Dear authors,

first of all I would like to apologise for the long time it took for this decision to be finalised: one of the original reviewers was unfortunately unable to re-review the paper again, so an additional reviewer had to be found. The last report on your modified manuscript consequently arrived not before the Christmas break.

Below you will find the two reports of the reviewers. You will see that both agree that the manuscript improved considerably and that it is in general ready for publication, but only if two important aspects are addressed: the first concerns the AAT model and a discussion of the uncertainties related to the lack of sufficient meteo stations at high altitude (referee 1); and the second concerns the better illustration of the classification scheme of rock glaciers in the Andes (active, inactive, intact, relict) and the subjectivity related to it (referee 3).

I agree with the reviewers and would like to ask you to adequately address these concerns in your modified manuscript.

Kind regards and my apologises again for the delay,

Christian Hauck
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Anonymous Referee #1:
Review of the manuscript “Permafrost Distribution Modeling in the Semi-Arid Chilean Andes” by Azócar, G. et al.

The study present relevant work in the area of spatial permafrost modeling in a region where only few studies or evidence of permafrost exist. The manuscript has improved over the first version, is well-structured, and the applied methods are adequate. However, there remain some issues that need to be addressed before publication. These issues mainly regard the modeling of the mean annual air temperature (MAAT) which is a main input to the permafrost model.

The low availability of temperature observations at high elevations (> 4000m) is a major weakness of the study. I assume that a great effort was made to gather temperature measurements in the region, and that no improvements in this direction can be made. However, there is a need to quantify the uncertainties regarding the AAT model:
From what becomes apparent by the results of the study (Figure 5), the climatic conditions for permafrost are favorable mainly at elevations above 4000m. However, almost no temperature data are available for these elevations – three stations (having one respectively two years of observations) lie around 4000m and only one station (4 years of observations) is located at 4900m. The main input to the AAT model (Eq. 1) is built from four stations accounting for 100 of the 116 AAT observations used in Model 1 (Eq. 1). These stations lie below 3519m, and are hence below the area of interest for permafrost occurrence in the region (according to Fig. 5). It is not clear whether the linear relationship determined by model 1 (lapse rate of -0.71°C per 100m) is valid at high elevations.

The authors are asked to determine the uncertainties of the AAT model (Eq. 1) at high elevation stations independently by applying a cross-validation (maybe station-wise). It would be interesting to know whether the model is biased at station "Frontera" (4 observation years) if the station is not included in the model. If there is a bias of the AAT model at stations at high elevations, the authors are asked to discuss its influence on the permafrost model more in detail (e.g., in page 11, lines 13-16). The estimated residual standard error (RSE) does not give an indication of the prediction error. Further, the comparison of the RSE with e.g., Hiebl et al. 2009 is not very meaningful due to the large difference in both climate and the data base underlying the models in the Alps and the Chilean Andes.

Further, a discussion of the quality of the station data used is missing. Temporal homogeneity testing and correcting are standard procedures required before estimating climate variables such as MAAT. The authors are asked to either show that the data underwent a quality control and homogenization process, or otherwise mention that the data used was not homogenized. I would not expect a large influence of the inhomogeneities on the estimated MAAT (in comparison to the uncertainties arising from the limited availability of observations in general). However, the uncertainties due to possible inhomogeneities should be mentioned in the manuscript.

Technical issues:
Subsections 3.1.2.1.1 & 3.1.2.1.2: include the text of subsections 3.1.2.1.1 and 3.1.2.1.2 directly in subsection 3.1.2.1 to avoid having another level of subsections.
Equation 1: Elevation and Northing do not depend on year j (same as the coefficients b_1 and b_2).
Equation 3: Elevation and Northing do not depend on station i, but are a function of x (same as MAAT), right? And the same for the residuals?
Equation 6: the notation [m] in the equation is confusing.
Page 9, line 19-24: Please rephrase the sentences.
Figure 1: could you include the meteorological stations in the figure?
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Anonymous Referee #3:
Comment from an additional reviewer 3, whose review became necessary as one of the original reviewers could not re-review the modified manuscript:

In my opinion, the manuscript is well structured and well written, and it seems to me that the authors took into consideration carefully all the comments of the previous reviewers.

The paper could be accepted as is but I strongly recommend to add a figure illustrating (picturing) what active, inactive, intact and relict rock glaciers are looking like. Not so many are familiar with rock glaciers in the Andes and, as the classification of rock glaciers is subjective, we need to know explicitly how the authors did it.

Dear authors,

many thanks for your revised manuscript and your responses to the questioons raised by the reviewers. In my opinion you clearly answered them and adapted your manuscript accordingly. The paper is now ready for publication except for some small technical corrections listed below:

(1) In your answer R1 you made an extensive cross-validation of the MAAT data to analyse the uncetainty of the AAT model. This you summarised in the manuscript as "Sensitivity analyses using leave-one-station-out cross-validation confirmed the validity of this value". Could you inlcude more details of this cross-validation in the text, i.e. by giving at least the maximal changes in predicted MAAT for the two reference elevations ? Otherwise, this one sentence is a bit vague for the reader.

(2) you answered R4 as "changed as requested", but in your manuscript the level 3.1.2.1.1 (Response and predictor variables) remained. This should be included in the text with a subheader without numbering to avoid to many section levels. the corresponding references on page 3 are wrong at the moment. Please carefully review and revise these section numbering.

(3) caption of Figure 1: here, the symbols of the figure should be explained; especially the symbols of the meteorological stations (as requested by reviewer 1) are not explained in the caption

(4) see also the comments/corrections in the annotated manuscript

kind regards,
Christian Hauck