This work considers the role of gravity waves in the evolution of the sudden stratospheric warming (SSW). In particular, the author makes use of the hydrodynamic equations to quantify the reflection coefficient of vertically propagating gravity waves (GWs) across the tropopause and stratopause during normal winter conditions compared with during an SSW in which the polar winter stratosphere warms significantly and the polar winter mesosphere cools. Consistent with previous work, the study suggests that the modification of GW flux from the troposphere to the stratosphere and from the stratosphere to the mesosphere lead to the anomalous temperatures observed in the polar stratosphere and mesosphere. The author suggests that during an SSW, the reflection coefficient significantly increases at the tropopause, leading to significantly fewer GWs entering the stratosphere from below, while the reflection coefficient increases at the stratopause compared with the no-SSW case. It is unclear how the stratopause is being defined, and how the temperatures used to define the reflection coefficient of GWs are chosen. The study could be worthy of publication as it will likely provide new insight into how GW forcing in the stratosphere and mesosphere is modified during an SSW. The study is well written, but some things could be clarified and improved. I recommend major revisions.

Overall, the introduction needs to be reworked and additional references should be added. The first paragraph is basically one long paragraph, with the exception of the transition to Section 2. More background should be given on what drives the temperature in the polar winter stratosphere and mesosphere, both during non-SSW and SSW conditions, as these temperatures drive the changes in GW reflectivity that is the crux of the paper. In particular, there is no mention of the global residual circulation nor how GW breaking relates to the descent and warming in the stratosphere/lower mesosphere, and ascent in the middle and upper mesosphere observed during non-SSW conditions. Also, explain how modifications to GW forcing leads to the strong descent and warming in the middle and lower stratosphere.

My other significant concern is in regards to the temperatures you are using for the tropopause/stratosphere/stratopause to define the parameter s, which drives the primary findings of this work. Where are these temperature values coming from, and what latitude/altitude are they referencing? Maybe more confusing is that you use a single temperature to represent each of these, and especially so for the stratosphere given the broad range of temperatures typically found there).

On line 150, you say that the stratosphere temperature can rise from 240 K to 290 K during an SSW. Do you have a reference for this? Manney et al. (2008) and France et al. (2012a, b) show the highest stratospheric temperatures during an SSW to be ~280 K. Also, polar-cap-mean temperature anomalies associated with SSWs are only on the order of 20 K (Vignon and Mitchell (2015). A 50 K increase in temperature is only valid if you consider the “maximum temperature anomaly (that occurs within the range of 30–90° latitude and 300 to 1hPa)” (Butler et el., 2017).

Another concern is that it is unclear how you define the stratopause. On Line 172 you say, “During the SSW, the stratospheric temperature rises to 290 K, causing a change in the parameter s =T1/T2, which becomes 1.1”. This implies that the stratosphere is warmer than the stratopause. Typically, the stratopause is defined as the layer of highest temperature, so during an SSW, the stratopause descends with the warming. Maybe you could consider referring to specific altitudes in your analysis, like 20 km, 40 km, and 50 km.

Finally, it is important to note that there is not a discontinuity in temperature across the tropopause or stratopause. Your analysis seems to require a large discontinuity across the boundary, but you are using layers 10s of km apart.

 Minor comments:

Line 14: “Temperature increases with ozone concentration”. Ozone actually peaks in concentration in the lower stratosphere (e.g., Gotz, 1933), but the warming peaks at the top of the stratosphere due to the strong absorption of UV (e.g., Pendorf, 1936).

Line 20: Also consider citing Matsuno (1971)

Lines 21-22: “rapid descent and warming of the air in polar latitudes, mirrored by ascent and cooling above the warming.” What altitudes?

Line 22: “…mirrored by ascent and cooling above the warming.” Ref: Limpasuvan et al. (2016)

Line 24: “About six times per decade” Ref: Charleton and Polvani (2007)

Line 33: “These effects span both hemispheres” How so? You could point to changes in the summer mesospheric winds and gravity wave filtering (e.g., Gumbel and Karlsson 2011; Karlsson and Becker 2016; Körnich & Becker, 2010), inertial instability and growth of the summer hemisphere 2-day wave (Lieberman et al., 2023; France et al., 2018; Sato et al., 2023), and resulting polar mesopause warming and reduction in polar mesospheric clouds.

Line 46: What did Cullens and Thurairajah (2021) find?

Line 51-53: The two “important points” here aren’t novel. It has been long understood that GWs play a critical role in the evolution of SSWs, e.g. Holton (1983), Liu (2017). Instead note how your findings provide new insight into how the temperature anomalies associated with SSW conditions modify the spectrum of GWs that propagate across the tropopause and stratopause.

Lines 225-228: Is this relevant for the dynamically-driven, polar winter stratosphere, since it’s in the dark?

Minor Changes:

Line 25: change “devided” to “divided”

Line 103-104: Consider rewording this sentence.

Brunt–Väisälä is misspelled in the Figure 1 caption and on Line 86.

Line 190: “atmosphere” is misspelled

References:

Butler, A. H., Sjoberg, J. P., Seidel, D. J., and Rosenlof, K. H. (2017), A sudden stratospheric warming compendium, Earth Syst. Sci. Data, 9, 63–76, https://doi.org/10.5194/essd-9-63-2017.

Charlton, A. J., and Polvani, L. M.: A new look at stratospheric sudden warming. Part I: Climatology and modeling benchmarks, J. Climate, 20, 449–469, doi:10.1175/JCLI3996.1, 2007.

France, J. A., V. L. Harvey, M. J. Alexander, C. E. Randall, and J. C. Gille, (2012a), High Resolution Dynamics Limb Sounder observations of the gravity wave-driven elevated stratopause in 2006. J. Geophys. Res., 117, D20108, doi:10.1029/ 2012JD017958.

France, J. A., V. L. Harvey, C. E. Randall, M. H. Hitchman, and M. J. Schwartz (2012b), A climatology of stratopause temperature and height in the polar vortex and anticyclones, J. Geophys. Res., 117, D06116, doi:10.1029/2011JD016893.

France, J. A., and Coauthors, (2018) Local and remote planetary wave effects on polar mesospheric clouds in the Northern Hemisphere in 2014. J. Geophys. Res. Atmos., 123, 5149–5162, https://doi.org/10.1029/2017JD028224.

Gumbel, J., & Karlsson, B. (2011). Intra- and inter-hemispheric coupling effects on the polar summer mesosphere. Geophysical Research Letters, 38(14), L14804. https://doi.org/10.1029/2011GL047968.

Holton, J. R. (1983), The influence of gravity wave breaking on the general circulation of the middle atmosphere, J. Atmos. Sci., 40, 24972507.

Karlsson, B., and E. Becker (2016), How Does Interhemispheric Coupling Contribute to Cool Down the Summer Polar Mesosphere?. J. Climate, 29, 8807–8821, https://doi.org/10.1175/JCLI-D-16-0231.1.

Körnich, H., & Becker, E. (2010). A simple model for the interhemispheric coupling of the middle atmosphere circulation. Advances in Space Research, 45(5), 661–668. https://doi.org/10.1016/j.asr.2009.11.001.

Lieberman, R. S., et al. (2021), The Role of Inertial Instability in Cross-Hemispheric Coupling. J. Atmos. Sci., 78, 1113–1127, https://doi.org/10.1175/JAS-D-20-0119.1.

Limpasuvan, V., Y. J. Orsolini, A. Chandran, R. R. Garcia, and A. K. Smith (2016), On the composite response of the MLT to major sudden stratospheric warming events with elevated stratopause, J. Geophys. Res. Atmos., 121, 4518–4537, doi:10.1002/2015JD024401.

Liu, H.-L, (2017), Gravity wave variation from the troposphere to the lower thermosphere during a stratospheric sudden warming event: A case study. SOLA, 13A, 24−30, doi: 10.2151/sola.13A-005.

Manney, G. L., et al. (2008), The evolution of the stratopause during the 2006 major warming: Satellite data and assimilated meteorological analyses, J. Geophys. Res., 113, D11115, doi:10.1029/2007JD009097.

Matsuno, T. (1971), A dynamical model of the stratospheric sudden warming, J. Atmos. Sci., 28, 1479–1494.

Sato, K., Tomikawa, Y., Kohma, M., Yasui, R., Koshin, D., Okui, H., et al. (2023). Interhemispheric Coupling Study by Observations and Modelling (ICSOM): Concept, campaigns, and initial results. Journal of Geophysical Research: Atmospheres, 128, e2022JD038249. https://doi.org/10.1029/2022JD038249.

Vignon, E., Mitchell, D.M. (2015), The stratopause evolution during different types of sudden stratospheric warming event. Clim Dyn 44, 3323–3337, https://doi.org/10.1007/s00382-014-2292-4