Dear authors,

I have now received the review for the revised manuscript. As you will see the reviewers indicate that the manuscript has improved but identified still several weaknesses especially in the presentation.
I ask you therefore to carefully revise your manuscript according to the review.
The revision should contain a response to each of the comments from the reviewers and explain how the comment was handled. If you disagree with a comment, please explain why. If the text was modified as a response to a comment, please indicate how the text was modified, including the new text and its position in the manuscript (line numbers) and highlight these in the revised manuscript.

I am looking forward to the new version of your manuscript.

Best regards,

Tobias Bolch -Editor-



Review

1 General comments
Revuelto et al. addressed most of my mentioned concerns. The presentation of wind measurements and the revised statistical analysis improved the manuscript. I understand the focus on the influence of topography on snow depth distribution and I think the focus on this topic alone is in general worth a publication. Some of my mentioned concerns are not well addressed, e.g. the quantification of persistence. The inter- and intra-annual persistence is a main conclusion in this manuscript although the chosen formulations are rather vague.

My major concern is the presentation. There are many hints that the manuscript is in a rather sloppy (type setting errors, missing white spaces, English grammar). I am not a native English speaker as well, but it seems that especially the new parts of the manuscript, and the discussion and the conclusion sections need editing.

2 Major comments
2.1 Quantification of persistence
In the abstract the authors mention their aim to assess if the contributions of topographic variables were variable over intra- and inter-annual time scales (line 30f). The chosen methods and results do not quantify the persistence, and thus all statements remain qualitatively and vague. For example in the discussion section line 559f (“...their contribution to the total explained variances are rather similar.”). I can see that the TPI is consistently explaining snow depth (Table 3 to Table 5), but with a quite variable contribution (e.g. from 49% to 83% for the TPI in Table 5). What I do not understand is, if the presented differences between survey days hint to a variable or a persistent contribution? Are these values similar or different? Here the manuscript is not able to quantify persistence.
Similarly, the authors mention that the models were consistent in the conclusions section (line 581ff) and concluded that this suggests a consistent effect of topography. Indeed some variables are always present in the models (line 559), but is a standardized coefficient for the TPI between -0.4 and and -.78 similar or different, especially if the model’s r2 is quite variable.
Since the time consistency of the influence of topographic variables is one main conclusion of this manuscript I expect a more detailed and quantitative investigation. This was already one of my major concerns in the first round. Here are some suggestions how this can be quantified:

• I understand that the authors do not want to present models that can be applied to other areas. They want to assess which topographic variable explains how much on a single day, and how does this contribution vary in time. This was mentioned as a reason for not training a model on one day and verifying the model on a different day, or training a model with all days (global model). But to my point of view, these investigations show how the single day models differ in relation to a global model. It could answer the question, are the presented ranges of coefficient rather similar or different to each other.
• Another way to obtain a relation is using Monte Carlo methods. In the first version of this manuscript this was used for to obtain confidence intervals for correlation coefficients. However, confidence intervals for the presented regression coefficients would quantify persistence: This would give a relation between a confidence per day and the variance between days.
• How often is the TPI the first variable in the trees (both in already analysed single day models, and in random subsamples of a single day)?
• What are the average and the range of the TPI’s critical value in the first node of the trees (both in already analysed single day models, and in random subsamples of a single day)?
…
2.1 Presentation quality
2.1.1 English grammar
Especially the new added paragraphs and the discussion and conclusion sections need editing. There are many long sentences which are hard to follow (e.g. line 536-540). Quite often the grammar is not correct, e.g. in line 519ff : “… the correlation …prevented us of potential problems of multicollinearity.”

2.1.2 Imprecise argumentation
In the following are only some examples presented, this is not a complete list:
The first sentence of the conclusion is not precise (line 572f), since only the TPI of one search distance was studied. All other search distances and also the curvature were excluded before the analysis.
Areas of snow free zones and areas maximum snow depth were not investigated, but mentioned in the discussion (line 562f) as a hint for time consistency.
The last sentence of the conclusion is not very precise: “Several interesting temporal evolutions ….were found…” (line 588 ff). Which evolutions are meant here? I can recall the temporal evolution of the SX parameter, not more. They can be mentioned here.
The authors have stated in the conclusions (line 584f) that “…terrain characteristics have shown a major role on snow distribution, as TPI explanatory capacity”. While this sentence is another example of not good English grammar, I also wonder about the expression “major role”, since only terrain characteristics were studied.
I mentioned Elsner and Schmertmann (1994) in my first review, which analysed cross-validation problems in time series. They do not analyse spatial autocorrelations as stated here (line 234ff). While the problems are related I think a longer explanation how these problems are similar and why this could be a problem here needs to be added.
Line 303f: “Upper areas of the map”.
Line 322f: I think the TPI showed the highest correlation for all days, not “nearly all”. See also Table 3. Similarly, I would say it is “significant on all days”, and not on “some” (Line 339).
Line 412f: When was snow not mobilized and how can the authors determine?
Line 431-439: This was already stated in the first review: Please cite the few studies which were mentioned in these lines. The authors mentioned “few”, but cite only one.
Line 451: Figure 3 is still not large enough that I can see snow in deep concavities. Maybe zoom into one example area.

2.1.3. Typesetting
Although there will be a typesetting correction after this second review, this manuscript has at this stage many typesetting errors. Sometimes there is a white space between numbers and units, quite often not (e.g. line 460). In line 239 is a white space after the “<” but not before.
The averaged Sx parameter (which I called very sloppy “Sx dash” in my last review, mainly because I copied and pasted this text into a browser window), should be consistently called in the manuscript with an averaging bar over the Sx, and not just “Sx dash (Sx further on)” (line 214), since this could lead to confusion. Thus, it will be consistent with the original paper of Winstral et al. (2002).
While many of those points are in general listed under “Minor comments”, the large number reduces the presentation quality. The large frequency only allowed me to show examples. In the second round of the review process I would expect more emphasis on this topic; otherwise this could give me an indication how sloppy other parts of the analysis were done which I have no direct insight to.

2.2 Minor Comments
I suggested in the first round that topographic variables can be studied in relation to other variables. This would allow conclude as in line 584f that “…terrain characteristics have shown a major role on snow distribution…” With the added wind analysis the authors have increased the value of the manuscript, although I would see a great value to include modelled melt rates, short- and longwave radiation in the analysis. Some points can be considered in this context:
2.2.1 “Net radiation”
The authors have added in Figure 2 net solar radiation. It is unclear if this integrates longwave radiation or only shortwave radiation.
The new information was never discussed in the text.
2.2.2 “Potential radiation”.
Similarly it is not clear to me if the used radiation introduced in line 193 integrates longwave radiation or only shortwave radiation.
If this is only shortwave, what I assume, I disagree with the explanation of the authors in their answer, that “…the use of the variable “potential radiation” is correct and useful for the main purpose of this
article, because it explain well the relative spatial variability of the incoming radiation
(independently of the magnitude) during specific periods of time.” During days with cloud cover it is not a matter of magnitude only, since diffuse and longwave radiation alter the spatial distribution of available melt energy.

2.2.3 Line by line
Line 136ff: What is the average number of observations set for a single day (to get an impression how small the 100 “SD cases” in a subsample is)?
Line 251ff: Not clear if the PCA was done for each day or for the global data set.
Line 301: Figure 4 is mentioned before Figure 3.
Line 312-315: Only a replication of the table.
Line 375ff: “Good agreement between models”? Do the authors mean a range between .25 to .65 of the r2 is a good agreement?
Line 444ff: The spatial scale of curvature and TPI is with 10 m (4 data points) and 25 m (25 data points) maybe too similar to come to this conclusion.
Line 190ff: As far as I know, ArcGIS takes for slope and curvature a 3 x 3 window. This would lead in the case of a 5 m resolution to a 15 x 15 m window.

Dear authors,

You have addressed the remaining concerns and I am happy to inform that the manuscript is now almost acceptable. However, I ask to once again carefully proofread the paper also regarding the punctuation. Please also check once again the formatting of the references.
Provide the figures (esp. Fig. 2 and 3) in better quality for the final publication. Figure 3 should also be enlarged. This could be achieved with omitting the outer frame.

Best regards,

Tobias Bolch
Editor TC