Dispersive modeling of the 2009 Samoa tsunami

In this study, we investigate the dispersive effects in the 2009 Samoa tsunami through numerical simulations. The wave propagation is first simulated with a weakly nonlinear and dispersive Boussinesq model and a non‐dispersive shallow‐water‐equations model. Comparison of the numerical results between these models indicates that tsunami propagation is significantly affected by the frequency dispersion east of Tonga Trench. Neglecting dispersive effects results in larger wave heights and speeds. The strong frequency dispersion is primarily attributed to the dramatic variation of water surface elevations generated by the earthquake doublet, and enhanced by the uneven bathymetry in Tonga Trench. Tsunami propagation is also simulated with MOST (“Method of Splitting Tsunamis”), which is based on the shallow water equations but uses numerical dispersion to mimic physical frequency dispersion at operational resolutions. A good agreement is observed between MOST and the Boussinesq model, as well as the field measurements in the leading wave. In the shorter trailing waves, agreement becomes poorer due to the mismatch between numerical and physical dispersions.