Surface-to-space atmospheric waves from Hunga Tonga–Hunga Ha’apai eruption

The January 2022 Hunga Tonga–Hunga Ha’apai eruption was one of the most explosive volcanic events of the modern era1,2, producing a vertical plume that peaked more than 50 km above the Earth3. The initial explosion and subsequent plume triggered atmospheric waves that propagated around the world multiple times4. A global-scale wave response of this magnitude from a single source has not previously been observed. Here we show the details of this response, using a comprehensive set of satellite and ground-based observations to quantify it from surface to ionosphere. A broad spectrum of waves was triggered by the initial explosion, including Lamb waves5,6 propagating at phase speeds of 318.2 ± 6 m s−1 at surface level and between 308 ± 5 to 319 ± 4 m s−1 in the stratosphere, and gravity waves7 propagating at 238 ± 3 to 269 ± 3 m s−1 in the stratosphere. Gravity waves at sub-ionospheric heights have not previously been observed propagating at this speed or over the whole Earth from a single source8,9. Latent heat release from the plume remained the most significant individual gravity wave source worldwide for more than 12 h, producing circular wavefronts visible across the Pacific basin in satellite observations. A single source dominating such a large region is also unique in the observational record. The Hunga Tonga eruption represents a key natural experiment in how the atmosphere responds to a sudden point-source-driven state change, which will be of use for improving weather and climate models.

1. The internal gravity waves studied here are very fast, moving at around 250 m/s. I confess that it is news to me that gravity waves can propagate this quickly! I am more used to speeds that are an order of magnitude slower than this, and I think many atmospheric scientists will be in a similar position, being familiar with the incompressible form of the dispersion equation on line 370, but not the full compressible form included here. The critical role of the speed of sound in setting the propagation speed makes me wonder whether these waves would not in fact better be labeled as "acoustic-gravity waves" rather than pure gravity waves. In any case, I think it should be clarified that these waves are different from what we usually think of as internal gravity waves in the atmosphere. For example, gravity wave drag parameterizations are not attempting to represent these very fast waves (are they?).
2. The claim that these observations will be useful for improving weather and climate models is speculative and would benefit from additional substantiation, if possible. Numerical models typically require the Courant number (Co=u*dt/dx) to be less than around 1 for stability, according to the The manuscript presents significant and timely results of the unique eruption event. The novelty of the work lies in the combined observational analysis of atmospheric waves at various heights and the finding of the global propagation of the atmospheric waves. The work contributes to the understanding of lithosphere-atmosphere-ionosphere coupling. However, I think the manuscript can be further improved by clarifying some ambiguities and incorporating more analysis/discussion on the result. My comments are listed below.
Major comments: 1. The vertical structure and propagation of the Lamb waves and gravity waves.
The vertical structure and propagation of atmospheric waves generated from volcanic eruptions have been rarely investigated previously, partially due to the lack of observations. For the Tonga eruption, the authors show clear wave signatures observed at various atmospheric heights, which offers a great opportunity to look into the vertical structure and propagation of the waves. If possible, I think the authors should take the full advantage of the observational data and investigate the vertical propagation of the waves. This would significantly improve the novelty of the work. The authors have mentioned the vertical wavelength in the manuscript. What about the propagation time? How much time it takes for each type of the waves to reach various observational heights? Does the vertical propagation speed of the wave varies with height? Can all the Lamb and gravity waves reach the ionosphere (possible atmospheric filtering of waves)?
2. The implications on weather and climate forecasting.
The impact of the result on weather and climate forecasting is not well justified. The Tonga eruption is a rare event, and its atmospheric impacts are extreme. It is unclear how the simulation of this extreme event would provide insights into the strengths and deficiencies of models for weather and climate forecasting, which are nearly always used for non-extreme conditions. The authors should clarify the applicability of the knowledge learnt from this extreme event to typical weather and climate forecasting.
Minor comments: 1. Lines 46 -47: The unit of energy is EJ or EJ^2? 2. Lines 54, "non-acoustic frequencies": what is the range of non-acoustic frequencies? Are the Lamb and gravity waves lower frequency than acoustic waves? 3. Caption of Figure 2: "Airglow inser" -> "Airglow insert"? 4. Line 78, "shockwave": where is it and how to determine that it is a shockwave? 5. Lines 137 -138: Extended Data Figure 3 should be Extended Data Figure 6? 6. Line 138: where are the "Two low-amplitude wavefronts"? Panels are not labeled in Extended Data Figure 5 (no 5b). 7. Line 147, "consistent in speed": please provide explanation. Which two speeds are consistent? 8. Line 151, "6.15am": what does it mean here? 9. Lines 221 -223: any references? 10. Lines 383-389 and Figure 2 airglow insert: Are the airglow images taken during the night or the day? The text seems to indicate that these are nighttime airglow images, while the figure shows daytime? Can the authors provide the original airglow images? 11. Extended Data Figure 3: There seems a gap between the TIDs at the west coast of USA and south-eastern USA. Why there is little TID in-between? Does this imply that the TIDs in south-eastern USA are induced by sources other than the eruption? 12. Supplementary Figures 1 and 2: it would be better to add timestamps and colorbar.
Referee #3 (Remarks to the Author): The manuscript presents an interesting compilation and analysis of various datasets that include observations of acoustic-gravity waves (AGWs) generated during the 2022 Tonga eruptions. Sources of AGWs and their excitation mechanisms are proposed and discussed. The advantage of the study is its multi-layer analysis of various measurements and discussion of their similarities and differences. I find this manuscript to provide the most complete (although very compressed due to page limitation) discussion of fluctuations from vertical evolution of AGWs after Tonga eruption up to now. I believe that the manuscript can be a great Nature report which will attract an attention to the problem of coupled processes in Earth's envelopes.
I provide some commentaries below that may help to improve the representation of the results, clearance of the discussion and story coherency. Overall, my main suggestion is to provide more quantitative analysis to support the discussion of the results and findings.
-L161-181, L202 -although this discussion and explanation can be valid, I would point to the fact that the eruption generated a tsunami. This tsunami could be a source of 1) AGWs of a wide range of periods and wavelengths and observed fluctuations in the near-field, 2) AGWs of a wide range of periods and wavelengths and observed fluctuations all over Pacific Ocean and thus 3) various traveling ionospheric disturbances. Among others, for example https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020JA028309 demonstrated that tsunami itself generates packet(s) of wide range of AGWs/GWs (see Figure -1 in the attachments). Although they may be less prominent at far-field in lower atmospheric observations, these waves may potentially be source of detectable fluctuations in near-field, as well as at far-field at ionospheric altitudes.
They also demonstrated that refracted/trapped/deflected ocean waves near the shore may drive AGWs/GW for hours. Similar was demonstrated with TEC observations (Tsugawa et al. 2011). Signals of ~200 m/s looks also comparable with speeds of tsunami propagations (see Figure -2  To summarize, for the sake of completeness, you may consider adding a tsunami because of undersea eruption and thus AGWs in the atmosphere as sources of detected fluctuations. -L86 -which panel of Figure 1 demonstrates 4 wavefronts? Can they be marked? I would also suggest adding here panels (a), (b), (c) to direct a reader to exact panels that are mentioned in the text.
Is it possible to provide more insight on the speeds with GOES data? A slowdown of waves over South America is mentioned , but it is not clear if waves were slowed down over South America or earlier, in the Pacific Ocean (not sure I can see it from Extended Data Figure 4,b). I think timedistance diagram could be useful to support this discussion. Does it mean that TIDs (2) arrived to US later than expected? I am looking at those fluctuations between lines (2) and (3) and distance range ~9000-11000 km. If those TIDs arrived later than (2) in New Zealand -are they driven by the same "source" or different? If different, why they are both named as (2)? How TID(4) consistent with eruption? Again, zooming of regions of discussion could be helpful.
Just an idea for the figure -see Figure -4 in the attachments (ignore if you don't like it). Meaning to put a pressure plot to the bottom of Extended Figure 3. From first try, the TIDs 4 is kind of consistent with 4th explosion, but not fully. By saying "TIDs 4 are consistent with the wave activity generated over Hunga Tonga in the hours after the primary eruption" -do you mean that TIDs 4 is from Lamb waves generated during explosion 4? I think some clarifications can be provided here.

. I confess that it is news to me that gravity waves can propagate this quickly! I am more used to speeds that are an order of magnitude slower than this... being familiar with the incompressible form of the dispersion equation on line 370, but not the full compressible form included here. The critical role of the speed of sound in setting the propagation speed makes me wonder whether these waves would not in fact better be labeled as "acoustic-gravity waves" rather than pure gravity waves. In any case, I think it should be clarified that these waves are different from what we usually think of as internal gravity waves in the atmosphere. For example, gravity wave drag parameterizations are not attempting to represent these very fast waves (are they?).
The gravity waves that follow the Lamb wave are indeed internal gravity waves -they are not intrinsically different from more commonly observed slower internal gravity waves except for their unusually deep vertical structure, which results from the unusually deep, strong source mechanism. Nevertheless, as the reviewer states, model parameterisations do not usually attempt to represent unusual internal waves of this type (although they do include waves of order 100 m/s, and our modified manuscript now states this explicitly) , and we address this in our next response.

The claim that these observations will be useful for improving weather and climate models is speculative and would benefit from additional substantiation, if possible. Numerical model stypically require the Courant number (Co=u*dt/dx) to be less than around 1 for stability, a c
-While the waves produced by the initial eruption are indeed extreme, models such as WACC M do routinely parameterise waves with phase speeds 100 m/s in the lower stratosphere (Richter etal, 2010, doi:10.1175/2009JAS3112.1), which are comparable to those produced by the convectiveac tivity following the initial eruption. In addition, a large fraction of gravity waves in the mesosphere and lower thermosphere do have phase speeds this large or larger, and study of these waves in ther elatively well-observed middle atmosphere could provide insight into their underlying physics. These points were not made in the original draft, and the reviewers are correct to fla this up. To clarify our meaning we have now modifie the text to make these statements explicitly, approx imatelydoubling the length of this section of the text. Yes: our analysis goes significantl deeper and further than Harrison (2022). The Harrison study focuses on measured pressure anomalies at ground level in the UK only. This provides local informa -tion on the propagation of the Lamb wave over the UK, with a particular focus on a specifi station in Reading. Our study is at the global scale, considers the whole depth of the atmosphere, and studies gravity waves generated across the entire day as well as the initial Lamb wave. The Harrison studyd oes provide useful additional evidence of repeated Lamb wave passages around the world whichwe do not show but do mention, and accordingly we have added it to our reference list.

Line 1: Perhaps the title should refer to *atmospheric* waves, unless that would violate a length limit.
The editor has suggested a new title which incorporates this suggestion.

Lines 30-32: Are these phase speeds or group speeds?
They are phase speeds, as clarified later in the paper. This has been made clearer in the modified abstract.

Line 66: Electrically neutral?
Yes: this has been clarified.

Line 337: What are the time limits on the integral?
Bounds have been added to the integral to clarify that this is over the duration of the observed pressure anomaly.

Line 349: The constant 20.05 must be dimensional (although its units are not stated in the manuscript). This means its value depends on the units of T and cs. Best to account for this, by perhaps stating that cs
This has been fixed as suggested by the reviewer.

Line 356: What are the altitude limits on the integrals?
Limits from 0 to have been added to the integrals to clarify this is theoretically over the whole depth of the atmosphere -but note the subsequent caveat that in practice we stop at 80 km due to data availability. This would indeed be fascinating, but sadly the spatiotemporal coverage of the satellite instruments used is not sufficien to observe vertical propagation of the initial large waves directly. This is becausethe fi rs gravity-wave resolving satellite instrument to pass close enough to observe these waves isIASI-C at aro und 8:00 UTC, 3.5 hours after the initial eruption (Figure 2). At this time the wavesare visible at all heights . This is consistent with a theoretical calculation of the vertical group velocityof waves with the observed p roperties, which we expect to propagate through the full depth of theatmosphere in less than an hour. 2.The impact of the result on weather and climate forecasting is not well justified The Tonga eruption is a rare event, and its atmospheric impacts are extreme. It is unclear how the simula-tion of this extreme event would provide insights into the strengths and deficiencie of modelsfor weather an d climate forecasting, which are nearly always used for non-extreme conditions.The authors should c larify the applicability of the knowledge learnt from this extreme event totypical weather and climate f orecasting. We agree with the reviewer comment, and have included our response to this in response to Review er 1's second major comment above.
C.2 Minor Comments 1. Lines 46 -47: The unit of energy is EJ or EJ^2? The "2"s are cross-links to reference number 2, i.e. Pyle et al 2000. This is admittedly a little confusin g in the current format of the text! To make this clearer the references have been moved to the textimm ediately before the bracketed values. 2. Lines 54, "non-acoustic frequencies": what is the range of non-acoustic frequencies? Are the Lamb and gravity waves lower frequency than acoustic waves? Yes. To make this clearer, "non-acoustic" has been modifie to "sub-acoustic".

Line 78, "shockwave": where is it and how to determine that it is a shockwave?
The term 'shockwave' was used a little informally here, and should not have been -while other published studies and the media have described the Hunga Tonga Lamb wave as a shockwave, this is not a technically accurate description of the physics involved and the reviewer is correct to flag this up. We have corrected the one instance of this term (line 78) to 'atmospheric wave' to avoid any implication of e.g. supersonic physics. Lines 137 -138: Extended Data Figure 3 should be Extended Data Figure 6?

5.
Yes -this has now been corrected. 6. Line 138: where are the "Two low-amplitude wavefronts"? Panels are not labeled in Extended Data Figure 5 (no 5b). The reference should have been to Extended Data Figure 4b, not 5b. In the correct figur they are indicated by dashed red lines overlaid on the panel. 7. Line 147, "consistent in speed": please provide explanation. Which two speeds are consistent?
The speed and direction of the wave across the observed portion of New Zealand, if propagated backwards in a Galilean framework, is consistent with an origin at Hunga Tonga in the specifie timer ange, assuming constant speed and direction -i.e. only one speed is involved, not two., To make th isclearer, the sentence has been slightly rephrased to "The speed and propagation direction of thes ewaves is consistent with ...". 8. Line 151, "6.15am": what does it mean here? Corrected to 06:15. 9. Lines 221 -223: any references? Two references have been added for each comparator. 10. Lines 383-389 and Figure 2 airglow insert: Are the airglow images taken during the night or the day? The text seems to indicate that these are nighttime airglow images, while thefigur show s daytime? Can the authors provide the original airglow images? The airglow observations are nighttime imagery, but with a brighter background than would be typic al due to a full moon on the night of the eruption. The images hence gives the impression of daylightat firs inspection, but on close examination stars are faintly visible in the far-field The image shownis t he original camera image without any treatment other than the superimposition of dashed lines tohi ghlight the otherwise weakly-visible phase fronts. See also the response to Reviewer 3 on the topic of the airglow images (below), for which we have added some text to the manuscript describing this analysis in greater detail. 11. Extended Data Figure 3: There seems a gap between the TIDs at the west coast of USA and south-eastern USA. Why there is little TID in-between? Does this imply that the TIDs insouth-e astern USA are induced by sources other than the eruption? We have replotted the data in this figur, which resolves this issue. The previous version of the figur considered data separately in the western US and southeastern US and the panel showed a spatial gap between these regions. The new version integrates data across the whole US, and thus the ga pis no longer present. Figures 1 and 2: it would be better to add timestamps and colorbar. The figures have been regenerated with colourbars and timestamps.

If possible, I think the authors should take the full advantage of the observational data and investigate the vertical propagation of the waves. This would significantly improve the novelty of the work. The authors have mentioned the vertical wavelength in the manuscript. What about the propagation time? How much time it takes for each type of the waves to reach various observational heights? Does the vertical propagation speed of the wave varies with height? Can all the Lamb and gravity waves reach the ionosphere (possible atmospheric filtering of waves)?
This would indeed be fascinating, but sadly the spatiotemporal coverage of the satellite instruments used is not sufficient to observe vertical propagation of the initial large waves directly. This is because the first gravity-wave resolving satellite instrument to pass close enough to observe these waves is IASI-C at around 8:00 UTC, 3.5 hours after the initial eruption (Figure 2). At this time the waves are visible at all heights. This is consistent with a theoretical calculation of the vertical group velocity of waves with the observed properties, which we expect to propagate through the full depth of the atmosphere in less than an hour.

The impact of the result on weather and climate forecasting is not well justified. The Tonga eruption is a rare event, and its atmospheric impacts are extreme. It is unclear how the simulation of this extreme event would provide insights into the strengths and deficiencies of models for weather and climate forecasting, which are nearly always used for non-extreme conditions. The authors should clarify the applicability of the knowledge learnt from this extreme event to typical weather and climate forecasting.
We agree with the reviewer comment, and have included our response to this in response to Reviewer 1's second major comment above.

Lines 46 -47: The unit of energy is EJ or EJ^2?
The "2"s are cross-links to reference number 2, i.e. Pyle et al 2000. This is admittedly a little confusing in the current format of the text! To make this clearer the references have been moved to the text immediately before the bracketed values.

Lines 54, "non-acoustic frequencies": what is the range of non-acoustic frequencies? Are the Lamb and gravity waves lower frequency than acoustic waves?
Yes. To make this clearer, "non-acoustic" has been modified to "sub-acoustic".

Line 78, "shockwave": where is it and how to determine that it is a shockwave?
The term 'shockwave' was used a little informally here, and should not have been -while other published studies and the media have described the Hunga Tonga Lamb wave as a shockwave, this is not a technically accurate description of the physics involved and the reviewer is correct to flag this up. We have corrected the one instance of this term (line 78) to 'atmospheric wave' to avoid any implication of e.g. supersonic physics.

Lines 137 -138: Extended Data Figure 3 should be Extended Data Figure 6?
Yes -this has now been corrected. Figure 5 (no 5b).

Line 138: where are the "Two low-amplitude wavefronts"? Panels are not labeled in Ex-tended Data
The reference should have been to Extended Data Figure 4b, not 5b. In the correct figure they are indicated by dashed red lines overlaid on the panel. Line 147, "consistent in speed": please provide explanation. Which two speeds are consis-tent? The speed and direction of the wave across the observed portion of New Zealand, if propagated backwards in a Galilean framework, is consistent with an origin at Hunga Tonga in the specified time range, assuming constant speed and direction -i.e. only one speed is involved, not two., To make this clearer, the sentence has been slightly rephrased to "The speed and propagation direction of these waves is consistent with ...".

Lines 221 -223: any references?
Two references have been added for each comparator.

Lines 383-389 and Figure 2 airglow insert: Are the airglow images taken during the night or the day? The text seems to indicate that these are nighttime airglow images, while the figure shows daytime? Can the authors provide the original airglow images?
The airglow observations are nighttime imagery, but with a brighter background than would be typical due to a full moon on the night of the eruption. The images hence gives the impression of daylight at first inspection, but on close examination stars are faintly visible in the far-field. The image shown is the original camera image without any treatment other than the superimposition of dashed lines to highlight the otherwise weaklyvisible phase fronts. See also the response to Reviewer 3 on the topic of the airglow images (below), for which we have added some text to the manuscript describing this analysis in greater detail.

Extended Data Figure 3: There seems a gap between the TIDs at the west coast of USA and south-eastern USA. Why there is little TID in-between? Does this imply that the TIDs in southeastern USA are induced by sources other than the eruption?
We have replotted the data in this figure, which resolves this issue. The previous version of the figure considered data separately in the western US and southeastern US and the panel showed a spatial gap between these regions. The new version integrates data across the whole US, and thus the gap is no longer present.

Supplementary Figures 1 and 2: it would be better to add timestamps and colorbar.
The figures have been regenerated with colourbars and timestamps. Figure -2

in the attachments).... To summarize, for the sake of completeness, you may consider adding a tsunami because of undersea eruption and thus AGWs in the atmosphere as sources of detected fluctuations.
The Lamb wave and fast gravity waves associated with the initial eruption had a speed and morphol -ogy highly consistent with an atmosphere-only pathway, and travelled substantially faster than thee stimated speed of the tsunami provided by the reviewer. Therefore, we believe it is unlikely thatthes e waves were generated via an oceanic pathway. From the reviewer's comment on the 200 m/sspe ed of the tsunami wave, we assume that the reviewer agrees with this, but mention it for clarityand c ompleteness. The slower far-fiel waves hours after the eruption in many (but not all) cases can be inferred to have speeds of order 200 m/s or lower, and therefore could be triggered by the tsunami. However, we wo uldargue against this on the grounds that the waves we observe are nearly perfectly concentric abo utHunga Tonga at all ranges*. An oceanic pathway would be very likely to introduce additional nois eto the 'secondary' atmospheric phase fronts produced later -see for example the bottom-topograp hyfocusing effects simulated by figur 9 of Inchin et al (2020, doi:10.1029/2020JA028309) and con-si der also interactions between the Proudman resonance effect and ocean trenches as discussedby Lynett (2022, doi:10.21203/rs.3.rs-1377508/v1) and Tanioka et al (2022, doi:10.21203/rs.3.rs-13200 93), which will generate new smaller tsunamis at trench locations. We do not see evidenceof these effects in our atmospheric wave measurements. However, we cannot rule this pathway outfrom our data, and accordingly, we have added a sentence discussing this possibility to the text, anda refere nce to Inchin et al. We have also added a sentence discussing evidence of meteotsunamisgenerate d in other basins by the atmospheric waves, highlighting the complex ways in which theoceans and atmosphere are coupled by waves.

For reader, it could be hard to see phases and their continuity to validate reported speed s from Extended Data Figure 3. Could some parts of the figure be zoomed in?
We agree that the phase fronts were difficult to resolve in the original version of the figure. This was due to plotting individual measurement points, which had a high level of scatter noise over small distances. To resolve these, we have recomputed the data in one minutes by 5 kilometre bins, which significant clarifies the figure. This binning does also reduce peak magnitudes, and the corresponding values have been changed in the body text to these new magnitudes to avoid confusion for the reader. The raw data used have not changed. each observation depicted (i.e., (a) Airglow,

Hawaii, (b) Surface Pressure Stations etc.).
This is a tricky one, as most other words that could be used here could also be potentially misleading (e.g. 'leading' could imply some form of guiding, 'front' could imply an association with weather, and' foremost' while probably fine for the Lamb wave would change as a function of time for the dispersive gravity waves.). As all three reviewers understood the meaning of 'initial' in this context, we have left it unchanged for now, but are very happy to change it if requested.
As suggested, lettering has been added to the panel, and is now used to refer to the individual panels in the text.

How you define the altitude of GNSS observations of 100-250 km? Could the signals be detected and discerned from the noise at such low altitudes as 100 km? Why then the shell height was set at the top boundary of 250 km?
The response of the electron density is a function of the neutral atmospheric perturbation, the geo- The GPS signals traverse the entire ionosphere and therefore they will experience the wave in electron density integrated along a line of sight from the satellite to the receiver and observed as fluctuations in the GPS TEC. Only high elevation satellites are used in our analysis to minimise errors in the assumptions necessary for mapping to a specific altitude (i.e. shell height) in the ionosphere. An ionospheric altitude of 250 km is used in our paper, which is commonly selected for TIDs in other works (for example see

the reader can find "mixed packet of waves with non-dispersive wavelengths and periods"? What periods and what wavelengths are estimated? What is meant by "large" amplitude? To summarize, it would be great to provide additional quantitative discussion
here and adjust figures accordingly.
The word 'shockwave' was poorly chosen and has been replaced in response to a comment from Reviewer 2 -the Lamb wave is the wave in question.
The clause containing the phrase 'mixed packet' has been removed from the text as it was unclear.
As the amplitude varies substantially by location due to the spreading of the wave, quoting a single value in the text would not be broadly representative, and accordingly we do not do so. The amplitude and temporal period of the Lamb wave at surface level are shown in Figure 1 and ED Figure 1a for the general case and ED Figures 1e and 8 for the specific cases of Broome, Australia and Tonga respectively. The horizontal wavelength is not stated directly, but can be computed from the period and speed of the data as presented. For the stratospheric general case, the amplitude is shown by Figure 2 and ED figure 5b and the horizontal wavelength is shown in ED figure 5c; note that a temporal period cannot be determined from these data as they are pseudo-instantaneous snapshots.

L86 -which panel of Figure 1 demonstrates 4 wavefronts? Can they be marked? I would also suggest adding here panels (a), (b), (c) to direct a reader to exact panels that are mentioned in the text.
The panels have now been lettered, and the relevant panels (m-p) identified in the text. The wavefronts are marked in these panels with black arrows. Figure 4,b).

I think time-distance diagram could be useful to support this discussion.
The possible South American slowdown is not easily visible in ED4b as the figure is a radial average and the effect is small and regional. It is also very close to the noise floor of GOES. To better highlight this feature, we have therefore added an additional ED figure (ED 10) of filtered GOES data showing the wave before and after the slowdown. The animated Supplementary Figure 2, where the possible slowdown is seen to take place over the east of South America as a mild bending of the primary phase fronts, also shows this effect as a function of time.

L98 -308 5 and 319 4 m/s -are these 2 numbers for 2 different locations or 2 different observations?
Different locations, as the text currently says ("a phase speed of between 308 5 and 319 4 ms −1 depending on location").

L102 how did you estimate phase speed of 318 m/s for hydroxyl airglow over Hawaii?
There are five visible wavelength cameras at the Gemini observatory in Hawaii, of which the results from one pointing northwards are shown in Figure 2b -results from the others are fully consistent with the chosen image, and accordingly the others are not reproduced both for brevity and clarity. Of the five cameras, one is aimed at a near-vertical angle (with a slight offset determined from study of the star field), and we use this image to identify the arrival time of the first wave packet using the image time stamp -this time is 08:48:53 UTC. At a distance of 4964 km and using an explosion time of 04:28:48 UTC, this gives a phase speed of 318.12 m/s. Further analysis using the other four cameras from the Gemini observatory gives results consistent with this. We use a horizontal view rather than the vertical view as our example in Figure 2b because the vertical image requires enhancement to make the red phase fronts visible, whereas the fully-temporally-consistent horizontal view shows the same signal without the need to modify the image. This information has been added to the methods section.

L103 -what is meant by "uniform" phase fronts? Uniform in what extent? I am not sure that any observations demonstrate vertical structure of fluctuation.
Our observations do provide vertical phase structure over a large chunk of the atmosphere, as described in the text.
To reiterate: for clarity of interpretation, the AIRS, IASI and CrIS data shown in Figure 2 have been shown at a different altitude level for each dataset, but (as described in the caption to Figure 2 and elsewhere) all three instruments each measure the same three stratospheric altitudes (approximately, 25 km, 39 km and 42 km) simultaneously. In each case, these measurements represent an average over a depth approximately 10-12 km centred at the specified height, and due to the strength of the signal and given its brief period it is likely that the phase front is at the same place across the full depth of the measurement. In all three datasets, no apparent phase difference is visible in the Lamb wave at different altitudes.
In addition, the arrival time of the Lamb wave at locations with surface pressure stations is consistent with the arrival time in the stratospheric measurements, as are the airglow images from Hawaii and the lower-troposphere-dominated GOES data. While our measurements do not provide complete coverage over some gaps (approximately 5-15km and 60-80km), based on both the large proportion of the height range covered and the our theoretical understanding of external wave modes, it is very unlikely that phase variations with heights in these parts of the profile are significant, and the vertical phase structure of the wave would have to be very morphologically unusual to only show divergences from uniformity in these altitude ranges.

L107 -Does any of demonstrated instrument or dataset have a sufficient precision to claim that Lamb wave propagated with 319 and 316 m/s in different directions? This is not following from the earlier discussion, where the speeds are suggested with an uncertainty of 6 m/s (L81) 3 m/s (L85), 5 m/s and 4 m/s (L98). What are the sampling rates of the data demonstrated?
The reviewer is correct -thank you for spotting this. We have clarified this by changing the text to say that "Our data may show evidence of a slightly different speed for propagation in different directions across the Earth..., but this is within the uncertainty range of our measurements". For completeness here, we note that strictly speaking the barometer data are not reporting errors but rather genuine variability, and that the uncertainty in the measurements depends on the time sampling of the data (which is variable) and the size of the pressure perturbation (also variable).

9000-11000 km. If those TIDs arrived later than (2) in New Zealand -are they driven by the same "source" or different? If different, why they are both named as (2)?
Yes, it is correct that the TIDs arrive slightly later than expected theoretically. Given their highly unusual magnitude and the relatively small 'delay', we believe this represents delays in propagation over large distances due to e.g. atmospheric refraction rather than a different source mechanism. For this reason, we also assign them the same identifying number. This is a very useful suggestion that has significantly enhanced our analysis shown in ED 3. We have now added the Tonga pressure signal to the figure as an additional panel, aligned to correspond temporally. This addition shows clearly that TID 4 is temporarily highly consistent with a pressure drop seen at Tonga possibly corresponding to a later smaller eruption. We have adjusted the text to mention this.