The referees have provided comments on your revised paper. Two referees (1 and 3) are now recommending accept after minor revision, though referee 1 sets more demanding conditions that referee 3. Referee 2, on the other hand, remains unconvinced by the robustness of the relationships between various physical quantities that you claim, and continues to recommend rejection.

Given that there are now 2 referees out of 3 in favour of publication, I am tending towards accepting this paper, but only after you have made further revision to address all Referees’ comments and the following in particular:

(i) Referee 1 raises a good question about why you have not shown results for a larger set of warmings. I might correspondingly ask why you have chosen to show composites in figure 5 which are identical to those already presented in Kodera (2006) when actually a further 10 years or so of data is now available and could be exploited.

(ii) Referee 2 is unconvinced by the relationships between physical variables that the paper claims to identify, is concerned about statistical significance and is skeptical of your claim that ‘convective overshooting clouds show a direct relationship to lower stratospheric upwelling at around 70-50 hPa’. (Note that when this referee refers to CALIPSO results in Fig 2 I think they mean CALIOP results in Fig 3.)

Please can you therefore provide a revised manuscript that addresses the referees comments as clearly as possible, together with itemised replies which make it clear how you have addressed each comment or justify why a comment has been ignored. I hope that after this I will feel that the paper is close enough to being publishable that I will not need to send it to referees again.

I have looked through the paper carefully myself and make the additional comments below. Again please can you address these as far as possible in your revision.

p2 l26: ‘how stability affects anvil cloud top height’ — stability at what level? lower stratosphere?

p2 l30: Eguchu et al (2014) — please update reference (in reference list) to give details of publication in ACP (not ACPD).

p3 l5: ‘decreases’

p3 l13: ‘statistical analysis’ > ‘composite analysis’

p3 l15: ‘exceptionally’ > ‘exceptionally’

p3 l21: ‘latitude of the wave breaking’ — expand a little, e.g. ‘latitude of the associated planetary wave breaking’

p3 l25: ‘and winds’ — including vertical velocity?

p4 l22: ‘An enhanced’

p4 l30: ‘In the tropics an increase in COV is synchronous with the stratospheric upwelling’ — personally I found it pretty difficult to see this (and therefore I have some sympathy with Referee 2) — anything you can say to support this statement would be helpful. Also the vertical velocity is noisy — how much of this structure is believable?

p5 l18-30: This ‘statistical test’ seems very ad hoc to me — in particular the second and third inequalities in (1) seem to be based on not much more than guesswork. Again bearing in mind Referee 2’s comments, I think it would be better based your arguments on e.g. identifying robust and coherent spatial patterns rather than on what seem rather spurious measures of statistical significance.

p7 l17: ‘COV clouds can penetrate above the tropopause’ — don’t they penetrate above the tropopause by definition?

p8 l13: ‘better’ > ‘stronger’

Figure 3 caption: second (c) should be (d). It would be easier to interpret this figure if the vertical axis for (b) was the same as for (a) and (c).

Figure 4 caption is not at all clear — you don’t properly identify the lower panels in each sub-figure as showing COV.

I believe that this paper is publishable on the basis that it is a study of two exceptionally strong sudden warming events which allow potentially interesting dynamical connections to be identified. As I have noted previously, one of the referees was unenthusiastic about the paper because s/he felt that the conclusions were speculative and not robust in any statistical sense. I don't think that you would quarrel with that view -- but it does not imply that the paper has now value. I would be prepared to accept the paper if those limitations are made a little clearer.

I recommend the following:

(i) You continue to use 'correlation coefficients' e.g. on p5. You have usefully clarified the text here but please can you insert a sentence that makes it clear that these correlation coefficients are simply being used to identify the relation between dynamical variables in two rather short-duration events.

(ii) On p8 you say 'it is clear that by adding the present two cases statistical significance increases' -- bearing in mind your response to a referee giving reasons why you had not extended the composite analysis, this seems like 'cherry-picking' to me -- choosing events that fit the pattern you want and not including others. I suggest that you delete the sentence mentioning 'statistical significance increases' and modify the following sentence to say something like 'Therefore the relationship that we have identified here in two particularly strong SSWs between the SSW and the enhancement of tropical convection is consistent with that previously identified from the composite analysis.

Adding one or two further sentences in the conclusions section saying something like 'The certainty of the dynamical connections identified here is of course limited by the small number and the relatively short duration of the events. Further certainty will come from future modelling studies and observational studies of a larger set of events.' would be good -- such sentences would not in any way lessen the value of the work, but they would introduce the appropriate note of uncertainty.

Once you have made these small changes, or changes in a similar spirit, I will be pleased to accept the paper.

Given that you have made the further changes that I recommended I am pleased to accept the paper for publication in ACP.