Long-term statistics of extreme tsunami height at Crescent City

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.