General Comments

Czekirda et al. present an interesting analysis to describe the evolution of permafrost in rock walls over the last 100+ years. The analysis is based on 2-D thermal modelling and measurements from rock wall temperature loggers along 9 profiles in Norway. The authors consider the various factors influencing the permafrost distribution and its evolution in the simulations and also assess their relative importance. The results of the simulations indicate an increase in ground temperatures since the 1980s and that the rate of change increases with elevation within a single rockwall section. Overall the analysis, interpretation of results and conclusion appear to be sound. The paper is for the most part, well written but some editorial revisions are required. The paper would be of interest to the general permafrost research community and especially those interested in mountain permafrost distribution and the stability of rockwalls. The paper is therefore worthy of publication following minor revision. I have a number of comments for the authors’ consideration.

It is good that field measurements such as the rock wall temperature measurements have been utilized in model calibration. However, there is not much comparison of the simulated results with observations. There is some comparison of the data (near-surface temperatures) derived from the rock wall loggers with the simulated temperatures but as the authors point out, these data were used for the calibration of the forcing input and only qualitative comparisons are done. There is not much comparison to observations of deeper temperatures, although a comparison to one borehole is mentioned. There appears from the information in section 2 and the references cited there are a number of boreholes with temperature cables (e.g. Christiansen et al. 2010) in the study area and also geophysical surveys have been done (e.g. Etzelmuller et al. 2021). It is not clear whether any of the boreholes or geophysical surveys are located on or close to the study transects. It would be good if the paper could include a comparison of these observational data with the simulated results. This could help strengthen discussion with respect to the relative importance of forcing factors (and limitations of the model) and other modes of heat transfer such as convection or advection along the various profiles.

Specific Comments

L17-18 – revision suggested: “…show the distribution of permafrost is sporadic to continuous along….”

L22 – It makes more sense to mention rock wall temperature before permafrost distribution since it is the ground temperature that determines occurrence of permafrost.

L33-35 – You could be clearer here that this was due to an extreme event rather than long-term change.

L38 – “permafrost-affected cliffs” or “cliffs underlain by permafrost” might be a better way of writing this.

L40-45 – Could you refer to the 3D (or multi-dimensional?) nature of heat flow and the higher thermal conductivity of the rock (compared to soil, unconsolidated sediments) here.

L53-56 – Aren’t freeze-thaw cycles important to this process (thermal contraction/expansion)? Would the frequency of these cycles change with climate warming?

L76-78 – Are you referring to the BTS approach here (e.g. Hoelzle 1992 https://doi.org/10.1002/ppp.3430030212; Gruber and Hoelzle 2001 https://doi.org/10.1002/ppp.374; Bonnaventure and Lewkowicz 2008 https://doi.org/10.1139/E08-013)

L85-86 – revision suggested: “…to simulate the thermal evolution since 1900 of mountain permafrost…..”  (I think you mean that you simulate thermal state since 1900 rather than rock walls being instrumented since 1900).

L89 – Why not just refer to limits of permafrost occurrence rather than near-surface permafrost.

L91-93 – How were the transects chosen – are they representative of the geological and climate conditions in the region?

L96 – Here and throughout text – just refer to “Western Norway” (delete “the”)

L98 – revise to “annual total precipitation” (revise elsewhere in text also)

L99 – revise to “mean air temperature” – is this “mean daily air temperature”? (note: important to be clear that this is air temperature since surface and ground temperatures are also mentioned in text). It would be useful to give the normal mean annual air temperature as well as the range, here and in description for the other study areas.

L102 – Do you mean “insulates” rather than “isolates”?

L103 – Revision suggested: “…2015-2017 nine loggers have been installed at selected rock walls to measure surface temperature in western Norway”. Since the data from these loggers appears to be used in your study, you should probably mention the type of logger and its accuracy and precision.

L 127 – Revision suggested: “ …areas in Norway, including its highest peak.”

L132-133 – Revision suggested: “..than western Norway with normal (1961-1990) mean precipitation typically less than 1000 mm per year (Lussana, 2018)…”

L135 – delete “the” before Central

L136–144 – Are these boreholes and geophysical surveys on or near the study profile?

L140-143 – Do you mean that permafrost occurs at least at elevation as low as 1559 m and that frozen conditions exist at all the boreholes down to this elevation? OR is it present at some boreholes but not others? Some clarification and revision of text required.

L145 – replace “whole” with “entire”

L155 – Here and elsewhere in text, delete “the” before “Northern”

L156 – revise to: “…with the highest annual total precipitation in….. where annual total precipitation was less than…”

L159-160 – Were these boreholes on or near the study profiles?

L195 – Define “GST”

L197 – Revision suggested – “Note that since CryoGrid 2D is a conductive mode, convective…”

L216 – Do you mean “surficial deposits”? also “all of” might be better than “the entire”

L239 – “positive trends” rather than “increasing”?

L249-251 – How far back before 1900 do you reconstruct SAT?

L259 – revise to “GST determined from rock wall loggers”. It isn’t clear what you mean by giving more reliability as SAT and GST are not the same thing and there are offsets which you mention later in the paper.

L268 – Be clear that freezing n-factors are used. Revise to “…..accounted for by using freezing n-factors (nF) that….”

L270 – revise to: “…assign various nF values along the….”

L288-289 – revise to: “…case of rock walls thawing n-factors (nT)….might not be able to….”

L301 – Revision suggested: “Model runs start around..”

L334 – What depth for GT are you referring to?

L339 – Although the video shows the evolution of the thermal regime over then entire 120 years it would be useful to include 1900 in Figure 4 so that the reader can easily compare current conditions to those at the start of the time period. This could also be done for the figures for the other two regions.

L357 – Do you mean permafrost degrades almost completely by 2020?

L381 – Revision suggested: “…blockfields, simulated GT is between -6 and -4°C.”

L382 – Here and elsewhere in text – It might be better to refer to range in GT rather than span.

L383 – Deep GTs – how deep? Revision also suggested “….glaciers has the smallest range in GT..”

L387-388 – Revision suggested: “GTs are simulated to be higher beneath warm-based glaciers with no permafrost beneath the thickest parts of the glaciers” – is this what you mean?

L408 – “lower” rather than “colder”

L441 – “The colder zones move rapidly” – not clear. It would be better to refer to rate of warming or cooling.

L455-458 – I may have missed this, but do you mention why you chose these time periods? I assume it is because they coincide with periods of warming and cooling in the SAT record. Also, be clear that you are referring to simulated GT.

L459 – revise to “GT at 20 m remained…”

L464 – “negative trend” might be better than “decreasing trend”

L465 – revise to: “At 20 m, GT….”

L469 – replace “raised” with “increased”

L481 – replace “larger” with “higher”

L484 – replace “coldest” with “lowest”

L545 – Shouldn’t you mention that the ice content is important?

L641 – Something else to consider in this section. Surface temperature in winter and therefore nF will not just be a function of the snow depth but will also depend on active layer thickness and substrate conditions (especially moisture content) as these will influence the latent heat effect (see for example Riseborough and Smith 1998, 7^th Int. Permafrost Conf. Proc.; Throop et al. 2012 doi:10.1139/E11-075).

L663-665 – Late-lying snow cover would delay or reduce the spring warming of the ground. Also, latent heat required to melt snow reduces amount of heat available to heat the ground.

L675-672 – Effect of thin or late onset of snow accumulation is also shown by Palmer et al. (2012 doi:10.1139/E2012-002). The temporary ground cooling related to low snow cover is also reported for the European Alps by PERMOS (2019) and Noetzli et al. (2020  https://doi.org/10.1175/BAMS-D-20-0104.1)

L705-707 – Are you referring to the thermal offset here which is related to the difference between frozen and unfrozen thermal conductivity (as well as the lag effects that mean that permafrost can still be present at depth when surface temperatures are above 0°C).

L709 – Are you referring to annual mean temperature here? Also revise to “..measured by the….”

L733- 735 – It would be useful to show this comparison, maybe in an appendix or supplementary information.

L737 – Has “RW” been defined earlier in paper?

L788-789 – Are these rates determined for the same time period?

L793 – Revision suggested – “Permafrost is likely discontinuous along most of the modelled profiles…” Do you really mean that for 2 of the profiles (Mannen and Ramanosi) permafrost is likely absent while 7 of the profiles are likely underlain by permafrost although it may be discontinuous in distribution.

L800 – Revision suggested: “..are warming by 0.2°C decade^-1…”

L803 – Replace “leaded” with “led”

L805 – revision suggested “…size appear to be important….”

L828 – revise to: “…colder than the rock wall…”

L840 – “positive trend” rather than “increasing trend”. Also, note the increase has largely occurred in the last 40 years.

L855 – You might also want to indicate the source of the data in the caption.

L1203-1208 – References out of order

The work presents results from 2D numerical modelling of heat conduction from several transects crossing steep rock walls in Norway. The aim of the study is not explicitly stated (it needs to be), but l.92-93 and the choice of sites suggest the aim is to investigate bedrock temperatures behind steep rockwalls and the adjacent landscape, including at or near the sites of known slope instabilities. At least one transect crosses an active instability (Gámanjunni).

Reliably modelling bedrock temperatures down to depths of relevance for the evolution of slope instabilities where permafrost may exist is very important and within the scope of TC. However, it seems that the model used has never been validated against borehole measurements even in simpler topographic settings and thermal systems. No borehole data for validation is presented here either. By its formulation, the model cannot account for effects that are especially important in landscapes susceptible to slope instability, where more pervasive and widening fractures are to be expected. Snow is also treated in a very simple way, and several parts of the transects are not oriented favourably to the topography for a 2D model. The resulting uncertainties are impossible to quantify through sensitivity experiments without real borehole data.

Boreholes data suitable for comparison do exist, and are claimed to agree 'quite well' with the model. But they are not shown. If the current level of detail in the presentation and discussion of the model results is to be preserved, the validation against at least this set of boreholes needs to be included. The good agreement would build some confidence in the model performance. Otherwise I suggest to significantly shorten the ms. and only focus on discussing those feature of the modelled bedrock temperatures that are broadly consistent across different sites or parts of different transects featuring similar conditions.

I am particularly concerned because one of the cited papers (Kristensen et al. 2021) already applied the same model, again without borehole measurements, to an unstable slope that it described as highly fractured and with seasonally varying permeability. As such, a site completely unsuitable for a model only accounting for heat conduction. We still know very little about the links between temperatures and slope stability, and false leads from unproven models can cause unnecessary confusion. More details on the limitations of the model and why some of the broadly accepted assumptions would not apply here are below in my comments to the text.

The ms. is not suitable for publication in its present form but see below for comments and suggestions that may make it acceptable after major revisions.

Throughout the text: improve the use of articles, e.g. l. 58 'the Northern Norway' -> 'Northern Norway', l. 100 'Permafrost limit' -> 'The permafrost limit', and in general improve the use of the English language and remove repetitions.

l. 15 'selected': explain (here or in §1 or §2 if there it takes more than a few words) selected based on what 

§1

l. 67 'attributing variations in mountain permafrost occurrence owing to' -> 'attributing mountain permafrost occurrence to'

l. 80 'selected sites', 'other sites' summarize how they chose those sites, as the choice can introduce biases in the derived works.

l. 87 the model uses forcing calibrated with observations but the model is not 'observation-constrained' because no subsurface measurements are used to constrain the 2D model results.

l. 91-93 this hints to the aims of the work but they need to be more clearly and explicitly stated.

§2:

This section needs to state clearly how the selected sites were chosen, how each transect was drawn, why none of the sites with boreholes were modelled, or if they were, why no comparison is shown between model and measurements.

Most of the place names mentioned in this section are not shown in fig. 1 nor any of the map so they aren't useful to any reader who isn't already familiar with these regions. Places that really need to be mentioned usually also deserve to be shown on a map.

Consider reducing unessential info on geography, tectonostratigraphic units and mineralogy, and descriptions of slope instabilities at other sites than the modelled profiles unless they share some fundamental similarity with the latter.

§3.1:

If CryoGrid 2D has been compared to actual borehole measurements, cite the relevant publications, summarize the observed performance of the model, and indicate any difference in the model configuration used here. If not, mention that the model has not yet been validated. The point here is that heat conduction and numerical solvers are well understood tools, but any new implementation needs to be proven correct. Additionally, the impacts of not accounting for convective and advective heat transport, fractures (both filled or open, with or without circulation of air or water), as well as the chosen ways of accounting for surface material and snow all reduce the accuracy of the model by an unknown margin. This is especially important in landscapes prone to slope instability and close to freezing temperatures, such as many of those discussed here, where more pervasive and widening fractures are to be expected and the any infiltrating surface waters can have a large impact on stability.

§3.2:

State how the exact trace of the profiles was drawn and how its geometric relation with the topography may influence the results. Fig. 1 seems to show that many of the chosen profiles have long sections running at a slant angle from the slope, e.g. the first half of Hogrenningsnibba and most of the Kvernhusfjellet profiles. The Mannen profile between 1000 and 1500 m even follows the top of a ridge. While some compromise is unavoidable when dealing with real topography, these profiles  are very far from the requirement of a 2D model that lateral heat fluxes though the plane of the model are zero. 

§3.3.1

l. 239-240 unclear whether the trend is with elevation or with time.

l. 243 'air inversions' -> 'temperature inversions'

l. 246 'coverage' -> 'resolution' (?) Also state what the resolution is.

l. 247 'each dataset' -> 'each profile' (?)

l. 252 (step 2) doesn't this bring back the problem that the nearby valley bottom meteo station or seNorge grid cell overestimate cold periods?

l. 254-255 (step 3) this lapse rate will be affected by inversions, is this intentional?

§3.3.2

The method used to make up for the lack of snow cover observations is reasonable, but it is quite simplified and uses many arbitrarily set values (Table 3) so again the model performance will be affected in an unknown way without borehole measurements.

§3.4

l. 302 'correlation'?

l. 318-320 Explain what is an uncertainty run, what a control run (never mentioned anywhere else in the text) and what are the uncertainty simulations mentioned in the text but not here. Are 'run', 'simulation' and 'scenario' synonyms throughout the text?

§4.1

l.326-328 'observations-constrained modelling...': it's more clear for the reader to call this 'calibration of GST forcing input using the measured SOs', similar to how it is already worded later on at l. 696. Once calibrated, of course the mean error is 0.00 for all 20 loggers, so the captions of figures S1 to S20 calling it 'validation' are misleading since the comparison and statistics are done against the same data used for calibration.

§§4.2-4.3-4.4 (l. 329-557)

These sections are much too long compared to what the reader gains from them. It's not necessary to describe in words everything that is visible in the figures, unless some feature contradicts other evidence or solves an open questions about some important point along a transect. Commenting each scenario and the details of each site is quite uninteresting because the model hasn't been validated using borehole data neither at these sites nor elsewhere (ortherwise provide reference). So the model outputs remain speculative and cannot be used to draw such detailed conclusions as described here about any one specific site.

I suggest these three sections are shortened and rewritten so that instead of discussing in unwarranted detail the state of each site under each scenario, they discuss how similar profile features (e.g. shape of the slope, presence of blockfields) and model scenario across different sites may lead (or not) to similar model outputs. This would show whether the model behaves consistently under similar conditions. Some of this is currently in §5.3. If instead your primary focus is on describing the conditions at each site, consider consolidating all info on each site in one subsection, discuss primarily the 'main' scenario and mention the other scenarios when they clearly improve the understanding of the 'main' scenario.

§5.1.1

Four major limitations are not mentioned:

- the correctness of the CryoGrid 2D code has not been validated against observations either in this study or in the literature. Magnin et al. 2017 notes that validation against boreholes measurements is rare due to lack of data and because established heat conduction models are assumed to be reliable under simple thermal systems. But CryoGrid 2D is not yet an established code. Myhra et al., 2017 didn't have supsurface measurements, Kristensen et al. 2021 applied it to an unstable slope without any validation dataset, and in a setting that is clearly not a simple thermal system based on the extreme heterogeneity of the unstable volume shown in their fig. 5 and on their finding that permeability varies with temperature.

- most of the sites chosen in this study are close to unstable slopes where fractures can be expected to be particularly frequent, pervasive and quite possibly open or filled with ice or water, i.e. not at all a simple thermal system that can be modelled with confidence by assuming heat conduction dominates below just a few metres. 

- the chosen profiles, especially (but not only) at Hogrenningsnibba, Kvernhusfjellet and Mannen have long sections where the geometric relationship to the slope (e.g. crossing it at a slant angle, or running along a ridge) is such that significant lateral heat flux through must be expected, violating a basic assumption of 2D models. Clearly this type of profiles and topography are not what Myhra et al., 2017 referred to when arguing for the suitability of 2D models in the Norwegian mountains because of their flat plateaus and long valleys.

§5.1.2

The use SOs calculated at each logger from GST measurements is mentioned in many places as a key strength of the study but where the SOs from different loggers are used is not well explained except for table 4. Each transect runs across a range of elevation, slope and aspect  widely deviating from those of the closest logger. It seems that most transect 'main runs' use different loggers for their easternmost and westernmost slopes, is this so? Then some are run with alternative loggers too. Calling these 'sensitivity scenarios' is confusing because they are not investigating the sensitivity to some pameter of the model configuration, but rather creating alternative forcing scenarios based on less realistic calculated SOs. Magnin et al. (2017) remarks that accurate GST are a prerequisite for a scheme without surface energy balance and without snow. Givn the mentioned frequent occurrence of temperature inversions, if GST is only calibrated at one logger along a transect (or one per mountain side) and than used everywhere along that transect or mountain side, accurate GST can't be assumed and the reference to the good performance below 6-8 m of the Magnin et al. (2007) model is unwarranted. See also my note to figg. S1-S20

§§5.1.3, 5.1.4

Because of the very effects described in these sections, snow is another element that makes it impossible to rely on the performance of the model without validation against borehole measurements. Especially when most of the nF values in Table 3 are rather arbitrary round numbers.

The claim that snow effects are in some measure also accounted for through the use of mean monthly SOs computed from GST measurements is significantly weakened if only one logger per scenario is used along each entire transect, or side of the mountain, as discussed in my comment to §5.1.2.    

§5.2

Is this section's primary focus on finding whether GST is a reliable indicator of permafrost by comparing where GST < 0 vs. where the 2D model predicts permafrost? Or on comparing the 2D model predictions vs. other studies that used SAT or GST predicted permafrost? Or is the aim is to suggest what the most likely conditions at each site are?

I recommend focusing on a brief and clear comparison between the permafrost/no permafrost prediction of the model match earlier published studies. 

l. 733-735 Given that the major weakness of the ms. is that the 2D model is unproven, mentioning the existence of data from some boreholes in Jotunheimen that are suitable for comparison without showing such comparison is disconcerting. Claiming they 'agree quite well' is unwarranted. The comparison with borehole data needs to be shown and documented, especially as the boreholes are said to span different snow conditions. If this is not possible, the existence of the data needs to be mentioned for future reference but without making unsupported claims of good model agreement.

§5.3

This is by far the most valuable part of all §5 and in fact the section of the manuscript that I feel provides most insight, even considering the limitations of the underlying model. It may be expanded a bit after other sections are shortened.

§6

These conclusions need to be qualified by stating that the model used has not been validated at depth and that it cannot account for effects that are especially important in landscapes prone to slope instability, such as many of those discussed here, where more pervasive and possibly open fractures is to be expected. Also mention (maybe in the Introduction) that a heavily fractured rock mass is thermally different and can be expected to have deeper reaching impacts on temperature compared to the local and shallow effect of a single fracture some metres below the rock face, like the one described in Magnin et al., 2005.

l. 803 'leaded' -> 'led'

l. 812-814 this contradicts the claims in the earlier sections that the model results below 6 m are insensitive to the details of how snow is treated.

l. 821 this confirm that the model isn't necessarily accurate accurate below a few metres if only one SOs calculated from one GST measurement is used over an entire transect or mountain side for each scenario.

    

l. 831-831 is any evidence for this discussed in the ms.?

fig.1: add some (labeled) elevation contour lines and any place name mentioned in the text. If other important place names have to be mentioned in the text but are outside these areas, add a map showing them. Or remove them from the text.     

fig.3: the meaning of each letter is in Table 1, not 2

fig. 4-5-6: The caption mentions both sensitivity and uncertainty runs but the differences between these two types of runs is not explained anywhere in the ms. Are they all in Table 5 where they are called sensitivity scenarios? Which ones are uncertainty runs? 

Please add to the main text an explanation of the meaning of the 'sensitivity test maximum range in the modelled maximum GT' and how it may relate to the actual uncertainty in the model. It seems quite optimistically low close to surface and surprisingly high at large depths. The maps need to be of the same style and they need to show clearly where the sites are in the broader orography and distance from the see. Roads etc. are not essential.

fig. 10, 12: individual lines are very hard to see

figures S1 to S20: these do not show validation of GST (here called RST which is not consistent with the rest of the ms.), they simply show that the calibration was correctly done, resulting in mean error of exactly 0.00 C at the site of each one of the 20 loggers.