scholar
  2. Berger JO, Sun D (1993) Bayesian analysis for the poly-Weibull distribution. J Am Stat Assoc 88:1412–1418CrossRefGoogle Scholar
  3. Cho Y-S (1995) Numerical simulations of tsunami propagation and run-up. Cornell University, IthacaGoogle Scholar
  4. Cho Y-S, Yoon SB (1998) A modified leap-frog scheme for linear shallow-water equations. Coast Eng J 40:191–205CrossRefGoogle Scholar
  5. Cho Y-S, Sohn D-H, Lee SO (2007) Practical modified scheme of linear shallow-water equations for distant propagation of tsunamis. Ocean Eng 34:1769–1777CrossRefGoogle Scholar
  6. Cho Y-S, Kim YC, Kim D (2013) On the spatial pattern of the distribution of the tsunami run-up heights. Stoch Environ Res Risk Assess 27:1333–1346CrossRefGoogle Scholar
  7. Choi BH, Woo SB, Pelinovsky E (1994) A numerical simulation of the East Sea tsunami. J Korean Soc Coast Ocean Eng 6:404–412Google Scholar
  8. Choi BH, Pelinovsky E, Ryabov I, Hong SJ (2002) Distribution functions of tsunami wave heights. Nat Hazards 25:1–21CrossRefGoogle Scholar
  9. Choi BH, Pelinovsky E, Lee HJ, Woo SB (2005) Estimates of tsunami risk zones on the coasts adjacent to the East (Japan) sea based on the synthetic catalogue. Nat Hazards 36:355–381CrossRefGoogle Scholar
  10. Choi BH, Hong SJ, Pelinovsky E (2006) Distribution of runup heights of the December 26, 2004 tsunami in the Indian Ocean. Geophys Res Lett 33:L13601. Google Scholar
  11. Choi BH, Kim DC, Pelinovsky E, Woo SB (2007) Three-dimensional simulation of tsunami run-up around conical island. Coast Eng 54:618–629CrossRefGoogle Scholar
  12. Choi BH, Min B, Pelinovsky E, Tsuji Y, Kim K (2012) Comparable analysis of the distribution functions of runup heights of the 1896, 1933 and 2011 Japanese tsunamis in the Sanriku area. Nat Hazards Earth Syst Sci 12:1463–1467CrossRefGoogle Scholar
  13. Clare MA, Talling PJ, Challenor P, Malgesini G, Hunt J (2014) Distal turbidites reveal a common distribution for large (> 0.1 km3) submarine landslide recurrence. Geology 42:263–266CrossRefGoogle Scholar
  14. Fukutani Y, Anawat S, Imamura F (2016) Uncertainty in tsunami wave heights and arrival times caused by the rupture velocity in the strike direction of large earthquakes. Nat Hazards 80:1749–1782CrossRefGoogle Scholar
  15. Geist EL (2002) Complex earthquake rupture and local tsunamis. J Geophys Res Solid Earth 107(B5).
  16. Geist EL, Lynett PJ (2014) Source processes for the probabilistic assessment of tsunami hazards. Oceanography 27:86–93CrossRefGoogle Scholar
  17. Geist EL, Parsons T (2006) Probabilistic analysis of tsunami hazards. Nat Hazards 37:277–314CrossRefGoogle Scholar
  18. Geist EL, Parsons T (2008) Distribution of tsunami interevent times. Geophys Res Lett 35:L02612. CrossRefGoogle Scholar
  19. Geist EL, Parsons T (2009) Assessment of source probabilities for potential tsunamis affecting the U.S Atlantic Coast. Mar Geol 264:98–108. CrossRefGoogle Scholar
  20. Gelman A (2006) Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Anal 1:515–534CrossRefGoogle Scholar
  21. Gelman A, Hill J (2006) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  22. Gelman A, Carlin JB, Stern HS, Rubin DB (2014) Bayesian data analysis, vol 2. Chapman & Hall/CRC, Boca RatonGoogle Scholar
  23. Gilks WR, Best N, Tan K (1995) Adaptive rejection Metropolis sampling within Gibbs sampling. Appl Stat 44:455–472CrossRefGoogle Scholar
  24. Go CN (1987) Statistical properties of tsunami runup heights at the coast of Kuril Island and Japan. Institute of Marine Geology and Geophysics, SakhalinGoogle Scholar
  25. Go CN (1997) Statistical distribution of the tsunami heights along the coast Tsunami and accompanied phenomena. Sakhalin 7:73–79Google Scholar
  26. González FI et al (2009) Probabilistic tsunami hazard assessment at seaside, Oregon, for near- and far-field seismic sources. J Geophys Res Oceans. Google Scholar
  27. Grezio A, Marzocchi W, Sandri L, Gasparini P (2010) A Bayesian procedure for probabilistic tsunami hazard assessment. Nat Hazards 53:159–174CrossRefGoogle Scholar
  28. Hagiwara Y (1974) Probability of earthquake occurrence as obtained from a Weibull distribution analysis of crustal strain. Tectonophysics 23:313–318CrossRefGoogle Scholar
  29. Hasumi T, Akimoto T, Aizawa Y (2009) The Weibull–log Weibull distribution for interoccurrence times of earthquakes. Phys A 388:491–498CrossRefGoogle Scholar
  30. Imamura F, Shuto N, Goto C (1988) Numerical simulation of the transoceanic propagation of tsunamis. Paper presented at the sixth congress of the Asian and Pacific regional division international association hydraulic research, Kyoto, JapanGoogle Scholar
  31. Justus C, Hargraves W, Mikhail A, Graber D (1978) Methods for estimating wind speed frequency distributions. J Appl Meteorol 17:350–353CrossRefGoogle Scholar
  32. Kajiura K (1983) Some statistics related to observed tsunami heights along the coast of Japan. Tsunamis–their Science and Engineering, Terra Pub, Tokyo, pp 131–145Google Scholar
  33. KEDO (1999) Estimation of tsunami height for KEDO LWR project. Korea Power Engineering Company Inc, GimcheonGoogle Scholar
  34. Kim YC, Choi M, Cho Y-S (2012) Tsunami hazard area predicted by probability distribution tendency. J Coast Res 28:1020–1031CrossRefGoogle Scholar
  35. Kim D, Kim BJ, Lee S-O, Cho Y-S (2014) Best-fit distribution and log-normality for tsunami heights along coastal lines. Stoch Environ Res Risk Assess 28:881–893CrossRefGoogle Scholar
  36. Knighton J, Bastidas LA (2015) A proposed probabilistic seismic tsunami hazard analysis methodology. Nat Hazards 78:699–723CrossRefGoogle Scholar
  37. Kulikov EA, Rabinovich AB, Thomson RE (2005) Estimation of tsunami risk for the coasts of Peru and Northern Chile. Nat Hazards 35:185–209. CrossRefGoogle Scholar
  38. Kumar TS, Nayak S, Kumar CP, Yadav RBS, Ajay Kumar B, Sunanda MV, Devi EU, Kumar NK, Kishore SA, Shenoi SSC (2012a) Successful monitoring of the 11 April 2012 tsunami off the coast of Sumatra by Indian tsunami early warning centre. Curr Sci 102(11):1519–1526Google Scholar
  39. Kumar TS et al (2012b) Performance of the tsunami forecast system for the Indian Ocean. Curr Sci 102:110–114Google Scholar
  40. Kundu D, Joarder A (2006) Analysis of Type-II progressively hybrid censored data. Comput Stat Data Anal 50:2509–2528CrossRefGoogle Scholar
  41. Legates DR, McCabe GJ (1999) Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241CrossRefGoogle Scholar
  42. Liu PL-F, Cho Y-S, Briggs MJ, Kanoglu U, Synolakis CE (1995a) Runup of solitary waves on a circular island. J Fluid Mech 302:259–285CrossRefGoogle Scholar
  43. Liu PL-F, Cho Y-S, Yoon S, Seo S (1995b) Numerical simulations of the 1960 Chilean tsunami propagation and inundation at Hilo, Hawaii. In: Tsunami: progress in prediction, disaster prevention and warning. Springer, pp 99–115Google Scholar
  44. Lorito S, Selva J, Basili R, Romano F, Tiberti M, Piatanesi A (2015) Probabilistic hazard for seismically induced tsunamis: accuracy and feasibility of inundation maps. Geophys J Int 200:574–588CrossRefGoogle Scholar
  45. Mazova R, Pelinovsky E, Poplavsky A (1989) Physical interpretation of tsunami height repeatability law. Vulcanol Seismol 8:94–101Google Scholar
  46. McCloskey J et al (2008) Tsunami threat in the Indian Ocean from a future megathrust earthquake west of Sumatra. Earth Planet Sci Lett 265:61–81. CrossRefGoogle Scholar
  47. Mimura N, Yasuhara K, Kawagoe S, Yokoki H, Kazama S (2011) Damage from the Great East Japan Earthquake and Tsunami-a quick report. Mitig Adapt Strat Glob Change 16:803–818CrossRefGoogle Scholar
  48. Mitsoudis D, Flouri E, Chrysoulakis N, Kamarianakis Y, Okal E, Synolakis C (2012) Tsunami hazard in the southeast Aegean Sea. Coast Eng 60:136–148CrossRefGoogle Scholar
  49. Muraleedharan G, Sinha M, Rao AD, Murty TS (2006) Statistical simulation of boxing day tsunami of the indian ocean and a predictive equation for beach run up heights based on work-energy theorem. Mar Geodesy 29:223–231. CrossRefGoogle Scholar
  50. Omira R, Baptista M, Matias L (2015) Probabilistic tsunami hazard in the Northeast Atlantic from near-and far-field tectonic sources. Pure Appl Geophys 172:901–920CrossRefGoogle Scholar
  51. Orfanogiannaki K, Papadopoulos GA (2007) conditional probability approach of the assessment of tsunami potential: application in three tsunamigenic regions of the Pacific Ocean. In: Satake K, Okal EA, Borrero JC (eds) Tsunami and its hazards in the Indian and Pacific Oceans. Birkhäuser Basel, Basel, pp 593–603. CrossRefGoogle Scholar
  52. Pasari S, Dikshit O (2014) Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure Appl Geophys 171:1251–1281CrossRefGoogle Scholar
  53. Pelinovsky E, Yuliadi D, Prasetya G, Hidayat R (1997a) The 1996 Sulawesi tsunami. Nat Hazards 16:29–38CrossRefGoogle Scholar
  54. Pelinovsky E, Yuliadi D, Prasetya G, Hidayat R (1997b) The January 1, 1996 Sulawesi Island tsunami. Int J Tsunami Soc 15:107–123Google Scholar
  55. Pishgar-Komleh S, Keyhani A, Sefeedpari P (2015) Wind speed and power density analysis based on Weibull and Rayleigh distributions (a case study: firouzkooh county of Iran). Renew Sustain Energy Rev 42:313–322CrossRefGoogle Scholar
  56. Rabinovich AB (1997) Spectral analysis of tsunami waves: separation of source and topography effects. J Geophys Res Oceans 102:12663–12676CrossRefGoogle Scholar
  57. Seguro J, Lambert T (2000) Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis. J Wind Eng Ind Aerodyn 85:75–84CrossRefGoogle Scholar
  58. Shin JY, Chen S, Kim T-W (2015) Application of Bayesian Markov Chain Monte Carlo method with mixed gumbel distribution to estimate extreme magnitude of tsunamigenic earthquake. KSCE J Civ Eng 19:366CrossRefGoogle Scholar
  59. Singh VP (1987) On application of the Weibull distribution in hydrology. Water Resour Manag 1:33–43CrossRefGoogle Scholar
  60. Sohn D-H, Ha T, Cho Y-S (2009) Distant tsunami simulation with corrected dispersion effects. Coast Eng J 51:123–141CrossRefGoogle Scholar
  61. Sørensen MB, Spada M, Babeyko A, Wiemer S, Grünthal G (2012) Probabilistic tsunami hazard in the Mediterranean Sea. J Geophys Res Solid Earth. Google Scholar
  62. Tanioka Y, Yudhicara Kususose T, Kathiroli S, Nishimura Y, Iwasaki SI, Satake K (2006) Rupture process of the 2004 great Sumatra-Andaman earthquake estimated from tsunami waveforms. Earth Planet Space 58:203–209CrossRefGoogle Scholar
  63. Van Dorn WG (1965) Tsunamis. In: Chow VT (ed) Advances in hydroscience. Academic Press, London, pp 1–48Google Scholar
  64. Vogel RM, Kroll CN (1989) Low-flow frequency analysis using probability-plot correlation coefficients. J Water Resour Plan Manag 115:338–357CrossRefGoogle Scholar
  65. Weibull W (1951) Wide applicability. J Appl Mech 103:293–297Google Scholar
  66. Wilks DS (1989) rainfall intensity, the weibull distribution, and estimation of daily surface runoff. J Appl Meteorol 28:52–58.<0052:ritwda>;2 CrossRefGoogle Scholar
  67. Yadav R, Tripathi J, Kumar TS (2013a) Probabilistic assessment of tsunami recurrence in the Indian Ocean. Pure Appl Geophys 170:373–389CrossRefGoogle Scholar
  68. Yadav R, Tsapanos T, Tripathi J, Chopra S (2013b) An evaluation of tsunami hazard using Bayesian approach in the Indian Ocean. Tectonophysics 593:172–182CrossRefGoogle Scholar
  69. Yoon SB (2002) Propagation of distant tsunamis over slowly varying topography. J Geophys Res Oceans 107:C10CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringHanyang UniversitySeongdong-gu, SeoulRepublic of Korea
  2. 2.Department of Civil EngineeringChonbuk National UniversityJeonju-siRepublic of Korea

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