Abstract
Historically, Crescent City is one of the most vulnerable communities impacted by tsunamis along the west coast of the United States, largely attributed to its offshore geography. Trans-ocean tsunamis usually produce large wave runup at Crescent Harbor resulting in catastrophic damages, property loss and human death. How to determine the return values of tsunami height using relatively short-term observation data is of great significance to assess the tsunami hazards and improve engineering design along the coast of Crescent City. In the present study, the extreme tsunami heights observed along the coast of Crescent City from 1938 to 2015 are fitted using six different probabilistic distributions, namely, the Gumbel distribution, the Weibull distribution, the maximum entropy distribution, the lognormal distribution, the generalized extreme value distribution and the generalized Pareto distribution. The maximum likelihood method is applied to estimate the parameters of all above distributions. Both Kolmogorov-Smirnov test and root mean square error method are utilized for goodness-of-fit test and the better fitting distribution is selected. Assuming that the occurrence frequency of tsunami in each year follows the Poisson distribution, the Poisson compound extreme value distribution can be used to fit the annual maximum tsunami amplitude, and then the point and interval estimations of return tsunami heights are calculated for structural design. The results show that the Poisson compound extreme value distribution fits tsunami heights very well and is suitable to determine the return tsunami heights for coastal disaster prevention.
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Annaka, T., Satake, K., Sakakiyama, T., Yanagisawa, K., and Shuto, N., 2007. Logic-tree approach for probabilistic tsunami hazard analysis and its applications to the Japanese coasts. Pure and Applied Geophysics, 164 (2): 577–592.
Choi, B. H., Hong, S. J., and Pelinovsky, E., 2001. Simulation of prognostic tsunamis on the Korean coast. Geophysical Research Letters, 28 (10): 2013–2016.
Coles, S., 2007. An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag, London, 45–183.
Cramer, H., 1999. Mathematical Methods of Statistics. Princeton University Press, Princeton, New Jersey, 575pp.
David, H. A., 1981. Order Statistics. 2nd edition. Wiley, New York, 384pp.
Dengler, L., Uslu, B., Barberopoulou, A., Borrero, J., and Synolakis, C., 2008. The vulnerability of Crescent City, California, to tsunamis generated by earthquakes in the Kuril Islands region of the Northwestern Pacific. Seismological Research Letters, 79 (5): 608–619.
Dong, S. L., 1989. Statistical analysis on parameter estimation method of Gumbel distribution. Journal of Hydraulic Engineering, 11: 35–42 (in Chinese).
Dong, S., and Hao, X. L., 2004. Statistical analysis of ocean environmental conditions with PTGEVD. The Proceedings of the 23rd International Conference on Offshore Mechanics and Polar Engineering. Vancouver, OMAE2004-51615.
Dong, S., Liu, W., and Ning, J. J., 2009. Return typhoon wave height estimation with Poisson-maximum entropy distribution. Shipbuilding of China, 50 (4): 13–21 (in Chinese with English abstract).
Dong, S., Tao, S. S., Chen, C., and Guedes Soares, C., 2014. Interval estimations of return wave height based on maximum entropy distribution. Journal of Coastal Research, 30 (5): 967–974.
Dong, S., Tao, S. S., Lei, S. H., and Guedes Soares, C., 2013. Parameter estimation of the maximum entropy distribution of significant wave height. Journal of Coastal Research, 29 (3): 597–604.
Fisher, R. A., 1922. On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of A Mathematical Physical & Engineering Sciences, 222 (1): 309–368.
Geist, E. L., and Parsons, T., 2006. Probabilistic analysis of tsunami hazard. Natural Hazards, 37 (3): 277–314.
Geist, E. L., and Parsons, T., 2011. Assessing historical rate changes in global tsunami occurrence. Geophysical Journal International, 187 (1): 497–509.
Geist, E. L., and Parsons, T., 2014. Undersampling power-law size distributions: Effect on the assessment of extreme natural hazards. Natural Hazards, 72 (2): 565–595.
González, F. I., Geist, E. L., Jaffe, B., Kânoglu, U., and Mofjeld, H., 2009. Probabilistic tsunami hazard assessment at Seaside, Oregon, for near-and far-field seismic sources. Journal of Geophysical Research: Oceans (1978–2012), 114 (C11): 507–514.
Greenwood, J. A., and Landwehr, J. M., 1979. Probability weighted moments: Parameters of several distributions expressible in inverse form. Water Resource Research, 15 (5): 1049–1054.
Hosking, J. R. M, and Wallis, J. R., 1987. Parameter and quantile estimation for the Generalized Pareto distribution. Technometrics, 29 (3): 339–349.
Hosking, J. R. M., 1990. L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society, Series B (Methodological), 52: 105–124.
Hosking, J. R. M., Wallis, J. R., and Wood, E. F., 1985. Estimation of the generalized extreme value distribution by the method of probability-weighted moments. Technometrics, 27 (3): 251–261.
Houston, J. R., Carver, R. D., and Markle, D. G., 1977. Tsunami-wave elevation frequency of occurrence for the Hawaiian Islands. (No. WES-TR-H-77-16) Army Engineer Waterways Experiment Station Vicksburg Miss.
Knighton, J., and Bastidas, L. A., 2015. A proposed probabilistic seismic tsunami hazard analysis methodology. Natural Hazards, 78: 699–723, DOI: 10.1007/s11069-015-1741-7.
Liu, D. F., and Ma, F. S., 1980. Prediction of extreme wave heights and wind velocities. Journal of the Waterway Port Coastal and Ocean Division, 106: 469–479.
Martins, E. S., and Stedinger, J. R., 2000. Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data. Water Resources Research, 36 (3): 737–744.
Parsons, T., and Geist, E. L., 2008. Tsunami probability in the Caribbean region. Pure and Applied Geophysics, 165 (11): 2089–2116.
Rao, A. R., and Hamed, K. H., 2000. Flood Frequency Analysis. CRC Press LLC, New York, 73–82.
Sun, S. Z., 2000. Lecture of Nonparametric Statistical Analysis. Peking University Press, Beijing, 141–155 (in Chinese).
Tao, S. S., and Dong, S., 2013. Interval estimation of return sea ice thickness in the northern arear of Bohai Sea based on maximum likelihood method. Engineering Mechanics, 30 (7): 294–298 (in Chinese with English abstract).
Tao, S. S., Dong, S., and Lv, H. M., 2012. Interval estimation methods of wave height for ocean engineering design. Shipbuilding of China, 53 (S2): 279–284 (in Chinese with English abstract).
Tao, S. S., Dong, S., and Xu, Y. H., 2013. Design parameter estimation of wave height and wind speed with bivariate copulas. The Proceedings of the 32nd International Conference on Ocean, Offshore and Arctic Engineering. Nantes, OMAE2013-10519.
Tao, S. S., Dong, S., Lei, S. H., and Guedes Soares, C., 2011. Interval estimation of return wave height for marine structural design. The Proceedings of 30th International Conference on Offshore Mechanics and Polar Engineering (Rotterdam, the Netherlands, OMAE2011), OMAE49421, 2: 305–311.
Wen, R. Z., and Ren, Y. F., 2007. Preliminary study on tsunami hazard analysis in China. World Earthquake Engineering, 23 (1): 6–11 (in Chinese with English abstract).
Woodruff, R. S., 1952. Confidence intervals for medians and other position measures. Journal of the American Statistical Association, 47 (260): 635–646.
Zhang, L. Z., and Xu, D. L., 2005. A new maximum entropy probability function for the surface elevation of nonlinear sea waves. China Ocean Engineering, 19 (4): 637–646.
Zhang, X. Z., 1996. Parameter estimation method application of Weibull distribution. Acta Meterologica Sinica, 54 (1): 108–116 (in Chinese with English abstract).
Acknowledgements
The study was partially supported by the National Natural Science Foundation of China (51279186, 51479183, 51509227), the National Key Research and Development Program (2016YFC0802301), the National Program on Key Basic Research Project (2011CB013704), and the Shandong Province Natural Science Foundation, China (ZR2014EEQ030). The authors thank Prof. Hajime Mase and Dr. Yong Wei for their constructive comments for the improvement of the manuscript.
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Dong, S., Zhai, J. & Tao, S. Long-term statistics of extreme tsunami height at Crescent City. J. Ocean Univ. China 16, 437–446 (2017). https://doi.org/10.1007/s11802-017-3259-y
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DOI: https://doi.org/10.1007/s11802-017-3259-y