Review Cadiou & Yiou WCDD by Paolo De Luca

In the paper the authors use rare-event algorithm for sampling and simulating cold spell events in France in order to evaluate their dynamics. They use winter DJF 1963 as a reference and then used a weather generator method to simulate the coldest winter that occur in two periods with less and more effect of climate change. Their results show that the frequency of cold spells is decreasing but their intensity remains stationary and that few simulated cold spells reach the intensity of the winter 1963. They also analysed the atmospheric circulation of the observed and simulated events.

The paper is highly technical and often hard to follow, with many grammatical errors so that I suggest to have it checked by an English native speaker. Said so, the topic is very interesting and I believe that this can be published in WCD after addressing some comments below.

Major comments

Abstract: the conclusion of the study is missing in the abstract. I suggest to add 1-2 sentences at the end, that resume the importance of the work.

L63 not clear what the bullet point states. “Reached without information…”? reached by who or what? Which information? Please clarify.

L102-109 if would be helpful if you could highlight in the figure the strongest cold spells mentioned.

If you focus on 90-day running means then why in Fig. 1b you show only 7-day running means?

Minor comments

L4-5 “significant computational resources”

L9 repetition of “France”, I suggest remove it

L8 “We focus first…”. Ok, but I don’t see the continuation of this in the remaining text. For example, “Secondly, we apply…” or “Then, we use…”. I suggest remove “first” or adapt the following text accordingly.

L11 “We applied..”, before you said “We find..”. Please check the tenses in all the Abstract and make sure to be consistent with the chosen one.

L31 “Arctic Amplification”, please remove “The”.

L33 “But…” change to “, but…”

L62 “the observational periods.”

L67 “200 years for simulations from the..” ???

L69 “2000-2050 decade” ?

L74 reference missing

L98 “have been”

L120 no need to repeat “Methods:”

Figures 2: not clear the meaning of blue and red histograms. Please add it in the caption.

In this manuscript, the authors study extreme cold spells over France using a stochastic weather generator. The interest of the manuscript is twofold. On the one hand, there is a strong methodological motivation, as rare event studies suffer from a problem of lack of data, and the proposed method is sufficiently general to potentially be applied to many other cases. While the idea of approximating the true dynamics of the atmosphere using circulation analogues is not new, the current study combines it with an additional ingredient, the idea of biasing the statistics towards extreme events, which they refer to as importance sampling.  On the other hand, the authors ask whether their tool allows to assess whether the probability of extremely cold winters such as the 1963 winter over France have been affected by climate change, which is a valid question in its own right. Hence, the motivations for this research seem robust to me, and the manuscript should be of interest to a sufficiently large audience. However, there are a number of points which I think should be clarified about the method and the validity of the results.

First I think the objectives of the paper are not framed in a very precise way, which makes it a bit difficult to assess to what extent they are reached. It is said in the introduction that the objectives are to examine: "1. whether a winter as cold as 1963 can be reached without information on this event 2. whether such a winter is still possible in the 21st century". The meaning of objective 1 is not clear a priori; if you were doing a simulation with a GCM for instance the answer would clearly be yes. So it seems this objective only makes sense within the framework of the stochastic weather generator used in the manuscript. If that is indeed the case I think the objective should be rephrased to clearly explain which property of the methodology is being tested.

I understand objective 2, but the word "possible" in this sentence seems a bit surprising to me. Similarly, the manuscript refers several times to "the coldest winters possible".

From the point of view of the true statistics of the climate system, it seems unlikely that a hard threshold exists (at least not within such bounds), it is more likely just a matter of how the probability of such an event changes with global warming. However, my impression is that the authors carefully avoid to talk about probabilities, and restrict themselves to qualitative statements. I understand that the probabilities obtained with the SWG are biased, but if I understand correctly it should be able to go back to the probabilities with respect to the unbiased distribution, and therefore the method should allow to make quantitative statements and estimate such probabilities. This, I think, makes the method quite interesting. For instance, it should allow to compare the probability or return time of an event with a given amplitude (or return level), like the 1963 winter over France, both in the factual and counterfactual worlds, and compare these two estimates. Is this correct or am I missing something?

A second, related aspect is that I am not sure I understand what is the basis for the conclusion that extremely cold winters such as the 1963 winter are not significantly affected by climate change, even in the careful terminology adopted by the authors.

As far as I understand, the conclusions are drawn on the basis of Fig. 5, which shows that the distribution of TG90d simulated from a SWG based on 50 years of data from the first part of the reanalysis dataset does not differ significantly from the one simulated based on the last 50 years of the reanalysis dataset.

By doing so, it seems to me that you are comparing two distributions which are both biased (due to the weights in the stochastic weather generator), but potentially not in the same way. Hence, I think the statistics should be unbiased before any conclusion can be made (for instance by computing the probability or return time of an event at the level of the 1963 winter). Do you agree, or did you make sure that the two distributions were biased in the same way?

Similarly, in section 2.5 and Fig. 2 you study statistics of the time derivative of Z500 and temperature, and compare the distributions obtained directly from data, using the stochastic weather generator, or some naive random sampling. But is it clear that we expect the distributions to be the same, or should the one obtained with the SWG also be biased ?

Finally, I have a number of more general questions on the methodological choices related to the SWG:

- what is the rationale for biasing using the rank of the temperature of the analogues rather their than absolute temperature value? Does it make any difference?

- is there a justification for the form of the biasing factor as a product of exponentials? Or is it empirical?

- is there a way to choose the parameters $\alpha_{cal}$, $\alpha_T$ a priori, or is it done entirely empirically?

- if I understand correctly, the SWG allows transitions from the current state to analogues of the image of the current state in the true dynamics. I guess it would be possible to do things differently and allow transitions from the current state to images of its analogues. Would it make any difference? Is there a good reason for making one choice or the other?

- the SWG seems like an interesting way to estimate properties of rare events, as mentioned above. Here the validation of such estimates is hindered by the fact that the dataset is quite small. Has the method been validated on a longer dataset, such as model data, and if so, for which type of quantities?

Specific comments

In addition to the above general comments, I have a number of questions on more specific points in the manuscript.

- The manuscript introduces a quantity, TGrd, which can be characterized by different event durations $r$. I understand that the paper focuses on the case where $r$ is the whole winter, and this is fair enough, but it would be interesting to illustrate how the distribution of TGrd changes for different values of the duration $r$. Presumably the distribution becomes closer to Gaussian at larger values of $r$, and the variance should also be reduced, as seems to be the case on Fig. 1a. A related comment is that some of the extreme events at large $r$ might be made of several extreme events at small $r$. It would be interesting to quantify this connection.

- ERA5 data is not stationary. It could seem natural to detrend it before constructing the SWG, but it seems like this was not done here. Is there a good reason for that? If the data indeed has a trend, is there anything in the SWG which prevents it from drifting, due to the biasing factor, towards earlier years in the dataset where low temperature extremes were more frequent?

- In section 2.6 and Fig. 3, you show the fraction of simulations for which the last day of the simulations falls after Feb 15. I am not sure I understand the rationale for this choice. What do you expect to be a measure of the quality of the stochastic weather generator based on this metric? Why not computing the climatology simulated by the SWG for instance?

- Fig. 4 shows that a SWG constructed without 1963 data simulates typically less cold winters than one including that data, and different simulations exhibit smaller variability. The first point seems like a drawback. Do I understand correctly that the benefit that you gain in return is the reduced risk of simulating minor variants of the 1963 winter, and therefore more strongly correlated events? How is this related to the smaller variability between independent runs obtained when excluding 1963? Do you know what is the fraction of days picked from 1963 in the simulations with the SWG constructed from data including that year, or do you have another measure of the degree to which they are correlated?

- Section 3.3 and Fig. 6; I would be curious to know whether composite maps are good representatives of individual events.

Technical details and typos

- Abstract: "societal impacts on society" is redundant

- p3, L68 "(e.g. in CMIP6 archive)" isn't the number of ensemble members missing in the parenthesis? (50?)

- p3, L74 broken reference for "Sippel et al. [REF]"

- p4, L104: "a upward trends" should be "an upward trend" I guess

- p4: it would be helpful if the formula defining TGrd based on TG could be written. Similarly on p6, the definition of the stochastic weather generator, which is currently described in words, might be easier to understand if the corresponding mathematical formulas were given, or if a reference to a paper where this is done was given.

- p6, L124 "K analogs days" should be "K analog days"

- p6, L139 "The goal is to simulate L day trajectories of a model while optimizing an observable", I am not sure I understand what the authors mean by "optimizing an observable".

- p8, section 2.6 title "Simulation protocole" should be "protocol"

- p11, caption of Fig. 4: second occurrence of "vertical purple dashed line": I guess you meant "horizontal"