The paper presents a detailed comparison of gravity wave characteristics in AIRS observations and in three high-resolution free-running numerical simulations initialized on January 20th, 2020. The study focuses on the ``DYAMOND (boreal) winter" period, which extends over three weeks starting from that date, and in the mid stratosphere (33 km). The authors employed advanced techniques to sample the numerical simulations as AIRS sample the atmosphere, which ensures an accurate comparisons between the four datasets.

Despite the few-km resolution of the numerical simulations, the authors still find lower amplitude gravity waves in the simulations than in AIRS observations. The agreement between observed and simulated waves is better in the winter (northern) hemisphere, where mountain waves dominate. In the summer hemisphere, with mostly convective wave sources, the spread in gravity wave characteristics between observations and models, as well as between models, is higher. The study also illustrates how gravity waves in free-running simulations diverge from those observed by AIRS in about a one-week timeframe, which is due both from differences in wave sources or large-scale circulation that filter the waves.

The study thus provides interesting insights in how state-of-the-art models are able to simulate atmospheric gravity waves. Except on a few places, the paper is generally well-written, and enables the reader to follow the argumentation. I would therefore recommend its publication, yet I have a number of remarks that should be addressed first.

Main comments

- I have some questions on how gravity waves characteristics are derived from AIRS observations. You use a fourth-order polynomial in the across-track direction to obtain temperature perturbations (l. 216). AIRS' swath is 1,800-km wide (l. 90). This polynomial thus typically excludes waves with wavelengths longer than 450 km in the across-track direction. On the other hand, there seems to be no similar filter applied in the along-track direction. Is there therefore an inherent anisotropy in the way you derive the temperature perturbations?

In line 224, you make a reference to the "dominant" wave. Could you be more specific here? Does it mean that you only retain the maximum coefficient of the 2-D horizontal Stockwell decomposition in each grid node? If yes, could you quantify the fraction of temperature variance that is discarded in this process? 

Last, Figure 3 looks very nice, but I am not sure to know which of the method shown in this figure (if any) is used in the paper. Furthermore, the wave packet shown in this Figure has occurred in 2008, i.e. outside of the time period addressed in this study. I would thus favour a figure that specifically applies to the methodology and time used in the paper (and the accompanying text could discuss the differences/pros and cons of this methodology with respect to previous ones).

- Fig 4: The y-axis in subfigures c), d) and e) is neither explicited in the subfigures nor in the caption. This seems to be a normalized count, but this is only a guess. In particular, I would like to know whether this is only a count or if there is some e.g. amplitude-weighted average in d) or e)?  

I am somewhat suprised by the horizontal wavelength figures. For instance, Figure d4 shows a narrow band of wavelengths shorter that 200 km in the center of the wave packet, and otherwise wavelengths longer than 400 km. This does not look so obvious in Figure b4: in particular, I am not able to distinguish a clear along-track gradient in wavelength as the one shown in d4. I have a similar comment on figure b1/d1 and b2/d2. Could you comment on this?

- Fig 5: I have the same comment on the horizontal wavelength here: for instance, I do not understand the dark blue patches in Figure d4.

I also note that the vertical wavelength histogram shown in Figure e) exhibits mostly wavelengths shorter than 16 km, while AIRS vertical resolution is between 7 and 13 km (line 97). Hence, the amplitude of those wave packets are likely significantly affected by AIRS observational filter. This may be stressed in the text.

Finally, the AIRS wave amplitude in this example peaks at about 1K, while it is stated in line 96 that the retrieval noise is between 1.4 and 2.1 K. It may be worth expliciting how the detected wave amplitude could be smaller than the noise level.

- In several instances, the study claims that gravity waves are underestimated in high-resolution simulations when compared to AIRS observations. I am not sure that this is fully supported by the material shown in this paper. This statement for instance appears in Section 4.3 (namely around line 370 and following ones), and is associated with Figure 8. Focusing on the first ten days of simulation (left column), this figure indeed shows higer gravity-wave amplitudes in observations mostly over Greenland, Iceland and Eurasia than in simulations. Yet, the previous section (especially Fig. 6) has shown that AIRS observations are biased toward higher-amplitude waves than the simulations. Hence, the conditional (wave-packet) mean, which is used to produce Fig. 8, seems to average both a mix of low- and high-amplitude waves in the simulations, while it averages mostly high-amplitude waves in the observations. I would be for instance curious of what would be the comparison if the same 1-K threshold that was used in Section 4.2 is applied here. The amplitude histrogram in Figure 4c furthermore illustrates my point: AIRS seems to compare well with simulations for higher amplitude waves, but underestimate lower amplitude ones.

I also note that the unconditional mean comparison (Figure 9) does not show a systematic difference in wave amplitudes between observations and simulations.

- The sentence that starts in line 392 seems to announce that diagnostics as those shown in Plougonven et al. (2017) will be shown. On the other hand, the following lines consist in a discussion based on several previous figures and relying on the reader's eye to compare them. This discussion is not very easy to follow (e.g. the sentence on line 401 looks odd). Wouldn't it be easier to show the pdf of wave amplitudes conditional to wind speed?

- line 445-446: I do not agree with this sentence: the lowest values associated with the NH peak in Figure 11e are those of AIRS and GEOS (not ICON), and I do not see the factor 3-4 difference between the 4 datasets.

- line 453, last sentence of Section 4.5: Yet, a small meridional displacement of the jet center in models with respect to the reanalysis might explain the feature discussed here. Maybe worth double checking.

- line 469-471: I am not sure to fully agree: waves approaching their critical level would see their vertical wavelength decreasing. In numerical models, this could result in decreasing amplitudes as they become sub-grid scale in the vertical. And those waves would soon break and thus contribute to the general circulation!

Specific points

- line 175: Rephrase the sentence that starts here.

- line 289: "Outside the main wave signal": do you mean in the hatched region?

- line 408: Rephrase the sentence that starts here.

- line 411: wavesm -> waves

- line 414: What does the second "this" of this sentence refer to?

- line 448: What do you mean by an "overall balanced flux"?

Please see my review in the attached pdf.