the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Aug 2026
Snowpack depth hoar impacts on the permafrost thermal regime in a land surface model
Abstract. In cold, dry regions, snowpacks can build a basal depth hoar layer that has a lower density that effectively increases the insulative ability and thus warms permafrost. However, the precise magnitude of the depth hoar insulation and the subsequent impact on permafrost thermal regimes remains highly uncertain. Current Earth and land surface models do not consider the depth hoar effect in their simulations. This study coupled a depth hoar scheme into the snowpack processes within a land surface model. The depth hoar effect on the permafrost thermal regimes in present (1980–2016) and future (2015–2100) climates was assessed by model simulations excluding and including depth hoar. Snow and soil thermal properties observed at the field sites were used to evaluate the model results. The modeling assessment revealed that the depth hoar produced permafrost warming of 2.5–4.0 °C in February under the present climate and deepened the active layer thickness by up to 20 cm. The insulative ability of depth hoar was further significant for colder air temperatures and a thicker snowpack. The effect was demonstrated by increased temperature differences between the air and soil depth at 20 cm with increasing snow depth under colder air temperature conditions. Under a future warming climate, the depth hoar functioned as an insulator enhancing permafrost degradation. Our analysis reveals a new perspective on the underlying influence of depth hoar as a driver of permafrost degradation in present and future climates. We recommend improvements to model representation to include the depth hoar process to improve simulations of the permafrost-related changes under warming climate.
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Status: open (until 29 Nov 2026)
- RC1: 'Comment on egusphere-2026-2767', Anonymous Referee #1, 21 Sep 2026 reply
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RC2: 'Comment on egusphere-2026-2767', Louis Védrine, 28 Oct 2026
reply
Summary and general assessment
The manuscript addresses an important question: how a basal depth hoar (DH) layer affects the insulation of the snowpack and the permafrost thermal regime. The authors implement a multilayer snow scheme with the DH parameterization of Yamazaki (2001) in the CHANGE land surface model. They compare simulations with and without DH at a single boreal larch site near Yakutsk, and extend them to 2100 under SSP5-8.5. The topic is relevant for The Cryosphere. However, three issues must be addressed before publication: (i) the physical representation of DH, and how much of the insulation results from explicit physics rather than prescribed parameters; (ii) the validation of individual mechanisms; (iii) the interpretation of the climate projections.
Major comments
1. Physical representation of depth hoar
The model should be examined in detail regarding DH formation, density and thermal properties, and the sensitivity of the results to the parameters. A central question is to what extent the insulating effect results from explicitly represented physical mechanisms or from assumptions built into the parameterization.
1.1 Densification.
A key ingredient of the insulating effect is slower densification of DH than of rounded grains (RG) at the same density. This is the core of the paper. Please quantify the DH-to-RG viscosity ratio over the density and temperature ranges encountered in the simulations, and compare it with available experimental and modeling estimates (e.g., Kojima, 1967; Calonne et al., 2017). In particular, clarify how this contrast controls the relative densification rates of DH and RG and, consequently, the persistence and thermal resistance of the basal DH layer.
1.2. Thermal conductivity (Eq. 9).
The decrease in thermal conductivity associated with DH formation in Eq. 9 requires stronger physical justification. Microstructure-based numerical homogenization studies (e.g., Calonne et al., 2011, 2019) show that snow thermal conductivity depends on density, microstructure and anisotropy. In particular, DH can exhibit substantial anisotropy, with vertical conductivity approximately twice the horizontal conductivity under the conditions considered in these studies. Please clarify how Eq. 9 was derived, identify the assumptions under which it is applicable, and compare its predictions with available microstructure-based estimates for DH and RG over the density range simulated. This comparison is important for assessing whether the modeled insulating effect follows from the assumed microstructure or is largely imposed by the parameterization.
1.3 Metamorphism model.
Please discuss the limits of the Yamazaki scheme in light of recent advances on snow evolution under temperature gradient (Dick et al., 2026; Braun, 2024).
1.4 Layering and DH thickness.
The upper layers have fixed thickness, so any change in snowpack thickness translates into a change in thickness of the bottom layer, and hence of the DH layer. Please discuss the sensitivity of the DH thickness (Fig. 5) to this discretization.
1.5 Compaction law.
Compaction is modeled with a linear law including a compactive viscosity. Mechanically, snow creeps with a power law of exponent close to 2 (Scapozza and Bartelt, 2003; Schleef et al., 2014). Védrine et al. (2026) showed that linear models implicitly assume a site-specific correlation between load and density; in the Arctic, a non-linear model densifies about six times more slowly than Crocus (Vionnet et al., 2012) for example . This choice must be discussed and is important for the insolation properties, particularly with low wind.
2. Model validation
Agreement between simulated and observed temperatures evaluates overall performance but does not independently validate each mechanism. Improved soil temperatures should be distinguished from specific validation of the DH conductivity and structure.
3. Vegetation
Domine et al. (2022) documented an increase in conductivity due to low vegetation in the Arctic tundra. Please characterize the vegetation more precisely in the discussion and state this limitation more clearly.
4. Climate projections
Atmospheric warming simultaneously affects snow-cover duration, snow depth, temperature gradients and the conditions favorable to DH formation. These changes interact and may modify both the persistence of the DH layer and its contribution to the ground energy balance. Please clarify how these competing effects influence the projected DH contribution. At a minimum, the discussion should distinguish the overall climate-driven change in ground temperature from the incremental effect of including DH. If the conclusions attribute a substantial role to DH in future permafrost degradation, additional sensitivity experiments would be needed to support this interpretation.
5. Consistency of the results and conclusions
- Numbers. The reported DH warming differs between sections: 2.5–4.0 °C in the abstract, up to 5–5.5 °C in Sect. 3.1.2, and 2–4 °C in Sect. 4.2. Please harmonize and specify the depth and period to which each value refers.
- Circular reasoning. L. 425–426 and L. 446, as already noted by Reviewer 1, present as confirmation or improvement what follows from the model configuration. At L. 483, the future simulations are said to "validate" the finding, but a simulation cannot validate a result obtained with the same model.
- Future projections. The DH effect is weaker in 2081–2100 than in the present climate (about 1.5 °C less in February in the surface layer), yet the conclusions state that DH enhances permafrost degradation. Please reconcile these statements.
- Generalization. The study relies on a single continental forest site, whereas the framing of the introduction is Arctic (tundra, wind slab). The abstract states that current models do not represent DH. This is overstated, since detailed snow models such as Crocus and SNOWPACK do represent it. Please specify that it is continental-scale land surface models that generally lack this representation.
Minor comments
- Snow types: please use Fierz et al. (2009), the reference in the snow science community, rather than Yamazaki (2001).
- 79: "SNOWPACK" designates the snow model of Lehning et al. (2002). Please clarify and cite it.
- Is the model code available upon request?
- Finally, I agree with Reviewer 1 that English editing would benefit the quality of the paper.
References
- Braun, A., Fourteau, K., Frei, S., Lehning, M., and Löwe, H. (2025). Toward a physically and microstructure-based equation for the evolution of the specific surface area in snow. Journal of Glaciology. https://doi.org/10.1017/jog.2024.109
- Calonne, N., Flin, F., Morin, S., Lesaffre, B., Rolland du Roscoat, S., and Geindreau, C. (2011). Numerical and experimental investigations of the effective thermal conductivity of snow. Geophysical Research Letters, 38, L23501. https://doi.org/10.1029/2011GL049234
- Calonne, N., et al. (2019). Thermal conductivity of snow, firn, and porous ice from 3-D image-based computations. Geophysical Research Letters, 46, 13079–13089. https://doi.org/10.1029/2019GL085228
- Dick, O., et al. (2026). Monitoring dry snow metamorphism using 4D tomography across 20 experimental conditions. Earth System Science Data, 18, 2875–2889. https://doi.org/10.5194/essd-18-2875-2026
- Domine, F., et al. (2022). Permafrost cooled in winter by thermal bridging through snow-covered shrub branches. Nature Geoscience, 15, 554–560. https://doi.org/10.1038/s41561-022-00979-2
- Fierz, C., Armstrong, R. L., Durand, Y., Etchevers, P., Greene, E., McClung, D. M., Nishimura, K., Satyawali, P. K., and Sokratov, S. A. (2009). The International Classification for Seasonal Snow on the Ground. UNESCO-IHP, Technical Documents in Hydrology No. 83, IACS Contribution No. 1.
- Kojima, K. (1967). Densification of seasonal snow cover. In Physics of Snow and Ice, Vol. 1, Part 2, pp. 929–952. Institute of Low Temperature Science, Hokkaido University, Sapporo.
- Lehning, M., et al. (2002). [Référence du modèle SNOWPACK à compléter à partir de l'article que tu souhaites citer.]
- Scapozza, C., and Bartelt, P. (2003). The influence of temperature on the small-strain viscous deformation mechanics of snow: A comparison with polycrystalline ice. Annals of Glaciology, 37, 90–96. https://doi.org/10.3189/172756403781815410
- Védrine, L., and Hagenmuller, P. (2026). Revisiting snow settlement with microstructural knowledge. The Cryosphere, 20, 1257–1277. https://doi.org/10.5194/tc-20-1257-2026
- Vionnet, V., et al. (2012). The detailed snowpack scheme Crocus and its implementation in SURFEX v7.2. Geoscientific Model Development, 5, 773–791. https://doi.org/10.5194/gmd-5-773-2012
- Yamazaki, T. (2001). A one-dimensional land surface model applicable to intensely cold regions and its applications in eastern Siberia. Journal of the Meteorological Society of Japan, 79(6), 1107–1118.
Citation: https://doi.org/10.5194/egusphere-2026-2767-RC2
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- 1
This manuscript presents a valuable and highly relevant investigation of how the representation of depth hoar affects simulated snow properties and the thermal regime of permafrost under present and future climatic conditions. The study is scientifically sound, the experimental design and methods are appropriate, and the analyses clearly support the conclusions drawn by the authors. In particular, the evaluation against observations demonstrates that the implemented depth-hoar formulation improves not only the simulation of snow depth and snowpack properties, but also the resulting soil temperatures. The manuscript therefore makes an important contribution to land surface modelling by addressing a consequential shortcoming in current representations of Arctic snow and by demonstrating the relevance of snow stratigraphy for simulating snow–permafrost interactions. I consider the study fully worthy of publication once the presentation has been substantially improved.
My principal concern is the quality and clarity of the English throughout the manuscript. In many places, I was able to infer the intended meaning because I am familiar with the subject matter. However, the wording itself is frequently unclear, imprecise, or potentially misleading, and readers who are less familiar with the topic may interpret some statements differently from what the authors appear to intend. This is therefore more than a matter of style or occasional grammatical errors: the language sometimes obscures the scientific reasoning and, in some cases, changes the apparent meaning of a statement. The manuscript requires thorough language revision, ideally by a fluent English speaker with sufficient familiarity with the subject to preserve the intended scientific meaning. My detailed comments below identify a number of examples, but they should not be regarded as an exhaustive language correction of the manuscript.
Please also find a number of detailed comments unrelated to the language issue below:
Abstract
Page 1, Line 13: I would suggest to mention which model here.
Page 1, Line 18: I find this sentence unclear. Do you mean that depth hoar had more impact in zour simulations under colder air temperatures and thicker snow packs than under warmer temperatures and more shallow snow packs? If so, please reformulate to make the sentence clearer.
Page 1, line 19: “soil at 20cm depth” instead of “soil depth at 20 cm"
Introduction
Page 2, line 35: “increase of snow depth in eastern” instead of “increase of snow depth in the eastern”
Page 2, line 47 “snow accumulation and usually found at the” instead of “snow accumulation and is usually found at the”
Page 2, line 48-49: This sentence is unclear to me. Do you mean to say that depth hoar increases the role of the snow pack as thermal insulator? Should be rephrased.
Page 2, line 53: Maybe consider adding Domine et al., 2019, who showed the same effects as Dutch at al with two other models, https://doi.org/10.1029/2018MS001445
Page 2, line 53: The term anomaly is ambiguous here. Maybe use biases, or even errors.
Page 2, line 60-63: I would suggest to add that the analysis in Dutch et al. is for one observational site in Canada.
Page 3, line 66: “depth hoar schemes within land surface models” instead of “depth hoar scheme within land surface models”
Page 3, line 68-69: Damseaux et al did not study how depth hoar forms, they only discussed physical depth hoar properties taken from other studies. This citation should be removed here.
Page 3, line 90-91: I would suggest to acknowledge here that most CMIP6 models don't represent permafrost carbon processes well (eg Schädel et al., 2024, https://doi.org/10.1038/s41558-023-01909-9), so projections of the permafrost carbon feedback have a high uncertainty (IPCC), which is intensified by biases in snow
2.2 Snow model
2.2.1 General description
Page 4, line 126-127: For a better flow of your argument, consider changing this sentence into something like "Since the density and liquid water content of the snowpack can in reality have vertically heterogeneous ..."
2.3 Study site and observation
Page 9, line 244: How is ALT monitored at these sites?
2.4 Model simulation
Page 9, line 249: Is there a reason why ERA-Interim was used instead of the more recent ERA5 reanalysis?
Page 9, line 270: From this sentence, it remains unclear whether you used the IPSL forcing downscaled by ISIMIP or forcing from another model.
3 Result
3.1.1 Snow depth and snow water equivalent
Page 10, line 285: Please make the mechanisms resulting in different snow depths and swe explicit here. I assume the differences between the snow depths in the two simulations arise from the difference in snow density, causing similar amounts of SWE to result in greater snow depths. If there is identical forcing, what causes the differences in swe during the build up of the snow pack?
3.1.3 Active layer thickness
Page 12, line 315: How exactly is active layer thickness derived from the model?
3.2 Seasonal variation of snow grain form
Page 13, line 335 (figure 5): Is this also an 11-year average? How is snow type averaged?
3.4 Correlation between air-soil temperature difference and snow depth
Page 16, line 402 (figure 9): In figure 8, and also in the text, you state that depth hoar has the strongest impact on insulation in the regime with the coldest air temperatures. Figure 9 seems to contradict that, the shifts in the pdfs of the moderate and warm air temperature regime are much more pronounced than those in the cold air temperature regime. Why is that?
Discussion
4.1 Impact of depth hoar on snow properties
Page 17, lines 425–426: The model was configured so that depth hoar has a greater insulating capacity; the simulation therefore does not independently confirm this. In addition, no observations from this study are presented in which depth hoar itself was measured. Please reformulate this statement.
Page 17, line 436: I find this formulation misleading. Parameterizations of snow thermal conductivity based on snow density are vulnerable to errors in simulated snow density, but this applies to any scheme that uses snow density as its basis. As you point out later, using different methods to estimate snow thermal conductivity can improve the results.
4.2 Impact of depth hoar on soil temperature
Page 18, lines 446–447: The differences between the two simulations show the impact of implementing depth hoar; they do not demonstrate that including depth hoar improved the simulation.
Page 19, lines 465–466: Does this statement contradict Figure 9, in which the probability density functions for the depth-hoar and no-depth-hoar simulations appear most similar at the coldest air temperatures?
Page 19, lines 486–488: In addition to reduced depth-hoar formation in a warmer climate, I would expect the shortening of the snow season to play a role. Could the reduced influence of the depth-hoar formulation during the shoulder seasons in the future projections also result from a decrease in snow cover itself?
4.3 Uncertainty and future work
Page 21, line 516: Did you mean ‘colder and warmer’?
Page 21, line 518: In the description of the model simulation, you write that ‘the soil organic carbon profile was simulated by CHANGE at each time step’. Does this mean that CHANGE calculates soil organic carbon, but that it does not affect soil heat capacity or soil thermal conductivity?