The study focuses on the response of atmospheric quasi-5-day oscillations (Q5DOs) to sudden stratospheric warmings (SSW). Westward and eastward traveling Q5DOs with zonal wavenumber 1 and 2 have been previously reported to enhance during some SSW. However, it has been difficult to accurately estimate the amplitude of the traveling Q5DOs under the presence of quasi stationary planetary waves (SPWs) whose amplitude can also rapidly change during SSW. To overcome this issue, the authors introduced a new methodology to determine the amplitude of the traveling Q5DOs that avoids the contaminations from SPWs. The authors applied the new method not only to synthetic data but also to the geopotential height measurements from Aura/MLS during major SSW events in 2006-2021. It is demonstrated that the amplitude of the traveling Q5DOs could be overestimated or underestimated during SSW if the conventional method was used.

The paper is well written and logically structured. The new method is well explained. The validity of the new method is demonstrated using synthetic data, and the limitation of the method is appropriately addressed. The comparison of the traveling Q5DOs obtained from the new and conventional method highlights the importance of taking into account the variability of SPWs during SSW.

I recommend this paper for publication basically in the present form. The following are minor comments that I believe the authors could easily address before publication:

Figure 1

The label for the horizontal axis is missing.

line 180

"does" should be "is".

line 187 "((Ak(t))"

One "(" should be removed.

line 235 "the original data Y'(x,t)"

Y' is not the original data. Rather, it is a reconstruction of the original data without rapid changes of SPWs.

line 291 "The fitting result is marked at the end day of each 20-day window."

This information should be provided when the 20-day window was first mentioned (line 142), because the information is needed in order to understand the timing of amplitude changes depicted in Figure 1.

Figure 6

It should be mentioned in the figure caption that these are composite results obtained from 8 major SSWs. Also, it would be informative if the authors could indicate either in the figure caption or in the figure itself that these results represent "new" minus "original", not the other way around.

Comments on “A new methodology for measuring traveling quasi-5-day oscillations during SSWs based on satellite observations” by Ma et al.

Summary

Ma et al. (2022) tried to establish a possible new methods of identifying travelling planetary waves in the stratosphere during sudden stratospheric warmings by removing the possible interference of stationary planetary waves. Compared with the traditional method, the authors claim they have several improvements in the identification method. However, a significance test is lack in the paper, and readers might wonder to what extent the results are trustworthy. The difference between the new method and old is also not large, which is also shown for the synthetic (man-made) data from Figures 1-3. Further, this paper focuses more in the mesosphere and upper stratosphere. The largest improvement is very likely not in the lower stratosphere. The results from 100 hPa to 10 hPa should be shown if possible. I did not see any discussion on the origin of the enhanced planetary waves during SSWs. Do they come from the lower atmosphere like troposphere or generate in the middle atmosphere directly? Due to those issues, I would suggest a substantial revision before the paper can be considered.

Major comments

1. The importance and significance of this study is not very persuasive. Only removing the interference of the stationary waves, I find it is hard to find any novelty of the results. The authors might add more discussion about the possible application of this new methods. Further, the stationary waves are much stronger than the travelling waves in their amplitudes. What is the ultimate aim of extracting the travelling the travelling wave amplitudes?

2. The difference between the old method and the new method is not very evident, especially for the synthetic method. If the authors have to present an example, why not use the real observation? The example shows that the curves extracted have some sawteeth, which might be a problem.

3. I am more concerned about the stratosphere. The amplitudes of the decomposed stationary waves and travelling waves in the stratosphere is more interesting, because SSWs occur in the stratosphere.

4. The origins of the stationary waves and travelling waves are worth mentioning in the paper. After reading, I did not find any information about the possible generation mechanism of the travelling and stationary waves in the middle atmosphere. Do all of them come from the troposphere? Is there any other mechanism of generating the travelling and stationary waves in the stratosphere and mesosphere?

5. The robustness of the results is a big problem. Can you provide any test for the composite difference?

Specific Comments

1. L46: This review paper was published in 2021. Changed to “Baldwin et al., 2021”

2. L47: two temperatures appear in this phrase, consider to rephase this sentence.

3. L54-56: There are too many publications discussion this point. Suggest to add more recent ones.

4. Figure 1. Please add the axis title for the x-axis. There are some sawtooth-shaped points for the extracted curves in Figure 1c, 1d. Can you present some explanation. Is there any method to remove those sawteeth in those plots?

5. L180: this criterion does not suitable for the … => …is not…

6. Figure 2b, Figure 3c, 3d: Similar problem as for Figure 1.

7. L310: The SSWs before 2013 were also studied in Liu et al. (2019; doi: 10.3390/atmos10110679) and Rao et al. 2019 (Table 1; doi: 10.1029/2019JD030900)

8. L336: Because we did not have the observations of the decomposed wave amplitudes, it is not strictly true to regard the results from the new methods as the baseline. But there is possibility that the amplitude in the old method is overestimated.

9. L352-353: If we use the old method as the baseline, the conclusion is reversed. The authors should be careful and cautious to summarize. I suggest to add more discussion. If there are some observed amplitudes for all waves, this comparison is more meaningful. Using the new method as the baseline, the old method is hypothesized to have problems. This bias might be not true.

10. Figure 6: Because this is a composite picture, I suggest to add the significant test. The largest problem of the paper is lack of test.