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As devastating and unpredictable tsunamis generated by underwater earthquakes are occurring more frequently, the need for tsunami disaster prevention measures is rapidly increasing. In this study, tsunami heights were estimated, and the best-fit distribution was examined through a combination of numerical analyses and statistical methods. A numerical model was employed to estimate the tsunami heights, and the parameters were estimated using the method of L-moments applied to the estimated tsunami heights. The best-fit distribution was determined by applying the estimated parameters to the L-moment ratio diagram. The study areas were the Imwon Port and the Sadong Port located in the eastern part of the Korean Peninsula. The tsunami height distribution was represented by a log-normal distribution for the Imwon Port, whereas the distribution was represented by a generalized Pareto distribution for the Sadong Port. The study indicates that the distribution most commonly suggested by previous studies, i.e., the log-normal distribution, is not always accurate. Therefore, when performing statistical analysis on tsunami heights, the assumption of a log-normal distribution should be considered carefully.

The reflection coefficients of monochromatic water waves over trenches with shear current are estimated analytically. The diffraction of waves by an abrupt depth change and shear current is formulated by the matched eigenfunction expansion method. The proper number of steps and evanescent modes are proposed by a series of convergence tests. The accuracy of the predicted reflection coefficients is checked by estimating the wave energy. Reflection and transmission characteristics are studied for various shear current conditions. The different combinations of strength, width of shear current, and incident wave angle with constant water depth topography are examined. The optimal figure of the trench with shear current is obtained by estimating the reflection coefficients for various sloped transitions. The resonant reflection of the water waves is found by multiarrayed optimal trenches and the interaction of sinusoidally varying topography with shear current.

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