The Tonga eruption provided an equivalent point source for observed atmospheric disturbances. We evaluated these disturbances based on the great-circle distance from the epicenter location (−20.5°N, −175.4°E) as identified by the US Geological Survey for the eruption induced magnitude M 5.8 earthquake origin (USGS, 2022). Figure 1 provides relevant geometry information and great-circle distance contours from the eruption location, as well as a great circle oriented at 26 and 206° azimuth from the epicenter. Superimposed is a background global map of GNSS TEC measurements at three post-eruption instances. Great circles assume 300 km height, characteristic of approximate ionospheric F region altitudes near the peak of the plasma population. The maximum great-circle distance is 21,000 km away from Tonga, located at (4.6°E, 20.4°N) near Sahara in North Africa. New Zealand was 2–4,000 km away, central US 12,000 km, South Africa 14,000 km, and Europe 18,000 km. Upper atmospheric perturbations beyond 10,000 km have never been able to be examined before this eruption.

Both northern (|Azimuth| < 90°) and southern (|Azimuth| > 90°) great circles pass high latitudes. The great circle is presumed to be the shortest path along which disturbance energy and momentum in the neutral gas will flow radially from the epicenter. We note that, although global TEC is not evenly sampled by ground receivers with large gaps over the oceans, each observation is useful in distance-time analysis. Thus, in contrast to typical TEC studies, the distribution of disturbance propagation observations do not suffer severe gaps as demonstrated in the following distance-time figures. Themens et al. (2022) also presented these type of distance-time figures, and our analysis is similar except that we provide propagation estimates also based on azimuth bearing of great circles. The approach allows us to precisely locate propagation signatures and clearly identify inbound waves.

The distance-time variation of dTEC illustrated in Figure 2 indicate dramatic development of disturbance global propagation over a prolonged period. The southward propagation from Tonga to Africa sectors via the southern high-latitude region shows a defined envelope, as marked by fiducial arrows bounding enhanced disturbance (in dTEC) as a function of distance and UT. The width of the envelopes is ∼ 8 h in time with ∼350 m/s slopes. Results show that dTEC fluctuations reached the furthest distance at ∼20,000 km via the southern polar region. Northward propagation is predominately similar as indicated by envelope lines and their slopes, and also reached ∼20,000 km distance where it encountered the southern outbound propagation. Although dTEC signals became weak at several distances of 14,000 km and 16,000 km, corresponding to European sectors and midlatitudes, propagation signals reappeared beyond those distances perhaps due to wave modulation. In the following discussion, we examine detailed regional characteristics in near-field and far-field regions and provide further evidence of ionospheric perturbation arrivals.

GNSS TEC measurements indicate immediate and vast near-field Tonga event atmospheric perturbations as demonstrated in Themens et al. (2022) and Figure 3. The earliest response was a clear positive dTEC occurring within 200 km of the epicenter almost instantaneously following the eruption at ∼04:15UT. This response, with ∼1 km/s radial propagation for the first 20 min, was an indication of supersonic infrasonic waves typically seen (as Rayleigh waves) during earthquake events (Astafyeva, 2019, and references therein). Immediately following, two enormous shocks occurred with dTEC magnitudes up to 3 TECu (1TECu = 10¹⁶ electrons/m²). Radial propagation initially occurred at ∼700 m/s speed, gradually slowing down to ∼450 m/s, and reached ∼5,000 km distance. The initial waves were clearly identifiable over the northern New Zealand area (∼1,500 km away from the epicenter) as early as ∼ 0500 UT (e.g., Figure 3) and, specifically, at ∼06:20 UT with 2-D fronts (Figure 1B). Subsequent waves were characterized by smaller amplitudes (0.1–0.2 TECu) at lower and relatively stable speeds of ∼360 m/s. These amplitudes were well within typical amplitudes for medium to large scale TIDs. These fluctuations had ∼10–30 min quasi-periodicity for at least 8 h (Figures 2, 3A–3C). The 2-D wave fronts exhibited horizontal wavelengths initially 500–1,000 km (Figure 1B) and later ∼300 km (Figure 1C).

Beyond the near-field, outbound ionospheric responses propagated into different regions of the world. Within 195–315° azimuth bearing of the great circles, the disturbance propagation signals were evident between 13–18,000 km (Figure 4A), particularly over South Africa, with large amplitudes and consistent ∼ 350 m/s propagation speeds. These disturbances lasted for at least 5 h with up to ∼10–30 min periods, arriving via southern great circles (Figure 1A). These results were derived as dTEC averages in time and distance with 1 min bins size in time and 10 km bin size in distance. 2-D wavefronts during the shock arrival showed well organized disturbances with 500–1,000 km wavelengths (Figure 4C), similar to Figure 1B in the near-field.

The continental US (CONUS) has dense receiver networks, therefore only a narrow range of azimuths (55–58°) are taken into account, to minimize decoherence of the wave signature due to regional deviations in the group velocity of the wave fronts. Such deviations can be caused by e.g., prevailing wind velocity, atmospheric pressure, propagation direction (Taylor, 1932), and the ionospheric conditions. Figure 4B shows the first sign of disturbance arrival in the west coast (8–9,000 km distance) at ∼11–12:00 UT, and the earliest front departed off the east coast at 13,000 km by ∼16:00 UT. Throughout, propagation speed remained at ∼350 m/s. Some samples of 2-D wavefronts are shown in Figure 4E. dTEC enhancements were aligned with iso-distance lines, and separated zonally by ∼500 km spacing (wavelengths).

Simultaneously, background TIDs were present, likely associated with geomagnetic disturbances during the recovery from a geospace storm with minimum Dst −94 nT at 23:00 UT on 2022-01-14 (according to WDC Kyoto, 2022b). The substorm activity measured by the AE index (WDC Kyoto, 2022a) indicated an onset after 1100 UT and multiple hourly enhancements reaching ∼500 nT throughout the rest of the UT day. Thus the ionospheric short-term disturbance was characterized by hourly enhancements of TID amplitudes almost simultaneously in latitude and longitude over CONUS, well correlated to AE activity. Post-sunrise TIDs were evident in the US east coast, propagating eastward at ∼300 m/s with 20–30 min periods, similar to what were reported in Zhang et al. (2021). Background TIDs include also gravity waves in certain region potentially linked to the strong stratospheric polar vortex (Sato and Yoshiki, 2008; Becker and Vadas, 2018; Bossert et al., 2020). These background TIDs occurred on the distance-time plot as simultaneous enhancement bands, slant bands, and possibly other features. The arriving eruption-induced fluctuations segmented these pre-existing TIDs fronts into smaller structures elongated along iso-distance lines, and had sharply different characteristics that can be distinguished in the distance-time plot (Figure 4B).

Ionospheric fluctuations continued to propagate through the eruption antipode in North Africa toward Tonga on the next day. These returning TIDs were most evident over South Africa (Figure 4D) where the disturbance phase was clearly toward shorter distance (light-blue arrows), starting at 03:00 UT at 15,000 km distance. The speed was ∼350 m/s. Figure 4E shows an example of wavefronts associated with the returning TIDs at 03:30 UT on 2022-01-16, close to local sunrise time. The timing of the returning TIDs is approximately consistent with propagation from the most distant point to South Africa along the great-circle Tonga—CONUS—Europe—South Africa—Tonga path (Figure 1A). Returning TIDs occurred also across the CONUS over a prolonged period for ∼ 8 h initially at ∼0600 UT at 13,000 km (the US east coast) (see light-blue arrows in Figure 4B), following a longer path of Tonga—southern high latitudes—South Africa—Europe—CONUS.

In the near field, clear indications occurred of the wave returning to New Zealand (Figure 3C) at 2,500–3,000 km distance from Tonga by ∼13:00 UT on 16 January (or to Tonga by ∼15:00 UT on 16 January), after traveling nearly 1.5 days along the complete great-circle. This timing is roughly consistent with a propagation at ∼350 m/s speed around the full great-circle.

During the TID global propagation, the horizontal phase speed varied between 300–350 m/s depending on propagation direction. For example, Figure 2 marks a southward propagation (red arrow) at 300 m/s. However, these speed estimations are generally consistent with infrasonic detection of pressure wave arrival at individual stations around the world, e.g., in northern Europe (Norstar Website, 2022) using the network established to monitor compliance with the Comprehensive Nuclear Test Ban Treaty and over CONUS using the pressure altimeter observations (Iowa Environmental Mesonet, 2022). Lamb waves travel at the sound speed, typically 300–350 m/s in the troposphere, and can exist at any period. Although their energy is confined to the troposphere, their amplitudes increase exponentially with height due to decreasing density. Their wave energy can leak into the upper atmosphere when Lamb waves with ∼300 m/s horizontal phase speed are resonant with the atmosphere, as can be the case with acoustic and gravity waves (Bretherton, 1969; Lindzen and Blake, 1972; Nishida et al., 2014). Lamb waves with ∼319 m/s phase speed were previously identified as an atmospheric wave response to the Krakatoa eruption (Symons, 1888; Taylor, 1932). Similar Lamb waves were also detected by very sensitive microbarographs during the St. Helens eruption (Mikumo and Bolt, 1985) and the Sumatra-Andaman earthquake (Mikumo et al., 2008).

A significant portion of our GNSS observations occurred inland, where direct tsunami wave contribution to these TID results may be ignored. Furthermore, an additional argument against the presumption of tsunami wave presence with 10–30 min periodicity and 300–350 m/s travel speed as noted earlier: Tsunami waves were reported to occur in the US west coast at 15:30–16:00 UT (NOAA DART and NOAA/NOS/CO-OPS Data, 2022) consistent with an anticipated 210–220 m/s propagation speed across the Pacific ocean. This is clearly different from observed ionospheric wave propagation which arrived at least ∼4 h earlier than the tsunami waves in the US west coast. Nevertheless, continued community study is recommended to further clarify the roles of tsunami and gravity wave interactions and the factors that are potentially responsible for their different propagation speeds (Makela et al., 2011; Kherani et al., 2016; Bagiya et al., 2017).

The earliest wavefronts could be seen traveling around the globe three times, passing six times over the CONUS over 100 h since the eruption (Figures 4B,F); the pass 6 over CONUS occurred at ∼05:00 UT on 2022-01-19 at 13,000 km (but is not shown here due to the space limit). The travel time around the globe in the direction of Earth’s rotation (eastward) was 34.8 ± 0.7 h and in the opposite direction 36.0 ± 0.7 h. The error standard deviations are roughly one order of magnitude estimates based on visual inspection. The measured propagation speed and the number of observed passes of the atmospheric wave are comparable to those reported with the Krakatoa eruption (Symons, 1888). Time periods before and after the eruption were processed with the same analysis, and no similar traces corresponding to ones shown in Figures 4B,F were observed before the eruption.