Until now, the analysis of long wave run-up on a plane beach has been focused on finding its maximum value, failing to capture the existence of resonant regimes. One-dimensional numerical simulations in the framework of the nonlinear shallow water equations are used to investigate the boundary value problem for plane and nontrivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, are used as forcing conditions to the boundary value problem. Resonant phenomena between the incident wavelength and the beach slope are found to occur, which result in enhanced run-up of nonleading waves. The evolution of energy reveals the existence of a quasiperiodic state for the case of sinusoidal waves. Dispersion is found to slightly reduce the value of maximum run-up but not to change the overall picture. Run-up amplification occurs for both leading elevation and depression waves.

Small islands in the vicinity of the mainland are widely believed to offer protection from wind and waves and thus coastal communities have been developed in mainland areas behind small islands. However, whether they offer protection from tsunamis is unclear. Do islands act as natural barriers? Recent post-tsunami survey data, supported by numerical simulations, reveal that the run-up on coastal areas behind small islands was significantly higher than on neighbouring locations not affected by the presence of the islands. To study the conditions of this run-up amplification, we solve numerically the nonlinear shallow water equations. We use the simplified geometry of a conical island sitting on a flat seafloor in front of a uniform sloping beach. By doing so, the experimental set-up is defined by five physical parameters, namely the island slope, the beach slope, the water depth, the distance between the island and the plane beach and the incoming wavelength, while the wave height was kept fixed. The objective is to find the maximum run-up amplification with the least number of simulations. To achieve this goal, we build an emulator based on Gaussian Processes to guide the selection of the query points in the parameter space. We thus reduce substantially the computations required to identify the run-up amplification. Our results show that the island acts as a focusing lens for energy and amplifies the run-up along the coastline behind its lee side, instead of protecting it, as popular beliefs suggest.