We sincerely appreciate the thorough review of this manuscript and the constructive feedback provided. The reviewer’s  comments have been very valuable for improving the clarity, structure, and depth of our work. Below, we address all comments in detail; reviewer comments are repeated in italic font.

General Comments:

1. Readability and Structure:

We appreciate the reviewer’s positive assessment of the manuscript and their recognition of its relevance and novelty. In response to the concern regarding readability and structure, we have carefully revised the manuscript to improve clarity and flow as well as language and grammar. Specifically, we restructured Section 3, “Description of study site and data”, Section 4, “Model simulations”, Section 5, “Results and discussion” and added an additional Subsection 5.4, “Model assumptions and limitations”, and we rephrased parts that previously may have been unclear.

1. Discussion Depth and Comparisons to Previous Studies:

We expanded the discussion and added comparisons to other studies as far as such studies are available. These sparse studies are now also mentioned in the Introduction section.

1. Conclusion vs. Discussion:

We appreciate the recommendation for strengthening the discussion. We reorganized the Discussion and Conclusion sections, moving and grouping elements of discussion into Section 5 (“Results and discussion”) and summarizing the principal findings in a now more concise Conclusion section.

Specific Comments:

L190: The observational permafrost temperature and atmospheric data sets of this site are largely sufficient -> “largely” based on what?

We reformulated the sentence specifying that the datasets are well suited for modelling purposes, because they include measurement periods of more than 20 years of meteorological forcing and permafrost temperature and distribution to be used to force the model or for comparison purposes. This has been stated in the updated version of the manuscript.

L219: The simulations have been run from June 2000 to January 2017-> Why this period? Explain, please.

This time frame was selected as it precedes the observed significant increase in ALT, aligns with available meteorological data, and is representative of long-term observations of permafrost temperatures at the site. Starting simulations in June avoids defining an initial snow cover and related uncertainties in its properties. The simulation of the selected  period allows to reconstruct the impact of  thermal stabilisation methods and to analyze the re-establishment of a new temperature equilibrium within the ground, while preserving permafrost and delaying an increase in ALT at the site. We incorporated this explanation in the manuscript.

L220: …an hourly time step-> Why hourly? Explain, please.

Meteorological data to force the model is provided at an hourly time step. This is a temporal resolution necessary to represent  fast-changing weather conditions and to simulate their impacts, for instance, on the energy balance and its various heat fluxes. For coherence, the model uses the same 1-hour time step. .Internally, the model interpolates the hourly forcing on a 15-minutes time step (accomplished by the MeteoIO library (Bavay and Egger, 2014))  to avoid abrupt step changes and to obtain higher temporal resolution simulations.  

L265: The objective of this experiment is to allow more efficient… -> Is that really the objective? It is not to analyze the applicability?

We removed this sentence. The objectives have been regrouped and reformulated at the end of the Introduction section.

L268: We simulate the presence of a 50-100 mm thick… -> Why that thickness and not a different one? Explain, please.

The thickness range was chosen such that efficient heat control in the context of this study was possible, that is, sufficient attenuation of the conducted heat while minimizing the use of insulation material. We also simulated a thinner slab, which was found to be insufficient to reduce heat transfer.

L273: The albedo of the isolation material is assumed to be 70%... -> 70% based on what? Explain, please.

We added an explanation stating  that the albedo of the insulation material is set at 0.7, representative of white styrofoam with a high-albedo reflective coating (Ramamurthy et al., 2015; Qiu et al., 2018; Chen et al., 2020) and comparable with the average albedo of a snow cover .

L299: …as evident in Equation (1).-> Not sure that “evident” is the right choice. If something is evident, there is no need to say it.

Correct. This statement has been reformulated avoiding the word “evident”.

L329: For some periods, measured snow depth is below the simulated one indicating that the model would underestimate melt or erosion.-> What is the reason for this? Can you support this statement with a reference?

This statement is supported for example in Lehning et al., (1999b).

Figures:

Maybe this is something on my side, but it is not clear to me why in some figures you choose daily averaged ground temperatures while in others you choose monthly averaged values.

We use monthly averaged ground temperatures when comparing the model to observational data because this provides a more reliable basis for evaluating the model’s ability to reproduce long-term temperature trends.. Monthly averaging reduces the influence of short-term variability, such as daily fluctuations, which can obscure lower frequency  temperature signals which may be of interest. This allows us to assess how well the model captures temperature trends over longer time periods.

We also used monthly averages when analyzing the impact on the ground temperatures from some passive thermal stabilisation methods, such as thermal insulation or the components affected by shading (influencing multiple environmental factors (e.g., solar radiation, precipitation, wind). Our goal was to understand the cumulative effect and the general effectiveness of these methods under varying conditions. Monthly averaging helps to emphasize the broader impact and detect the effect of the methods within the overall trend.

In contrast, we used daily averaged data when the focus was on the dynamics (variability) and evolution (trend) of the system over time—for instance, to explore how quickly equilibrium is reached following a change in forcing or how ground temperature is affected by the individual cooling method applied. In these cases, daily resolution is essential to capture the thermal response of the soil to temporal variations in the meteorological forcing in greater detail.

In Figure 1 I miss some location references (lat, lon or UTM).

We added the UTM.

In most of the figures, it is really difficult to distinguish the numbers within the blue color areas.

We also improved the visibility (contrast) of numbers on the graphs.

Technical Corrections:

• We corrected all issues with citation formatting.
• Improvements of sentence structure and clarity have been applied to L153, L212, and L290.
• We removed redundant wording in L132-136 , L332-333, and L334-335.
• Figure A2, Figure B2, and Figure 2 have been revised to remove redundant information.
• The incomplete reference at L637 has been corrected.

Final Remarks:

We greatly appreciate the reviewer’s insightful comments, which have significantly improved the quality of our manuscript. We hope that the revisions address all concerns and suggestions satisfactorily.

We sincerely thank the reviewer for the thorough and constructive review of this manuscript. We are pleased that the topic is considered relevant and the study design scientifically valuable. We have carefully addressed all major and minor comments, which has led to significant improvement of the clarity, structure, and scientific quality of our work. Reviewer comments are repeated in italic font.

Major Comments:

1. The introduction is too long and contains non-essential information.

Without specific indication, it is difficult to identify what the reviewer considers ‘non-essential’ information. Nevertheless, we tried to focus the introduction on information particularly relevant for this paper and write the introduction more concisely. Note however, that Referee 1 and the Editor have asked for some additions, e.g. the discussion of Alpine vs. lowland permafrost, and a comparison with previous studies discussing the stabilization of Alpine permafrost, which we  included in the introduction. Therefore, the introduction still has a certain length.

1. The fieldsite description lacks detail regarding permafrost and climate data.

We thoroughly revised Section 3 and added more information regarding the site description such as permafrost ALT trends and changes in it, mean air temperature, snow depth, and snow season specific for the site.

1. Recommend adding an overview table comparing natural conditions with thermal stabilization experiments.

Thanks for the suggestion. A summary table ( Table D1) has been included in the Appendix, highlighting key outputs of the ALT in different modelling simulation scenarios, enabling easier comparison across model results.

1. A dedicated section on model limitations is missing.

We added a new section which discusses related points (Section 5.4, “Model assumptions and limitations”).

1. The Discussion is limited; comparison to literature is missing.

Thank you, also Referee 1 raised the same point. We briefly mentioned comparative studies in the Introduction and discussed their results in comparison to our findings in the Discussion section. In addition, some parts of the former “Conclusion and outlook” section have been moved into the revised “Results and discussion” section, resulting in a more complete discussion of results  and more concise and structured conclusion.

Minor Comments:

I would recommend proof-reading the manuscript for grammatical mistakes.

The manuscript has been proofread for grammar and clarity, and corresponding corrections have been applied.

The title does not reflect that the assessment and comparison are based on numerical simulations and not field experiments.

The title has been revised mentioning the simulation-based nature of the assessment.

L23: Include newer rates of Noetzli et al. (2024): Enhanced warming of European mountain permafrost in the early 21st century, https://doi.org/10.1038/s41467-024-54831-9

The reference to Noetzli et al. (2024) has been added, and based on it, the corresponding most recent information regarding the temperatures and melting rates.

L36: Not only thawing but already warming permafrost can be a risk for the infrastructure. L36: Why “built” infrastructure? L37: What is meant with “such” infrastructure? Infrastructure on permafrost? L49: What includes “other destructions”?; L54: Improve the clarity of this sentence.

We reworded and clarified these sentences to remove ambiguity regarding the terms of infrastructure, thawing risks, and types of destruction.

L108: also CryoGrid community model, https://doi.org/10.5194/gmd-16-2607-2023 

We included the CryoGrid community model citation.

L138: Did you include drainage / seepage in combination to your bucket water scheme? Your simulated fieldsite is on a slope (Fig. 1), so this might be an important effect. If not included, discuss it in the uncertainties.

Yes, drainage is included indirectly, given the slope of the terrain. It is assumed that percolating water is not only seeping vertically but also following potential slope flow draining water from the site in the underlying substrate. We have mentioned this in the revised manuscript.

L166: Not clear, so it calculates the surface energy balance? What does it mean that it avoids the connection with the surface temperature?

In SNOWPACK, boundary conditions can be set using a Neumann type BC, calculating the heat fluxes and the resulting temperature at the surface, rather than relying on a prescribed surface temperature as an input. This approach allows the surface temperature to evolve naturally based on the energy balance and the applied cooling methods. This BC provides a more accurate representation of the heat exchange between the ground and the atmosphere, with a better representation of the heat flux at the soil-atmosphere interface. We have explained this in the manuscript.

L174: Which permafrost parameters? Ground temperature and active layer thickness?

By the permafrost parameters we refer to ground temperatures, volumetric water content, bulk density, thermal conductivity, heat capacity, temperature gradient, etc. These are now explicitly mentioned in the revised manuscript.

L175: How is the snow simulated? Based on the precipitation of the atmospheric data? On a mountain top that might be extensive snow redistribution due to wind. Is that considered? Furthermore, you are on sloping terrain, which may affect the snow accumulation. Do you take this into account? How is the melting handled? Is meltwater just removed from the system or can it infiltrate the ground?

SNOWPACK can simulate the evolution of the snow cover either by prescribing measured snow height values or by calculating the new snow depth based on observed precipitation and air temperature. When the snow cover is prescribed from measured values it takes into account local drifting snow, since that is included  in the snow height measurements.

L178: This sentence does not make sense. Do you mean: We selected this site because it us representative and because of the infrastructure?

We corrected the sentence stating that we selected this site because it is representative of many alpine permafrost locations and because the nearby infrastructure could be affected by permafrost thaw.

L180: Give time period and active layer thickness before and after. What about the variability of ALT from year to year?

The ALT at this site has doubled, during the past decade (Hauck and Hilbich, 2024). Hauck and Hilbich (2024) indicate a general deepening of ALT from 4–5 m before 2008 to 5–7 m by 2016, with subsequent increases leading to 13 m after the extreme summer of 2022. This approaches the threshold (about 14 m) beyond which full winter refreezing may no longer be possible. We added this information regarding the ALT variability during the studied period into the manuscript.

L193: Atmospheric data from which time period? Also refer here to table 1, as it is only listed in this table which parameters have been used and not mentioned in the text.

For simulations, we used atmospheric data (Table 1) from the PERMOS meteorological station next to the borehole for the years 2000 to 2017 (Swiss Permafrost Monitoring Network, PERMOS,  Hoelzle, 2021; Hoelzle et al., 2022). Long-term observations (Hoelzle et al., 2022) state that the mean air temperature observed at Schilthorn (1998-2018) is -2.60 °C, the mean snow height -0.87 m, and the snow season usually lasts from October to June (Swiss Permafrost Monitoring Network, PERMOS, and Hoelzle, 2021). We added this information  in the paper.

L198: How was the spinup performed?

We clarified in the paper that SNOWPACK needs a proper initialization but not a spin-up if the ground temperature profile is initialized with corresponding observations.

L199: Is this data from the borehole? Then add it to table 1 where you describe the borehole. and L205: You say in line 199 that you have observational data for volumetric ice and water content, voids, density, thermal conductivity and heat capacity. Now you say it is based on borehole temperatures (?) and modelling. Which is true?

We do not have measurements of volumetric ice and water content, voids, density, thermal conductivity and heat capacity. Instead, we estimated these based on previous studies and parameters of substrates typical for this site. In the text we added a clarification and reference to Table 2 stating: “We set up the model using the following set of parameters: volumetric ice, water, substrate, and voids content of the ground, substrate density, thermal conductivity, and heat capacity. Based on the available data from the borehole temperature measurements and previous modelling experience (Marmy et al., 2013; Ekici et al., 2015; Wagner et al., 2019; Hoelzle et al., 2022), we use the substrate parameters listed in Table 2.”.

Table 2: Are the 3 layers divided into gridcells? What is the thickness of the gridcells and do they vary with depth?

We added a description of layer discretization and grid cell thickness in the text of the manuscript.

Each layer was divided into grid cells with a vertical extent of 0.1 m for the natural conditions and for thermal stabilization with shading.

The thermal insulation layer was divided into grid cells of 0.05 m and 0.1 m for 50 mm and 100 mm material thickness, respectively.

Additionally, to accurately represent the placement of cooling pipes and the active cooling process, the grid cell thickness for layers between 0.2 m and 0.4 m was refined to 0.01 m. This information is included in the manuscript in Sections 3, 4.2.2, 4.2.3.

L226: For those not familiar with Schmucki, please state the main principle so that one does not have to google the paper: is it e.g. an albedo aging factor?

Schmucki’s albedo aging parameterization estimates the albedo based on the time elapsed since the last snowfall, grain size and liquid water content. This brief explanation has been added in the paper.

L242–257: Would fit better in the discussion section than in the methods.

We appreciate the suggestions, however, we think it makes sense to keep it as part of the Methods section. This paragraph explains the specific adjustments made to the model—namely, the coefficients changed to simulate the thermal stabilization through shading. We think that this information is essential upfront for understanding how the method is implemented and the model is configured.

L253: Partly based? Which of the numbers were not based on Loktionov et al., 2022?

We clarified that the choice for parameters (1) wind speed decreased by 70% and (2) the ground completely protected from snow and liquid precipitation, is based on previous modelling results investigating thermal stabilisation by Loktionov et al., (2022). However, Loktionov et al. (2022) applied a value of solar radiation that decreased by 95% from global horizontal irradiance (GHI). In the present study, we can revert to the modelled components of direct and diffuse solar radiation. Using only the diffuse solar radiation component is a simplified and idealised case, which allows to reproduce the effect of the solar panels on ground temperature distribution, without applying an additional empirical coefficient. This is explained in the revised manuscript.

L309: Where does the number -7.5 dC come from?

This choice corresponds to the mean temperature of the coolant circulating in the pipes, and was experimentally tested in Loktionov et al., (2024a).

L329: What about redistribution of snow by wind?

We forced the model with available snow depth measurements from the site, avoiding the calculation of the snow depth from precipitation data (Table 1) which includes only rainfall. We have clarified that in the text .

Figure 1: I recommend several improvements in this figure:

• Add lat / lon or UTM
• It is very difficult to see the permafrost conditions / solar radiation close to your fieldsite. I would recommend to zoom much closer to your fieldsite in your maps with solar radiation and permafrost distribution.
• Another possibility would be to display the permafrost distribution into the map on the right instead of only showing the topographic map.
• Change the colorbar of the solar radiation as the lower values are not applicable.
• Furthermore, make the green dots for the stations better visible.

Thanks for these suggestions. We adjusted Figure 1 accordingly, namely: (1) zoom in on the fieldsite; (2) made the station markers more visible; (3) included the UTM in the figure caption; (4) changed the colorbar of the solar radiation.

Comments concerning Figures 2, 4, 5, 6, 7, 8, 10, 12, 13, A2 :

Following the suggestions, we made the following changes:

• Improved visual clarity (e.g., removed redundant 0°C isotherm labels).
• Updated colorbars to use perceptually uniform scientific color scales.
• Increased depth range in Fig. 12b to show the entire active layer.

L342: Could it be that this is true because you used the bucket water scheme? Do you think your results could look different using Richards equation? Discuss the uncertainties.

We added a clarification in the manuscript to acknowledge the role of the bucket scheme in our results. While using Richards equation may provide a more detailed simulation of capillary-driven water flow, we argue that this may not be appropriate in our study context. The permafrost soils in mountains are typically rocky, with large voids and cracks, where capillary forces play a small role for water flow. Under such conditions, it is not clear whether the Richards equation would better represent water movement compared to the bucket scheme. We discuss this point and the associated uncertainties in the revised manuscript (Section 5.4, “Model assumptions and limitations”). 

Fig. 4b / L343: In your simulations, reduced wind speeds lead during the entire year to lower ground temperatures. I am wondering: if you reduce wind speeds, this will reduce latent heat fluxes during summer, decreasing the evaporation and thus the cooling of the ground? Or is evaporation not included in the model?

The revised manuscript states that evaporation is included in SNOWPACK via the latent heat flux. However, with the bucket scheme, only the surface layer contributes to evaporation, and once this moisture has evaporated, the process will stop. This may limit the evaporation over a longer time. Additionally, we note that latent and sensible heat fluxes can compensate for each other depending on the atmospheric conditions. Increased evaporation and cooling often lead to stronger sensible heat fluxes due to enhanced temperature gradients between the surface and atmosphere, and vice versa. We have incorporated this explanation into the revised manuscript text (Section 5.4, “Model assumptions and limitations”).

L350: “affects negatively ground temperatures” can be misleading as temperatures are increased. Change the wording.

We changed the wording removing the misleading part.

Final Remarks:

We are grateful for this  thoughtful and insightful feedback. The implemented revisions based on the reviewer’s suggestions have significantly improved the structure, clarity, and scientific rigor of this manuscript. We hope the revised manuscript adequately addresses the raised concerns.