The manuscript presents an interesting exploration of European windstorm extremes, how these can be statistically modelled, and their dependence on NAO. The manuscript poses several useful and relevant questions, motivated by identified knowledge gaps. I think overall the manuscript is well structured and provides some useful insights into the answers to the questions posed. I appreciate the discussions of the limitations of the analysis but think in some places the methods could be better justified to strengthen the credibility of the conclusions made. I would thus recommend the manuscript for publication after moderate/major revisions. Below are some suggestions for improvement which I hope the authors may consider in preparing a final version.

MAIN POINTS

• Sections 3.1 and 3.2 state that the scale parameter is ‘independent of large scale patterns such as the NAO’ and there is an ‘undetectable signal in the α parameters’. It seems that these statements are made based purely on a visual inspection of Figure 4. My concern is that this these are possibly strong statements without justification based on further exploration. Could it be possible that there is an NAO signal in some regions and not in others (e.g. over some parts of Northern Europe where α₁ is ~-3)? Could the authors provide a test of significance for this relationship, at least for the three most studied locations (Bergen, London, Madrid)? This would give greater credibility to this assumption and the results that follow, which are based on this assumption (e.g., the conclusion that the relative importance of NAO decreases with increasing return period in all locations).
• Please provide some additional justification/explanation in Section 3.3:
  • Please could you add some additional justification of why you use a 5-year validation period. This seems like a very short window/small sample for estimating a 200-year return period.
  • Are your results in Figure 7 conditional on the fact that you calculate the MSE based on a baseline 5-year period? Would this change if you used e.g. a 10-year window, changing your conclusions?
  • The increase in variability in the MSE in Madrid with catalogue length is not mentioned. Do you have any thoughts on this you could add? E.g., Is this due to the difference in NAO phase between the two periods being compared (e.g., similar to the results in section 3.4)?
  • Would the conclusion that ‘historical catalogues longer than 5-15 years do not yield improvements in the return level estimation’ be made if a different validation period length were used, or is this statement relative to the 5-year based estimate? Please could you clarify? I.e., Is the conclusion of this section that only 5-15 years of footprints are needed to reliably estimate the 200-year event? I’m not sure I am convinced of this from this analysis.
• Please provide more clarity in Section 3.5:
  • The exploration of a future NAO state of +1.5 is interesting, but please can you make it clearer that this is a theoretical demonstration rather than a value that has been derived from climate projections. E.g., in the conclusion (line 283) you state ‘under future NAO states…’, which implies over-confidence in this evolution to a +1.5 state.
  • I am not totally clear on the approach taken in this section and which parts of Figure 10 relate to which method. There is the discussion of ‘simulated events’ and ‘theoretical return levels’. Am I right in thinking that the same approach as in Section 3.4 is used to simulate events with varying NAO state and these make up the box plots, and then the approach in Appendix B is used to calculate the theoretical return levels shown by the red crosses? My confusion comes from lines 251-253 where you reference Appendix B when talking about the event simulation. Please could you clarify this and provide more detail in these lines.
  • In the text you describe simulating events with reference NAO 0 and +1.5, but the plots in Figure 10 also include a box plot for reference NAO -1.5, this is slightly confusing. It is also a bit confusing using sigma again in this part of the method (because you use sigma to represent the tail scale parameter earlier in the manuscript). Could this be changed to another symbol?

OTHER MINOR POINTS

• Abstract – The abstract jumps to describing results related to the location and scale parameters but does not mention prior to this that an EVA model is used. Could this be mentioned briefly to set the scene e.g. in line 4?
• Line 64 – ‘..for a 72-hour period of each ...’ typo?
• Lines 75-77, could you include references for the ‘spatial Gaussian filter’ method, and the validation results?
• Line 83 – do you take the NAO index for the middle day of the 72-hour footprint window, or an average over the 72 hours? Could you add this detail here?
• Line 85 – My understanding is that the statistical model is applied to locations separately. Please could you add this to the beginning of Section 2.3 for clarity (i.e., ‘for any given location…’)?
• Lines 90-91 – please could you include clarity on why you introduce a separation between footprints with and without strong winds. Is this to justify the model being suitable for WISC footprints which only include strong winds?
• Line 98 – I appreciate that you discuss the limitations of assuming a shape parameter of zero, but maybe this could be referenced on this line too to reassure the reader you have considered this to be an assumption. The models in Fig 2 look good though, supporting this assumption – did you find a similar good fit in other locations?
• Line 110 – for completeness it would be appreciated if the combining and rearranging of equations 1-5 to produce equation 6 could be included in the appendix.
• Figure 2 – How were the 95% confidence intervals calculated (e.g. bootstrapping)? Please could you add this detail to the caption? The same is true for a few the other figures.
• Line 175 – The manuscript notes that the 200-year return levels are higher when using the NAO covariate, and this seems to be the case for both NAO=0.5 and -0.5. Do you have a hypothesised explanation for this? Is this linked to your conclusion at the end of Section 3.5 (line 261)?
• I appreciated the additional plots in the supplementary material. E.g. fig S2 was useful for demonstrating the relative contributions of the components of the model for different return periods.
• Line 197 – ‘5- year validation period to quantify of..’ typo?
• Line 220 – it is noted that the simulated gusts exceed the WISC dataset considerably. Could you add a statement as to whether this is to be expected, and if so, why? Is it due to the much longer simulation period?
• Conclusion – where appropriate please caveat the conclusions made in the bullet points based on your answers to my questions/comments above
• Line 304 – there as been some recent exploration of wind-gusts in the UKCP convection permitting model projection that it might be good to reference here, e.g., https://link.springer.com/article/10.1007/s00382-021-06011-4#Sec13

Review of: Return levels of extreme European windstorms, their dependency on the NAO, and potential future risks.

This paper presents a new statistical method to estimate extreme wind gusts across Europe from dataset of high resolution, historical wind storm footprints. The model allows the authors to answer interesting questions about the role of the phase of the North Atlantic Oscillation in the magnitude of extreme gust events, and the optimal length of historical dataset that is required to estimate return levels.

Please note that I am a climate scientist, not a statistician. So I leave it to other reviewers to analyse the method in critical detail, but to the best of my knowledge the method seems well formulated and is well presented. I find this study a useful addition to the literature and particuarly to the insurance community. The study is well written, the results are nicely presented, and the limitations are clearly identified. Following minor revisions below I’d be happy to accept this paper for publication.

• ‘from the WISC project’ could be removed from the abstract to save defining the acronym.
• L6: ‘setting the tail location parameter’ and ‘tail scale parameter’ comes a bit out of nowhere in the abstract as we don’t know what type of statistical model this is. Suggest revising how the statistical model is introduced to provide slightly more context.
• L21: I’m not sure how the long-range predictability links to natural variability. Perhaps convert into multiple sentences?
• L33: You could also add (in support of this kind of framework) that if you take multiple 100 years of climate model data or century-long reanalysis to use for this exercise substantial calibration is needed, and long observational records may contain spurious trends – managing all of this is a lot of work before you even start to create a hazard event set.
• L36: It feels like your conclusion counteracts this point as you say ~20 year observation periods are long enough, maybe you could reflect on the record lengths you suggest and past studies on decadal variability in the conclusions?
• L51: Are the WISC gusts still openly available? The data availability statement implies an author must be contacted to access them. Can you gain permission to host them on a repository or encourage the original source (C3S?) to continue to host them. They’re clearly useful for the community!
• L54: The introduction currently doesn’t mention the impact of climate change on the NAO, shifting some of the text from section 3.5 to this section would help motivate your final research question.
• L62: Was there any comparison of the ERA-int/ERA20C WISC footprints over the common period in their validation? It would be very useful to confirm that they are not substantial biases when the boundary forcing is changed as this would influence your results.
• L76: Did any issues arise in the validation of the WISC footprints that might be relevant here?
• L82: Just to confirm, the daily teleconnection index is calculated from monthly derived EOFs, or is it one pattern for the whole year? The sentence is currently unclear. Also do you not have data out to 2014?
• L90: Can you confirm if you did any separation on the WISC footprints into ‘strongest’ events or if this implicit in using the extreme footprint dataset?
• L98: The discussion of the limitation around the shape parameter could be moved to here for clarity. As someone who’s not an expert on these methods I found that helpful to know at this point.
• L101: Is the method of moments a standard technique? If so can a reference be provided?
• L111: I followed the method well, but it might help at line 111 to quickly recap the key parameters that the method boils down to, as there are a lot of symbols introduced and it’s very important for the reader to get the form of this equation clear in their mind.
• L132: Is there are a reason for the focus on the 10 year return period level? 200 years makes sense with the solvency 2 requirements but is this one driven by industry partner interest?
• L140: sigma_hat is defined FROM the mean excess in line 101? Confirm symbols/description are correct.
• L140-146: Could you do a statistical test (e.g. pattern correlation) to confirm the NAO influence rather than the visual analysis. I had to look at this for a long time to confirm I agreed with you. To me subplots (a) and (c) look very similar but (b) looks more like (d) with the extension of high winds towards northern Spain? Is this because the 1 in 200 year return periods have a smaller influence from the NAO?
• L167: ‘Strong positive’ relationship seems quite generous as there is still quite a spread of gust values with a single NAO index value. Can you include some more verification? (e.g. strength of correlation/model fit)
• L174: ‘Return levels are higher for the 200-year return period (Fig. 6b) than the 10-year (Fig. 6a)’ This could be removed as the result is expected?
• L194: Are the results the same if the 5-year test period is instead swapped for 2 or 10 years? This feels quite important for your result around length of historical catalogue that is required.
• L204: Mentioning in the methods on average how many footprints per year there are in the WISC dataset would help with the interpretation here.
• L206-210: ‘Therefore, historical catalogues longer than 5-15 years do not yield improvements in the return level estimation at these three locations.’ This is the only result in the paper that I’m struggling to see from the Figures. To me the uncertainty bands are large, and the MSE seems relatively similar throughout the whole period for Norway. It seems similar for years 10-40 for London, and similar throughout for Madrid. Can you provide more information on how you’ve defined a ‘limited improvement’? And highlight that the data record needed seems very location dependent?
• L276: ‘the largest gust speeds feature stochastic noise’ – Can you clarify what you mean here and how it relates to the model?
• In the abstract and conclusions it’s mentioned that the framework can assess high return period losses without the complexities of a catastrophe model. I’d note that this method allows you to replace the event set component of a catastrophe model, but it doesn’t get you to the losses (e.g. inclusion of exposure and vulnerability). A CAT model would still be required for that. So please revise where appropriate.
• In the conclusions can you comment on how the NAO-based results could likely be used in a CAT modelling framework? Within a given winter the NAO index can vary wildly, even though it has general cycles of high/low. Given one of your results is that you only need a 20 year period for analysis, is there a preferred historical 20-year period based on historical NAO variability, or is literally any period fine?
• Similarly, given the CAT modelers issues with thinking about impacts of climate change in their backward-looking models, this is a method that could be used to think about this without grappling with full climate model simulations.

Figures:

• Figure 1: the colour scheme of (d) doesn’t display well on my screen. Can you confirm that it’s emphasisng the features you need it to?
• Figure 2 (and similar ones): The differences between line types are hard to distinguish (the three dashed ones). Consider revising the colours/styles?
• Figure 3: Matching colourmaps for (a) and (b) would make it easier to compare how much stronger the gusts are with increasing return period.
• Figure 6: Including a difference plot to show the impact of the NAO states could be nice here/in the supplementary material.
• Figure 10: Can a different symbol be used for NAO state so not to conflict with previous use in the methods?