This paper uses reanalysis data primarily ERA-5 data to determine if stratospheric circulation branches may be defined based on wave-forcing. Three science questions are posed: (1) Can different branches in the stratospheric circulation be dynamically defined based on the wave driving? (2) Did different branches of the stratospheric circulation change differently over the past decades? (3) How robust is the representation of the circulation structure and its changes in different reanalyses? Results identify two robust branches: a deep branch predominantly driven by waves with wavenumbers 1 to 3 and a shallow branch predominantly driven by waves with wavenumbers 4 to 180. Results also find a long-term trend in these branches.

My main issue is that the paper performed the calculations based on a definition of atmospheric waves solely in terms of wavenumber. This paper quantifies the contributions of atmospheric waves on these deep and shallow circulation branches. The waves are separated based on their wavenumbers. There’s a category of waves comprising those with wavenumbers 1 to 3 and another for waves with wavenumber 4 to 180. There is no mention of phase and periodicities. Taking this approach, the paper doesn’t properly decompose the dynamical variables into real physical atmospheric wave phenomena. Hence, there is questionable physical meaning/significance to the results.

The deep and shallow circulation branches that are reported in the introduction seem to allude to winter circulation. Hence, a proper analysis should’ve focused on real physical planetary-scale waves (e.g. wave-1 VS wave-2 and/or Stationary vs travelling waves) that are known to occur when these branches form. The analysis should have involved processing daily reanalysis data. The paper actually doesn’t clearly state how the problematic decompositions are made. Some sections indicate the decomposition was done on monthly-means which isn’t sufficient. Either way, defining waves solely in terms of wavenumber was a major flaw. Consequently, the analysis of long-term changes are rendered wrong. Owing to this, I cannot recommend this paper for publication. I suggest the authors take guidance from papers like Yasui et al [2021] and Koval et al [2023] on how to properly quantify the role of atmospheric waves on any middle atmospheric phenomena. You’ll see all of them properly acknowledging different kinds of physical planetary-scale waves (e.g. Rossby waves, kelvin waves, etc). 

Other issues:

• This paper is centered on the deep and shallow circulation branches that are centered on a TAL between 20 N/S and 40 N/S. In the introduction, the paper acknowledges previous studies identifying shallow and deep branches in the stratospheric circulation. However, the science questions made it seem as though this paper aimed to find other very distinct kinds of circulation. The science questions need to be re-written to clarify that this paper still focuses on these deep and shallow circulation branches.
• Add a paragraph at the end of section 2.2 that explains how each science question can be answered using these parameters (and any accompanying methodology)? This will help readers immediately know what to look out for.
• The authors need to introduce figures first before reporting on results found in the figures.
• The authors need to make use of the mathematical symbols of terms (that they already introduced). Some sections are too wordy because instead of using the short-cut symbols, the authors still write the complete name/phrase of the parameter.

References:

Koval, A. V., Toptunova, O. N., Motsakov, M. A., Didenko, K. A., Ermakova, T. S., Gavrilov, N. M., & Rozanov, E. V. (2023). Numerical modelling of relative contribution of planetary waves to the atmospheric circulation. Atmospheric Chemistry and Physics, 23(7), 4105-4114.

Yasui, R., Sato, K., & Miyoshi, Y. (2021). Roles of Rossby waves, Rossby–gravity waves, and gravity waves generated in the middle atmosphere for interhemispheric coupling. Journal of the Atmospheric Sciences, 78(12), 3867-3888.

Review for ‘a dynamical separation of deep and shallow branches in the stratospheric circulation’ by Rasul et al.

This work uses 4 reanalysis data to separate the deep and shallow branch of the Brewer-Dobson circulation, concluded that the shallow branch is mainly driven by wave number smaller than 180, and the deep branch is mainly driven by wave number larger than 180. The past trend over 1980-2017 is also presented. Overall, the analysis of this work is clear, and the paper is well written. I recommend accept this work after a minor revision.

Major comment:

The trend that the authors calculated from all reanalysis data over 1980-2017 are not statistically significant. I think this might because over 1980-2017, the Brewer-Dobson circulation could be divided into two eras with an opposite trend: slower during 1980-2000, and faster during 2000-2017 (Polvani et al., 2018, Fu et al, 2019). I suggest that the authors check the trend over the individual time periods.

Also, throughout of this paper, there are too much wording like ‘maybe’, ‘appears’, which sounds not very scientific and professional, please try to avoid it.

Specific comments:

Line 31, ‘two-way mixing’: need citations

Line 50 ‘the stratospheric circulation is expected to increase’: ‘increase’ could be misleading, ‘strengthen’ is better

Line 116 ‘EP flux’: needs a citation here

Equation 4: a more detailed calculation method should be described here. Do you calculate the EP flux of each wave number, and then calculate the mean value for wave 1-3, and 4-180? Do you need to perform an inverse Fourier transform from the wavenumber-frequency domain to longitude?

Line 133 ‘nyquist criterion’: citation here.

Line 172: DeltaT = 86400s. I think to make the calculation balanced; the unit should be 86400 s/day. And there should be a space between the number and the units. Please also check other numbers in this manuscript.

Figure 1 caption: Is white contour arrows only in figure 1a, and black contour arrows only in figure 1b-c? Why choose to compare different variables?

Line 179 ‘the wind threshold’: is there a relevant citation?

Line 185: this sentence is not Grammarly correct.

Figure 2: green line: you might want to name it ‘TEM residual’ instead of ‘TEM’ to avoid possible confusion.

Line 240: ‘ERA5 is able to resolve gravity waves better than other reanalysis’: need a citation here

Line 267: ‘we expect a higher..’: can you explain more about this sentence?

Figure 6: it will be helpful to include error bars to the mean value?

320: ‘compareed’ typo.

429: ‘we find out the deep branch’, the deep branch of the Brewer-Dobson circulation.

References:

Polvani, L. M., Abalos, M., Garcia, R., Kinnison, D., & Randel, W. J. (2018). Significant weakening of Brewer-Dobson circulation trends over the 21st century as a consequence of the Montreal Protocol. Geophysical Research Letters, 45, 401–409. https://doi.org/10.1002/2017GL075345

Fu, Q., Solomon, S., Pahlavan, H. A., & Lin, P. (2019). Observed changes in Brewer–Dobson circulation for 1980–2018. Environmental Research Letters, 14(11), 114026.