  Employing a linear shallow water equation (LSWE) model in the spherical
coordinates, this paper investigates the tsunami waves generated by the
atmospheric pressure shock waves due to the explosion of the submarine volcano
Hunga Tonga-Hunga Ha'apai on January 15, 2022. Using the selected 59
atmospheric pressure records in the Pacific Ocean, an empirical atmospheric
pressure model is first constructed. Applying the atmospheric pressure model
and realistic bathymetric data in the LSWE model, tsunami generation and
propagation are simulated in the Pacific Ocean. The numerical results show
clearly the co-existence of the leading locked waves, propagating with the
speed of the atmospheric pressure waves (~1,100 km/hr), and the trailing free
waves, propagating with long gravity ocean wave celerity (~ 750 km/hr). During
the event, tsunamis were reported by 41 DART buoys in the Pacific Ocean, which
require corrections because of the occurrence of atmospheric pressure waves.
The numerically simulated tsunami arrival time and the amplitudes of the wave
crest and trough of the leading locked waves compare reasonably well with the
corrected DART measurements. The comparisons for the trailing waves are less
satisfactory, since free waves could also have been generated by other tsunami
generation mechanisms, which have not been considered in the present model, and
by the scattering of locked waves over changing bathymetry. In this regard, the
numerical results show clearly that the deep Tonga trench (~ 10 km) amplifies
the trailing waves in the Southeast part of the Pacific Ocean via the Proudman
resonance condition.
