Best-fit distribution and log-normality for tsunami heights along coastal lines

The best-fit distribution of the tsunami height was investigated along the Eastern Coast of Korean Peninsula. Firstly, the tsunami heights corresponding to the nine probable undersea earthquakes were obtained along the coastline using the numerical simulation. The method of L-moment ratio diagram was used to identify the best-fit probability density function of the tsunami heights caused by each undersea earthquake. The result indicates the generalized Pareto distribution is the best-fit distribution representing the tsunami heights regardless of the characteristics of the undersea earthquakes. This is particularly because the area of high tsunami heights and its relative magnitude to the adjacent locations were similar for the most simulations cases. In addition, this study further investigated the reason why the tsunami height distribution is not represented by the log-normal (LN) distribution as suggested by the previous studies. Result of the investigation indicates that the log-normality of the tsunami heights can be preserved when the length of a coastal line is not long such that the homogeneity of the length of the wave propagation paths reaching at different locations of the coastal line is preserved. This subsequently secures the central limit theorem making the distribution of the tsunami heights have the LN distribution. As the length of the coastal line increases, the deviation of the tsunami height distribution from the log-normality increases.