General comments

The paper “Identification of stratospheric disturbance information in China based on round-trip intelligent sounding system” by Yang He et al. presents statistical analysis of observational data obtained from specific balloon measurements at six sites in China.  The extraction and analysis of the stratospheric gravity wave disturbance is an important topic, as more knowledge on gravity waves and their interactions is needed for the improvements of gravity wave parametrisations. Regarding the methodology of the paper, I am not entirely satisfied. During the procedure, for example, steps leading to reduction of the datasets were applied, without any discussion and verifications on possible impacts on the results. Also, I have the impression that too strong implications are sometimes deduced from rather ambiguous results. The structure of the paper might be improved by moving the methodology out from the result section and adding a discussion section. Finally, as for the language and notation, I think the paper needs to be carefully read through and cleaned.

Specific comments

L91: How large is the integer multiple of the swing period? Could smoothing have an effect on elimination of GWs?

L95: How exactly is defined which data are used and which not (i.e., what is “several hundred meters”)? This might possibly have an impact on the results, as only the cases with certain atmospheric conditions are taken. How do the results change if these limitations are set to be for example stricter?

L106: Can the rising and flat-floating stages be considered to contain concurrent effects? I am thinking whether the conditions could change during the rising or flat-floating motion. How long is the rising stage?

L117: I have no experience with such an analysis but from an intuitive point of view, I have a problem with the definition of the separation direction. If the trajectories were mostly zonal or meridional, I would understand that it makes sense to take this direction. The trajectories depicted in Figure 1 are, however, often in some angle that does not seem to be parallel with either of these directions, so taking the projection to them will modify the multi-order structure function. Did you consider taking some fitted direction of the trajectory as the separation direction?

L166: Discarding some more cases makes me suspicious, these things could really bias the results. Did you study why K(1) is not close to 0 in these cases? Are the trajectories somewhat special? If you make some change to the analysis (for example, taking another separation direction), does this change?

L215: The difference between the distributions might be just an effect of the trajectory directions being more diverse in autumn, i.e., due to the mean flow?

L229: The figures displaying the “intuitively seen” results of the wind speed disturbance do not look convincing to me. Could you argue your observations more, e.g., by highlighting the parts of the plot that should illustrate this fact? Also, I guess that the roughness of the delta u_L sequence should depend on the angle of the trajectory, as the projection to the separation direction could make for example distant points closer to each other, depending on the angle.

L266 and further: “As KHI increases…” – I strongly disagree with this interpretation of the plots. In my opinion, these “trends” are deduced just from a few outliers. In some cases, they are not visible for both seasons, even leading to an opposite “trend” for one of the seasons than the one stated in the text (Figure 7i for autumn). To make these results plausible, I believe that it is necessary to

1. look at the trajectories of these outliers if they are somehow special and
2. test all the previous steps in the analysis that lead to a decrease of number of considered data – maybe, they would produce another group of outliers that might change/support the trend (none of which would support the interpretation).

L287: Does it make sense to average over the area? Did you test for an example that the results are similar to averaging over the actual trajectory, which would be probably the correct but more complicated way?

Technical corrections

L20, L74: Use commas as elsewhere.

L22, L27, L28, L111, L156, L160 and further: Check the notation of gravity waves. GWs is defined in plural but afterwards, often (not always) GW is used for the plural form.

L22: Article needed before wave amplitude.

L23: Use instability instead of unstable.

L27: Plural in general circulation models.

L28: Please formulate more carefully the sentence “The scale of GW is relatively small and…” Just a part of the gravity wave spectra cannot be resolved.

L31: “GW parametrisation…” Add an article or switch to plural.

L34: Use the abbreviation GWs.

L43: Models instead of model.

L44: Some one-sentence explanation of the RTISS system is definitely needed at this place. The description of the three stages is confusing if I do not know that it is some kind of balloon measurement.

L52: In scientific texts, plural for data (“data used in the paper are…”) might be better.

L53: Define the abbreviations of the sites.

L55: I am missing the information on the approximate number of releases in winter and summer.

L64: Description of the colours in Figure 1 (c-h) is missing.

L71: “several hours apart in the vertical direction” What does it mean? How long is the rising and falling – how many values are there?

L74: Define abbreviation for relative humidity (and use it at L77), RH is used further in the text.

L75: Missing article before “meteorological sensor”.

L97: “separation distance direction” is used before it is defined. I suggest using just the distance of the measured points instead of it here. In any case, it would be more suitable to state if the motion is quasi-horizontal or not.

L100: It is not clear to me here what kind of interval you interpolate to (temporal/spatial).

L108: Is the Text S2 available somewhere or is it an old reference? Also, there is no reference to S1.

L110, L114, L120, L155, L159, L172, L174, L175, L176: The math symbols in text (r, r^2, r^3, q) should be in math style.

L115: I recommend moving the sentence “The balloon trajectory…” together with the definition of r (L118) before the second paragraph of the subsection.

L117: Some interpolation already mentioned in section 2.2. Is it the same interpolation or is it something else?

L117: Is the last value of n surely N and not N-1?

L117, L118: It would be better readable if the sentences do not start with a math symbol.

L125: If I understand the equations correctly, Eq. (2) for q=3 is not equivalent to equation (3) unless δu_T is very small, which is probably not the case with your definition of separation direction (might be solved by interpolating to the fitted trajectory direction, as mentioned above). It is not clear in the paper which equation is used as the third order structure function.

L125: Explain δu_L before and omit here. Also, x is not defined.

L125: Dot after the equation.

L126: “a position-independent statistical results” – either omit the article or use singular.

L133: Probably something like “we define” instead of “we choose”. The sentence is not well understandable.

L133: Why does the value of H1 have to be between 0 and 1?

L138, L139: Different meaning for symbols epsilon and l? Renaming would make it more comprehensible.

L149: Is C1 the same as C_1? It is not defined. And again, it is not clear for me why the values are between 0 and 1.

L166: “discard” instead of “discarded some”.

L169: Capital T.

L171: Change “to illustrate” to “we illustrate”.

L173: Article before “third-order structure function”.

L173: “from the third-order structure function” probably accidentally twice.

L173: an r^3 slope

L178: I don’t understand how the GW scale is quantified. According to the previous section, I thought that R_w should be < 5 km?

L180: Consider unifying the axis label style in Figure 2 a – d (changing for example 10^5 to 5 or vice versa).

L180: “The red dots represent negative values” – does this mean that the plot actually displays -S3? Would be more understandable for me in the axis label.

L181: What are the dashed lines in Figure 2d?

L182: Figures 2e and 2d are, to my understanding, not really connected to the remaining subplots in Figure 2 and they are even first referenced after Figure 3. I would consider moving them to a separate figure.

L184: Either “an unstable GW” or “unstable GWs”.

L185: The notation of H1 and C1 in brackets is not defined before, it doesn’t have to be completely clear.

L186: Change “coexist” to “coexisting”.

L199 – L217: I have the feeling that these paragraphs do not fit into the subsection (not about disturbance parameters).

L205: “distinguish between”

L220: Missing description of colours in Figure 4.

L226: “no matter whether”

L227: Maybe change “with lower latitude” to “at lower latitude”?

L242: Wrong description of Figure 6, same as for the previous figure.

L253: Three spaces between “between” and “H1”.

L254: Delete the backslash symbol.

L260: Would be more comprehensible if you state here you are writing about variables from figures 7 d – f.

L264: I would prefer the sentence “Considering…” to be reformulated. For example, “Next, we consider that (…) the Kelvin Helmholtz instability. The ratio of (…) representing the instability is used to explore (…)”.

L264: Explain KHI here + add an article.

L265: “between 15 and 25 km” might be more understandable.

L276: Small o.

L278: Regarded.

L280: Use “aim” instead of “hope”.

L284, L285: What do the words “basically” and “exactly” mean here? I am confused. Does it mean that the release is done approximately at let’s say 23 UTC, so that it arrives upward at exactly 00 UTC? Please reformulate this part. Also, I believe that this information should be rather in the data or methodology part and not in results.

L290: What is the height range where small-scale GWs are detected?

L310: Is correlation coefficient 0.5 from 12 values so significant? How large is the p-value for these levels?

L321: “that is closely related”?

L328: Regarding the right part of the figure, unfortunately, I don’t understand it at all. Could you perhaps consider supplementing some description to the red arrows? On the other hand, I really like the left part of the figure - it is very nice and illustrative and could be very useful for an introductory (methodology) part of the paper.

L344: Add an article before “wave dissipation”.

L357: Appendix is not referenced in the paper.

General comments:

The high-resolution atmospheric sounding from the round-trip intelligent sounding system is an interesting novel option to investigate atmospheric disturbances in the stratosphere. The present study by He et al. applies the structure function and singular measure to these soundings in attempt to quantify the stratospheric small-scale gravity wave (SGW) over China by Hurst parameter and intermittency parameter, and to analyze its relationship with inertia-gravity wave (IGW).

Although the authors’ dataset and observation could be of very high scientific value, the study in its present form suffers from several flaws and I recommend publication pending the following specific revisions.

Specific comments:

1. The dynamics of a sounding platform and its response to atmospheric motions is of necessary knowledge before interpreting atmospheric disturbances parameter such as structure functions and intermittency parameter. In the present case, the expected behavior of the balloon in the flat-floating phase remains unclear. From the introduction (L84-89), it is implied that this phase is characterized by quasi-horizontal motion similar to superpressure balloons (Hertzog et al., 2002; Boccara et al., 2008). Whether their detection principles are consistent? the authors should further explain the uniqueness of the detection system, and strongly recommend that the dynamic process of detection be further elaborated.

2. The authors carry out their structure function analysis in space coordinate (longitudinal distance) after interpolation, in my intuition, time is the appropriate and most commonly used coordinate in which to perform the analysis similar to a quasi-Lagrange measurement. Of course, this may be treated differently from the linear fitting mentioned in the first point, I am well aware that different methods have their own rationality and limitations, and it may be interesting if the author can compare the results of different methods here. For example, compare the results in space and time coordinates? If the data can be analyzed in time coordinates, there is no need for interpolation since the measurements were sampled regularly.

3. L95-L97: The flight segments used for analysis should be chosen carefully in order to be quasi horizontal. For example, in part of the profile in Figure A1, after the burst of the outer balloon, the platform adjusts to its equilibrium level a few hundred meters below the burst altitude. In my understanding, the authors are nevertheless using that initial segment in their analysis, even though it is contaminated by altitude variations. I would recommend to discard it.

4. L115-120：Using structural functions, the calculation of the longitudinal velocity (Parallel to separation distance), requires careful consideration. Why not directly use the original flat drift data? what is the purpose of decomposition? Specifically, what criteria is used for reference to decompose according to the longitude direction or the latitude direction? Can the data analysis performed after the decomposition still represent the characteristics of the fluctuation?

5. L154-L161: Why was the gravity wave scale chosen to be 5km? Considering the different horizontal resolutions of different data, the specific scale of gravity waves selected should be different. Therefore, I understand that the author here should choose the wave parameter closest to 5km, and suggest that the author give the statistical distribution results of the actual scale. In addition, considering that the flat-floating distance is long enough, why not choose a longer scale, and whether this will cause a difference in the analysis results?

6. L167-L169: How does the author determine this conclusion? It is suggested that the author add relevant explanations (figures or tables) in this work.

7.  In Figure 2, according to my understanding, the Hurst parameter H1 and intermittency parameter C1 both come from the calculation of the slope. If so, the slope of H1 is easily understood, which comes from the linear fitting of the structure function spectrum in Figure 2a. However, how is the slope of C1 calculated in Figure 2d?Also, how to determine the premise of Eq. (9)? Given a nonstationary random atmospheric process with stationary increments that is scale invariant from some outer scale R down to some inner scale η, I wonder whether the relationship K(1)=0 can always be satisfied when calculating the intermittent parameter C1? In other words, how is approximately close to 0 (L166) defined, and does it eliminate part of the result?

8. L173-L175: “From third-order structure function, a downscale energy cascade (from large to small scales) can be seen from the third-order structure function”. How do you know this conclusion? Do red dots (negative values) represent downscale energy cascade, corresponding to a drag of gravity wave on background, while blue dots (positive values) denote upscale energy cascade corresponding to an increase in turbulent kinetic energy? I think the authors should use more approachable language that explains its physical meaning

1. L180: The curve in Figure 2d increases as q increases. Could you make more explanations on the physical meaning of K(q)? What does the larger or smaller K(q) (i.e., intermittent parameter) mean?

1. l90-192: This statistical result is very interesting, and it is recommended that the author supplement its physical explanation.

1. Explanation of the jagged structure in the spectral shape.

By comparing the results of Figure 2 and Figure 3, we can see some differences in the results:

1) Compare (a) in Figure 2 with (a) and (e) in Figure 3, multi-order structure function has obvious spectral shape difference on large scale (larger than 10km). What is the difference behind this difference in the actual observed wind field? It is suggested that the authors add relevant explanations.

2) Compare (b) in Figure 2 with (b) and (f) in Figure 3, third-order structure function has obvious the sawtooth structure in the spectral shape in Figure 3 (b) and (f), while the spectral shape in Figure 2 (b) is much smoother. Can sawtooth be considered a special spectral structure that appears when atmospheric disturbances are strong?

1. L199-L206: I think the author's method here for calculating inertial gravity waves and turbulence is too simplistic. The author is strongly advised to further elaborate on the details. Taking into account the specific nature of the journal, detailed and complete discussion is encouraged.

For example, what is the calculated altitude interval of the turbulence parameter? Are the statistical results from the regional average or the regional sum?

In addition, considering that there are already many observations of inertial gravity waves and turbulence, it is recommended to increase the comparison between the relevant parameters of this article and the existing results to further illustrate the rationality and reliability of the results.

1. L255: In Figure 7, the authors illustrate the correlation between the different parameters by drawing a scatter plot. However, due to the limited sample size, some linear relationships are not obvious, which makes some of the author's statements seem a little absolute. For example, L267-L270: The trend of increasing first and then decreasing is not obvious, so it is suggested that the author delete this expression.

Also, If the author tends to discuss the relationship between inertial gravity waves and small-scale gravity waves, the relatively absolute wording is modified to a mild expression. Because in the present work of the authors (if the number of current observations cannot be significantly increased), due to the limitations of the sample, it is also necessary to discuss the possibility that the maximum or minimum value of the edge region in the scatter results is caused by the wild value.

1. L282-L283: “Based on the ERA5 reanalysis data, the ozone mass mixing ratio (OMR) and PV at different pressure layers that matched the detection are selected”

How this is matched needs to be further explained.

1. L354: What exactly do fingerprints mean here?

Minor comments:

1. L65: The two colors in Figure 1 are not marked with seasons, please add.

1. L168: Where is Text S2?

1. L200: 18–25km → 18–25 km

1. L213: “critical layer filtering” should be further explained, for example, how are gravity waves affected here by the background wind field.

1. L220: The display in figure4 e and f is incomplete and the authors should readjust the boundary values.

1. L220: The two colors in Figure 1 are not marked with seasons, please add.

1. L235: The size of the ordinate scale in Figure 5b is inconsistent with other subgrams.

1. L253: between H1 → between H1

1. L321-L324 100hPa → 100 hPa, 10hPa → 10 hPa

Please check for similar errors elsewhere.

Unfortunately, neither my abilities nor my time allow me to find all the grammatical problems throughout the manuscript. Therefore, I ask the authors to check the full text by themselves, and preferably seek advice from a native English speaker.