Dear Dr Koumoutsaris,
I have read your detailed answers to the comments of the reviewers and I am asking you to provide a revised version corresponding the major revision that is required in this case. Please submit the revised version and a description of the changes implemented in the manuscript following the suggestions/requests of the reviewers. The revised manuscript and your answers will be passed to the reviewers for their further comments. The final publication of your manuscript in NHESS is conditional upon the positive evaluation of the reviewers.
Looking forward to receiving your revised manuscript
Best regards
Piero Lionello

Dear Dr. Koumoutsaris,
Thanks for the revised version of your manuscript and the description of the changes implemented following the suggestions/requests of the reviewers. I am passing the revised manuscript and your answers to the reviewers for their comments.

Best regards
Piero Lionello

Dear Dr. Koumoutsaris,
Both reviewers appreciate the improvement of the revised version of your manuscript. However, reviewer 1, has still some concern on how uncerainties are computed. Please, consider Reviewer 1's comment and answer/modify your manuscript accordingly.
Your manuscript will be returned to reviewer 1.
Best regards,
Piero Lionello

Dear Dr. Koumoutsaris:
Your manuscript is returned for a minor revision.
Please consider the following main issues a) to d) to be properly clarified:
a) There is an apparent inconsistency in your manuscript
Note the following. At lines 9-10 of the abstract and lines 9-10 of page 24 in the Conclusions you write that “The model suggests that the occurrence of such extreme cold events have increased approximately two times during the course of the 20th century as a result of anthropogenic climate change”. Instead, at lines 24-25 you write that “the non-stationary model suggests that under current climate conditions, such an extreme event, is approximately 2 times less likely to occur than in the 1960s“. Table 4 also suggests an increased (doubled) return time of the “1962/63 winter freeze event”.
Please correct this inconsistency or clarify
b) In the “Methods” section, defend your choice of using the change in radiative forcing from CO2 in the nonstationary model (first main comment of the reviewer)
c) In the methods section, add that the non-stationary model does not consider the potential non-stationarity in the dependencies described by the joint pdf (first part of the second comment by the reviewer)
d) It is not clear which variables the nonstationary model is actually using. Please, make this clear in the methods section (second part of the second main comment of the reviewer)
Moreover, please consider all minor points raised by the reviewer

Finally consider also the following comments:
i. I agree with the reviewer that at line 9 of the abstract “”such extreme cold events” is not immediately clear and the sentence should be rephrased (I presume it refers to events as anomalous as the “1962/63 winter freeze event)
ii. Line 8-9 of the conclusion “According to the model, such a cold winter is estimated to occur once every approximately 400 years under current climate conditions in the UK.” I see this in table 4 (please, in the text, specify that you refer to the South UK). However, this result contradicts the empirical evidence. You write at lines 20-22, page 20 that “only two other winters (1683/84 and 1739/40) have been colder than 1962/63 in the last 350 years”, suggesting a return period in the range of 110-120 years. Please clarify this inconsistency.
iii. The definition of AFI in expression (2) at page 5 is not clear. Specify the meaning of the subscript “i” and specify appropriately the upper and lower limit of the sum
iv. Consider whether moving the first part of section 3.3 (describing copulas) to an appendix could improve readability of your manuscript and help the readers to focus on the novelty of your study

Please, provide a revised version (which accounts for all reviewers’ comments), and a copy of your manuscript where all your changes are annotated and the list of your detailed answers to the reviewers’ comments.

Best regards,
Piero

Dear Dr. Koumoutsaris:
Thanks for the revised version of your manuscript, which I am happy to recommend for publication in NHESS. However, please note that, possibly because of incorrect internal references or processing of the manuscript, some references are missing (The pdf reports several “??”). Please submit a corrected version of your manuscript.

I thank you for having considered NHESS for the publications of your research.
Best regards,
Piero Lionello