Magnetic Field Signatures of Tropospheric and Thermospheric Lamb Modes Triggered by the 15 January 2022 Tonga Volcanic Eruption

Intense eruptions of the Tonga volcano activated prominent traveling atmospheric disturbances (TADs) at 04:05UT on 15 January 2022. Himawari‐8 satellite images depict that TADs of the tropospheric Lamb wavefront propagate with a speed of 315 m/s and arrive in Taiwan at 11:30UT. Networks of 98 barometers, 28 tide gauges, an ionosonde, and 10 magnetometers are used to study the responses of magnetic fields to TADs in Taiwan. The horizontal components in magnetic field changes of the Taiwan magnetometers all point toward and away from the Tonga volcano at 11:00–12:00UT upon the tropospheric Lamb wavefront arrival and at 22:00–23:00UT when the thermospheric Lamb wavefront with speeds of 487 m/s coming, respectively. Analyses of the raytracing and beamforming techniques on the horizontal components in magnetic field changes of 69 INTERMAGNET magnetometers show that both tropospheric and thermospheric Lamb waves efficiently activate traveling ionospheric disturbances and modify ionospheric currents of the globe.


• Tropospheric and thermospheric
Lamb waves of the Tonga volcanic eruption activate dynamo currents and electric fields • Traveling atmospheric disturbances of the Tonga volcanic eruption significantly uplift the ionosphere • Tropospheric Lamb waves of the Tonga volcanic eruption modulate ground-based air pressures and sea levels Supporting Information: Supporting Information may be found in the online version of this article.
At 04:05UT, intense eruptions of the Tonga volcano generated prominent TADs of atmospheric shocks, pressure disturbances, and tsunamis on 15 January 2022.Himawari-8 satellite images depict prominent TADs of a Lamb wavefront (cf., Liu et al., 1982) propagating worldwide (Figure 1a), which provides a good chance to study tele-volcanic magnetic signatures induced by TADs in the ionospheric E-layer.Networks of 10 three-component magnetometers, 98 barometers, 28 tide gauges, and an ionosonde are employed to examine the atmosphere-ionosphere coupling upon the arrival of TADs/TIDs, especially Lamb waves, over Taiwan.Meanwhile, 69 global magnetometers of INTERMAGNET (https://www.intermagnet.org/index-eng.php)(Kerridge, 2001) are used to study responses of the horizontal component magnetic fields to TIDs on the globe.

Observations and Data Analyses
Himawari-8 is a new generation of Japanese geostationary meteorological satellite, which carries state-of-theart optical sensors with significantly high radiometric, spectral, and spatial resolution (Bessho et al., 2016).The wavelength of 6.2 μm infrared band (#8) with a spatial resolution of 2 km and the time resolution of 10 min clearly observes worldwide TADs of upper-level tropospheric water vapor at 344 hPa (http://cimss.ssec.wisc.edu/goes/OCLOFactSheetPDFs/) at about 8.2 km altitude (https://www.weather.gov/epz/wxcalc_pressurealtitude)(Otsuka, 2022) during the Tonga volcanic eruption.Figure 1a displays TADs of the tropospheric Lamb wavefront in the double difference of Himawari-8 band#8 images, which traveled with an average speed of 315 m/s away from the Tonga volcano and arrived in Taiwan at about 11:30UT, as well as locations of the Taiwan magnetometers, barometers, tide gauges, and an ionosonde.
Figures 1b-1d display ionograms, ground-based atmospheric pressures, and tide-removed sea level fluctuations on 15 January 2022, respectively.When the tropospheric Lamb wavefront in Himawari-8 images arrives in Taiwan at 11:30UT, the pressures start to increase and reach their maximums at about 11:50UT (Figure 1c); the sea levels begin to fluctuate and become prominent after 14:00UT and reach their maximums by 14:30-17:30UT (Figure 1d).The maximums of ground-based pressures and sea level fluctuations lag the tropospheric Lamb wavefront by 20 min and 3-6 hr, respectively.The short lag of 20 min could be due to the ground friction to the tropospheric Lamb wavefront, while the long one of the 3-6 hr may be caused by atmospheric pressure-sea surface interaction and/or tsunami waves.Based on the maximums, the horizontal speed of ground pressures is about 286 m/s (Figure 1c), while due to the maximums being complex, the horizontal speed of sea level fluctuations is difficult to estimate (Figure 1d). Figure 1b shows ionograms on top each hour that the F-layer appears clearly at about 220-300 km virtual height during 00:00-11:00UT, reaching a maximum altitude at about 10:00UT.After the tropospheric Lamb wavefront arrival at 11:30UT, the range-spread-F appears at 280-300 km at 12:00UT, 375-395 km at 13:00UT, 190-220 and 275-300 km at 14:00UT; reaches the highest altitude of about 275-520 km at 15:00-16:00UT; starts descending to 270-330 km at 17:00UT and 220-290 km at 18:00UT; becomes very faint after 19:00UT; finally disappear at 21:00UT; and typical F-layer with non-physical fluctuation traces appears at 250-350 km during 23:00-24:00UT (Figure S1 in Supporting Information S1, Movie S1).
Figure 2a from top to bottom illustrates the condensed rapid-run ionograms with 6 min resolution (Movie S1), magnetic field changes, subtracting the reference from the observation of ΔB x and ΔB y , the azimuth of magnetic horizontal changes (ΔH), the upper/lower envelops of sea level fluctuations, and those envelopes of atmospheric  Let the northward, eastward, southward, and westward be 0, 90, 180, and 270°, respectively.The azimuth θ of magnetic horizontal changes of ΔH = (  Δ 2  + Δ 2  ) 1/2 can be expressed as, Figure 2a displays that ΔB x yields a rapid decrease at Zone A, a maximum at Zone H, a minimum at Zone B, and a maximum at Zone C, while ΔB y depicts a minimum at about 03:00UT, a maximum at Zone H, and a prominent minimum at Zone C. The azimuths of ΔH of the 10 magnetometers lie between 120° and 330° on 15 January 2022.We further compute the median of azimuths of ΔH with 3,600 (=60 × 60) datapoints for each magnetometer every hour on 15 January 2022 (Figure S2 in Supporting Information S1 and Movie S2). Figure 2b shows that the 10 median azimuths pointing of 120.0-130.5°(290.1-307.0°)at Zone H (Zone C), which is about the direction toward (away from) the Tonga volcano at 124.8° (304.8°).
To see whether the toward-pointing signature specifically occurs in Taiwan or not, we select 10 out of 69 magnetometers of INTERMAGNET to examine the horizontal magnetic field changes in the eastern Asia region and globe upon the tropospheric Lamb wavefront arrival.The sample rate of the INTERMAGNET magnetometers is 1 Hz. Figure 3a illustrates the locations of INTERMAGNET and the tropospheric Lamb wavefront at 11:30UT on 15 January 2022, while Figure 3b depicts ΔB x , ΔB y , and azimuth angles of the 10 selected magnetometers, 5 in regional (KAK, KNY, MMB, CYG, and DLT) and 5 in global (GNG, TUC, VIC, HER, and CNB) areas.At Zone A, while Figures 1e and 2a depict that ΔB x in the Taiwan magnetometers suddenly decreases at about 06:30UT, Figure 3b shows similar changes in the 10 selected magnetometers, which confirms that global effects have been detected.Note that the Dst index reaches a local maximum of −43 nT at 06:00UT during the storm period.At Zone H (10:30-12:00UT), while the ΔB x and ΔB y and azimuth angles of the magnetometers in Taiwan respectively reach the maximums and point toward the Tonga volcano (Figure 2a), those in the regional magnetometers at KAK, KNY, MMB, CYG, and DLT also yield the similar maximums and pointing toward the volcano (Figure 3b).For the globally selected magnetometers, at Zone H, despite no extrema in ΔB x or ΔB y , upon the tropospheric Lamb wavefront arrival, the horizontal components at GNG, TUC, and VIC also point toward the Tonga volcano, while those at HER change rapidly.It is interesting to find that the horizontal component at CNB points away from the Tonga volcano, which might result from the site being in the southern hemisphere, where the magnetic vertical component (B z ) is upward.The horizontal components pointing toward and away from the Tonga volcano as well as changing rapidly show that the tropospheric Lamb wavefront plays an important role in the magnetic field perturbations.At Zone B, the ΔB x component of the 10 Taiwan magnetometers, the five regional magnetometers, and one global magnetometer (GNG, around the conjugate point of KNY) yield very similar tendencies, simultaneously reaching significant large reductions at 15:40UT, which suggests that regional and conjugate effects have been observed.It is surprising that at Zone C, the ΔB x and ΔB y of both Taiwan and regional magnetometers reach the maximum and the minimum, respectively, which further results in the azimuth angles suddenly changing and pointing away from the Tonga volcano (Figures 2, 3b, and 3c).
To find responses of the magnetic field to the tropospheric Lamb wavefront of the globe, we examine the azimuth of ΔH within 1.5 hr before and after the wavefront arrival recorded by the INTERMAGNET magnetometers.
When the azimuth points within 15° of the toward or away Tonga volcano direction for more than 15 min, or fast changes more than 90° in 5 min, we then can consider that TADs/TIDs induced by the tropospheric Lamb wavefront have been observed.Upon 1.5 hr before and after the tropospheric Lamb wavefront arrival, ΔH azimuth angles of the 10 Taiwan magnetometers all (100% = 10/10) point toward the Tonga volcano, while those of 25.4% (=16/63), 9.3% (=6/63), and 25.4% (=16/63) of the INTERMAGNET magnetometers yield toward, away, and fast change signatures (Figure 3a; Figures S3 and S4 in Supporting Information S1, Movies S3 and S4).Note We further adopt the ray tracing and the beam forming techniques (Liu et al., 2006(Liu et al., , 2010(Liu et al., , 2019(Liu et al., , 2020b) ) on the INTERMAGNET data associated with Zone H and Zone C signatures (Figures 3a and 3c), and construct two global grid searches to see whether the tropospheric Lamb waves and the 487 m/s TIDs are triggered by the volcanic eruption or not.Figures 4a and 4b illustrate that when the tropospheric Lamb wavefront speed of 315 m/s (the volcanic eruption time of 04:05UT) is given to the ray tracing (beamforming) technique, the location at the minimum standard deviation in the travel time of ±34 min with the average eruption time of 03:53UT (the minimum standard deviation of ±27 m/s with the average travel speed of 329 m/s) appears near the Tonga volcano, which confirms the tropospheric Lamb wavefront triggered by the Tonga volcanic eruption can prominently change the horizontal magnetic field in the globe.Similarly, Figures 4c and 4d depict that when the speed of 487 m/s and volcanic eruption time of 04:05UT are set, locations of the minimum standard deviation in the travel time of ±37 min with the average eruption time of 04:15UT and that in the travel speed of ±22 m/s with the average travel speed of 482 m/s are near the Tonga volcano, which again confirms that the Tonga volcanic eruption can trigger the 487 m/s TIDs and prominently disturb the horizontal magnetic field on the globe.

Discussion and Conclusion
Scientists find that the atmospheric response to excitations at tropospheric heights, such as by volcanic eruptions, is dominated by Lamb waves because their wave energy is mainly distributed at lower heights of the atmosphere  (Francis, 1973;Jones, 1970;Lin et al., 2021;Lindzen & Blake, 1972).These modes can propagate a long distance with a horizontal speed slightly above 300 m/s and little attenuation.Figure 1a shows that the tropospheric Lamb wavefront activated by the Tonga volcanic eruption at 04:05UT travels 8,500 km with a horizontal speed of 315 m/s and arrives in Taiwan by 11:30UT, which agrees with the characteristics of Lamb waves induced by volcanic eruptions (Kubota et al., 2022;Liu et al., 1982;Zhang et al., 2022).Figures 1c and 1d show that upon the tropospheric Lamb wavefront arriving in Taiwan at 11:30UT, the ground-based pressures and sea levels start to increase and fluctuate.The pressures reach their maximum at about 11:50UT.The 20-min lag of the pressures suggests that the tropospheric Lamb waves mainly travel in the upper-level troposphere.In contrast, when the Taiwan and regional magnetometers register the passages of 487 m/s TADs/TIDs at 08:50UT and Zone C, no fluctuations can be detected by the barometers and tide gauges (Figure 1), which suggests the 487 m/s TADs/ TIDs traveling in a higher atmosphere at about 150 km altitude and being related to thermospheric Lamb waves (Forbes et al., 1999;Meyer & Forbes, 1997).
The median azimuths of the 10 Taiwan magnetometers, each obtained with 3,600 datapoints, of 120.0-130.5°together with that of the five regional magnetometers almost exactly point toward the Tonga volcano (124.8°,azimuth in Taiwan), which strongly suggests that intense dynamo ionospheric currents in southwestward during the of the tropospheric Lamb wavefront arrival at 10:30-12:00UT (Zone H).The beginning of the eastward electric field at 11:30UT lags that of the dynamo current at 10:30UT by about 1 hr.Based on Kelley (2009), the most usual form of the current equation can be expressed as where σ, E, U, and B E are the conductivity, electric field, neutral wind, and Earth's magnetic field in the Earth-fixed coordinates, respectively.B E consists of horizontal (B H ) and vertical (B z ) components.Here, σ is a 3 × 3 tenser and functions of electron/ion density, gyro frequency, mass, and collision frequency.Around the Lamb wavefront arrival, the current can be expressed as When the conductivity is very high, the dynamo current, J d = σ U d × B E , will be quickly canceled by the motor current of the dynamo electric field, σE d .However, if an impact very suddenly occurs, for example, a Lamb wavefront, the dynamo current could lead the dynamo electric field by minutes to hours.The median azimuths of the 10 Taiwan magnetometers and the five regional magnetometers pointing toward the Tonga volcano indicate that the intense J d in southwestward occurs around the tropospheric Lamb wavefront arrival in Taiwan and the regional area at 10:30-12:00UT (Zone H in Figures 2a and 3b).The intense J d in the southwestward results in the dynamo electric field, E d , in the northeastward.It is the E × B upward drift owing to the eastward component of E d and the Earth's magnetic field, B E , causing the prominent ionosphere ascendence during 11:30-15:30UT (Figures 1b and 2a).These indicate that the dynamo current leads the dynamo electric field by about 1-2 hr in Taiwan and Japan after the tropospheric Lamb wave arrival.Figure 5 sketches that due to the cross product of the neutral wind velocity activated by the tropospheric Lamb wavefront and the Earth's magnetic field, the dynamo currents result in the azimuth angle pointing toward and away from the Tonga volcano in the northern and southern hemisphere (e.g., CNB), respectively.Moreover, owing to the competition and time delay between dynamo currents (J d ) and motor currents of the dynamo electric field (σE d ), the azimuth angle could point toward/away from the Tonga volcano or abruptly fluctuate.In total, 100% of Taiwan and 60% of INTERMAGNET magnetometers experience the tropospheric Lamb wavefront disturbing the magnetic field in the ionosphere (Figure 3a, Figures S3 and S4 in Supporting Information S1).
Each INTERMAGNET magnetometer could experience one tropospheric and two thermospheric front passages on 15 January 2022.In total, the magnetometers experience 63 tropospheric and 113 thermospheric front passages (Figures S3b and S4-S6, Table S1 in Supporting Information S1).About 60% and 58% of front passages register the tropospheric and thermospheric Lamb mode signatures, respectively.Approximately, 65% and 58% (55% and 60%) of the front passages register the tropospheric (thermospheric) Lamb mode signatures in daytime and nighttime, respectively.Meanwhile, about 35% of the first pass and 86% of the second pass register the thermospheric Lamb mode signatures.In nighttime, more than 96% of the second pass registers the thermospheric Lamb mode signatures.In short, regardless of daytime/nighttime; the first/second pass, more than 55% of front passages register the tropospheric and thermospheric Lamb mode signatures.Almost all the second passages in nighttime register the thermospheric Lamb mode signatures.
The nighttime conductivity at midlatitudes is generally low, and however, the Es layer with foEs of 2.0-5.0MHz at 120-150 km altitude (Movie S1) shows that the conductivity could be much greater than its typical value during 14:30-16:30UT (=22:30-00:30LT-8 hours).Figures 1b and 2a reveal that the ionosphere monotonically descends during 14:30-18:00UT.This indicates that the ionosphere experiences prominent westward electric fields which further activate westward motor currents, and cause significant decreases in the northward magnetic field of B x in the Taiwan, regional, and conjugate areas during 14:30-16:30UT (Zone B in Figures 1e, 2a, and 3b).Figures 2a and 3b depict that at Zone C, the azimuth angles point away from the Tonga volcano, which suggests that northeastward dynamo currents and southwestward dynamo electric fields have been induced by the thermospheric Lamb waves toward the Tonga volcano (i.e., away from the antipode).The Es-layer descends to the lowest altitude of about 90 km around 22:20-22:30UT, confirming the westward component of the southwestward dynamo electric field.We further examine the azimuth angles of the INTERMAGNET magnetometers and find that in total, 86% (=43/50) of the magnetometers register the thermospheric Lamb front signatures of the magnetic field and currents in the ionosphere.The source origins derived by the ray tracing and beamforming techniques are near the Tonga volcano, which confirms that the eruptions trigger both tropospheric and thermospheric Lamb waves traveling worldwide.It is interesting to find that the thermospheric Lamb waves propagate almost 1.5 times faster than the tropospheric Lamb waves do.In conclusion, TADs of the tropospheric Lamb wavefront result in the ground-based atmospheric pressure peak and cause sea level prominent fluctuations.The signatures of pointing toward, away, or fast changes indicate that the TIDs triggered by the tropospheric and thermospheric Lamb waves can further induce dynamo currents and the associated dynamo electric fields on the globe.

Figure 1 .
Figure 1.(a) Locations of Overhauser magnetometers (red triangles), tide gauges (dark blue asterisks), barometers (blue diamonds), and an ionosonde (magenta square, 121.0°E, 25.0°N) as well the Himawari-8 satellite image at 11:30UT on 15 January 2022.The magenta star presents the Tonga volcano and red arrows denote the variations of the horizontal component of the Earth's magnetic fields during the 14:00-15:00UT on 15 January 2022.The (b) ionogram, (c) differential pressure disturbances recorded by 98 barometers, and (d) sea surface heights recorded by the 28 tide gauges and those fluctuations after the tidal removal have been displayed.The time sample rates of the ionograms, atmospheric pressures, and sea levels are 6, 1, and 1 min (6-min interpolation), respectively.The red vertical line denotes the tropospheric Lamb wavefront arrival time in Taiwan at 11:30UT.Note that the trace around 480 km altitude is the "double hop" of the trace at about 220 km altitude at 11:00UT in the ionogram.(e-f) Variations of the magnetic northward (B x ), eastward (B y ), and downward (B z ) components on 15 January (red curves) as well as on the reference days of 16-18 January (thin gray curves) 2022 and their associated median (dashed curves).The sampling rate is 1 Hz.The red vertical lines denote the arrival time of the tropospheric Lamb wavefront arrival in Taiwan at 11:30UT on 15 January 2022.The black, magenta, black, and blue dotted squares denote the time zone of Zone A, H, B, and C, respectively.

Figure 2 .
Figure 2. (a) From top to bottom show that the virtual height of the E-, F-, and sporadic Es-layers, deviations of the magnetic northward (ΔB x ) and eastward (ΔB y ) component, and the azimuth of the deviated magnetic horizontal component (ΔH) of arctan(ΔB y /ΔB x ) of each magnetometer, the sea level and pressure with detrended data as well as their upper/lower boundary.ΔB x , ΔB y , and the azimuth angle are denoted by blue, green, and red curves, respectively.Sea level and pressure fluctuations with the detrended data, upper and lower boundary, and the envelope between upper and lower boundary are indicated by gray curves, red curves, magenta curves, and black curves, respectively.(b) The azimuth angles at 11:00-12:00UT (Zone H) and 22:00-23:00UT (Zone C) on 15 January 2022 are represented in red and blue arrows, respectively.The black dashed arrows indicate the toward/away directly to the Tonga volcano.

Figure 3 .
Figure 3. (a) The map of 10 Taiwan magnetometers (combine into one) and 69 global magnetometers with red, blue, green, and black squares denote the toward, away, fast changes, and none signatures on each station, respectively.Tonga volcano is pointed out with magenta stars, and the red curve indicates the tropospheric Lamb wavefront at 11:30UT.The 10 selected global magnetometers are specified with cyan circles.(b)The ΔB x , ΔB y , and azimuth angles are denoted by blue, green, and red lines, respectively.The vertical red lines indicate the arrival of the tropospheric Lamb wavefront on each magnetometer, and the precise location of each magnetometer is labeled vertically in the form of (Latitude (°N), Longitude (°E)) on the left, with the distances (km) to Tonga notes on the right-top.The right-hand-side table denotes whether the critical variation can be observed in the corresponding time zone, symbol "○" and "×" represent "Yes" and "No," respectively.At Zone H, the different time zones depend on the distance between the Tonga volcano and the magnetometers.The notations of "T," "A," and "F" indicate the toward, away, and fast changes signatures.(c) The map with the same illustration as (a), but at 22:00UT.The blue curve denotes the thermospheric Lamb wavefront.

Figure 4 .
Figure 4.The ray tracing (a and c) and beamforming (b and d) techniques apply to Zone H and Zone C. The magenta solid star, halo star, and white cross indicate the location of Tonga volcano, the antipode of Tonga volcano, and the location of minimum standard deviation.The minimum standard deviation, associated mean, and distance from the minimum to Tonga are listed on top of each panel.

𝐉𝐉
=   +   =   +  ( +   × ) =   +   +   (3) which consists of the ambient J 0 and the triggered J t currents.U d , E d , and J d are the neutral wind disturbed by the Lamb wavefront, dynamo electric field, and dynamo current, respectively.U = U 0 + U d , where U 0 denotes the background neutral wind velocity.The dynamo current and the dynamo electric field are in opposite directions.

Figure 5 .
Figure 5.A sketch of neutral winds (U d ) activated by the tropospheric Lamb wavefront, dynamo-generated electric fields (E d ), dynamo current (J d ), and the induced magnetic fields (ΔH, red bold arrows) in the lower ionosphere.Magenta arrows denote the Earth's magnetic field (B E ).