Statistical analysis of three-dimensional run-up heights using Gaussian process emulator of particle method

This study presents that an emulator of a particle method has the potential to be applied for the statistical analysis of tsunami run-up phenomena. The emulator follows a Gaussian process to model a particle method specifically for estimating wave heights of tsunami run-up in front of buildings on the ground. In general, Gaussian processes have the advantage of designing statistical emulators to reduce the computational cost required by simulators. Although statistical analysis using computational models requires a considerable number of simulations, Gaussian process emulators can address this challenge. In contrast, particle methods are advantageous for simulating free-surface flow problems including tsunami run-up. The mesh-free methods discretize the Navier-Stokes and continuity equations without mesh generations as opposed to mesh methods, and thus they can simulate tsunami behaviors near ground buildings. In this study, we simplify tsunami run-up as three-dimensional dam-break problems where the collapse of a water column owing to gravity moves in a slope and impacts on two buildings. Although these problems are not exactly tsunami run-up phenomena, the study intends to show the possibility of applying the Gaussian process emulator for such phenomena. The sensitivity analysis of the wave heights is carried out using the emulator to observe how the run-up heights are influenced by the initial size of the water column. Consequently, it predicts the tendency of the wave heights based on the initial settings and demonstrates the effectiveness of the emulator for the run-up analysis. In addition, this study illustrates the frequency and quartiles of the run-up heights near ground structures, which can be applied for tsunami evacuation planning.