General comments:

The authors have addressed most of my concerns in this round. I appreciate the efforts and hard work by these authors. Nevertheless, some new problems emerge due to the substantial made to the original version, which mainly lies at the non-efficient discussion for the result interpretation. Moreover, several figures need to be modified for their unclear labels. I will recommend its publication after adequately addressing the following concerns.

Specific comments:

Figure 1: I am confused and surprised that the authors did not correctly show the geographic coordinates for the whole study area – Antanctic continent. It is supposed to have equal latitude and longitude grid. Nevertheless, I can not see the label of latitude for this map.

Section 2.1:  The literatures on the robustness and accuracy of radiosounding measurements used here are missing, making it hard to convince the readers to believe the analysis results based on these observations. Some necessary discussion regarding this issue can be added by referring to the following references:    DOI:10.3390/rs13020173 and https://doi.org/10.5194/acp-21-17079-2021.

Figure 7: There exists silimar issues like Figure 1.  

Figures 8 and 9: My hunch is that the labels for the lines shown in Figure 7 is not correct considering the longitude information is missing (there appears only latitude coordinate in the Abscissa, and is not enough to accurately describe the coordinates).

L340: I can not find Figure 12 throughout the manuscipt.  If my guess is right, the authors may want to refer to Figures 8-9.

In section5: The authors discussed the potential influential factors, including temperature inversion, katabatic winds and polar vortex. The nature for the latter two factors is concerned with the shear-induced turbulence. Nevertheless, the authors did not mention wind shear at all. This is supposed to be avoided. Besides, recent study (Xue et al., Q.J.2022, doi:10.1002/qj.4262) indicated that katabatic winds could be linked to trapped lee wave and result in enhanced turbulence, which can be added in attempt to increase the readability and scientific level.  

Also, buoyancy, cloud cooling, convection, gravity wave (and its breaking) could be other variables that are ignored in this section. The authors can refer to the following references:

doi: 10.1088/1367-2630/aa5d63

https://doi.org/10.1016/j.envpol.2021.116534

https://doi.org/10.1029/2018JD029479

https://doi.org/10.3390/s20030677

https://doi.org/10.1088/1748-9326/abf461

doi: 10.1016/j.uclim.2022.101151

https://doi.org/10.1029/2022JD037174

https://doi.org/10.1007/s00382-021-06075-2

General Comments

Overall, this paper is very interesting, and I think provides a benefit to the scientific community. The analysis is thorough, and the authors provide context as to how the results of the study are useful. Largely, it is well-written, with some grammatical issues, for which I provide some suggestions in the Technical Corrections section below. My biggest concern is that the authors consistently equate Richardson number to atmospheric stability, however, this is not entirely correct, as a statically stable atmosphere can still be turbulent with an Ri value below critical. If the authors re-word this discussion throughout the paper, and address my other comments, I am happy to see it published.

Specific Comments        

I am missing a description of why 1/Ri is useful, as opposed to simply using Ri. To me, it is odd that you would use 1/Ri as a metric for turbulence and to determine PBLH rather than simply Ri, as is more standard in previous literature. You need to provide a solid argument as to why you use 1/Ri instead, including a discussion of previous literature which supports your argument.

Line 64-66. This sentence implies that Ri is a direct measure or stability, but this is not true. Stability can exist in the presence of turbulence, and strong turbulence usually leads to either a neutral or unstable layer. Thus, Ri in itself does not determine static stability, though it does provide some insight into the stability of a layer. With regards to Antarctica, the PBLH is almost always either near-neutral or stable, with very few instances of instability. These near-neutral PBLHs are still turbulent, and usually, so are the stable PBLHs. Make sure here, and throughout the paper, you don’t claim that a lack of turbulence (as indicated by Ri) equals a stable layer, and the presence of turbulence equals an unstable layer. Instead, contrast between turbulent and laminar, or clarify that Ri gives insight into the stability of a layer, but is not a direct measurement of stability.

Line 68. Please clarify bullet point #3. Particularly, it is unclear to me what you mean when you say the analysis was extended for three sites to two vertical cross-sections at a high horizontal resolution. More description of what this means is necessary.

Line 11 and throughout paper. Ri should be calculated using potential temperature and wind speed, not temperature, which you show with Eq. 1. Make sure to specify in the text throughout the paper that Ri is calculated using potential temperature.

Sect. 2.1. Add the frequency with which the radiosondes were launched. I see that you use data from March 2021 to February 2022, but how often within that year were radiosondes launched? Does this differ for the different sites?

Sect 2.1. Did you remove questionable radiosonde measurements near the surface? Usually, near-surface radiosonde measurements are unreliable due to the radiosonde needing time to equilibrate to the outside temperatures once it is launched, so the temperature values reflect warmer values than reality. Thus, below about 20 m, radiosonde measurements are usually unreliable, and make it look like the atmosphere is unstable, when it really isn’t. Make sure you are taking this into account.

Figure 1. Add latitude values. Also, in this figure caption is the first time you introduce Dome A. You should introduce the significance of the Dome A site earlier on in the introduction or methods.

Line 116. You need to be careful with statements like this. As mentioned in an earlier comment, Ri does not directly determine atmospheric stability. Instead, the change in potential temperature with altitude is a direct indicator of stability (see Sect. 2.2 of https://amt.copernicus.org/articles/15/4001/2022/amt-15-4001-2022.html). A layer can have an increase of potential temperature with altitude (indicative of a stable layer), but wind shear still provides some turbulence, and Ri is below the critical value. Change your wording here and throughout the paper to avoid claiming that Ri is directly indicative of stability.

Line 121. As I previously stated, the production of turbulence does not always equate to an unstable atmosphere. A truer statement is that buoyantly driven turbulence often leads to instability, but mechanically driven turbulence often does not lead to instability. In Antarctica, the turbulence is dominated by mechanical rather than buoyant forcings, so I would not make this claim.

Line 126. Why does 1/Ri provide better evidence of atmospheric stability? 1/Ri would provide the same evidence as would Ri. Is it because 1/Ri may be easier to interpret, since larger 1/Ri means more turbulence? Clarify this.

Sect 3. Please explain how 1/Ri profiles were calculated. Do you calculate this at each altitude by comparison with the lowest measurement? Or do you calculate it between consecutive vertical levels?

Fig. 2. Since potential temperature, rather than temperature, is the variable that directly feeds into calculating Ri, I would recommend plotting this figure with potential temperature rather than temperature. Additionally, potential temperature is a more standard and helpful variable used to visual atmospheric stability.

Line 165-168. Do you have any evidence to support this hypothesis? Because, with your reasoning, the opposite theory could also be formed. Make sure you support this hypothesis with evidence, otherwise remove it.

More examples of issue directly inferring stability from Ri:

Line 171

Line 186

Line 214

Line 291-292

Line 358

Line 376-377

Line 379-380

Fig. 4. Why do you show the median profiles from the observations here, but you show the difference between the model and observations for Fig. 2 and 3. I would try to remain consistent, but otherwise give an explanation as to why you show them differently.

Fig. 6. This is difficult to interpret. Please provide more discussion of what is shown in this figure, and what the significance is.

Fig. 7. It is not necessary to include the color bar twice. This would look neater if you just had one centrally located color bar. Also, add latitude numbers.

Fig. 8. It may not be necessary to explain how wind barbs are interpreted, as this is standard practice in meteorology. Additionally, I again suggest just showing the color bar once, to clean up the figure a little bit.

Line 281-283. Give some examples of why one might want to know when the atmosphere is turbulent in Antarctica in order to avoid it. For example, aviation, certain scientific activities, etc.  

Line 351. Explain why a turbulent atmosphere over the ocean is expected. Oceanic waves? Heat flux from open ocean or sea ice leads?

Line 384. Give more examples of why these results will be useful to others, aside from astronomy. Aviation is an important one.

Technical Corrections

Line 11. The statement in parentheses is not grammatically correct. Consider “Ri; a critical parameter which determines the possibility that turbulence could be triggered.”

Line 17. Instead of “gains” perhaps use the word “increases.”

Line 46. It is improper to start a sentence with the word “And”. Remove this word.

Line 46-47. The sentence would read better as “Presently, monitoring a wide range of atmospheric turbulence over the Antarctic continent is tremendously difficulty, while the atmospheric Richardson number…”

Line 47-48. The statement in parentheses is again improper grammar. See my comment on Line 11 above and apply a similar fix here.

Line 48. Should be “calculated from” instead of “calculated by”

Line 49. What do you mean by “sketchy?” Use a more descriptive word or statement here. The word “sketchy” is too colloquial for a scientific journal.

Line 52. Would read better as “However, their research has some specific shortcomings (or problems that need further study)…”

Line 80. It would be more appropriate to say “Sect. 6 summarizes the main findings and primary takeaways of this study.”

Line 92-93. It is not necessary to say “depending on the ascent speed” if you don’t give a range of what the ascent speed could be. Instead, comment that with a typical ascent rate of 5 m/s, and a logging frequency of 1 Hz, the vertical resolution is approximately 5 m.

Line 132-133. Not necessary to again state the time over which the analysis is done, as this is already stated in the methods.

Line 195. This wording is not ideal. I don’t think you should call other researchers “afraid.” Please rephrase to explain why this analysis has not been done before.  

Line 199. Say “Additionally” instead of “Besides.” The word “Besides” does not make sense in this context.

Line 222. Say “which suggests” instead of “this suggests.”

Line 341. Say “shallower” instead of “thinner.” (Also apply this to Line 372).

Line 348. Say “laminar” instead of “calm.” (Also apply this to Line 372).

Line 378. Don’t start a sentence with “And.”

Please see the attached pdf supplement file for my full comments.