This study provides a systematic characterization of Rossby wave activity during the 25 sudden stratospheric warming (SSW) and 31 strong polar vortex (SPV) events that occurred in the period 1979-2021 using space-time spectral analysis. The results reveal the Rossby wave behaviors during two situations of stratosphere-troposphere coupling. Overall, this study is very interesting and worth of publication on WCD. I only have some few concerns or comments.

General comments:

The significance of some results are not robust due to limited composite samples used here. Although the authors made efforts to comprehensively analyze these cases, I think they may use the ensemble runs derived from SNAPSI (Hitchcock et al., 2022) to support the key findings during SSW events, particularly for the ‘rule-of-thumb’ proposed by the authors. The authors may compare differences in the wave activities during control runs and nudged runs.

In addition, as the authors said, using 48 m/s as a threshold value is arbitrary. I suggested replacing it with 1 standardize deviation of zonal wind climatology as the threshold to select SPV events.

Specific comments:

L6: concomitant -> simultaneous

L44: complicated -> complex

L83: ‘SSW events’ should be ‘SPV events’.

L63: What do you mean about this sentence ‘periods around SSW and SPV events are not excluded’? Please clarify it.

L81:The words ‘rapidly’ and ‘rapid’ are not appropriate. The description of ‘transient wave’ is enough to describe the faster wave than stationary wave.

L91: ‘We not here that also’ -> ‘Also note that’

L237: This may be related to stronger stratosphere-troposphere coupling over the North Atlantic Ocean. Please refer to Garfinkel et al (2013) and Zhang et al. (2022).

L258: Is the positive anomaly caused by the internal variability or the sample error of composite cases? Does it also appear in large-ensemble experiments? Please see my general comments.

L325:It is confused why the heat flux co-spectra with higher-wavenumber westward propagating waves for SSW events are so noticeable at 10hPa in the upper stratosphere at which there only occurs wave 1 and 2. Please give more explanations.

L356:This sentence should correspond to Fig. 11a and d.

L366: Fig.11b should be Fig.11a

References:

Hitchcock, P., Butler, A.H., Charlton-Perez, A.J., Garfinkel, C.I., Stockdale, T.N., Anstey, J.A., Mitchell, D.M., Domeisen, D.I., Wu, T., Lu, Y., Mastrangelo, D., Malguzzi, P., Lin, H., Muncaster, R., Merryfield, B., Sigmond, M., Xiang, B., Jia, L., Hyun, Y., Oh, J., Specq, D., Simpson, I.R., Richter, J.H., Barton, C.A., Knight, J.R., Lim, E., & Hendon, H.H. (2022). Stratospheric Nudging And Predictable Surface Impacts (SNAPSI): a protocol for investigating the role of stratospheric polar vortex disturbances in subseasonal to seasonal forecasts. Geoscientific Model Development.

Garfinkel, C.I., Waugh, D.W., & Gerber, E.P. (2012). The Effect of Tropospheric Jet Latitude on Coupling between the Stratospheric Polar Vortex and the Troposphere. Journal of Climate, 26, 2077-2095.

Zhang, J., Zheng, H., Xu, M., Yin, Q., Zhao, S., Tian, W., & Yang, Z. (2022). Impacts of stratospheric polar vortex changes on wintertime precipitation over the northern hemisphere. Climate Dynamics, 1-17.

Review for "Opposite spectral properties of Rossby waves during weak and strong stratospheric polar vortex events" by Schutte et al. WCD

This manuscript by Schutte et al. (2023) uses observations and a novel technique (which has not been applied before to SSWs) to examine the spectral properties of Rossby waves throughout the lifecycles of SSW events and strong polar vortex events. The technique picks up on large spectral changes throughout the lifecycle with SSWs being characterized by a reduction in the eastward phase speeds in the stratosphere before the event, along with an increase in westward phase speeds, before being associated with an overall reduction in all phase speeds sufficiently far after the onset. This is consistent with enhanced upward propagating waves before the onset (although their characterization of this as being due to stationary waves requires further explanation; see my point below), and planetary wave suppression after the onset throughout the stratosphere and troposphere. SPV events seemingly show opposite-signed results. Although the stratospheric response is very clear, the tropospheric response to such events is less clear using this method which I suspect is due to the small number of observed events and thus strong inter-event variability, particularly given the more chaotic nature of the tropospheric flow.

The paper is well-written and I found it novel and interesting to read. I have only minor comments and so that is my suggestion. I do hope the authors will use a longer dataset or model simulations to better test the method, though!

Minor Comments:

Lines 46-49: This sentence is a bit too flippant in its summary of the role of planetary and synoptic waves in the surface impact. 

A large consensus in the community is that something initially brings the stratospheric influence to the surface and maintains an exogenous forcing to the troposphere. The two main such processes are 1) related to the changes in the meridional circulation, initially by the wave-induced meridional circulation during the onset stage (the 'downward control' idea), but later by the radiatively-driven circulation due to the persistent lower-stratospheric anomalies (e.g., Thompson et al. 2006 whom you already cite, and White et al. 2022, JAS). On the other hand, planetary wave suppression throughout the entire column can also provide the continued exogenous forcing (e.g., Hitchcock and Simpson 2016, JAS; Hitchcock and Haynes 2016, GRL). However, to amplify the tropospheric response due to the above mechanisms, it is generally well-accepted that the synoptic wave feedback in the troposphere is necessary to yield the wind dipole associated with the negative NAO (the meridional circulation nor the planetary wave effect can yield the full dipole). Both Song and Robinson (2004) and the aforementioned White et al. (2022) show this downward response being caused by the meridional circulation, but with an additional effect by the planetary waves (though much stronger in Song and Robinson and in Hitchcock and Simpson 2016), followed by a synoptic-wave-induced tropospheric amplification. 

Although this is likely too detailed for your paper introduction, comparing the planetary and synoptic wave effects and determining which is the 'main modulator' of the surface response is not well-founded nor the correct to phrase it, as they both play important, but crucially, very different roles in maintaining the tropospheric response.

Lines 75-76: Did you also use the other parts of the SSW definition defined in Charlton and Polvani? I presume that because you used dates directly from the Butler et al. paper, that you did. But for self-containment maybe state the extra conditions for SSW identification mentioned in the Charlton and Polvani paper. For clarity, the definition makes sure that the winds return to westerly for a 20-day period post easterlies, and must also return to westerly before the end of winter (end of April, I think).

Line 80: Presumably you excluded the 22nd Feb 1979 event because there are not 60 days in that calendar year before the event occurred? Maybe state it directly? 

Line 84: Why is 48ms-1 chosen? As you state, it is arbitrary, but without reading the Oehrlein et al paper, I do not know why it has been chosen? How sensitive are your results to increases or decreases in that value? I would think that a better and less arbitrary criterion would be to use some kind of standard deviation definition (although perhaps that is what the cited paper did already do)

Line 117: Why do you use an extra 10degree in the tropospheric average compared to the stratospheric? For consistency across levels, maybe the same should be used? It is fine to do what you have done, but maybe just clarify why you chose those different bands for the reader.

Lines 145-150: I think this quantity was plotted in figure 2 but it was not clear from the text or figure caption. Can you clarify? Perhaps define this hemispherically-averaged phase speed as a different variable or just make sure to refer to it properly in the figure (also figure 7, for instance).

Line 163: Is there a reason you did not exclude the SSW and SPV event days from the resampling procedure? 

Line 213: You divide the anomaly for a particular SSW or SPV by that season's mean? Or by an overall climatological seasonal mean?

Lines 222-224: To clarify, a stationary wave pattern is suggested because the anomalies are dominated heavily by westward-propagating wave anomalies with a reduction in the climatologically-dominated eastward-propagating anomalies, and so this would lead to a more stationary pattern? I see that you said the reduction of all wavenumbers simultaneously likely indicates a weakening of the background flow, but the 'stationary' part is not clear to me.

Figure 4 (and other relevant figures): Why did you choose 250hPa as the 'tropospheric' level? 250hPa is already in the lower stratosphere at sub-polar latitudes. I guess your latitudinal average of 35-75N will be dominated by the lower latitudes when weighted. But if you stick with 250hPa, can you address how sensitive the results in this and other figures are to surrounding levels?

Lines 232-239: This reduction in upward-propagating low-wavenumber waves strikes me as supporting the idea that planetary waves after an SSW onset become suppressed throughout the entire atmospheric column (not just the stratosphere) in agreement with Hitchcock and Haynes (2016: GRL) and Hitchcock and Simpson (2016; JAS). 

Also, can you clarify why this reduction in the V'V' spectra provides evidence of a more persistent tropospheric flow post onset? I would have thought momentum fluxes would indicate this phenomenon. I understand V'V' to be more of an eddy kinetic energy-type 

quantity and given the reduction at low wavenumbers only, it indicates more of a planetary wave suppression in my eyes. I am happy to be 

proven wrong though!

Line 240: This looks to only be slightly significant at lags 10-20 days and is only sporadically positive at other lags. 

Lines 268-269: yes, but 250hPa is already in the lower portion of the vortex (see my point above).

Lines 273-279: This gradual reduction in the (significant) phase speed anomalies from the middle stratosphere to the lower stratosphere is reminiscent of the downward propagation of critical lines from the upper to lower stratosphere post SSW, a la Matsuno (1971) and Hitchcock and Haynes (2016).  

Figure 9: Any ideas as to why the synoptic waves at k=4+ or so, also show a strengthening of westward phase speeds? To me, I wonder if it essentially represents the breaking up of the vortex and filamentation of potential vorticity streamers from the edge of the vortex as planetary waves break, leading to smaller-scale features. In any case, it would be good to mention the interesting, albeit confusing, synoptic-wave features so high up in the stratosphere.

Lines 322-323: Is this because the vortex has weakened (post SPV maximum) to an extent that it is more receptive to upward-propagating waves

from below?

Grammatical Comments:

Lines 29-32: I would rewrite this opening sentence. It is a little confusing to read and disjointed (especially the part before the colon). The part after the colon I would just write as a new sentence. 

Lines 40-43: The opening sentence is again a bit disjointed. The NAM and AO you put in the first set of parentheses are zonally-averaged themselves, whereas you add about zonally-averaged quantities directly after, and using Hall et al. (2021) as an example. The Baldwin and Dunkerton 2001 and Thompson et al 2006 papers also use zonally-averaged quantities. Multiple sets of parentheses (in this case, 3!) can be confusing and break up the sentence too much. I suggest: 

"The impact of SSW and SPV events on the tropospheric circulation is most often analyzed in terms of circulation indices of zonally averaged quantities (such as the Arctic Oscillation or the Northern Annular Mode, e.g., Baldwin and Dunkerton, 2001; Thompson et al., 2006), or in terms of changes in the frequency of weather regimes (e.g., Charlton-Perez et al., 2018; Domeisen et al., 2020c; Hall et al., 2023)."

Line 121: update end of line to: '...allow ONE to neglect...'

Line 214: change to '... a value twice as large. '

Line 359: 'reflect' --> 'lead to' or 'result in'

References:

Hitchcock, P., and Haynes, P. (2016), Stratospheric control of planetary waves, Geophys. Res. Lett., 43, 11,884–11,892, doi:10.1002/2016GL071372.

Hitchcock, P., and I. R. Simpson, 2016: Quantifying Eddy Feedbacks and Forcings in the Tropospheric Response to Stratospheric Sudden Warmings. J. Atmos. Sci., 73, 3641–3657, https://doi.org/10.1175/JAS-D-16-0056.1.

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

White, I. P., C. I. Garfinkel, and P. Hitchcock, 2022: On the Tropospheric Response to Transient Stratospheric Momentum Torques. J. Atmos. Sci., 79, 2041–2058, https://doi.org/10.1175/JAS-D-21-0237.1.