The paper presents a thorough analysis of concentric GW patterns in the middle atmosphere and deep convection as a potential source. The investigation methods are sound and the figures of generally high quality. Much emphasis is given to the development of the convection in the potential match time and how large an emission erea and match error might be. This distinguishes the current work from previous studies and I recommend to publish the current study for ACP. However, I think that the structure of the paper needs to be improved. In particular, the MCS tracking analysis is never shown together with actual brightness temperatures, which would elucidate which structures are actually tracked. Some real zooms would be helpful, so the details close to the source can be distinguished. There are quite a number of repitions (please remove), but sometimes a motivation why the next step in the analysis chain is performed whould be helpful.

Major comments:

The presentation logic needs to be improved. The tracking data are shown on several figures, but never become really clear. My suggestion would be:

Introduction: Please skecth your multi-step approach: a) back-traces, b) coparision with instantaneous map c) area region + tracking => likelihood for a specific convective event / MCS  in short. Do so without providing results but refer to (sub)sections. Then one gets a plan of what you are going to do  

Figs 3-6

 a) remove the inlay showing the tracking

 b) add a new panel showing a real zoom of the core circle with the RT and the symbols,

    use red and blue for the respective tropopause crossing of the ray

Do a new combined Figure where you show for one fixed time the BT -90 -> -50 °C, the tracking position at this time with a larger symbol and the tracks for the other time with smaller symbols. For a second panel of each wave-event: Combine this with tracks overalyed on winds as in F11. For the tracks the area of the circle / zoom region is sufficient and this would allow to resolve the movements. The large area including the observation side is not required, on the other hand.

For the tracking run from C #1 to C # 9, don't repeat C #1 - #4 for the second / third event. Then it becomes immediately clear that these are not the same!

Summary: Please provide a more generic summary. Describe the new points of your method (combing RT and tracking, error estimates) first. Briefly summarize what you found. 

More to the details of the writing: You quite often present a result in something like two sentences where you don't have the details. One or two paragraphs later you then explain this. That is unhelpful, becuase one gets sidetracked. Rather than having preliminary results a motivation at the head of the section where you are in the general plan would be helpful. 

Section 3.5:

There are several problems with this section:

A) The observational filter of GPS-RO allows only to see GWs with wavelengths larger than 100~km, actually even longer than 200-300km for the fast waves discussed here (cf. comments to LL170 below). That is for along-LOS wavelength, still one would need a very favourable viewing geometry to see the waves. As every MCC also emits longer horizontal scales it is much more likey you sound these (cf. horizontal wavelengths of GWs determined from AIRS). This makes the approach faulty from the beginning.

B) Which vertical wavelengths did you determine? They are not shown! Are they compatible with the extremly high phase speeds you gain directly from the OH observations. At least at the OH layer they must be long (lz>15km) or you couldn't observe the waves from an OH layer. In the stratosphere refraction by the background wind is negligible (your own argument), thus they the GWs have long lz their, too. In that case you need to spedify how you sepeareted between GWs and background.

C) A lot is missing in the descrition. What did you take for the propagation direction? Radial from a center would be my approach ...

This section does not contribute much to the overall results. Thus I suggest to simply remove section 3.5 from the paper rather than trying to fix the points.

Specific comments:

L257 Please omit or reformulate the statement: "It is worth ... " Convective GWs can have a wide range of phase speeds. Considering previous works by Hye-Yeong Chun and Joan Alexander you would assume the spectrum to peak at phase speeds of 20-30 m/s. Actually, such lower phase speed CGWs drive the QBO. Therefore, the statement must not be made in such generality. I would rather say, the waves observed here have phase speed sufficiently large that the winds below do not introduce major disturbances in the wave fronts and that they hence can be still recognized as concentric wave structures.

In all maps: You show circles in lon/lat. Shouldn't it be circles in terms of (km)? So close to the tropics the difference is only 15%, still ...

Fig 10 and description. This repeats a lot between legend and text, but it does never become really clear to me what you are after. Please try to reformulate. In particular, it is not the tropopause diameter, but the diameter of something at the tropopause and it remains unclear to me whwther you try to estimate backward from the observed rings or forward from the source or both.

Minor comments and technical corrections:

L23 of the GWs -> omit the

L24 if you consider it from the view point of the mesosphere - otherwise mountain waves are probably more important and spontaneous imbalance for higher latitude of similar importance

L27 has -> have

Since you give a quite comprehensive overview, perhaps add something of the following: There are also some studies linking satellite observations with OLR. That includes work by McLandress et al., JGR, 2000, Jiang et al., JGR, 2004 for MLS, Choi et al 2009 (introducing a CGW source model), Preusse et al. 2001 (IR limb sounding). Also, a typhoon may act as a source to quasi-circular waves of much larger scales -> Kim, Chun and Wu, JGR, 2009)

L74,L75 repeats 1024 pixels

L105 this is horizontal and time? Please say so

Eq1 / 2. This would be more meaningful if you also provide the dispersion realtion

L144 Omit the sentence The backgrounds ... That's coming in the next paragraph comprehensively

What does happen, if you have a bias? A potential bias could induce a locally enhanced / reduced buoyancy frequency. Would it be worth correcting for that first?

L155 Since you use this as stopping condition: What is your actual conserved quantity? In GROGRAT it would be wave action flux.

L158 module -> sounds a bit strange, simply omit?

L164 I am missing the point of the "Therefore". You mean unusual cold so you want to see whether both lead to the same deviation?

L167 / 169 repeats

LL170 With that you very likely see different horizontal wavelengths than the ones you find in the airglow. The observational filter of GPS is given in

@Article{lange_2003,

  Author =       "M. Lange and Ch. Jacobi",

  Title =        "Analysis of gravity waves from radio occultation measurements",

  Journal =      "Springer Berlin",

  Pages =        "479-484",

  Year =         2003

}

They actually come to the same values as found by the analytical approach in Preusse et al. JGR 2002. With that you need very favourable viewing conditions (angle between LOS and wave fronts) to see the same wave. More likely you are observing longer parts of the wave spectrum emitted from the same event.

How did you remove the large-scale background in the GPS profile?

L177 That sentence is a bit ambigious. Do you mean: A large overshoot results in a particular cold tropopause? Or do you mean: If the tropopause is already particularly cold you need more energy to create an overshooting? Please insert one more sentence making this more specific.

L203 Why T_{core}/2 and not \Delta T_{core}/2 ?

L220 regions have been

L237 Suggestion:  The blocking diagram hence visualizes where the background winds induces a zero vanishing intrinsic frequency of the GWs.

LL243 I like the 3D blocking diagram as it shows the altitude structure, but swap introduction of 6b and discussion of phase speed: the quantitative argument is much better seen from 2D. (Or reading further, just omit the in-advance statement L244).

L265 There is Taylor and Hapgood (1988) as well (please include, it's the first) - and then I think you have the full list. Maybe "Numerous" is a bit strong. Anyway, you here repeat from the introduction.

L277 That sentence is too long and too warped.

Fig10 diameter of the tropopause: what do you mean?

 diameter of circular wave fronts at tropoapuse altitude?

 diameter of overshooting?

Fig11 You don't need three grey-scale bars, only information is time

L353 Take your own values! You should be able to just take them out of e.g. F7

Literature:

For backward raytracing: Some work by Pramitha?

In their manuscript “Sources of Concentric Gravity Waves Generated by a Moving Mesoscale Convective System in Southern Brazil”, the authors combine measurements from multiple instruments at multiple altitudes with ray tracing models to connect gravity wave observations in the OH layer with their sources at the tropopause. Single cores of a moving mesoscale convective system are identified as most likely sources of the concentric gravity waves observed in the OH layer.   

This work is quite impressive from the amount of data used and the analysis performed. However, I would suggest to better explain the reasoning behind all the measurements taken and the analysis performed. Both the introduction and the summary/conclusion section are missing clear scientific research questions motivating the work. At the moment the paper seems a bit like a data dump without a clear motivation behind. This impression could possibly be overcome by refining the introduction and conclusion. Additionally, I would suggest to revise all the sections / figures for their necessity to support the findings and possibly remove some of them.

A detailed list of minor comments is given below.

L24: Better: „in the tropical troposphere“, as otherwise one might start arguing about the importance of orographic versus convective gravity waves.

L27: Maybe better: … mechanism is known to generate concentric gravity waves … (or remove at least “natural”, you probably do not want to start a discussion about non-natural GW sources)

L27: Most […] cases […] have […]

L38: … imgaes … have been used …

L42: ray tracing models

Introduction: You are nicely describing what was done before and what you are doing, but you are missing to describe the difference and provide a reasoning for your study. Why do we need this paper? What does it bring new to the world?

L101-103: This is a hypothesis which will be confirmed later. Maybe rephrase: According to previous studies (…), the appearance of concentric structures in the airglow hints to: 1) point-like convective overshooting of the tropopause and 2) weak intervening background wind.

Table 1: What is the exact definition of the propagation direction? Degree measured clockwise from North? And how do you define the propagation direction of a concentric outward propagating wave? Is only the value of the centre fit shown for the propagation direction?

L105: One parenthesis too much.

Figure 2 (+ description): Maybe do this as an example on top of one of the plots from Figure 1, so one can better understand what you are doing. Maybe explain the crest/trough part already at point 1. Makes it easier to follow. In 2: The 3 circles have to have the same radius, no? In 5: Why so complicated? Why not directly measure from P to where one of the lines from 3 crosses the black circle? Are all these steps done manually for each case or is there an automated software?

Chapter 2.1 – raytracing part: How is the vertical wavelength / wave number determined, which is necessary for the raytracing? All 4 stopping criteria seem a bit arbitrary. Can you explain in more detail why you chose these four stopping criteria? What is the physical reasoning behind each of them?

The advantage of this ray-tracing method (variable background wind over this large altitude range) should be made clear somewhere in the text.

L186ff: Please reorder for better readability:

Adapting Equation 3 from Griffin et al. (2016), the overshooting top height (OT_Height) is estimated using the brightness temperature (BT) and the lapse rate (LR) of the overshooting top (OT), the tropopause height and temperature:

Eq. (3)

Here H_Trop is the tropopause height, OT_BT is the brightness temperature of the OT, T_Trop is the tropopause temperature and OT_LR is the OT lapse rate.

The cloud top brightness temperature was obtained from the Advanced Baseline Imager (ABI), which is an imaging radiometer of GOES-R satellite. The ABI has 16 different spectral bands, including two visible channels, four near-infrared channels, and 10 infrared channels with a spatial resolution of 0.5-2 km. Among the weather and climate products of these channels, the CTBT product is derived from the 11, 12 and 13.3 µm infrared observations.

The OT lapse rate was estimated using the radiosonde profile and the CTBT. The OT lapse rate for the days considered in the determination of the tropopause temperature and altitude were averaged and was found to be -7.35 Kkm^-1.

L160: Why do you state this here, as you are not tracing any waves forward to the thermosphere?

L220: […] regions have been used to identify […]

L221 & 222: I am confused by the use of references in this sentence. Why are you referencing other papers for things you have done here in your paper?

L231: Maybe better “deployed”

Figure 6: The description of the different colours and vectors belongs to the caption, not the text.

L258f: If this criterion is not applicable to the cases you show, why do you introduce it?

L284: Maybe use “shown” instead of “demonstrated”?

L284: How is the CAPE calculated?

L290ff: Is this an observation from your data or from Kim et al.? I would suggest to rephrase: It was observed in previous studies that the presence of deep convection with colder cloud tops brightness temperatures further decreases the tropopause temperature (Kim et al., 2018). In our data this also happens between 12:00 UT on September 30, 2019, and 12:00 UT on October 3, 2019, when the cloud top temperature ranges between -40◦C to -90◦C.

Reorder Figures 10 & 11 according to their first mentioning in the text.

L315ff: Please rephrase. The first and second sentence seem to be in contrast to each other. Were all four cores there or only core 3 & 4?

L344 - 355: Please explain better where you get the diameter of the plume at the tropopause from (31 km you state, but not where you extracted this value from).

Chapter 3.4: This chapter seems a bit like unnecessary information to me. Please either remove or explain why it is necessary for your findings (e.g. mention it in the summary section).

L441: Is signifies the correct word here?

L482f: spectra (plural) -> were

Figure 15: Please use a more intuitive colour scale for a continuous (not around 0 centred) range. See also Crameri, Shephard, Heron (2020) for hints on good colour scale usage.

L524: *Rossby*

Figure A1: For better comparability, the colour scale (extend) for the upper plots should be kept constant. Additionally, please add an x-axis. Otherwise the points in the lower panels are really hard to interpret. Is the tropopause here defined by thy laps rate?

Please check citation formatting throughout the whole manuscript.

Crameri, F., Shephard, G.E. & Heron, P.J. The misuse of colour in science communication. Nat Commun 11, https://doi.org/10.1038/s41467-020-19160-7, 2020.