Tsunami propagation over varying water depths

The linear Boussinesq equations are an ideal model for transoceanic propagation of tsunamis. However, they are impractical for real-time application because Boussinesq-type equation models rely on a fine grid system and therefore require a huge computational domain. Thus, shallow-water equations models are the preferred method of predicting propagation and run-up of near- and far-field tsunamis since they produce fairly accurate results with a much smaller computational requirement. There may be an additional benefit in including physical dispersion effects in numerical models since shallow-water equations theoretically neglect the effect of dispersion on the transoceanic propagation of tsunamis. In this study, a modified finite difference scheme was proposed that adds terms to the linear shallow-water equations in order to account for varying water depths. The proposed model was verified by applying it to tsunami propagation over a submerged shoal and the results were compared with those of the well-known Boussinesq equations model, FUNWAVE. The proposed model was further tested by simulating transoceanic tsunami propagation on real topographies and comparing the numerical results with available observed data.