Hydrostatic versus non-hydrostatic modeling of tsunamis with implications for insular shelf and reef environments

Dispersion is known to separate frequency components and reduce the amplitude of tsunami waves in the open ocean. The present paper elucidates a reverse process, in which the dispersed wave components from trans-oceanic propagation of the 2011 Tohoku tsunami regroup over the insular shelves and reefs of Hawaii. The non-hydrostatic and hydrostatic modes of a nonlinear long-wave model describe the pertinent processes with and without dispersion using the same system of two-way nested grids for direct comparison. Both solutions have very similar amplitude spectra across the ocean and reproduce the dominant components of recorded surface elevations and currents in Hawaii despite their markedly different offshore waveforms. The hydrostatic solution shows early arrival of short-period signals from nonlinear scattering around the Hawaiian Islands and faster attenuation of the amplitude due to their local source. The short-period trailing waves from dispersion more effectively excite shelf and reef oscillations giving rise to better agreement with both the amplitude and phase of the recorded data. Even with larger offshore wave amplitude, a hydrostatic model trends to underestimate the surge elevation and current velocity at coastlines fronted by shallow reefs susceptible to resonance oscillations associated with edge waves.