General comments

The paper of Damseaux et al. presents improved soil temperature and permafrost extent estimates using a new snow thermal conductivity scheme within CLM5.0. They highlight the importance of improved pan-arctic parametrisation in ecosystem models to achieve more realistic and robust predictions on permafrost thaw-related emissions and their impact on a regional and global scale.  This study is within the scope of the journal, addresses a relevant research question, and will be of interest to the broader modelling community. I find that the article is well-written, and the results are clearly presented and discussed, however, I have some comments for the authors.

Specific comments

1. The authors discussed the improved model performance using the Sturm et al. (1997) instead of the Jordan (1991) scheme to calculate snow thermal conductivity. I think it would be relevant to highlight that even though the implementation of the Sturm scheme is an efficient way of addressing the insulation capacity and soil temperature bias, the effects on model outputs will need to be re-evaluated after structural developments in the snow schemes (especially if those affect snow density, which is the basis of thermal conductivity calculation).
2. How would changes in snowpack properties e.g. snow density, liquid water content and snow depth change the preferential fit of the Sturm scheme over other thermal conductivity schemes e.g. when looking at conditions under different future climate scenarios?
3. Consider discussing the potential consequences of the significant soil temperature changes on a pan-arctic scale already in the Discussion (currently, these are brought up shortly in the Conclusion section, L339).

Minor comments

L115: Can you specify why you have chosen the 0.8 m SWE limit e.g. was this motivated by observations?

L142: What is the uncertainty in the permafrost classes defined by the ESA-CCI data and how is it compared to the uncertainty of your model-data deviation?

Figure 1. Please add the data references in the figure caption.

Figure 2. The Celsius sign missing next to the colour bar.

L193-: Please revise this long sentence for improved readability.

L206: What causes the cold bias gap in the control run?

Figure 3. I suggest adding an observed winter offset sub-figure next to the Control and Sturm run sub-figures to compare the model fit directly to observations using the two parametrisations.

Section 3.3. How did the limitation of SWE to 0.8 m affect the simulation of permafrost fringe areas e.g. in mountainous regions? (or were these areas filtered out from your spatial analysis?)

L248: Consider rephrasing “This observation is particularly remarkable…”. As I understand this finding supports your hypothesis that the Sturm scheme provides an improved simulation of winter offset (as you mention in L249).

L362: typo: Brown et al. (data)

Figure A3.: Please consider changing the colour scale for increased readability (e.g. to a gradient from light to dark with increasing effective snow depth). Add “depth” and the unit (m) on the colour bar and figure caption. Alternatively, you could present a figure with the difference in effective snow depth between the Control and Sturm runs instead of the absolute values, to better visualise the spatial differences.

Figure A3. caption: missing word “depth” in: “Period (1980 to 2021) average of effective snow depth…”

The paper introduces a new snow thermal conductivity parametrization in CLM5.0, which is believed to be more adapted to Arctic snow. The default (Jordan) and new parametrization (Sturm) are compared to one another, to ESA CCI products and to in situ soil temperature data. The authors argue that the new parametrization is more representative of tundra snowpacks and is an important development in understanding changes in permafrost.   

The response of permafrost and its stored carbon stocks to climate change is an important topic and a huge source of uncertainty. One of the many reasons for this uncertainty is the role of snow thermal insulation in models. As such, the topic addressed in this paper is important.

Nevertheless, there are two major issues I would like to see addressed, both of which are related to one another and to the only variable used in the Sturm parametrisation i.e. snow density:

1. The authors state that snow density in the Arctic is poorly represented in most LSMs, including in CLM. Given that their new parametrization is based on measurements, wouldn’t it require snow densities simulations to be representative of Arctic snowpack in order to be effective? In lines 239-246, the authors suggest that snowpack insulation in CLM4.5 was “acceptable” due to errors in snowpack density being compensated by high thermal conductivity. This error compensation was then disrupted with the introduction of the new snow scheme. By proposing to us a snow thermal conductivity parametrisation that works with snow densities that are still not well simulated by CLM5.0, is the Sturm parametrization also not compensating for an error elsewhere? Compensating for errors in models is widespread and can be valuable, but since CLM5.0 is widely used by the scientific community, the authors need to address this clearly in the manuscript in order for future users to understand fully the limitations and compensations involved in the new parametrization.
2. There is no attempt to evaluate the variable (snow density) upon which the new parametrization depends at any stage in the manuscript. Comprehensive data on Arctic in situ snow density measurements are lacking, and, even if there were any, similar scale issues as highlighted by the authors in lines 276-284 with regards to soil data would likely arise. As such, a sensitivity analysis of the snow thermal conductivity parametrization to modeled snow density is essential. This analysis would help determine whether the new parametrization is robust and will remain effective even if the cold bias introduced by the new fresh snow density function is later corrected, or if it is merely a temporary fix with some underlying empirical grounding that compensates for an error elsewhere.

For consideration: Although I would like the authors to consider the following questions, they may choose to ignore them if they wish, as these questions pertain to the study's legacy and broader impact. Was this study done in collaboration with the CLM5.0 team? Does this paper document the introduction of the Sturm parametrization in CLM5.0 i.e. has it already been or will soon be added as an option for users? If so, clarification on this would be useful and would assist future users as this would contribute to good research practice as part of ongoing model documentation. If the CLM5.0 team was not involved or is unaware of this study, I wonder if the authors may be willing to explain the reasons for that; I would expect that it is easier to work with the group of the model one is trying to improve rather than in isolation.

Minor comments:

• Section 2.1 includes a brief model description of the snow module, but lacks details on soil representation. While I obtained some of this information from Lawrence et al. (2019), the reviewed paper includes “permafrost” in its title, therefore I don’t think it would be superfluous to include some critical information about how soil is represented e.g. how many soil layers are there in CLM5.0, and what are their thicknesses and depths? Given the different thermal properties of mineral and organic soil, concise information about their representation would also be welcome. Such information is essential for context, particularly for statements like "the improvement is less pronounced in deeper layers, as the properties of soil increasingly dominate snow insulation properties at depth" (L210-212).
• L180 What does “approximately” linear” mean? L240 what is “acceptable” snow insulation? These terms are rather vague. Please define.
• L225 “bias increase”: do you mean “warm” bias, “positive” bias…?
• Lines 290-292: Doesn’t snow type depend on meteorological conditions? In this case, one might argue that in a physically-based model like CLM, it may be more logical to incorporate various snow thermal conductivities based on the meteorological conditions/variables that result in different snow types rather than including different snow types explicitly. Additionally, whether different snow schemes are needed in LSMs to represent different snow types or whether improved snow physics is required is open to debate. The authors may want to nuance these statements.
• L320- As well as, perhaps, the spatial (horizontal and vertical) variability of soil properties? Referring to my first minor comment, it is important that a paper about permafrost does not forget soil properties and the potential sources of errors coming from the soil representation.