Tsunami Inundation Modeling

A tsunami's wavelength — tens to hundreds of kilometers — is far larger than even the deepest ocean, so the wave is a long wave for which vertical accelerations are negligible and the flow can be averaged over depth. This reduces the full three-dimensional fluid equations to the shallow-water equations in the water-surface elevation and depth-averaged velocity, making basin-scale simulation feasible. Titov and Synolakis built their solver on this approximation. The trade-off is that the standard shallow-water form omits frequency dispersion, which matters for shorter-wavelength waves such as those from some submarine landslides, where Boussinesq models are preferred.

Offshore, the computational domain is always wet, but inundation modeling must follow the shoreline as it moves inland during runup and retreats during drawdown, so cells switch between wet and dry. The wetting-and-drying algorithm classifies each cell by whether its total water depth exceeds a small threshold and updates the moving boundary every time step. This is the technical core of inundation (as opposed to propagation) modeling, because the quantities of interest — how deep and how far the flooding reaches and the runup height — are precisely the behavior of this moving shoreline. A poor wetting-and-drying scheme produces spurious oscillations or unphysical flooding.

Tsunami inundation maps inform evacuation and design decisions, so an inaccurate model can cost lives. After the 2004 Indian Ocean tsunami, several published inundation predictions made with unbenchmarked models diverged sharply from measured paleotsunami and survey data, undermining confidence in modeling generally. Synolakis and colleagues responded by defining a benchmark suite spanning analytical solutions (verifying the equations are solved correctly), laboratory experiments such as runup on a conical island, and field measurements of historical tsunamis (validating geophysical realism). A model is accepted for operational and hazard use only after passing these standard tests, and results are expected to report this validation.