The paper by Le Roux et al. analyses past trends in snowfall extremes in the French Alps based on the SAFRAN regional reanalysis. Several non-stationary extreme value models are considered, and the best performing model according to the Akaike information criterion is chosen for each individual case to model the parameters of the underlying GEV distribution. The study finds a diverse spatial pattern of changes in annual maximum snowfall with variability both in the vertical (elevation classes) and horizontal space (individual mountain ranges). A general pattern, however, is an increase of return levels of extreme daily snowfall at higher reaches, and decreases at low elevations. The results have implications for the design of infrastructures that are potentially affected by heavy snowfalls.

Overall, the paper is well thought-through and well written. All details of the different statistical methods employed are provided. The figures are informative, and the conclusions are well based on the results obtained. Regarding the general scope, I certainly consider the paper relevant for the reader of The Cryosphere. The single main deficiency of the work is the missing validation of the SAFRAN data with respect to extreme snowfall amounts and their temporal trends. Several previous works are cited, but much more information is necessary in my opinion. Potential deficiencies of the reanalysis dataset in representating extreme snowfall woudl ultimately affect the conclusions of this work. I strongly suggest that the authors try to better motivate the use of this reanalysis dataset for their purpose. Apart from this, several minor issues are listed below which also should be improved in a revised version of the paper.

Overall, I suggest to return the paper to the authors for minor revisions before considering a publication of this work.

Minor issues:

Line 28: Skip "globally"

Line 30: You probably mean "maximum atmospheric water vapor"

Line 31 : I suggest to replace by" … the observed global mean temperature scaling for annual maxima …"

Line 55 : Meaning of "max-stable" is unclear

Line 58 : " … by assessing past temporal trends"

Line 70: Change to "… observations and provides, among others, snowfall data for each …" (SAFRAN provides more than snowfall data)

Line 78-80: This section is far too short, a much better motivation for using SAFRAN instead of, for instance, station series, needs to be provided (see above). A dedicated validation exercise would help.

Chapter 3.1: The information that block maxima are used (instead of POT) should be clearly given.

Equation 1: The meaning of y is not ultimately clear and needs to be defined

Line 95: "… represents an annual maximum …"

Line 104: "represent" instead of "represents"

Chapter 4.1 and further: I'm not sure if the term "pointwise" should be used here. I understand the meaning and the difference to "piecewise" in statistical terms, but pointwise could be misunderstood as being based on observations taken at individual locations/points (which is not the case here)

Lines 189-199: This section is basically a very brief description of one figure after the other. It should be extended and some more information on each figure and a brief description of what they show and what this means) needs to be provided.

Chapter 5.1: This chapter is very important as it highlights potential limitations of the work. However, the implications of these limitations for the interpretation of the results and for the conclusions remain largely unclear. Are the conclusions valid nevertheless or do they have to be questioned?

Lines 244-245: This implication does actually only hold if the past trends would continue into the future. Do you have any evidence for this?

Lines 275-277: What this basically means is that mean temperature is not the only control. This could be written much clearer.

The paper analyzes changes in heavy snowfall events in the Alps for the period 1959-2019. The topic is of interest and the methodology very robust and well presented. The manuscript is well written and the figures are very easy to be understood.  In my opinion the paper can be a very good contribution for TC. I do not particular critizisms to the work as is. I only have some minor comments and some curiosities that perhaps could be adressed by authors or at least discussed in a revised manuscript. 

-The first comment is about the selection of the 100 yr return period, as targeted intensity of heavy snow event in this work. Perhaps authors should justify more why this recurrence (that involves very rare events) was chosen. I think that replicate some of the analysis (i.e. Figure 6) for a more frequent recurrent time (i.e. 5-10 yr) could give good information about the sensitivity of the results to the return period selection, and in case there are significant diferences the results of the paper could be more interesting for a management point of view. At least, I think this question should be discussed.

- Another question is that the assignation of existing trends to warmer climate or changes in precipitation intensity is discussed in a very qualitative way (based on some references) when this is a very interesting topic from a climate change perspective, as associated uncertainties of precipitation intensities are much larger than the ones for temperature warming. Perhaps simply presenting a map of temperature and 100 yr precipitation intensity during the snow season, and may be simple cross tabulation test could answer much of this question. The works cited about changes in extreme precipitation over the Alps do not present in most cases their respectives study periods. They should be presented as trends on this parameter may change a lot depending on the selected period, and only those covering a similar time span than this study can be used as reference.

- It would be also good to have an idea in which period of the snow season happen more frequently the very intense heavy snowfall events. The sensitivity of these events to climate change is supposed to be very different if they tend to happen in the coldest part of the snow season, or during the shoulder periods. This could be also a explanatory factor the the spatial heteregoneity shown between massifs.

- In line 25, and later in discussion,  is mentioned that optimal temperature for heavy snowfall events is slightly below 0ºC. Probably in Alps may be tru, associated to the humid arrival of oceanic/mediterranean air masses, but this is not generalizable worldwide (I guess that heavy sowfalls in Colorado or Hokkaid will happen well below 0ºC). I would just clarify the sentence.

- In line 66 is said that the study area is typically divided in 23 massifs/units. I think this classification is typicall for SAFRAN but probably not very geografical (may be I am wrong). I would again clarify or slightly modify the sentence.

- I agree with the other review that a stronger validation of the dataset would be desiderable, but I also wonder how to make it properly, as for my knowledge the best observations of snow in the region have been use to be assimilated in the SAFRAN-CROCUS. This difficults a comparison with observations. May be this question should be mentioned in methods or discussion section.

Hoping my comments will result useful,

Ignacio López-Moreno

The submitted manuscript describes how the 100-year return level of daily snowfall water equivalent from Safran reanalysis has changed in the French Alps between 1959 and 2019 based on non-stationary GEV distributions. The study demonstrates an elevation dependent result with mostly decreasing values below 2000 m and mostly increasing values above. However, the investigated regions and elevation ranges often show a high regional variability.

I liked reading the manuscript, which has a clear structure and illustrative figures. The language is with a few exceptions easy to read. The topic is definitely of high interest for readers of TC. I suggest to accept the manuscript as soon as the following points, have been addressed:

• Extreme snowfall or even snowfall in general from Safran reanalysis, at least to my knowledge, has so far never been evaluated with measurements as e.g. described in Gaume et al. (2013) or Nicolet et al. (2016). I believe it’s necessary to show at least some comparisons with the available time series.
• Moreover, the following points are missing, which are both important in case of comparisons with measured snowfall water equivalents:
  
  a) Is the reanalysis able to reproduce rain-on-snow-events within a 24 h time period?
  
  b) Are the reanalysis data refer to the same 24h period as the measurements?
• The examples of extreme snowfall or roof collapses provided are used to justify the use of the 100-year level, although all these examples are not caused by one extreme snowfall alone. Most of the examples also concern elevations below 600 m, which are not analyzed in this study at all. Please elaborate. Furthermore, instead prominently mentioning avalanche defense structures, which are not impacted by one extreme daily snow fall; I’d suggest to mention snow breakage.
• The linear elevation dependence considered in L100 is in contradiction to doi.org/10.1029/2009WR007916. Please elaborate.

Minor:

Title: I’d suggest to extend the title with «based on reanalysis» as the used snowfall data are not measured.

L18: “power lines” instead of “electric systems”

L20: Rather cite : doi.org/10.5194/nhess-8-1-2008

L53: previous studies (see next sentence)

Table 1: Why is Faranda et al (2020) not listed?

               S_nd: Why the mean of maximum? It’s just the annual maximum snowfall in N consecutive days.

L61: Does 600 m elevation mean the 300 m elevation band between 450 and 750 m? Please clarify?

L66: Please explicitly mention that the reanalysis provides the daily snowfall amount in kg/m2 in contrast to measured height of snowfall, which usually is given in cm.

Figure 1: Why is the m^-2 of kg m^-2 written italic?

L113: “Appendix A”

L118-119: Please rephrase.

L151: Fig. 3b

L156: I count 7 massifs?

                Fig. 3c

L160: In Figure 2d…, while in Figure 3d…

L167: “Further” instead of “Then”

            Xi instead of Zeta

L172: “at 500 m” instead of “at low elevations”

L173: “at 2500 m” instead of “between 2000 and 3000 m”

L179: “Appendix B”

L199: “with an increasing or decreasing trend”

L205: What means “short”?

L214: “we always have at least two time series…”

Figure 8: Could you please indicate the non-significant massifs with a white-dotted pattern.

Fig 9: “..illustrated with colors (elevation range dependent scale)..”

L234: “..literature (see next paragraph)…”

L242: I don’t find the 1.5 kg m-2/100 m in Blanchet et al. (2009)?

L243ff: This study is about annual maximum snowfall, which is only at low elevation a concern in regard to infrastructure. Avalanche defense structures or settlements in the mountains are endangered by annual maximum snow depth and not one snowfall event. Please rephrase!

L244: What means red? Reddish, dark red?

L250: “combined with liquid precipitation, which is not considered in this study”

L251-252: Is there a specific reason you distinguish here below 1000 and above 3000 m, in contrast to the separation below and above 2000 m in the abstract and the conclusion?

L254-262: It seems strange that you write in these lines about increase in “extreme precipitation”, “high latitude” and “moderate extreme snowfall”, which all have so far not been analyzed in this study.

Please rephrase the last sentence and make clear to what elevation you refer.

L257: “1.4 billion Euro of damage”

L266-274: This might be true for moderate extreme snowfall but not for the annual maximum.

L283: “Faranda (2020)”

L295: “For the four investigated elevation ranges…”

L305-307: See my comments to lines to L243ff.

L325: How is a “good” fit defined in numbers?

What did you do for those cases, where no good fit could be obtained?