Parameterization of the snow fracture energy to model the onset of crack propagation in snowpack models

Monteiro, Diego; Viallon-Galinier, Léo; Fourteau, Kévin; Dick, Oscar; Hagenmuller, Pascal

doi:10.5194/egusphere-2026-733

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https://doi.org/10.5194/egusphere-2026-733

Preprints

25 Feb 2026

| 25 Feb 2026

Status: this preprint is open for discussion and under review for The Cryosphere (TC).

Parameterization of the snow fracture energy to model the onset of crack propagation in snowpack models

Diego Monteiro, Léo Viallon-Galinier, Kévin Fourteau, Oscar Dick, and Pascal Hagenmuller

Abstract. Snowpack models are widely used to complement field observations in avalanche risk forecasting. They help estimate key indicators related to dry-snow slab avalanche triggering processes, such as failure initiation and crack propagation. In recent decades, several models have been developed to predict crack propagation propensity, typically characterized by the critical crack length (the cut length beyond which an initial crack self-propagates), measurable in the field using the Propagation Saw Test (PST). However, these models often depend on poorly constrained parameters, particularly, the weak layer fracture energy w_f. In this work, we relate the fracture energy to snow properties that can be measured directly or simulated by detailed snowpack models. To this end, we first exploit microstructural knowledge and data by computing the min-cut on about 300 three-dimensional snow microstructure images. The min-cut represents the smallest ice interface that would need to be fractured to separate two opposing sides of the structure, thus providing a quantitative proxy of fracture energy at the microscale. We fitted a relation between the min-cut and snow properties that can be measured or simulated, namely density and grain morphology. The min-cut is then linearly related to the fracture energy w_f using measurements from Richter et al. (2019), which track weak layers across multiple seasons and sites using PST and observed profiles. We retrieved w_f by inverting the state-of-the-art slab model WEAC (Weißgraeber and Rosendahl, 2023), based on manual measurements and snowpack simulations from the Crocus model. After calibration, w_f is evaluated in two slab models of different complexity for their ability to reproduce observed critical crack lengths, using both observed data and Crocus outputs. Although the correlation between min-cut and w_f remains moderate (i.e. R of 0.5 at most), likely due to measurement and modeling uncertainties, the parameterization demonstrate a clear added-value over the use of a constant w_f in reproducing realistic critical crack lengths (i.e. R = 0.59 and RMSE of 12.5 cm against R = 0.39 and RMSE = 14.5 cm). Moreover, the proposed parameterization performs well for identifying and monitoring weak layers over the course of the season. Its consistent performance across slab models and strong results using Crocus outputs highlight its potential for operational dry-snow slab avalanche hazard monitoring.

Received: 06 Feb 2026 – Discussion started: 25 Feb 2026

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Diego Monteiro, Léo Viallon-Galinier, Kévin Fourteau, Oscar Dick, and Pascal Hagenmuller

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CC1:
'Comment on egusphere-2026-733', Valentin Adam, 25 Mar 2026 reply
Dear authors,
The topic is highly relevant for avalanche forecasting and aims to bridge microstructural physics with operational snowpack models. In particular, the analysis of the CT dataset is valuable and extensive, contributing to an improved understanding of how microstructural properties relate to macroscopic properties.
However, the manuscript currently suffers from conceptual inconsistencies, unclear physical interpretation, and methodological gaps that limit the strength of its conclusions.
1. Critical energy release rate vs. critical crack length
From a fracture mechanics perspective, it remains unclear what is meant by the term “critical crack length.” One could interpret it as the finite crack size required for the onset of crack propagation within a coupled criterion framework (Leguillon, https://doi.org/10.1016/S0997-7538(01)01184-6), but this is not the case here. Renaming this quantity to “critical cut length” would help avoid this ambiguity.
Furthermore, the manuscript neglects the second condition required for fracture initiation, namely that the stress must exceed the strength of the weak layer (Leguillon). The context of coupled criteria is therefore missing.
“The stability of a snowpack and the critical length above which a crack spontaneously propagates depend on both the fracture energy of the weak layer w_f and on the mechanical behavior of the overlying slab”. What critical length is ment here, the finite length of a coupled criterion which needs to be exceeded (like everyone with a mechanical background reads) or the “critical crack length” of a PST (like snow practitioners reads it) ?
“The fracture energy itself is known to be a function of the snow layer density and microstructure”. This has never been stated in the mentioned reference Adam et al., https://doi.org/10.1038/s41467-024-51491-7
The magnitude of the “critical crack length” derived from a PST does not provide direct information about crack propagation propensity. It is a geometric measure rather than a material property. For the same weak layer, different critical cut lengths can be obtained depending on slope inclination, slab stratification, and cutting direction (see Adam et al., https://doi.org/10.1038/s41467-024-51491-7).
"A small a_c means that the weak layer below the slab is prone to crack propagation.” This statement is incorrect. A small “critical crack length” is not a direct indicator that the weak layer is prone to crack propagation, but a configuration-dependent system response of the slab–weak layer–geometry setup as you partly mention: “The critical crack length ac thus depends on both how the slab deforms when it loses support from the weak layer, and the specific fracture energy of the weak layer “. Same applies for “Finally, we examine the potential of predicted critical crack lengths to discriminate between weak layers and more stable layers within a profile.”
The “critical crack length" has so many geometric and material dependencies which scale differently that its nearly impossible to interpret it. E.g. a longer “crack length” can be related to a stiffer slab due to a crust and even though the weak layer might be potentially dangerous. Vice versa how should be the small “crack length” at lower slab height be interpreted in Figure 9 without knowledge? Those interactions makes the interpretation highly complex, particularly for operational applications or practitioners.
The profiles in Figure 9 mainly reflect the effect of slab stiffness, which causes the “critical crack length” to increase more or less linearly with depth. The observed discontinuities are introduced by the min-cut parameterization associated with different grain types. If the min-cut parameterization were plotted with the corresponding calculated critical energy release rates, this would contain essentially the same information but would be easier to interpret. In this context, the level of “critical cut length” is unnecessary. These values are absolute and configuration-dependent, and therefore not intrinsic material properties. As such, they are not suitable quantities to describe or predict fracture initiation or propagation.
The terminology “crack propagation propensity” is vague. The critical energy release rate describes fracture initiation (or “onset,” as stated in the title). If crack propagation itself is to be addressed, a steady-state framework (e.g., Rosendahl et al., https://doi.org/10.5194/nhess-25-1975-2025) or dynamic fracture processes (e.g., Bergfeld et al., https://doi.org/10.5194/nhess-23-293-2023) must be considered. From a fracture mechanics standpoint, the PST-derived “critical crack length” is not a valid indicator of crack propagation and has historically been misinterpreted in the snow science community.
Since PST measurements are partly conducted on inclined slopes, the relative contributions of mode I and mode II should also be clarified. A brief statement quantifying that the loading is predominantly mode I (e.g., ~95%) and that the analysis is therefore restricted to mode I-driven initiation would improve clarity.
2. Missing physical justification of the min-cut → fracture energy link
No direct experimental validation is provided to support a correlation between min-cut and critical energy release rate.
The argumentation of the parameterization follows an indirect route via the “critical crack length.” The comparison with a constant energy release rate primarily shows that, within the PST dataset, the inferred energy release rate is not constant but varies, likely with density. Since density is also a primary input to the min-cut formulation, the resulting improvement in modelled “critical crack length” does not constitute a robust justification for a physically meaningful parameterization between min-cut and fracture energy.
Rather, this highlights the need for a controlled experimental campaign combining fracture mechanical field tests with direct CT measurements across different grain types.
The correlation on which the parameterization is based remains only moderate.
It is unclear whether the PST dataset alone is suitable to validate such a relationship across different grain types. It should first be demonstrated that grain types can be statistically correlated with fracture energy derived from the PST dataset itself. If this is not possible, the dataset may not be appropriate for validating the proposed parameterization.
In addition, it is unclear whether the PST dataset contains a sufficient diversity of grain types to support such validation.
The assumption of a fixed weak-layer thickness in the PST analysis is not explained, as this information is available in the original dataset. Similarly, the weak-layer elasticity is parameterized via density relationships derived for general snow types rather than specifically for weak layers. It is not stated which parametrisation is chosen (AC, CT, SMP) from Gerling 2017. This would improve clarity. Furthermore, density-based parameterizations reflect an apparent stiffness rather than the theoretical Young’s modulus. Consequently, the experimental method used to derive such parameterizations should be consistent with the actual loading conditions, particularly with respect to strain rate and time-dependent behavior. For example, formulations such as Gerling (2017) may yield Young’s modulus values several times higher than the effective modulus relevant for PST-type configurations (see Schöttner et al., 2025, Fig. 13a). In addition, more appropriate parameterizations exist for specific weak layer grain types (e.g., Schöttner et al., 2025). A clear separation between the derivation of weak layer and slab elastic moduli is necessary.
Since the weak-layer Young’s modulus strongly influences the calculated energy release rate (see sensitivity study Adam et al., https://doi.org/10.1038/s41467-024-51491-7), it is important to assess whether the observed correlation between min-cut and fracture energy isn’t in fact primarily a density correlation. Given the multiple sources of uncertainty in deriving fracture energy from PSTs, this should be explicitly tested. For example, a direct comparison between weak-layer density and min-cut may already yield similar or even stronger correlations.
The manuscript itself acknowledges that density is the main variable controlling min-cut and that measured densities exhibit strong scatter: ” Since the density of the weak layer is the main variable used to estimate the min-cut in the parameterization Eq. 5,” and “we assume that the min-cut can be related to a macroscopic quantity, in particular the snow density.” A sensitivity analysis quantifying this effect would therefore be highly valuable.
While the min-cut may indeed be a promising proxy for fracture energy, the current approach does not convincingly demonstrate this. It would be more straightforward to directly test correlations between fracture energy and other available microstructural descriptors (e.g., from CROCUS or grain-type parameterizations) rather than introducing an additional layer of assumptions via min-cut.
3. Further comments
The inclusion of the Heierli model does not add clear value to the manuscript. The WEAC model is state-of-the-art and computationally efficient, and the comparison does not contribute significantly to the overall argument.

Figure 1 is misleading, as the slab is not represented as a true Timoshenko beam; the boundary conditions do not allow for rotational freedom at the slab end.

The nomenclature should be used consistently (e.g., a_c vs. AC in figures). Indexing of Units should also be checked carefully m^2 “squared” instead of just m2.

Introduced variables should appear consistently in figure labels (e.g., min-cut with ζ).

Figure 5 contains redundant labeling (headers and x-axis labels).

Figures 3 and 4 appear redundant; one should be removed. Additionally, labeling inconsistencies (“min min-cut” vs. “min-cut”) should be corrected.

Avoid using red and green with identical marker shapes due to accessibility concerns.

Use consistent terminology throughout (e.g., “min-cut” vs. “mincut”).

A schematic overview of the full methodology (similar to Mayer et al., 2023, Fig. 1 https://doi.org/10.5194/nhess-23-3445-2023) would greatly improve readability.

The treatment of sphericity and SSA is difficult to follow. It is only briefly mentioned in a figure caption (Fig. 6) and appendix. A1 clearer methodological description of how different grain types are handled is needed.

Key contextual explanations currently presented in the first section of the discussion should be moved to the methods, this would help to better follow the conceptual idea.

Figure 2 would benefit from additional labelling of the weak layer of interest

3.2.2 (Fig. 6Y) ?

Figure 7: Indicate clearer within the plots that a) b) are observed and c) d) are simulated. This can only be know with reading the caption.

Figure 6 c) to f) x axis label is missing or can not be required to be transferred by the reader from g) because its another scale and plot.

Figure 6: what are the units for time ?

The inconsistency in error use and their origin is confusing think about adding errors in the whole model chain as well.

Figure 7 a) where does the different errors measured for a_c come from? They are rather relativ nor absolute.

The general approach of estimating the resistance of each snow layer against crack propagation using snowpack models such as Crocus, which resolve microstructural properties, is very promising.
However:

a) The methodological justification of the min-cut parameterization for fracture energy is currently insufficient.

b) The use of the geometrical measure “critical crack length” introduces conceptual ambiguity and reinforces a historically misinterpreted quantity in the snow science community.
A more appropriate framework would directly assess, for each layer, how the available energy release compares to the intrinsic fracture toughness of that layer. This ultimately calls for a physically consistent approach in which fracture toughness is determined through controlled fracture experiments across different grain types combined with direct CT measurements.

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Citation: https://doi.org/10.5194/egusphere-2026-733-CC1
RC1:
'Comment on egusphere-2026-733', Philipp Rosendahl, 14 Apr 2026 reply
This manuscript addresses an important and operationally relevant problem: how to parameterize weak-layer fracture energy for snowpack models from variables that are actually available in Crocus-like systems. I find the overall idea promising. The strongest aspect of the study is the multi-scale workflow: the authors start from min-cut calculations on 271 µCT snow images, derive a density–morphology parameterization, map this to weak-layer fracture energy through WEAC inversions of PST data, and then test the resulting formulation in both WEAC and a simplified Heierli-type model. This is a sensible and practically useful direction. The reported improvement over a constant w_f is real, especially for observed profiles, and the manuscript benefits from explicit reproducibility efforts through shared data/code.

I also view the use of WEAC as methodologically appropriate. Weißgraeber and Rosendahl (2023) present WEAC as a closed-form layered-slab mechanics framework that delivers slab deformations, weak-layer stresses, and energy release rates in real time, while explicitly not making it itself a crack-growth criterion. In that sense, using WEAC here as an inversion/forward mechanics engine is sound.

My main concerns are how strongly the manuscript interprets the resulting parameterization as a physically established fracture law, and how it interprets PST-derived critical cut lengths in light of the recent fracture-mechanics literature.

Please consider the following general, overarching remarks.

1. Critical cut length should be treated more carefully as a system response, not as a material property.

Recent work makes this point very clearly. Adam et al. (2024) state that the critical cut length a_c marks the onset of unstable crack growth, but it must not be misinterpreted as a material property because it depends on cutting direction, slope angle, slab layering, and load. Bergfeld et al. (2025) further show that PST geometry alone can change measured critical cut lengths substantially, with slope-normal ends yielding up to 50% shorter values than vertical ends. Recent ISSW guidance by Rosendahl et. al (2024) makes the same point even more directly: the measured critical cut length alone does not allow comparison across different experimental conditions and should be used to derive fracture toughness (not vice versa) if comparability is desired. Against that background, I encourage the authors to consistently frame a_c as a configuration-dependent system quantity. Within one standardized setup it is a legitimate model target, but it is not itself the weak-layer fracture resistance.

2. The manuscript should more clearly separate onset of propagation from sustained propagation, crack arrest, and avalanche release.

The title is appropriately limited to the onset of crack propagation, and that focus is scientifically defensible. However, several passages broaden the interpretation toward general “crack propagation propensity” and operational hazard monitoring. Literature shows that these are not the same problem. Bergfeld et al. (2023) distinguish onset from the subsequent dynamic propagation phase and separately quantify dynamic fracture and compaction. Rosendahl et al. (2025) then show that slab touchdown can reduce the energy release rate after onset and contribute to crack arrest, so onset and sustained self-propagation are mechanically distinct stages. In my view, the paper would be stronger if the claims were narrowed accordingly: this is a promising parameterization for onset models, but not yet a complete description of crack propagation or release probability.

3. The recent mixed-mode literature raises an important limitation of the scalar w_f formulation used here.

The manuscript states that WEAC accounts for mixed-mode conditions, but in practice the inversion setup uses upslope PST cuts, no touchdown, and a fixed weak-layer height of 3 cm. Adam et al. (2024) provide a first mixed-mode anticrack interaction law and show that fracture toughness is significantly larger in shear than in collapse. They also note that the historical PST literature contains almost no mode-II-rich data. Conference work by Walet et al. (2024) and Rheinschmidt et al. (2024) points in the same direction: accurate fracture-toughness estimates require better elastic-property retrieval, and fracture resistance is mode-dependent, potentially including mode III for cross-slope propagation. I therefore think the authors should explicitly discuss what their scalar w_f represents. As currently formulated, it looks more like an effective PST-based fracture parameter for a limited loading regime than a general weak-layer fracture-energy law. At minimum, the authors should report the mode mixity of their inverted cases and explain why a scalar w_f is acceptable for this dataset.

4. The min-cut idea is physically attractive, but the paper does not yet establish a strong physical law linking min-cut to macroscopic fracture energy.

Here I see both a strength and a limitation. The strength is that the authors do not rely on density alone, and recent work by Schöttner and co-authors strongly supports the general idea that weak-layer mechanics are shaped by microstructure in addition to density. The limitation is that the actual evidence presented here for the specific min-cut → w_f link remains moderate: the reported correlations between min-cut and inverted w_f are only R ≈ 0.31 .. 0.36 for observed profiles and R = 0.47 for Crocus profiles. Recent mechanical studies also suggest that the relevant microstructural controls are richer than sphericity and SSA alone. In Schöttner et al. (2026), stiffness is linked primarily to anisotropy and tortuosity, while strength is more sensitive to local interface geometry; distinct grain-type regimes are also reported. That does not invalidate the present parameterization, but it does suggest that it should be presented as a pragmatic empirical proxy rather than a physically established constitutive law for fracture energy. Moreover, since µCT scans are available, I encourage the authors to consider the recent findings on links between microscructural and macroscopic properties and look further than min–cut.

5. The validation strategy needs to be strengthened, and stronger baselines are necessary.

As I understand the workflow, the Richter PST dataset is used to invert pseudo-observed w_f, then to fit the min-cut–w_f relation, and then again to evaluate predicted a_c. This is not an independent validation. A leave-one-weak-layer-out, leave-one-season-out, or leave-one-site-out cross-validation would materially strengthen the paper. This matters especially because the performance gains are uneven: for observed profiles the improvement over constant w_f is substantial, but for the Crocus case that is closest to the intended operational application, the gain is modest (R = 0.76 versus 0.73; RMSE 10.1 versus 11.1 cm). In addition, given the recent literature showing that density is the dominant first-order predictor of weak-layer mechanical behavior, I think the key missing baseline is a density-only w_f model. Without that comparison, it is difficult to quantify the actual value added by the morphology term. A second useful baseline would be density plus discrete grain type. The present comparison against a constant w_f is necessary, but not sufficient.

6. The inversion is likely sensitive to elastic and geometric assumptions, and this deserves a more systematic uncertainty analysis.

The manuscript fixes several quantities that recent work suggests are influential: weak-layer height is set to 3 cm, weak-layer modulus is taken from a density-only Gerling relation, the WEAC setup assumes upslope cuts, and the Heierli implementation uses an equivalent modulus derived from the WEAC mode-I formulation. Bergfeld et al. (2023) showed that slab layering materially affects inferred stiffness, weak-layer modulus, and fracture-energy partitioning; Adam et al. (2024) and Walet et al. (2024) likewise emphasize the importance of retrieving elastic properties more directly from experiments. I therefore encourage the authors to add a sensitivity analysis for weak-layer thickness, modulus parameterization, and touchdown assumptions, or at least to propagate those uncertainties into the inferred w_f. At present, the uncertainty bands for observed profiles mainly reflect the assigned Table A1 ranges of sphericity and SSA, which are themselves taken from 5th–95th percentile ranges in long-term Crocus reanalysis rather than from co-located microstructural measurements.

7. The applicability across weak-layer types should be stated more cautiously.

The validation data are dominated by faceted crystals and depth hoar, and the single surface-hoar layer in the Richter dataset was not reproduced by Crocus. At the same time, Adam et al. (2024) derived their mixed-mode interaction law on surface-hoar weak layers, while Schöttner et al. (2026) report distinct scaling behavior across FC&DH, DF&RG, and SH categories. I therefore do not think the present manuscript yet supports a broad statement about “snow fracture energy” in general. What it supports best, in my reading, is an effective parameterization for PST-like onset calculations in persistent FC/DH-type weak layers under the specific modeling assumptions used here. The conclusions should be narrowed accordingly.

Please also consider the following specific remarks.
When referring to the PST measurement, I suggest to consistently use critical cut length rather than critical crack length, except where the latter is explicitly defined as a modeled fracture-mechanics quantity.

Please report the mode-I / mode-II share of the energy release rate for the inverted WEAC cases, not only the final scalar w_f. This would greatly help readers position the results relative to Adam et al. (2024), even if dominated by mode I.

Please add density-only and density-plus-grain-type baselines, and perform held-out validation by weak layer or season. That comparison is central to the paper’s main claim that morphology materially improves prediction.

Title: The title currently promises a general parameterization of snow fracture energy (fracture toughness), which suggests applicability across mixed-mode fracture, compression, tension, shear, and related cases. The manuscript does not support such a broad scope. As presented, the study is limited to compression fracture toughness of weak layers. I therefore recommend a shorter title that reflects this narrower scope more accurately (see comment 2 above).

l5: The critical crack length measured in PSTs is specific to the PST configuration, i.e. the cut length beyond which a crack self-propagates in that particular setup. It should not be interpreted as directly transferable to skier-triggered anticracks in an effectively infinite domain. The energy release rates in these configurations differ substantially; this can be demonstrated, for example, with the Heierli model or WEAC. Because the free boundaries in PSTs increase the energy release rate, enclosed anticracks in the same weak layer would generally require much longer critical lengths for propagation. This is a central methodological issue in the manuscript. Critical lengths are configuration- and geometry-dependent and therefore have limited predictive value on their own. For modeling and forecasting, they are better used to infer material properties such as fracture toughness, not treated as transferable physical properties themselves. By contrast, fracture toughness is a material property and is, in principle, transferable across geometries, slope inclinations, and slab configurations. This distinction should be stated clearly and introduced much more carefully.

l13: The meaning of "inverting" becomes clearer later in the manuscript, but in the abstract the term is too vague. I suggest stating more explicitly what is being inverted and for what purpose.

l46: This statement is not correct, and the clarification given in l50 points in the opposite direction. Critical crack length depends on geometric, elastic, and bulk properties of the system and is not, by itself, a reliable predictor of crack propagation. For example, a flat slope and a 60 degree slope with the same weak layer and slab can yield very different cut lengths because the slab deformation is fundamentally different. A short cut length measured at 60 degrees does not imply easy propagation on flat terrain. I recommend revising this passage carefully and making these limitations explicit. This comment is closely related to my remark on l5.

l52: The energy release rate is a system property, reflecting the change in total energy, and should not be attributed to the slab alone. I agree that beam theory can provide a useful modeling framework here, but the wording should be more precise.

l55: I find this statement too strong in its current form. Whether slab compliance or weak-layer compliance dominates depends strongly on their respective elastic properties. Please qualify the statement more carefully.

l63-l65: This section requires much more careful framing. In its current form, the method appears insufficiently justified. For instance, how sensitive are the results to changes in SMP diameter, layer thickness, or tip shape? Would a doubled diameter, doubled layer thickness, or a much sharper tip yield the same inferred fracture toughness? I am not sure. These concerns should be addressed.

l68: The method of Richter et al. (2019) relies on highly simplified weak-layer stress representations and a long chain of assumptions that now appear dated. I suggest acknowledging these limitations more explicitly when citing this work.

l77: I see a conceptual tension between "physics-based" and "parameterization" in the way these terms are used here. A physics-based model aims to represent causal physical mechanisms, even if approximately. A parameterization, by contrast, is generally phenomenological and correlation-based. I recommend clarifying this distinction.

l89-l90: This statement is an oversimplification. Crack propagation also depends on weak-layer elastic properties, geometry, slope angle, and related system characteristics. Please revise accordingly.

l110: The equation appears to lack physical dimensions or units. In particular, considering E but not weak-layer thickness t directly affects the modeled w_f, since w_f = sig^2 / k where sig is stress and k = E / t weak-layer stiffness. This should be discussed explicitly.

l169: Does the Richter dataset include weak-layer thickness? If so, I strongly recommend using it. If not, please provide an error-propagation analysis to quantify the effect of assumed versus measured weak-layer thickness.

l193: The opening sentence of the Results section is unclear. Please rephrase for clarity.

Figure 3: This figure appears redundant. In my view, Figure 4 already conveys the necessary information, so Figure 3 could be omitted.

Figure 4: Please consider using a more accessible color palette.

Figure 6: Does this figure not suggest that a single parameter is insufficient to model w_f? Have you considered additional parameters? Since µCT data are available, I encourage you to examine recent work by Schöttner et al. on informative microstructural descriptors and to test parameterizations based on those variables. I understand the motivation to develop a practically usable model with easily measurable inputs. However, even if the eventual goal is a reduced operational model, it is still important first to identify the best-performing physically meaningful model rather than starting from assumptions that may already be too restrictive.

l274: I cannot follow the equation in its current form. Please define the variables explicitly.

Figure 7: Adding row labels such as "observed" and "simulated" would improve readability.

l301: With constant t, the Heierli and WEAC models will naturally give very similar results. Variability in layer thickness would likely provide a stronger basis for discriminating between the models.

Figure 8: I would appreciate uncertainty estimates for both the data points and the model curves.

l348–l349: This is presented as an advantage, whereas I would view it more as a limitation in terms of physical representation. I suggest rephrasing accordingly.

l360: This assumption appears insufficiently supported by fracture-mechanics reasoning, especially for highly porous media, and your own results seem to contradict it. I therefore recommend rewording this point more cautiously.

l366: Given that µCT data are available, I encourage the authors to go beyond noting the "lack of complexity in the proposed parameterization" and to provide a more advanced analysis.

l427: The Heierli model does not focus on physical processes at the crack tip. Rather, it only describes slab deformation in regions not supported by the weak layer. This should be stated more accurately.

Overall, I view the manuscript as promising and potentially useful, particularly for operational snowpack modeling. However, I think substantial revision is needed before publication. The key changes are conceptual rather than cosmetic: the paper should more carefully distinguish system-level PST observables from material properties, onset from sustained propagation, and empirical operational parameterization from physically established fracture law. With those revisions, plus stronger baselines and more defensible validation, the study could become a valuable contribution.

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Citation: https://doi.org/10.5194/egusphere-2026-733-RC1

Diego Monteiro, Léo Viallon-Galinier, Kévin Fourteau, Oscar Dick, and Pascal Hagenmuller

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Short summary

This research aims to improve dry-snow slab avalanche forecasts, particularly the propagation of cracks in weak layers, as current models rely on uncertain and difficult-to-measure parameters. We combined snowpack simulations with field measurements to link fracture energy to measurable and modelable snow properties. This new approach better reproduces observed crack lengths and allows weak layers to be tracked throughout the season, thereby improving operational avalanche risk assessment.


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