The paper "Explaining the period fluctuation of the quasi-biennial oscillation" by Kim is an excellent work that addresses the long standing issue of explaining the variations in the length of the QBO period. Explaining variations of the QBO period are of great interest given the relevance of the QBO as one of the major modes of atmospheric interannual variability that has effects not only in the tropics, but also on the surface weather and climate in the extratropics. Several authors tried to explain variations of the QBO period by correlation with the solar cycle. Analysis of longer data sets, however, were less conclusive. The suggestion in this work, relating QBO period changes to variations in the forcing by small scale (gravity) waves, is therefore an interesting new explanation. The author presents a convincing chain of arguments for this mechanism.

The paper is very well written and the figures are adequate and of good quality.

The paper is therefore recommended for publication in ACP after minor revisions.

Further, the paper is recommended to be highlighted in ACP.

My main comment is that some more discussion should be added to further strengthen the paper and to provide a somewhat broader view.

Detailed comments are given below.

MINOR COMMENTS:

(1) In the introduction:

It should be mentioned that several papers write about the QBO period depending on the 11-year solar cycle (e.g., Salby and Callaghan, J. Climate, 2000), while analyses using longer data sets are less conclusive (e.g., Fischer and Tung, JGR, 2008; Kren et al., ACP, 2014).

Variations of wave mean flow interaction as an alternative mechanism being responsible for QBO period variations is therefore quite convincing.

Do you think that wave momentum fluxes near the tropopause could be affected by the solar cycle and thereby contribute to QBO period variations related to the 11-year solar cycle?

Salby, M. and Callaghan, P.: Connection between the Solar Cycle and the QBO: The Missing Link, J. Climate, 13, 2652-2662, doi:10.1175/1520-0442(1999)012<2652:CBTSCA>2.0.CO;2, 2000.

Fischer, P. and Tung, K. K.: A reexamination of the QBO period modulation by the solar cycle, J. Geophys. Res., 113, D07114, doi:10.1029/2007JD008983, 2008.

Kren, A. C., Marsh, D. R., Smith, A. K., and Pilewskie, P.: Examining the stratospheric response to the solar cycle in a coupled WACCM simulation with an internally generated QBO, Atmos. Chem. Phys., 14, 4843–4856, https://doi.org/10.5194/acp-14-4843-2014, 2014.

(2) l.54, 55: Did you use ERA5 model level data, or pressure level data provided by ECMWF?

(3) l.67-70:

Please explain in more detail how wave momentum fluxes and in particular phase speeds are determined. For phase speeds the wave frequency is needed.

In l.68 it is mentioned that 2D FFT was applied for this. Usually, this requires windowing in the time domain. How was this performed? How many days were combined to perform the 2D FFT?

(4) l.120: It could be mentioned that some observational evidence for critical level forcing as the main main mechanism for the gravity wave forcing of the QBO is seen in the gravity wave spectra shown in Ern et al., JGR, 2014.

(5) After l.212:

You should give some reasoning why the descent of the QBO westerly phase is much more continuous than the descent of the QBO easterly phase.

Do you think that this is a combination of:

(a) a weaker seasonality in the sources and low-altitude filtering of the small scale waves, and

(b) large scale Kelvin waves contribute significantly to the downward propagation of the QBO westerly phase (Ern and Preusse, GRL, 2009; Kim and Chun, ACP, 2015b). Possibly, large scale Kelvin waves may have a different seasonality than the small scale waves, and the dissipation mechanism of large scale Kelvin waves is mainly radiative damping, and not critical level filtering as for the small scale waves (Ern et al., ACP, 2009; Krismer and Giorgetta, JAS, 2014).

Ern, M. and Preusse, P.: Quantification of the contribution of equatorial Kelvin waves to the QBO wind reversal in the stratosphere, Geophys. Res. Lett., 36, L21801, https://doi.org/10.1029/2009GL040493, 2009.

Ern, M., Cho, H.-K., Preusse, P., and Eckermann, S. D.: Properties of the average distribution of equatorial Kelvin waves investigated with the GROGRAT ray tracer, Atmos. Chem. Phys., 9, 7973-7995, https://doi.org/10.5194/acp-9-7973-2009, 2009.

Krismer, T. R. and Giorgetta, M.: Wave forcing of the Quasi-Biennial Oscillation in the Max Planck Institute Earth System Model, J. Atmos. Sci., 71, 1985-2006, https://doi.org/10.1175/JAS-D-13-0310.1, 2014.

(6) l.189/190: This is not entirely true:

It has been pointed out before by Ern et al. (2014) that during easterly shear gravity wave forcing in satellite observations and in estimates from reanalysis occurs in a series of bursts in accordance with the stepwise descent of the easterly QBO phase, while gravity wave forcing acts more continuously during westerly shear.

(7) l.227-232: Some discussion about how realistic ERA5 resolved small scale waves are, and whether this matters, should be added:

It was shown by Preusse et. al. (2014) that convective gravity waves in the ECMWF model are not very realistic and could not be traced back to potential sources. Similarly, Okui et al. (2023) showed that in another gravity wave permitting model (JAGUAR) the agreement between model and AIRS observations in convectively dominated regions is poor.

Therefore it should be noted that for the mechanism steering the QBO period it is likely not required that the representation of convective gravity waves in ERA5 is overly realistic, as long as the spectrum of gravity waves contains the range of phase speeds interacting with the QBO. This is also confirmed by Fig.5d showing the zonal wind tendency with the contribution of advection subtracted.

Preusse, P., Ern, M., Bechtold, P., Eckermann, S. D., Kalisch, S., Trinh, Q. T., and Riese, M.: Characteristics of gravity waves resolved by ECMWF, Atmos. Chem. Phys., 14, 10483-10508, doi:10.5194/acp-14-10483-2014, 2014.

Okui, H., Wright, C. J., Hindley, N. P., Lear, E. J., & Sato, K. (2023). A comparison of stratospheric gravity waves in a high-resolution general circulation model with 3-D satellite observations. Journal of Geophysical Research: Atmospheres, 128, e2023JD038795. https://doi.org/10.1029/2023JD038795.

(8) l.239, 240:

Please add data availability statements for ERA-Interim and MERRA2 that are used in Appendix B. Further, a statement for JRA-3Q should be added if JRA-3Q results will be provided in the revised manuscript.

TECHNICAL COMMENTS:

l.132: in independece variables -> in additional independent variables

The paper Explaining the period fluctuation of the quasi-biennial oscillation is an interesting work investigating the connection between variations in the length of the QBO period and variation of small-scale waves.  

The paper is well-written and presents a compelling argument that variations in small-scale waves are the dominate drivers of the variation in QBO descent rates. After minor revisions towards justifying choices made in the analysis, the paper is recommended for publication in ACP. 

- Hampson and Haynes 2004 posits the SAO to be a possible of the period fluctuation of the QBO (as well as upwelling and wave forcing). Can this analysis also investigate this possibility?

- Figure 2: To further emphasize the argument, it would be nice to see the W-descent period plotted here as as well, even if varies little.

- Why use monthly rather than weekly means? In (page 5, line 107) the limitations of lower frequency sampling is noted.

- 4.1, page 6, 120-133: Please justify choice of F70 (rather than say, F50). Do these show similar annual evolution? Similarly, comment on column averaged w* rather than w* at several levels. In particular, I would naively expect that height at which w* is measured/regressed would matter for descent rates.

- page 6, 138-139: Please clarify the phrase "the selected time series were standardized."

- Figure 5 (and similar): Could the y-axes be adjusted to be consistent throughout the figure? I think this would aid in comparison between panels 5d and 5e greatly. 

- Figure 5 (and similar): Can comment on why the wave forcing estimates (panels d and e) appear to be "out of phase" with one another in the first half of the year? If the variations in wave-forcing are primarily driven by the seasonal cycle, I would expect this not to be the case. (Something like ENSO perhaps?).

- Appendix A: I don't understand why we get to separate the purple and orange lines, as they seem to "start" at the same place.