© 2022 Elsevier LtdOn January 15, 2022, the Hunga Tonga-Hunga Ha'apai volcano's huge eruption generated tsunami waves globally due to an unusual source in this unique event: fast-traveling air pressure disturbances originated from the explosion of the volcano. Here we investigate the global propagation of the pressure waves (first cycle) and the consequent ocean waves. The analysis of the measured air pressure waves shows that the speed of air pressure linearly increases with time. The peak and trough amplitudes of the pressure wave exponentially decrease with the traveled distance until half the overall distance; then, it restarts to increase, reaching a peak towards the apogee. Two different modeling approaches are followed to solve the air pressure waves and the resulting ocean waves: i) a synthetic pressure forcing model based on barometric measurements and ii) a numerical model based on nonlinear shallow water theory using an initial disturbance at the volcano. We forced the hydrodynamic model by the produced pressure fields to compute the resulting tsunami waves globally. We present the modeling results, discussing the possible sea level amplification mechanisms and affecting factors. Fairly well agreement between the computed and measured air pressure waves and sea levels around the globe is promising.