Numerical Simulation of Atmospheric Lamb Waves Generated by the 2022 Hunga-Tonga Volcanic Eruption

manuscript submitted to Geophysical Research Letters Numerical simulation of atmospheric Lamb waves1 generated by the 2022 Hunga-Tonga volcanic eruption2 Angel Amores1, Sebastian Monserrat2, Marta Marcos1,2, Daniel Arg¨ueso2,3 Joan Villalonga3, Gabriel Jord`a3and Dami`a Gomis1,2.4 1Instituto Mediterr´aneo de Estudios Avanzados (UIB-CSIC), Esporles, Spain.5 2Departament de F´ısica (UIB), Palma, Spain.6 3Centre Oceanogr`afic de Balears, Instituto Espa˜nol de Oceanograf´ıa (IEO-CSIC), Palma, Spain7 Key Points:8 •The underwater Hunga-Tonga volcano exploded generating Lamb waves that trav-9 eled around the Earth several times.10 •We simulate these waves using a hydrostatic shallow water equation oceanic model.11 •The results closely follow the observations of atmospheric pressure perturbations.12 Corresponding author: Angel Amores, [email protected] –1– Accepted Article This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1029/2022GL098240. This article is protected by copyright. All rights reserved. Accepted Article This article is protected by copyright. All rights reserved. manuscript submitted to Geophysical Research Letters Abstract13 On January 15th, 2022, around 4:30 UTC the eruption of the Hunga-Tonga volcano, in14 the South Pacific Ocean, generated a violent underwater explosion. In addition to tsunami15 waves that affected the Pacific coasts, the eruption created atmospheric pressure distur-16 bances that spread out in the form of Lamb waves. The associated atmospheric pressure17 oscillations were detected in high-frequency in-situ observations all over the globe. Here18 we take advantage of the similarities in the propagation and characteristics between at-19 mospheric Lamb waves and long ocean waves and we use a 2DH ocean numerical model20 to simulate the phenomenon. We compare the outputs of the numerical simulation with21 in-situ atmospheric pressure records and with remote satellite observations. The signal22 in the model matches the observed atmospheric pressure perturbations and reveals an23 excellent agreement in the wave arrival time between model and observations at hun-24 dreds of locations at different distances from the origin.25 Plain Language Summary26 The underwater explosion of the Hunga-Tonga volcano in the South Pacific Ocean27 generated atmospheric pressure disturbances, known as Lamb waves, that propagated28 and surrounded the globe several times. In this study, we exploit the similarities between29 atmospheric Lamb waves and long waves in the ocean (e.g., tsunamis) to simulate their30 propagation using an ocean numerical model. The comparison of our results with remote31 satellite data and in-situ atmospheric pressure records reveals that our model correctly32 reproduces the propagation of the atmospheric disturbances generated by the volcano33 explosion.34 1 Introduction35 On January 14th, 2022 the underwater Hunga-Tonga volcano, located in the South36 Pacific Ocean, erupted in a one-in-a-thousand year event (Klein, 2022). The volcano, lo-37 cated between the uninhabited islands of Hunga Tonga and Hunga Ha‘apai of the King-38 dom of Tonga, is part of the Tonga–Kermadec Islands volcanic arc and has been active39 since its first historical eruption in 1912 (Global Volcanism Program, 2022). The volcano40 had emerged after an eruption that started in December 2014. This recent eruption re-41 sulted in material being deposited and merged with the Hunga Ha’pai island, creating42 an area of around 2 km of diameter and maximum height of 120 m above sea level (Cronin43 et al., 2017). According to the Global Volcanism Program (2022), the strongest erup-44 tion began on January 15th around 17:30 local time (4:30 UTC) with a plume reaching45 30 km in the atmosphere and 600 km in diameter, making it visible by multiple satel-46 lite observations. Observations of Sentinel-2 satellites revealed massive changes in the47 surface area and the disappearance of the formerly deposited volcanic material. The ex-48 plosive eruption, whose power has been estimated to be equivalent to somewhere between49 4 to 18 megatons of TNT (https://earthobservatory.nasa.gov/images/149367/dramatic50 -changes-at-hunga-tonga-hunga-haapai), generated tsunami waves (warnings were51 issued across several countries in the Pacific coasts) and also atmospheric shock waves52 that propagated across the globe and were detected by the NASA Aqua satellite as con-53 centric wave patterns (Adam, 2022).54 Such amount of energy liberated into the atmosphere by the violent eruption is ex-55 pected to generate various types of atmospheric waves with different spectral energy con-56 tent, including inertia gravity waves, infrasound waves and Rossby waves, making the57 atmospheric wave pattern close to the source very intricate. Among these atmospheric58 perturbations, the type of wave which is expected to optimally transfer energy over long59 distances, and therefore the one expected to dominate far away from the source, is the60 Lamb wave mode, which was first introduced by Horace Lamb (Lamb, 1881). This has61 been observed in earlier similar events, as for example the well-known Krakatoa volcanic62 –2– Accepted Article This article is protected by copyright. All rights reserved. manuscript submitted to Geophysical Research Letters eruption in 1883 (Symons, G. J. (ed.), 1888; Press & Harkrider, 1966). The explosion-63 induced atmospheric waves after Krakatoa eruption circled the Earth three times (Murty,64 1977) and generated tsunami waves which, at many locations, were coupled with the tsunami65 generated by the ocean surface perturbation provoked after the eruption (see Monserrat66 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 rotation72 and travel at the speed of sound in the media (Gossard & Hooke, 1975). Assuming an73 isothermal troposphere, the phase velocity of the Lamb waves, CT, is only affected by74 the air temperature and is defined as:75 CT=rγ·R·T M,(1) where γ= 1.4 is the ratio of specific heat of air corresponding to the range of atmo-76 spheric temperatures, R= 8314.36 J·kmol−1·K−1is the universal gas constant, M=77 28.966 kg·kmol−1is the molecular mass for dry air and Tis the absolute temperature.78 Due to their particular characteristics, the propagation of Lamb waves through the79 atmosphere with spatially varying temperature is analog to the behavior of oceanic long80 waves propagating over an ocean with variable depth. Long waves in the ocean are also81 non-dispersive barotropic waves traveling with a phase velocity, CH, given by82 CH=pg·H , (2) where g= 9.81 m·s−2is the gravity acceleration and His the ocean depth.83 Long waves in the ocean have been successfully simulated using 2DH shallow wa-84 ter equation models, as for example, the propagation of tsunami waves and their arrival85 times at remote coastal locations (e.g. Titov et al. (2005)).86 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-88 Tonga volcano explosion using a vertically-integrated hydrodynamic ocean model. To89 do so, a simple relationship between the vertically integrated atmospheric temperature90 and the equivalent ocean depth is obtained from eq. (1) and (2)91 H=γ·R·T M·g,(3) This study is organized as follows: in Section 2 the data and the model used for92 the simulations as well as the way it was initialized are described. Results of the sim-93 ulations are compared with remote and in-situ observations in Section 3 and a summary94 and conclusions are presented in Section 4.95 2 Data and Methods96 The numerical ocean hydrodynamic model SCHISM (Semi-implicit Cross-scale Hy-97 droscience Integrated System Model, V5.9.0; Y. J. Zhang et al. (2016)) was used to sim-98 ulate the atmospheric Lamb waves generated by the volcano explosion. We have used99 its dynamic core, which is a derivative product built from the original SELFE (v3.1dc;100 Y. Zhang and Baptista (2008)), in 2DH barotropic mode. It solves the vertically-integrated101 hydrostatic Navier-Stokes equations with shallow water approximation. The model do-102 main covers the entire globe with an unstructured triangular computational grid of 0.25◦ 103 –3– Accepted Article This article is protected by copyright. All rights reserved. manuscript submitted to Geophysical Research Letters resolution with 1036800 nodes and 2070720 elements. The simulation starts on January104 15th 2022 at 04:30 UTC coinciding with the volcano explosion and has a duration of 5105 days. The computational time step was set to 1 min and the variables were saved ev-106 ery 5 min at each computational grid point. We decided to use an oceanic model because107 the atmospheric models suited for this kind of simulations include filters that remove fast108 waves, such as sound waves, to avoid numerical instabilities and to allow larger time-steps.109 It would be necessarily to adapt an atmospheric model by modifying its dynamical core110 to represent Lamb waves. On the other hand, the numerical model we are using here is111 specifically designed to resolve high-speed long waves, such as tsunami waves. Because112 Lamb waves and tsunami waves behave similarly in many aspects, it was immediate to113 adapt the model configuration to solve Lamb waves generated by the volcano explosion.114 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.116 To define the equivalent water depth in the model (see equation 3), we used the117 atmospheric temperature fields obtained from ERA5 reanalysis . ERA5 is a comprehen-118 sive reanalysis that spans from 1979 to near-real time and integrates historical observa-119 tions into global estimates using advanced modeling and data assimilation systems. ERA5120 data is provided at 1-hour temporal resolution and 0.25◦spatial resolution. A time-varying121 temperature field over the domain was defined to represent the vertically-averaged at-122 mospheric temperature. For the results shown, the simplest approach was taken. The123 temperature field has been computed as the average between the temperature at 2 m (ob-124 tained from ERA5 data on single levels; Hersbach et al. (2018b)) and the temperature125 at the top of the troposphere. Assuming an almost constant temperature in the strato-126 sphere, a fixed altitude, high enough to be above the tropopause in the whole globe, has127 been taken. This level has been choosen at 100 hPa, obtained from ERA5 data on pres-128 sure levels; Hersbach et al. (2018a)). The results do not vary significantly when more com-129 plex algorithm is used to define the temperature field. Tropospheric temperatures were130 translated into equivalent depth fields using eq. (3), which in turn were incorporated into131 the model through the bathymetry. As such, the bathymetry field was updated every132 hour to take into account air temperature variations estimated from ERA5 hourly data.133 The initial perturbation created by the volcano eruption was simulated using an134 equivalent atmospheric pressure perturbation of 50 hPa. In the model, this was intro-135 duced as an instantaneous sea level perturbation at the start of the simulation, which136 had a cylinder-like shape of 60 km radius and 50 cm height. The intensity and the ex-137 tend of the initial perturbation were chosen to match the amplitude and frequency of138 the available atmospheric pressure records from Fig. 2. Other shapes such as a Gaus-139 sian and semi-spherical perturbations were also tested for the initial forcing with sim-140 ilar results.141 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 an143 atmospheric pressure signal. This approach corresponds to a decrease of 1 hPa for ev-144 ery cm of water elevation, and vice versa. The simulation took a total of 6 h to complete145 with 23 CPU.146 The simulation was validated against in-situ surface atmospheric pressure records147 obtained from different sources (see the map in Fig. 2 to see the spatial distribution of148 the stations). A total of 889 station were retrieved from NOAA Automated Surface/Weather149 Observing Systems (ASOS/AWOS) spread across all United States, including Hawaii,150 Alaska and Puerto Rico. A time series of atmospheric pressure from Ciutadella (Balearic151 Islands, Spain) with a temporal resolution of 30 seconds was obtained from the Balearic152 Islands Coastal Observing and Forecasting System (SOCIB). Another time series from153 Kadhdhoo, in the Maldives, with a 10 minutes temporal resolution was also used to com-154 pare with the model outputs. Atmospheric pressure records where also obtained from155 the Australian Bureau of Meteorology at three locations (Sydney Observatory Hill, Perth156 –4– Accepted Article This article is protected by copyright. All rights reserved. manuscript submitted to Geophysical Research Letters Airport and Darwin Airport) with 1 minute temporal resolution. Among all the atmo-157 spheric pressure records, only those with less than 10% of missing values were retained,158 which left a total of 719 stations (20% of them were removed). Since the period of the159 generated Lamb wave was around 40 minutes, the atmospheric pressure records were band-160 pass filtered with cut-off periods between 2 hours and 15 minutes. In each record, the161 first pass of the atmospheric perturbation was identified as the first maximum of the time162 series after the explosion (this peak was required to exceed 3 times the standard devi-163 ation of the filtered time series). In 42 of these time series no peak was larger than the164 threshold imposed and were consequently discarded. Additional 56 time series were also165 discarded because the detected peak clearly corresponded to a different atmospheric pro-166 cess. The total number of stations used was 621.167 The simulation was also qualitatively compared to satellite observations to further168 assess the realism of the wave propagation. Infrared data from the Geostationary Op-169 erational Environmental Satellite (GOES-R) program and the European Organisation170 for Exploitation of Meteorological Satellites (EUMETSAT) were used at 15-min tem-171 poral resolution for the first 24 hours since the eruption. The Pacific region was repre-172 sented by the GOES-17 satellite with imagery from the IR10.3 channel with a spatial173 resolution of 5424×5424 pixels. The 0-degree region was observed by the Meteosat-11174 satellite (High Rate SEVIRI Level 1.5 Image Data) with data from the IR10.8 channel175 with a spatial resolution of 3712×3712 pixels. For the sake of visualization of the at-176 mospheric pressure wave footprint in the satellite IR observations we used, at each time177 step, their second time-derivative. These fields were subsequently spatially filtered with178 a 50 (100) pixel window for GOES-17 (Meteosat-11) satellite observations with the fil-179 ter described in Amores et al. (2018).180 3 Results181 A qualitative comparison of the model results with satellite observations during the182 first travel of the Lamb waves (from the origin to the antipodes in Northern Africa) re-183 veals that the simulation closely follows the spatial pattern of the satellite measurements184 (Fig. 1). Note that we are comparing the observed and modeled spatial footprints of the185 waves, but using different variables. The relevant parameter here is thus the location of186 the wave rather than its amplitude. Panels a-fshow the propagation of the Lamb wave187 over the Pacific captured by GOES-17 satellite from 15 minutes after the explosion un-188 til January 15th 10:30 UTC. The wave is clearly observed in satellite images that also189 display a close agreement with the observations. Panels g-jshow the travel of the wave190 captured by Meteosat-11 satellite from 17:30 to 20:30 UTC. In this case, although still191 identified, the wave signal is surrounded by noisier data probably due to a larger cloud192 coverage and/or lower spatial resolution offered by this satellite in comparison with GOES-193 17. The wave is observed at 17:30 and 18:30 and it is still visible at 19:30 and 20:30, co-194 inciding again with the pattern of the simulation.195 Fig. 2 shows the comparison of 10 high-frequency atmospheric pressure records (col-196 ors help matching dots in the map and time series in the lower panel) at different dis-197 tances from the volcano (indicated with a red star in the map) between January 15th 198 04:30 UTC until January 18th 02:40 UTC. In addition, the temporal evolution of the sim-199 ulation is available in Movie S1 in the Supplementary Material. The modeled time se-200 ries (in grey) were extracted from the closer grid point to each station. At all locations201 the numerical simulation matches very well the time of arrival of the Lamb wave. At each202 site, 4 different passes are observed, except in the Ciutadella station (dark red), the clos-203 est to the volcano’s antipodes in our database. In this station only two passes occur be-204 cause of the overlapping of the northern and southern waves (see Movie S1 for a better205 visualization). The model better captures the first wave pass, as shown by both the ar-206 rival time and the wave amplitude. Once the Lamb wave has traveled farther distances207 –5– 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.209 Using all available atmospheric pressure records, we have quantified the performance210 of the approach by comparing the time of arrival of the first Lamb wave. To do so, we211 have determined the time when the first atmospheric pressure maximum is found at in-212 situ pressure records and in the model simulation. Fig. 3 represents the scatter plot of213 modeled vs. observed arrival times of the first wave. There is an excellent agreement be-214 tween model and observations at all sites, with a R2larger than 0.98 and a root mean215 square difference (RMSD) of 10 minutes (we remark here that the temporal resolution216 of the simulation is 5 minutes).217 4 Summary and Conclusions218 After Hunga-Tonga volcano explosion on January 15th, 2022, atmospheric pressure219 records around the world measured high-frequency perturbations that traveled around220 the globe several times and that were consistent with the presence of atmospheric Lamb221 waves. We have numerically simulated the atmospheric Lamb waves generated by the222 volcanic eruption taking advantage of their similarities to ocean long waves. Namely, both223 types of waves propagate through the fluid as vertically integrated waves, with 2D hor-224 izontal motion and share the same dispersion relation. The analogy consists of defining225 an equivalent bathymetry in the ocean shallow water model that corresponds to the ver-226 tically averaged air temperature, which has furthermore temporal variability.227 The results of the simulation mimic satellite and in-situ observations. In partic-228 ular, when the outputs of the model are compared to atmospheric pressure records at229 different distances from the source, they display excellent matching in the arrival times230 of the perturbation. Therefore, the results confirm that the observed high-frequency sur-231 face pressure oscillations are the footprint of non-dispersive atmospheric Lamb waves orig-232 inated by the eruption of the Hunga-Tonga volcano.233 Despite being an idealized simulation, which neglects various factors that may af-234 fect different characteristics of the wave, the close agreement between the observation235 and the model suggests that the main physical mechanisms are well represented in our236 experiment. For example, our model does not consider the effect of orography. High moun-237 tain systems such as the Andes or Himalayas may cause reflections of the Lamb waves238 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. For240 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 to242 estimate the equivalent depth. We also assumed the air to be dry and thus, we consid-243 ered that water vapor and humidity changes have only a minor effect on the propaga-244 tion of the wave. In summary, we have shown how a vertically integrated hydrodynamic245 ocean model can be used to investigate and anticipate the propagation of atmospheric246 Lamb waves across an isotherm troposphere.247 Conflict of Interest248 The authors declare no conflicts of interest relevant to this study.249 Open Research250 Data Availability Statement:251 •ERA5 dataset can be downloaded from https://cds.climate.copernicus.eu/.252 –6– Accepted Article This article is protected by copyright. All rights reserved. manuscript submitted to Geophysical Research Letters •NOAA atmospheric pressure time series were downloaded from https://mesonet253 .agron.iastate.edu/request/asos/1min.phtml#).254 •SOCIB data is available in https://www.socib.es/?seccion=observingFacilities&facility=255 mooring.256 •Information regarding the Maldivian atmospheric pressure record can be found257 in https://mv.geoview.info/kadhdhoo,7909905.258 •The GOES satellite data can be downloaded from https://www.ncdc.noaa.gov/259 airs-web/search.260 •The Meteosat-11 data was obtained from https://navigator.eumetsat.int/261 product/EO:EUM:DAT:MSG:HRSEVIRI.262 The numerical simulation can be downloaded from: https://doi.org/10.5281/zenodo.5948860263 Acknowledgments264 This study was supported by the MOCCA project RTI2018-093941-B-C31 funded by MCIN/AEI265 /10.13039/501100011033/ and by FEDER Una manera de hacer Europa. It was also sup-266 ported by grants PGC2018-099285-B-C21 and PGC2018-099285-B-C22 funded by MCIN/AEI/267 10.13039/501100011033 and by “ERDF A way of making Europe” NextGenerationEU/PRTR.268 Angel Amores was funded by the Conselleria d’Educaci´o, Universitat i Recerca del Gov-269 ern Balear through the Direcci´o General de Pol´ıtica Universit`aria i Recerca and by the270 Fondo Social Europeo for the period 2014–2020 (grant no. PD/011/2019). Daniel Arg¨ueso271 was funded by Spanish Ministry of Science and Innovation through the EPICC Project272 (PID2019-105253RJ-I00) and the Beatriz Galindo Programme (BG20/00078). The au-273 thors are grateful to NOAA, EUMETSAT, the Australian Bureau of Meteorology and274 SOCIB to make their data freely available. Finally, we also thank to Dr. Ali Shareef for275 providing the atmospheric pressure data from the Maldives.276 References277 Adam, D. (2022). Tonga volcano eruption created puzzling ripples in Earth’s atmo-278 sphere. 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Panels ato fcorrespond to observations from GOES-17 satellite while panels gto jcorrespond to observations from Meteosat-11 (see in the Data and Methods sections the details of the postprocessing performed). The colorscales are different for each satellite and numerical simulation and are fixed to provide a correct visualization. –9–