Switanek et al. provide an analysis of the multivariate dependence of relative snow depth anomalies over the Austrian and Swiss Alps to temperature and precipitation anomalies. Besides showing past trends of relative snow depth trends, they use the estimated sensitivities to predict snow depth and compare it to a degree-day snow model. The multivariate approach is interesting and has a lot of potential for understanding past changes and predicting future changes. However, some major reservations need to be addressed or discussed first. Finally, it is unclear what the paper is mainly about. I tended to follow what was written in the title. But there are also other elements within that need to be linked to the research aims (a lot of trend analysis of relative changes and comparison to a degree-day model).

The paper’s structure is somewhat unfamiliar, because it does not follow the standard approach of intro, methods, results, discussion, but instead guides the reader through a research journey with a lot of motivation used, e.g., in the methods description. Personally, I enjoyed reading it. But, a major drawback is that methods are sometimes difficult to find, since they are spread out. Furthermore important elements are missing, the research questions/aims and the discussion. I honestly don’t know, if I should recommend a standard paper structure or not, but definitely the missing components need to be added.

Major points

1. I would expect temperature and precipitation to have different effects in the accumulation and ablation phases of the snow cover. But in your model, using seasonal averages, accumulation and ablation are treated together. Did you perform tests for differences in sensitivities between start and end of the snow season?

2. One major drawback of your method is the strong need for extrapolation of the sensitivities in “unknown” climatological terrain. In my opinion, the chosen approach using local linear regression produces unrealistic values, especially at the boundaries and beyond the training domain (Fig 5a-d). Moreover, it smoothes out a lot of local effects (Fig 5 comparing the different columns); this might be a reason why SnowSens does not capture interannual variability. I don’t know a simple remedy to this, but at least this needs to be discussed.

3. I understand the choice of elevation bands, but in a changing climate context, I could also imagine a lot of potential for statistical methods to learn across elevation, at least what concerns temperature, given its strong dependence with elevation. However, this probably requires going away from anomalies to absolute temperature and snow depth values. Did you test the multivariate dependency also for “raw”, ie., absolute values of temp, precip and HS? Would it work? Also without subdividing by elevation?

Minor points:

• L1: What climatic cycles do you? Maybe better rephrase, since climatic cycle can mean something like the Milankovitch cycles.

• L40ff: Might be worth mentioning doi:10.1002/joc.8002 who also attempted something similar for snowfall

• L49-54: this belongs into methods. Please provide here a more conceptual statement how you go beyond the state-of-the-art and what your research questions, aims, or hypotheses (choose one) are.

• L99: so y_clim,i should not be a time series but a fixed value for every station, right? Maybe state it explicitly. Also your RMSEs are then the average over all stations?

• Sec 3 is more than just methods, it contains a lot of background information and motivation

• L126: Not sure I agree that Nov-Mar performance should equal to Nov-May. See also Major point 1.

• Sec 3.2. is unclear. Please describe better how you performed the interpolation. Eg, “function of the inverse distance”? “adjusted to match”? Also not clear if your interpolation takes into account the effect of elevation? The five nearest stations might not be equally representative in that regard.

• Related: Why did you not use LAPrec or the gridded HISTALP to extract this information? They use homogenized input, but at least for LAPrec, the spatialization is much more complex and takes topography well into account.

• L150ff: Seems like research questions to me, not methods.

• L156: which correlation coefficient (Pearson, Spearman)?

• Fig 4: Please do not use rainbow scales, since the changing colors introduce artificial visual breaks. Use a continuous scale such as viridis, scico (https://www.fabiocrameri.ch/colourmaps/), or similar. Moreover, figure looks quite overplotted, maybe it could help to sub-divide by elevation bins? Ok, I see this comes as Fig5. So maybe in Fig4 you could focus on a few single stations instead or omit?

• L209: how did you define “nearest quartile” in 2d?

• L210: Why did you not use the actual values for your localized linear regression instead of the bins? In that way, you can maximize the information better, and also include information beyond empty bins (< 50 values). Moreover, in statistics, extrapolating beyond the range of training data is controversial. Personally, I would not trust the values far beyond (>1degC, 50% prec) what one sees in Fig 5e-h. Finally, since you want to get 2d-surfaces, GAMs (generalized additive models) seem like a prime tool to be used (with a 2d tensor product smooth); it would not require to bin your data, and would also work in 3d with elevation as third predictor.

• L242 Please explain, why the bias correction is needed.

• Sec 4.1. Why this? Not related to the main paper goal, I guess? Also there are some methodological concerns, and missing descriptions: related to data coverage, usage of linear regression for multiple stations (not recommended, because of their correlation, better to a regional/elevation series first), why the arbitrary split in two periods given the know non-linearity of change (papers by Marty and co.).

• L307: What test did you use to assess this significance of skill?

• Fig10 a) and b) scales do not match but should? a) has -0.4 to 0.4 and b) has -0.2 to 0.6

• L341: Does this also hold for the single series? Would be interesting to see some single stations time series and not only regional averages.

• L350: Very interesting application of your method. However, 3.2degC is beyond your training range for that elevation range, so the accuracy is highly questionable. Especially, since your numbers are very different compared to previous studies (a comparison with existing literature would be very useful, there are a lot of studies using regional climate models, or snow models forced with climate models).

• Discussion of results missing.

Please see report attached