Characteristics of Tsunamis Observed in Japan due to the Air Wave from the 2022 Tonga Eruption

A large eruption of the Hunga Tonga-Hunga Ha(cid:0)apai volcano in Tonga on January 15, 2022 generated air-sea coupled tsunamis observed at the ocean-bottom pressure sensor network along the Japan Trench (S-net) in Japan. Initial tsunamis from the 2022 Tonga eruption, detected by 106 ocean bottom pressure sensors, were well modeled by an air-sea coupled tsunami simulation, with a simple atmospheric pressure pulse having a half-wavelength of 300 km and a peak amplitude of 2 hPa. A one-dimensional air-sea coupled tsunami simulation having a simple bathymetry shows that an input atmospheric pressure pulse with a short half-wavelength of 50 km, which is shorter than the length of the slopes, caused an amplitude increase via the Proudman resonance effect near the deep trench. The wavefront distortion due to the separation of the air-sea coupled wave (v=312 m/s) and sea wave (v= sqrt(gd)) is also signicant near the shore. In contrast, these effects are not signicant for the half-wavelength of the input atmospheric pressure pulse of 300 km. These results indicate that observing the wavelength of an atmospheric pressure pulse due to an eruption is important for forecasting the heights of air-sea coupled tsunamis.


Introduction
A large eruption of the Hunga Tonga-Hunga Ha apai volcano in Tonga on January 15, 2022, caused devastating disasters in nearby areas. The eruption generated air waves coupled with seawater waves propagating through the Paci c. Tsunamis, long-waves in the ocean, generated by the air wave from the eruption were observed in tide gauges and ocean bottom pressure sensor network along the Japan trench (S-net) in Japan. The network, which includes 150 pressure sensors connected by a cable with 30 km intervals, is operated by the National Research Institute for Earth Science and Disaster Resilience (NEID) in Japan (Uehira et al. 2012;Kanazawa 2013). A maximum tsunami amplitude of 1.2 m was observed at Amami in Japan, and thus, a tsunami warning was issued by the Japan Meteorological Agency.
Similar air-sea waves had previously been generated by the Krakatoa volcano eruption in 1882 (Harkrider and Press 1967), and the authors indicated that the air wave propagated at a velocity of 312 m/s. This kind of air-sea coupled waves, which is often called to meteotsunamis, has already been studied without (2021) suggested that meteotsunamis are ampli ed when the velocity of the air waves is similar to that of the tsunami waves. This is called the Proudman resonance effect (Williams et al., 2021). In the case of the tsunami caused by the air wave from the volcanic eruption, the tsunami propagated near a deep trench should be ampli ed.
In this paper, the tsunami waves observed at ocean bottom sensors of S-net in Japan were modeled by the air waves generated by the 2022 Tonga eruption. We discuss the characteristics of tsunami propagation, including the tsunami ampli cation near the Japan Trench, which has a depth of approximately 8 km.

Data And Method
Ocean bottom pressure data observed at 113 sensors at S-net (National Research Institute for Earth Science and Disaster Resilience, 2019) were downloaded ( Figure 1). The observed data are ltered in the periods between 100 and 3600 s using the bandpass lter in Seismic Analysis Cord (SAC) developed by Goldstein et al, (2003) (Supplement S1).
The governing equations to be solved by the numerical simulation is brie y explained. Linear approximation of Euler`s momentum equation is: where u, v, and w are the velocity in x, y, z-direction, respectively, p is the pressure, g is gravity acceleration, and ρ is the water density. By using longwave, or shallow water, approximation, third equation in (1) becomes Then, pressure p is p = − ρgz + c where c is a function of x, y, and t. At the ocean surface where z is a wave height (h), pressure (p) becomes atmospheric pressure (p 0 ) which is an input for the air-sea coupled wave in this study. Pressure, p, then becomes p = ρg(h − z) + p 0 . The momentum equations (1) (3) for air-sea coupled waves and continuity equation (4) were numerically solved using a staggered grid system with an input of the atmospheric pressure gradient at each time step. The grid sizes of the numerical computation were set at 1.5 km in both x and y directions.
The atmospheric pressures observed at approximately 3000 points in Japan (Weathernews, https://jp.weathernews.com/news/38708/, 2022) showed that the pressure pulse (a peek amplitude of approximately 2hPa, and the duration of 20-15 mins) passed through Japan from southeast to northwest with a strike of -44°. The shape of the pressure pulse was assumed to be half the wavelength of sine wave. The half-wavelength was set to 300 km, which corresponded to a duration of 16 mins. The peek amplitude was set to 2hPa. First, numerical computation in one dimension with a constant ocean depth of 5500 m was carried out to obtain the steady state of air-sea coupled initial wave. The pressure pulse and the steady state initial wave are entered into the two-dimensional computational domain from the low boundary along the x-axis ( Figure 2). The pressure pulse is continuously propagated in y-direction with a constant velocity of 312 m/s. The bathymetry was rotated 44° clockwise (Figure 1 and 2) to match a strike of the pressure wave from Tonga.

One Dimensional Tsunami Simulation
A one-dimensional tsunami simulation was carried out to understand the tsunami waveform deformation due to the existence of a deep trench. A simple bathymetry was set to compute the tsunami ( Figure 4): a shore 100 km away from the left boundary; a slope of 1/25 from the shore to 200 km away, where water depth is 8,000 m (trench); a slope of 1/12.5 from 200 to 400 km away, where the water depth is 5,500 m; and a at bottom from 400 to 900 km away. For an input of the atmospheric pressure pulse, three different half wavelengths, 50 km, 100 km, and 300 km, were tested for this simulation. 8,000 m depth to the shore increased the amplitude of tsunami. Shortening of the wavelength by the shoaling is not obvious. However, the shape of the wave front is distorted. This is due to the separation of air-sea coupled wave (v=312 m/s) and sea wave (v = √ gd).
For a half wavelength of 300 km (Figure 4c), three snapshots from 400 to 800 s show that the shapes of the waves are distorted with time, while the amplitudes of the waves are not signi cantly increased. In contrast, the shoaling effect from 8,000 m depth to the shore is clearly seen in both the amplitude increase and wavelength shortening. The distortion of the wavefront is visible but not signi cant.
The snapshots from a half-wavelength of 100 km (Figure 4b) show that the characteristics of the waveforms are between those for half-wavelengths of 50 and 300 km. Three snapshots from 600 to 1000 s show that the amplitudes of the tsunami increased slightly when the depth of the water increased to 8,000 m. The shoaling effect is also observed in both the amplitude increase and wavelength shortening.
The distortion of the wavefront is also observed from 1400 to 1800 s (Figure 4b).

Conclusions
Initial tsunamis from the 2022 Tonga eruption observed at 106 ocean-bottom pressure sensors in S-net, Japan, were well modeled by the air-sea coupled tsunami simulation with an atmospheric pressure pulse having the half wavelength of 300 km and the peek amplitude of 2hPa.
A one-dimensional air-sea coupled tsunami simulation with a simple bathymetry shows that an input atmospheric pressure pulse with a short half wavelength of 50 km, which is shorter than the length of the slope (200 km), caused an amplitude increase by the Proudman resonance effect near the deep trench. The wavefront distortion due to the separation of air-sea coupled wave (v=312 m/s) and sea wave ( v = √ gd) was also signi cant near the shore. In contrast, when the half wavelength of the input atmospheric pressure pulse was 300 km, which is longer than the length of slops, the wave shape distortion due to those effects became small. It is important to observe the wavelength of an atmospheric pressure pulse due to an eruption to forecast the heights of air sea coupled tsunamis. Figure 1 Location of ocean bottom pressure sensors in S-net (red circle) used in this study. The blue rectangle denotes the air-sea coupled tsunami computation area.

Figure 2
A snapshot of an air-sea coupled computed tsunami at 145 mins after 18:00. Circles represent the locations of ocean bottom pressure sensors used in this study. Red circles represent the sensors where observed and computed waveforms are compared in Figure 3. Comparison of observed and computed waveforms at nine sensors is shown in Figure 2. Black lines represent observed waveforms, and red lines represent computed waveforms. Long period waves in the rst 100 mins in the observed waveforms are an effect of the bandpass lter.