An empirical solution for tsunami run-up on compound slopes

Deterministic numerical models for tsunami inundation provide the most accurate means for estimating tsunami run-up when the bathymetry/topography and water-level time history at the seaward boundary are well known. However, it is often the case that there is uncertainty in both the bathymetry/topography and water level at the seaward boundary. For these reasons, empirical solutions for tsunami run-up may be preferred because the run-up can be computed quickly allowing a probabilistic estimate the tsunami run-up risk. In this paper, an empirical solution for tsunami run-up is developed based on an analytic solution and calibrated using a Boussinesq wave model for plane-sloped and compound-sloped cases, including the effects of bottom friction, wave breaking, and the slope of the inundated land area. The new relation is a function of the tsunami wave amplitude at a specific water depth (100 m) to provide clear guidance for practical application, and of two values of the surf-similarity parameter to account for a compound slope. The model comprises three equations for three regions: breaking, transition, and non-breaking. The model predictions are compared with survey data from the 2011 Tohoku tsunami in Japan without recalibration. The new equation provides reasonable estimates of run-up height and is generally conservative.