Log-normality of the Tsunami Run-up Heights along the Eastern Coastal Line of Korean Peninsula

Abstract

While tsunami is one of the most dangerous disasters threatening the survival of human being, the analysis of tsunami often requires the numerical simulation which needs tremendous amount of input data such as the ones related to sea bathymetry, terrain, and undersea earthquakes. To overcome this problem, the statistical approaches are often used. In this study, the method of L-moment ratio diagram was used to identify the best-fit distribution of the tsunami runup height along the eastern coastline of Korean Peninsula, which can subsequently be used as the reference distribution to analyze the risk due to tsunami attack. The result of the analysis indicates the generalized Pareto (GPA) distribution is the best-fit distribution representing the tsunami runup heights regardless of the characteristics of the undersea earthquakes. This is particularly because the tsunami runup height is influenced not only by the characteristics of the undersea earthquakes but also highly by the bathymetry and the terrain of the area near the tsunami attack. Further analysis was performed to figure out why the tsunami runup height does not have the ideal theoretical form, which is the log-normal distribution. Result of the investigation indicates that the log-normality of the tsunami runup heights can be preserved when the length of the 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 principle of the central limit theorem making the distribution of the tsunami runup heights follow the log-normal distribution. As the length of the coastal line increases, the deviation of the tsunami runup height distribution from the log-normality increased.