The article by Jonas Spaeth and Thomas Birner entitled “Stratospheric Modulation of Arctic Oscillation Extremes as Represented by Extended-Range Ensemble Forecasts” discusses the influence of the stratospheric polar vortex on the surface climate. This topic has been discussed a lot in the literature and it is well established that extreme states of the polar vortex tend to shift Arctic oscillation towards certain states with implications for regional weather conditions. However, the strength of the link between stratospheric conditions and surface weather is poorly estimated because of a low signal-to-noise ratio. To address the low signal-to-noise ratio problem the authors turned their look towards model simulations which provide much more data sufficient to obtain robust estimates of the stratosphere-troposphere coupling. The underlying assumption is that the models provide a reasonable representation of the real atmosphere. The assumption seems to be violated at least in some cases because some estimates obtained from the two different models considered (ECMWF and UKMO) diverge significantly. Which of the two models is closer to the real world is difficult to establish. Therefore, the interpretation of the results should be done carefully. Nevertheless, the article presents novel results which in my opinion go beyond state-of-art. I believe the article can be published in Weather and Climate Dynamics after revision. My main criticism concerns the causal analysis. This should be better described and, in case if the approach used by the authors is a well-established one (I apologize for my ignorance), proper references to background literature should be made. Additionally, I strongly recommend a language check before publication.

Major comment:

1. The authors distinguish between increased probability of AO extremes following stratospheric events (their question 2) and how often stratosphere can be considered a cause of extreme AO events (question 3). Both questions are addressed in terms of probabilities (e.g. Figs. 6,7,8). While I understand the difference between the two questions in principle, I do not understand how you manage to solve them separately, given that both questions can only be answered in statistical sense. In figure 7 you show probability of at least one SSW day preceding a randomly sampled day; however in Figure 8 this probability becomes a probability of AO extreme preceded by a SSW day by chance (left panel of Figure 8). This is not the same, clearly. Assume hypothetical world in which all AO extremes are caused by an SSW occurred during previous 30 days. Then dashed lines in Fig. 7 would reach 1 by day -30. However, this would not affect your climatology because it only measures probability of SSW. As a result, you would never be able to correctly answer question 3 using your methodology. For day 30 you would only obtain the difference between 1 and an SSW probability, which is not the right answer to question 3. Figure 11 illustrates the same problem – there is no evidence in data that AO>3.5 can occur without an SPV within previous 40 days, yet only about half of those events that occurred after SPV can be attributed to SPV following your methodology. I believe the methodology needs to be revised (or I miss something).

Other comments

L18: What does it mean: “up to a degree of 27%”

L31: Please clarify whether you cite daily AO index value, monthly value or seasonally value.

L34: Do Kim et al discuss wildfires in winter or in another season?

L54: “are needed” for what?

L146: Please explain what does “dynamical SSW” mean and provide reference if it has been introduced elsewhere.

L151: “we therefore do” what?

Figure 1: Although interannual variability of predicted SSW frequency is not the main point of your article I wonder if upper panel of Fig. 1 could show relative frequency of p-SSW rather than absolute numbers. It is quite exciting to see so small number of p-SSWs in 2008/09, a winter in which an SSW occurred in the real world.

L165: “the event was generally very rare” sounds strange to me

L175: Please provide equation which you apply

L197: A rather complicated deseasonalization approach has been used. Why not used a simpler approach in which climatology is estimated using other hindcast years? For example, for ECMWF hindcasts this would provide 19x11=209 realization to build a climatology for each date and lead time. Why do you think it is not enough?

L219: “occur only few days after the event” can you provide the exact lag?

L223: I do not think NAM1000 distribution is significantly different from 0 at negative lags.

L226: the trend goes to weaker negative values, not positive.

L234: I am not sure the name “ECMWF S2S model” is correct.

L236: “most phases of negative NAM1000”, perhaps: “most cases of negative NAM1000”

L243: I do not think NAM1000 in ERA5 follows AR1 process either, or have you checked it?

L258: Should not probability of negative NAM be exactly 50%, by construction?

Figure 6: What is the period used for calculating the probability increases?

L429: I do not think that increasing number of models would help to make definitive quantitative statements unless you know which models are right and which models are wrong. Since all models are different you could only possibly increase the spread.

Review of manuscript WCD-2021-77: “Stratospheric Modulation of Arctic Oscillation Extremes as Represented by Extended-Range Ensemble Forecasts”, by Jonas Spaeth and Thomas Birner.

The authors used a large set of extended-range ensemble forecasts within the sub seasonal-to-seasonal (S2S) framework (namely ECWMF and UKMO models) to obtain an improved characterization of the modulation of AO extremes due to stratosphere-troposphere coupling. Within this framework, they investigated how much stratospheric polar vortex extremes increase the probability of persistently AO phases and their extremes. They found that following potential SSW events, persistently negative AO states (> 1 week duration) are 16% more likely, and the likelihood for extremely negative AO states (< −3σ) is enhanced by at least 35%. How the stratospheric polar vortex extremes can be considered as the cause of the subsequent AO extremes was also quantified and discussed. Despite the straightforward analysis presented in this paper, I still found the results are interesting and the diagnostics can be useful for the forecast model assessment. The main issue I have is a lack of dynamical analysis to explain the differences in the two models in representing the AO extremes followed by stratospheric events (SSWs and SPVs) and the results regarding causal relationships between AO extreme and stratospheric polar vortex extremes. Hence my suggestion is major revisions. Once my points below are answered, I can recommend this work to be published in WCD. 

General Comments:

1. Two S2S forecast models (ECMWF and UKMO) used in this study showed some quantitative disagreement (i.e., the results diverge significantly e.g., Figs. 5, 6, 7. 8 etc). However, there is no dynamical analysis and explanations to address the issue rather than simply comparing the results in a statistical sense. It would make the results clearer if you could address this issue in the paper.
2. I am not convinced about the causal analysis in this paper. As you are aware, the extreme AO events are not only proceeded by extreme stratospheric events, but also by mid-latitude winter circulation such sea-level pressure, sea-ice and remote forcing from the tropics. How can you isolate the possible stratospheric influence alone from these other factors (since this may not direct/linear statistical relationship)? I believe that not all stratospheric polar vortex extremes lead to AO extremes. You probably need to revise your methodology to address this question.

Other Comments:

 L143: Will be the results sensitive to the WMO’s definition that includes the reversal of the meridional temperature gradient?

Figure 3. Please also add a similar histogram for UKMO model next to this figure. Also please add the uncertainty in this plot.

L175: Please delete this and just mention the number. Otherwise, please provide a full equation before inserting the number.

Figure 4. Do you have a similar figure for ERA5? How does it look like compared to UKMO and ECMWF models? It’s hard to get definitive quantitative statements since both the model are probably not right.

L429: I dont think you will get a definite answer for this rather than a spread of the quantification of the probability of extreme AO events following extreme strat. events in different model configuration.