Reply to Review of “Intensity and dynamics of extreme cold spells of the 21st century in France from CMIP6 data” (Reviewer #1)

We thank the reviewer for carefully reading our manuscript and for their constructive remarks (in italics). Our replies are in red (see pdf).

General comment

This paper investigates the evolution of 15-day cold extremes over France in 11 CMIP6 models, using a Stochastic Weather Generator (SWG) to increase the sample size and thereby allow conditioning on very extreme events. The authors argue that this provides something like a statistical equivalent of ensemble boosting, which is a method applied within a physical model. The methodology used here was introduced in a companion paper (Cadiou and Yiou, https://doi.org/10.5194/egusphere-2024-612) where it was applied to reanalysis data. However, I cannot ascertain the current status of that paper, which is unfortunate. I have to admit that I do not have a good feel for the meaning of the statistics being produced by this methodology, but since the same methodology is applied across different epochs, I understand that the differences between epochs are meaningful (i.e. we are perhaps more interested in precision than in accuracy here). The particular choice of region and cold-extreme length were motivated by implications for energy system demand, and the choice of CMIP6 models by the ready availability of the output data. That might all seem a bit arbitrary, but the subject of cold extremes has been rather neglected until recently (except for a reduction in cold extremes being a classical indicator of climate change), and I can’t imagine that the results would change with the inclusion of more CMIP6 models. Thus I believe that this study will be of interest to the climate science community.

I personally find the most interesting result to concern the connection between the WCC circulation pattern (which is not one of the canonical North Atlantic circulation patterns) and 15-day cold extremes over France. If I understand correctly, the fact that conditioning on temperature or on WCC appears to yield pretty much the same cold extremes makes the WCC a unique predictor of those cold extremes (i.e. both necessary and sufficient). Moreover, the WCC pattern appears to be reasonably well simulated in the CMIP6 models, and to not exhibit a robust response to climate change up to the warming levels investigated. These findings support the value of storyline approaches for this phenomenon, and the use of CMIP6 models, both of which are useful things for researchers to know.

My only criticism of the study is that it does seem a bit perverse to throw away ensemble members and then try to increase the sample size statistically from the single remaining member! This data set would seem to provide a perfect opportunity for validation of the SWG, to see whether it can reconstruct the missing variability, since for some models there are presumably reasonably large ensembles available.

Thank you for this comment. The reason why we only used 1 run per model (and the first in lexicographic order, if runs are labelled as rXiYfZpU) is very prosaic: some studies in bias correction “just” use one GCM run (e.g. François, B., Thao, S. & Vrac, M. Adjusting spatial dependence of climate model outputs with cycle-consistent adversarial networks. Clim Dyn 57, 3323–3353 (2021). https://doi.org/10.1007/s00382-021-05869-8; Bohan Huang et al 2024Environ. Res. Lett. 19 094003, DOI 10.1088/1748-9326/ad66e6).

We checked the IPSL ensemble (~33 members, with a convenient file format). The run we used in the paper (r1i1p1f1) seems to be warmer than the 32 others (see Fig. 1 in the attached pdf), although it has been often used in several other studies. A few members contain 15-day events that are much colder than what has been observed (in ERA5), and colder than what is simulated with the SWG based on the r1i1p1f1 run. We checked that the cold events in all CMIP6 simulations yield similar atmospheric patterns. We also checked how the SWG simulations based on the “r1i1f1p1” run compare with the other cold extremes of 1950-2000. We will discuss this issue in the revised manuscript, and use the SWG from CMIP6 runs that indeed show the coldest TG15d events. A new figure will be added to the next, and a discussion on the necessity of using large ensembles (rather than long simulations) to sample extremes. 

Minor comments

My other comments are all minor:

Line 10: You should say what the outcome was of this analysis of the CMIP6 models.

Ok, we will clarify the abstract about the results.

Line 57: Blackport and Screen (2020) is a curious citation to support this statement since it argues precisely the opposite.

Indeed. The sentence will be corrected.

Lines 122-125: Was the K-S test applied to the raw model data or the bias-adjusted model data? The latter would be more informative, I think.

The K-S test was applied to the raw model data. This will be clarified in the text. We will also perform a K-S test on the bias adjusted climate model time series, which could allow keeping more models.

Lines 255-256: Is this after bias adjustment? That is what the caption to Figure 2 suggests. If so, that seems to be quite an interesting finding.

Yes, this is after bias adjustment. This will be clarified in the text.

Figure 3: Can you clarify how the whiskers are constructed? The caption says the lower whiskers are constructed symmetrically to the upper whiskers, but they don’t look symmetric in the figure. Also, in a few cases (notably IPSL for the middle epoch of SSP3-7.0) there would appear to be a very large number of outliers in the cold tail, which seems highly relevant for this study; what do you make of those?

The whiskers are constructed with a symmetric formula (i.e. min[max(T ), q75 + 1.5 × (q75 − q25)] for the upper whisker and min[max(T ), q25 - 1.5 × (q75 − q25)] for the lower whisker), which, depending of the distribution, will not necessarily result in symmetric boxplots. This is a standard formula for boxplots. With this formulation, non-Gaussian distributions can lead to many “outliers”.

Lines 305-306: This is an interesting point, since it is quite common to look at the correlation between circulation indices and seasonal mean temperatures across the entire distribution. Can you say a bit more (rather than just a caveat, which is not so informative) about the extent to which the correlations in the tail that you are analysing are related, or not, to correlations across the entire distribution? That would be useful information for the reader, because it would guide any subsequent studies.

The text will be enriched, as correlation is generally obtained from the core of the probability distributions, and might not be very informative on the tails.

Lines 364-366: This statement is based on Figure 8, but I am having trouble reconciling Figure 8 with Figure 6. In Figure 6, I can hardly see any difference between the four panels for the third epoch, which is where one should presumably see the sensitivity to scenario.

Figure 6 (now figure 4) displays the WCC for SWG simulations, so conditioned on extreme cold events. These figures show that the atmospheric configuration associated to extreme cold events is indeed little affected by the scenario and level of warming. Figure 8 shows the evolution in the frequency of a low WCC index in the daily circulation. So a model could see a decrease in the frequency of low WCC days with warming while still displaying a low WCC when an extreme cold spell occurs.

Figure 7: It looks by eye as if the difference between the coldest events (those conditioned on either tas or WCC) and the rest increases as climate warms, which would seem to go against the general expectation of the coldest extremes over western Europe warming faster than the overall distribution (because of the reduced temperature difference with the Arctic). Can you comment on this? More generally, it would be useful to place this analysis within the context of the wider literature on projected changes in temperature extremes.

We will add references on trends on extremes vs. trends in the mean. In our case, the “conditional” (to NAO, AR1…) SWG simulations do not reflect significant trend differences. For instance, the trends are detailed for SSP1-2.6 and KACE-1-0-G in the table below. The control (AR1) simulations exhibit a higher trend than the tas-SWG and WCC-SWG simulations, but not the simulations without importance sampling (“None”). Furthermore, the confidence intervals are very wide because there are only three periods. Therefore, we cannot conclude that there is a significant difference in warming between the mean and extremes.

Table 1: Trend in warming in the SWG simulations depending on the variable used for importance sampling.

Lines 654-656: This submitted version of Sippel et al. should be deleted since the published version is provided by the very next entry in the reference list.

Ok, this will be corrected.

Reply to Review of “Intensity and dynamics of extreme cold spells of the 21st century in France from CMIP6 data” (Reviewer #2)

We thank the reviewer for carefully reading our manuscript and for their constructive remarks. Our replies are in red (see pdf).

General comment

Reviewer’s comment on “Intensity and dynamics of extreme cold spells of the 21st century in France from CMIP6 data” by Cadiou and Yiou (2025)

The authors study historical, present and future extreme cold spells over France in ERA5 and CMIP6 models. They use a stochastic weather generator based on circulation analogues and importance sampling, which is a sort of stochastic rare event sampling algorithm. The paper concludes that the intensity of extreme cold spells decreases in the future as global warming progresses, however impactful cold spells may still occur in the near future and should not be overlooked. Furthermore, the paper evaluates the ability of CMIP6 models to realistically simulate the circulation anomalies leading to extreme cold in France.

The risk of future extreme cold spells is understudied and tends to become underestimated due to the focus on the increasing frequency and intensity of hot extremes as a consequence of global warming. This might exacerbate the general vulnerability of our society to cold extremes. Thus, the topic and the message of this paper is highly relevant. Furthermore, the paper is well written and clearly structured.

Minor comments

I suggest that the authors implement following minor corrections/changes:

1. The authors do not discuss the limitations of the methodology, but point instead to already published work. Since the rare event algorithm is the essential element of this study, I think that the authors should extend the paragraph about limitations in Sec. 5 and discuss, in a concise way, the main assumptions/limitations of the algorithm in this work as well. For example, this stochastic rare event sampling algorithm cannot generate new atmospheric states, but is based on a resampling of already explored atmospheric configurations. This and similar limitations should be mentioned and discussed.

Ok, the caveats of the SWG are more thoroughly discussed in section 5.

1. This shall be an independently published work, thus I ask the authors to shortly summarise what they have done in the first paragraph of Sec. 5, instead of only referring to Cadiou and Yiou (2024).

Ok, the results of the previous paper Cadiou and Yiou (2025) will be summarized.

1. It is confusing that Fig. 6 is discussed before Fig. 4 & 5. I suggest to reorder the figures: what is now Fig 6 should be shown before Fig 4 and Fig 5.

Ok, the Figures will be reordered to match the text.

1. L 136-137: Was the linear trend removed grid-point-wise?

Yes it was. This will be clarified in the text

1. L 174-178: I don’t understand how the content of this paragraph leads to the final statement: “In essence, we are evaluating …”. Some additional clarifications would be helpful.

We will develop the paragraph to make it clearer.

1. L 247-250: The paragraph on testing causal relations could be clearer. For example instead of writing “here several atmospheric indices”, please mention the actual indices.

The paragraph will be clarified by displaying the atmospheric indices used and explaining the “do” action of Hannart et al. (2016).

1. L 6: sentence is not clear, should be rephrased. Past events cannot re-occur, but events similar to past events can occur in the future.

Ok, this sentence will be rephrased.