Interpretation of global tsunami height distribution due to the 2022 Hunga Tonga-Hunga Ha’apai volcanic eruption

Tsunamis generated by atmospheric pressure waves due to a volcanic eruption were investigated based on both the proposed estimation formulas and numerical calculations. First, assuming linear shallow water conditions, estimation formulas were proposed for the maximum possible amplitude and the resonance distance. Second, the fundamental properties of tsunamis generated by atmospheric pressure waves were examined numerically using both the nondispersion and weak dispersion models. Based on the numerical results, a ridge and shelf can amplify tsunamis due to atmospheric pressure waves beyond the limits of the Proudman resonance. The estimated and numerically determined maximum possible amplitudes agreed well when the dispersion of tsunamis was not large. Third, the distribution maps of the maximum possible amplitude and the resonance distance for various traveling velocities of atmospheric pressure waves were generated using the proposed formulas. The maximum tsunami amplitude depends on both the length of the excitation area and the resonance distance along the path of atmospheric pressure waves. The worldwide distribution of both the tsunami height and the appearance time of the maximum tide level fluctuations due to the 2022 Tonga volcanic eruption and several historical eruptions were interpreted based on the distribution maps. In the historical large eruptions, the period of the atmospheric pressure waves was shorter; thus, the dispersion effect was larger, resulting in a smaller tsunami amplitude.