Intercomparison of hydrostatic and nonhydrostatic modeling for tsunami inundation mapping

Abstract

Nonhydrostatic modeling has emerged as an effective tool for seismological and tsunami research for over a decade, but its general application in hazard mapping and engineering design remains a topic of discussion. The approach incorporates the depth-averaged vertical velocity and nonhydrostatic pressure in the nonlinear shallow-water equations that provide a Poisson-type equation via the conservation of mass for quasi-three-dimensional flows. After the 2011 Tohoku tsunami, the State of Hawaii augmented the existing inundation maps to account for probable maximum tsunamis from Mw 9.3 and 9.6 Aleutian earthquakes. The use of both hydrostatic and nonhydrostatic modeling with a common set of telescopic computational grids covering 1330 km of shorelines facilitates a thorough intercomparison under distinct extreme events over a range of tropical island terrain and bathymetry. Including vertical flow dynamics can enhance the formation of a slowly attenuating trough behind the leading crest across the ocean as well as drawdown of receding water over steep nearshore slopes. The nonhydrostatic approach consistently gives lower predictions of the offshore tsunami amplitude due to frequency dispersion but can produce more severe coastal surges from resonance of the leading crest and trough over insular slopes as well as trapping of tsunami waves by wide shelves. Despite the potential for underestimating coastal surges, the lack of vertical inertia in hydrostatic models can result in substantially larger runup over steep terrain. The tsunami processes leading to inundation are complex with a strong dependence on the waveform and topography that can be well elucidated by the nonhydrostatic approach.