Numerical simulation of atmospheric Lamb waves generated by the 2022 Hunga‐Tonga volcanic eruption

13 On January 15, 2022, around 4:30 UTC the eruption of the Hunga-Tonga volcano, in 14 the South Pacific Ocean, generated a violent underwater explosion. In addition to tsunami 15 waves that affected the Pacific coasts, the eruption created atmospheric pressure distur16 bances that spread out in the form of Lamb waves. The associated atmospheric pressure 17 oscillations were detected in high-frequency in-situ observations all over the globe. Here 18 we take advantage of the similarities in the propagation and characteristics between at19 mospheric Lamb waves and long ocean waves and we use a 2DH ocean numerical model 20 to simulate the phenomenon. We compare the outputs of the numerical simulation with 21 in-situ atmospheric pressure records and with remote satellite observations. The signal 22 in the model matches the observed atmospheric pressure perturbations and reveals an 23 excellent agreement in the wave arrival time between model and observations at hun24 dreds of locations at different distances from the origin. 25 Plain Language Summary 26 The underwater explosion of the Hunga-Tonga volcano in the South Pacific Ocean 27 generated atmospheric pressure disturbances, known as Lamb waves, that propagated 28 and surrounded the globe several times. In this study, we exploit the similarities between 29 atmospheric Lamb waves and long waves in the ocean (e.g., tsunamis) to simulate their 30 propagation using an ocean numerical model. The comparison of our results with remote 31 satellite data and in-situ atmospheric pressure records reveals that our model correctly 32 reproduces the propagation of the atmospheric disturbances generated by the volcano 33 explosion. 34

generated by the ocean surface perturbation provoked after the eruption (see Monserrat 66 et al. (2006) and other references mentioned there). 67 Lamb waves are non-dispersive atmospheric waves, whose energy is optimally trans-68 mitted far away from the source with minor losses. They arise as solutions of the mo-69 mentum equations with zero vertical velocity, meaning that Lamb waves have purely hor-70 izontal motion, occupying the full depth of the troposphere and with a maximum pres-71 sure signal at the surface. These waves are only slightly affected by the Earth's rotation 72 and travel at the speed of sound in the media (Gossard & Hooke, 1975). Assuming an 73 isothermal troposphere, the phase velocity of the Lamb waves, C T , is only affected by 74 the air temperature and is defined as: where γ = 1.4 is the ratio of specific heat of air corresponding to the range of atmo- where g = 9.81 m · s −2 is the gravity acceleration and H is the ocean depth.

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Long waves in the ocean have been successfully simulated using 2DH shallow wa-

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Given these similarities between atmospheric Lamb waves and oceanic shallow wa-87 ter waves, we propose to simulate the atmospheric Lamb wave generated after the Hunga-

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Tonga volcano explosion using a vertically-integrated hydrodynamic ocean model. To 89 do so, a simple relationship between the vertically integrated atmospheric temperature 90 and the equivalent ocean depth is obtained from eq. (1) and (2) This study is organized as follows: in Section 2 the data and the model used for 92 the simulations as well as the way it was initialized are described.

Accepted Article
This article is protected by copyright. All rights reserved. Lamb waves and tsunami waves behave similarly in many aspects, it was immediate to 113 adapt the model configuration to solve Lamb waves generated by the volcano explosion.

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Moreover, the numerical model used here is vertically integrated, which makes it com-115 putationally less demanding than using a full 3-D atmospheric global model. The outputs of the hydrodynamic model are provided as sea surface displacements. 142 We apply the inverted barometer equivalence to convert the sea level response into an

Accepted Article
This article is protected by copyright. All rights reserved. manuscript submitted to Geophysical Research Letters and has interfered with its own and the environment, the patterns become more com-208 plex. However, the model is still able to correctly capture the arrival time in most cases.

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Using all available atmospheric pressure records, we have quantified the performance tically averaged air temperature, which has furthermore temporal variability.

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The results of the simulation mimic satellite and in-situ observations. In partic- that are not represented in our simulation. We also made some assumptions in our ap-239 proach, but they do not prevent us from correctly simulating the wave propagation. For 240 example, we assumed the temperature to be constant in the vertical through the tropo-241 sphere, but we found that using the average temperature was a good approximation to 242 estimate the equivalent depth. We also assumed the air to be dry and thus, we consid-