the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Aug 2023
Snow mechanical properties variability at the slope scale, implication for snow mechanical modeling
Abstract. Snow avalanches represent a natural hazard for infrastructures and backcountry recreationists. Risk assessment of avalanche danger is difficult due to the sparse nature of available observations informing on snowpack mechanical and geophysical properties and overall stability. The spatial variability of these properties also adds complexity to the decision-making and route finding in avalanche terrain for mountain users. Snow cover models simulate snow mechanical properties with good accuracy at fairly good spatial resolution (around 100 m). However, monitoring small-scale variability at the slope scale (5–50 m) remains critical given that slope stability and the possible size of an avalanche are governed by such scale. In order to better understand and predict the spatial variability at the slope scale, this work explores existing linkages between snow mechanical properties and microtopographic indicators. First, we compared covariance models and scaling properties. Then, we predicted snow mechanical properties, including point snow stability, using GAM spatial models (Generalized Additives Models) with microtopographic indicators as covariates. Snow mechanical properties such as snow density, elastic modulus, shear modulus and snow microstructural strength were measured at multiple locations over several studied slopes using a high-resolution snow penetrometer (SMP), in Rogers Pass, British-Columbia, and Mt Albert, Québec. Point snow stability such as the skier crack length, critical propagation crack length and a skier stability index were derived using the snow mechanical properties from SMP measurements. Microtopographic indicators such as the topographic position index (TPI), vegetation height and proximity, Up-wind slope index (wind exposed/sheltered area) and potential radiation index were derived from Unmanned Aerial Vehicles (UAV) surveys with sub-meter resolution. We computed the variogram and log-log variogram of snow mechanical properties. The comparison showed some similarities in correlation distances fractal dimensions between the slab depth and slab snow density and also between the weak layer microstructural strength and the stability metrics. GAM models suggested several significant covariates such as TPI, VRM, Winstral index, vegetation height and distance to vegetation. The point snow stability maps generated represents good teaching material in avalanche skill training and awareness course. The difference in spatial pattern between the slab and the weak layer should be considered in snow mechanical modeling.
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RC1: 'Comment on egusphere-2023-1586', Anonymous Referee #1, 18 Aug 2023
General comments
This paper explores slope-scale patterns in snowpack stability. Four field surveys were conducted at different locations where snowpack properties were measured with a snow microprenetrometer and terrain properties were measured with a UAV. Three snowpack properties (slab depth, slab density, weak layer strength) and three stability indices (skier crack length, critical crack length, skier stability index) were derived from the SMP measurements, and their spatial patterns were explored with variogram analyses. Trrrain properties (slope angle, convexity, etc.) were used to fit regression models to predict stability patterns across the slopes and explore which terrain factors were most influential. The results suggest slab properties were more variable than weak layer properties and recommend ways slab variability could be accounted for in mechanical models of avalanche release.
The study is well designed, relevant, and interesting; however, I think its presentation needs to be improved before publication in the Cryosphere. Some of the methods and concepts are not described in sufficient detail, the use of terminology and symbols should be more consistent and organized, and the overall contribution and relevance of the study should be clarified.
Specific comments
- Novelty of research methods. Line 105 states “no studies have linked snow stability and mechanical properties with microtopography indicators in spatial modeling”, but I would argue that Reuter et al. (2016) perform a similar study where SMP data was used to spatially predict a failure initialization criteria and critical crack length based on terrain and snowpack data. While the specific properties and terrain predictors differ, as do the type of regression models, the methods are conceptually quite similar. Sect 4.3 of that study specifically discusses spatial prediction of stability indices. I think the similarities and differences between this study and previous studies needs to be clearer in the Introduction (several distinctions are made throughout the section, but not presented in a complete succinct way that links to their objective), and any relevant comparisons with past studies should be added to the Discussion.
- Incomplete methods. Methods section 2.5 does not describe how the covariates were derived or how the GAM models were fit to the data in enough detail to reproduce the study. The technical comments below list some specific examples.
- Description of terrain variables. The microtopographic indicators (covariates) are not sufficiently described. The topographic position index and vector ruggedness measure are not common terms used to describe avalanche terrain and should be described with plain language interpretations. It’s difficult to interpret why these were significant explanatory variables without understanding what they represent. Similarly, some of the other terrain variables are not described in enough detail to understand how they were derived or how to interpret them (e.g., wind-exposure index).
- Relating results to terrain/snowpack influences. A strength of this study is that it was conducted at multiple sites with different terrain and snowpack characteristics. I think the results could be more impactful if the influence of these characteristics were discussed in more detail. For example, what were the main differences between the wind-exposed versus forested slopes and persistent versus non-persistent weak layer grains? Understanding how these factors influence slope-scale variability would be directly relevant to avalanche risk management.
- Consistency and organization of terms and symbols. In general, there were quite a few places where consistent and complete use of terminology and symbols needs to be improved. Many examples are provided below.
Technical comments
Abstract/Introduction
- Line 4: True in some contexts, but “can simulate with good accuracy” is better.
- Line 11: These were not “measured” on the slopes but estimated from SMP measurements.
- Lines 8-19: Some of these sentences are a little vague “models suggested significant covariates”) and would benefit with being a little more specific about what types of variables were included in various parts of the study (e.g., “covariance models and scaling properties”) and some plain language interpretations (e.g., what does it mean that “GAM models suggest significant covariates”?).
- Line 19: Winstral index as not defined in the abstract, so perhaps use wind-exposure index.
- Lines 26-27: Perhaps more general triggers such as “person” instead of “skier” and “stresses from snowfall or warming” instead of just “new snowfall”.
- Line 30: The conceptual model decomposes hazard into 4, not 2, factors (problem type, location, size, likelihood).
- Line 44: Is there a word like “depth” missing in “spatial pattern of snow”?
- Line 48: Can you describe what is meant by “roughness” in a way that links the concept to avalanche release? The interpretation of the fractal distances is unclear in the results.
- Line 52: Start new paragraph here?
- Line 110: Can you briefly describe this “knockdown effect”?
Methods
- Line 127: “receives” instead of “received”.
- Lines 131-136: Please provide consistent details for each site. For example, the text for the site in Quebec does not name it Arete de Roc or provide the abbreviation AR used later in the manuscript, no slope angle is provided for JBC, and shouldn’t “the other site” in line 131 be “the first site”?
- Fig 1: Very nice images to illustrate the study sites. Please add the word “survey” prior to green and red in the caption for consistency.
- Line 165: Provide a bit more detail about the weak layer criteria. It sounds like one weak layer was identified for each survey, was this the uppermost result in a compression test of any fracture character, the uppermost result with a sudden fracture character, an expert interpretation of the primary layer of concern, or something else?
- Line 167: Please clarify if the winter imagery was collected on the same day as the survey.
- Line 181: I would consider layer depth, thickness, and density to be structural rather than mechanical properties.
- Line 183: Missing “density” between slab and rho.
- Line 187: Out of curiosity, does this method of averaging the density of each slab layer account for the varying thicknesses of these layers so that it would be conceptually the same as a bulk density measurement made with a sampling tube, or is this a more abstract slab density?
- Line 191: State “… shear strength of the weak layer…” so it is clear this is in reference to how you will derive tau_p.
- Line 194: Macroscale strength is not defined or explained anywhere, so the justification for this assumption is unclear.
- Fig 2: This figure is helpful but could potentially be simplified with a bit less text (e.g., green boxes) and more consistent formatting (has a mix of serif and sans serif fonts and sizes, bold and non-bold font, why is some text red?).
- Line 201: You could consider just saying “the SPI is the ratio of two lengths” rather than “defined by”.
- Line 207: It’s not clear to me what “the surface beneath the skier” refers to in the definition of alpha.
- Eq 6: Missing right bracket at the end of the numerator.
- Lines 262-264: This sentence is confusing and perhaps belongs later in this section. Aren’t the microtopographic indicators defined by more than the second order derivates as listed in Table 1? And it’s not clear how these moving windows are applied or relevant to the analysis.
- Sect 2.4: The fitting of spherical and gaussian variogram models should be described here since they are discussed in the results. Also, the results suggest you pick the best fitting model.
- Sect 2.5.1 and Table 1: Some of the microtopographic indicators could be defined more clearly. Specifically, TPI and VRM should have plain language descriptions because they are not everyday terms used to characterize avalanche terrain with intuitive meanings. How should canopy height be interpreted if you masked areas with vegetation? How are the concepts of “potential of incoming solar radiation” and “Winstral index” quantified? How was prevailing wind direction determined? What is meant by moving windows represented with two values such as 5/15 and 25/50?
- Line 284: The symbol Sx has already been used to describe a slab layer (line 177).
- Sect 2.5.2: This section is not clear what data is used to fit GAM models. My interpretation is that Y is the 6 properties previously analyzed and the X are the ~13 covariates listed in Table 1. I also assume the model was fit (and cross-validated) using data from the 60-80 SMP profile locations, but this is not stated. While the concepts behind the statistical modelling are explained well, it should be clearer and more explicit how they were applied to this data.
- Eq 12: The asterisk for multiplication is not necessary.
Results
- Fig 3: It would help if the 4 surveys were presented in a consistent order throughout the paper (methods, table 2, figures, etc.). The y-axis is not labelled.
- Table 2: Based on the methods, 3 x 2 = 6 compression tests were done with each survey, so why is only a single test reported. Since the tests were performed following Canadian Avalanche Association (2016), they should also be reported following those standards: “CTM 15 (RP) down 25”. How was ac_PST derived from PST test results? These don’t seem like cut lengths from a 100 cm long column. The mix of words and symbols in the column headings is confusing, I suggest using words. Units can be specified in the column headings. Consider separate columns for slab depth and density. Dates should probably be in YYYY-mm-dd format.
- Line 311: Are the lengths reported for each weak layer the (average) observed grain size with a crystal screen and loupe or the thicknesses derived from SMP measurements?
- Line 315: What is meant by the slab is made up of one layer? Doesn’t the SMP identify very thin layers?
- Line 340: “slab thickness” used here but referred to as “slab depth” in other parts of the manuscript. Check manuscript for consistency.
- Line 340: Is there any relevant interpretation to gaussian versus spherical variogram models?
- Fig 3: Interesting that AR had some longer correlation lengths given it sounds like it was the most wind exposed site.
- Line 353: “surface roughness” could be misinterpreted to mean the physical texture of the snow surface, which is why I think the interpretation of fractal distances needs to be explained. What does a value of 2.7 mean?
- Line 360: Please be more specific about what variable or property the “variance” refers to.
- Fig 6/7: Please explain the grey vegetation in the caption. Consider presenting the RMSE and MAE as rounded values with units to improve interpretability. The prefix “CV” is unnecessary. In general, these are very interesting figures and I agree could be valuable teaching material.
- Line 368: “same” or “similar” variation?
- Line 370: This sentence is confusing and partly contradictory.
- Line 378: This could be the start of a new subsection on microtopographic indicators.
- Table 2 and 3 are not cited in the text. The asterisks next to covariates are not defined, but I assume refer to significance levels.
- Table 2/3: Interesting that the wind exposure index Sx was more frequent for the models at the Fidelity sites than the AR site which was apparently more wind exposed. This result could be better understood of the derivation of Sx was explained better.
- Fig 8: What is meant by “pondered” in the caption. Consider vertical gridlines to make it easier to align the labels with the upper chart.
Discussion
- Line 388: Again, “variance” of what variables?
- Line 395: Should this be “< 0.5”?
- Line 401: Consider “slope angle” instead of just “slope”.
- Lines 402-406: These interpretations of TPD and VRM are difficult to understand when these variables have not been described in plain language.
- Lines 408-434: These seem to be new results presented in the Discussion section, which is unconventional. Also, the relevance of these comparisons could be introduced initially (instead of lines 435-445) so it is clearer why estimating density and strength from slab depth/thickness is helpful for mechanical models.
- Results were not compared with the similar studies such as Reuter et al. (2016).
- Fig 9: It’s odd to present new datasets in the caption of a discussion figure (EP20, EP19). Also, caption should have plain text names for all symbols presented. The 2 subfigures should be labelled and cited as 9a and 9b. Consider using different colours for the McClung and Bazant curves, it initially appears they are from the same study.
Citation: https://doi.org/10.5194/egusphere-2023-1586-RC1 - AC1: 'Reply on RC1', francis meloche, 18 Nov 2023
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RC2: 'Comment on egusphere-2023-1586', Anonymous Referee #2, 18 Oct 2023
The paper "Snow mechanical properties variability at the slope scale, implication for snow mechanical modelling" present both experimental measurements and modelling results of the horizontal variability of mechanical properties and stability indicators at the slope scale, that is to say from 1 to 100m typically. The scientific question is of high importance as this variability can be of paramount importance for the avalanche hazard for two main reasons. Variability can lead to weaker areas compared to the mean properties of the slope. In case a skier (or other trigger) meet this area, it could trigger an avalanche that would not have been released elsewhere (the knock-down effect). Moreover, the variability of mechanical properties also influence the propagation of cracks in weak layer and could promote or arrest long propagations. The originality of this paper is to combine measurements and, from these measurements, a method to estimate the values anywhere in the slope by the inference of statistical relationships between some chosen predictors (terrain information, absolute position, snow depth, incoming solar radiations) and the mechanical and stability metrics. Both scientific question and used methods seems relevant and at the cutting edge of the avalanche hazard research field and adapted for the readership of EGU journals. However, the paper would benefit from additional efforts before publication as all elements are not provided to the reader to estimate the impact of such research and to reproduce the results. In particular, sections methods and discussion may be easily improved. I detail below my main concerns as well as some minor comments I identified while reading the paper.
Main comments
The main limitation to estimate the impact of this research is that the model transferability is not addressed in the paper. Being able to estimate the horizontal variability of mechanical properties in a slope is of very high interest for the community. However, the impact of the method depend on the minimal set of knowledge to be able to apply in a different situation. It would be interesting to discuss these requirements of the method in the discussion for better reuse of the results.
In relation with the first point, a 10-fold cross-validation is used to estimate the error. However, in the paper, you point out that mechanical properties are correlated in space (and measure a correlation length). Hence, a random draw of an evaluation group does not seem sufficient to be able to have an independent evaluation set. It would be necessary to ensure that points from evaluation and training sets are at least spatially separated by a correlation length (or more). This may introduce complexity in the method but ensure a stronger evaluation. In any case, a discussion of the impacts of chosen evaluation method would be welcome.
When studying correlation lengths of the values of mechanical properties and stability metrics, you used the R function to perform a fit. It would be interesting to know the model used (function that is used for the fit) and provide the fitted parameters to quantitatively compare the results. It would also strengthen the results. On Figure 3 and 4, it would be possible to plot a vertical line for correlation length. It would also be interesting to provide a reproducible table of fitted values (at least the correlation length) that is extensively used. On Figure 3 and 4 it may also be possible to provide a small insert on each graph to represent the log-log variogram and provide data for the fractal dimension.
The results are convincing for the mechanical properties but I wonder what could be the use of critical crack length and skier crack length with less interesting results. Could you comment it in the discussion? Moreover, it is possible to imagine two ways of inferring stability indices: it is possible to infer from mechanical variables or to use a statistical model to predict directly these final variables. Could you comment the choice you made ? There is good reasons to choose one or the other, and it could also be interesting to compare both methods.
The GAM model is evaluated on the basis of maps and scoring of Fig. 6 and 7. However, the choice of covariates and what do we learn from the frequency in GAM may be of interest for further use of such techniques. In particular, authors chose a set of covariates and perform different tests (e.g. with different moving windows for TPI and VMR). I would be interested in recommendations from the authors on choice of covariates for further use of similar methods.
The discussion is quite short and do not discuss the relative interest of the information provided by measurements and by the GAM modelling. The study gather a large amount of data and a brief summary of the main guidelines of the studies would help the reader at the beginning of the discussion (the start seem quite steep for me).
Additional minor comments are detailed below:
page 1, line 10-12: "snow mechanical properties [...] were measured". SMP does not provide a direct measurement of density or elastic modulus. Maybe it would be better to use the word "estimated" rather than "measured". Same remark for page 3, line 67.
page 1, line 16: I am unsure whether the mention to log-log variogram is useful in the abstract, especially as it is not shown in the article.
page 1, line 19: VRM is not defined in the text before page 24. It would be better to define at first occurrence and at least in the methods section. Moreover, an very short reminder of what are VRM and TPI variables would be welcome.
page 2, line 42: lacking space before parenthesis.
page 7, line 183: The method used to identify the weak layer and the influence of this expert identification on the results may be enhanced. We have very few information on how this have been done, how this choice can impact the results and what consequences do this manual interaction have on the transferability of the method.
page 7, equation 1: replace "+-" by "-".
Table 1: How is justified this choice of variables ? In particular, the use of variable xy limits the transferability. It would be interesting to understand what lead you to this presented set of variable.
Page 13, line 326: Isn't there also low correlation length for slab density?
Page 13, line 331: Please define in the methods clearly the method to compute the correlation length and show it on the plot as Figure 3 does not allow to clearly know the correlation length for slab density at JBC22-SH.
Figure 5: Could you provide the number of elements in each boxplot ? It may be interesting to provide a similar figure for correlation length.
Page 17, line 360: The percentage of deviance is not defined or presented in the methods section.
Figures 7: The computation of lsk and ac with the analytical equation suppose that the snowpack is sufficiently homogeneous on the horizontal axis. From what I see on the figure, the computed values are here relatively low compared to the scale the model is applied. However, such a check may be important to mention for further use of this method.
page 23 line 431: the usefulness of dataset EP20DF and EP19FC are not fully clear for me. Results are not shown, so we do not have an idea of the performance the method could have on such different areas.
Page 17, line 375-376: Could you identify the outliers and the two weak spots (I clearly see on the north side but I am unsure of the second one you identified).
Page 17, line 383-384 and page 19 line 401: How do you explain that snow depth is not an interesting predictor? Maybe the dataset is too homogeneous ?
Page 22: A lot of use of 'Our result' or 'this result'. It is not always perfectly clear to what you intent to refer. In the same idea, line 426 and 429 you refer to Fig.9, maybe precise the variable you are interested in and/or add a) and b) to the two subfigures to point more precisely the data you want.
Figure 9 : You introduce a new dataset and new results in the discussion which is quite unusual. This may be moved in methods and results section.
Citation: https://doi.org/10.5194/egusphere-2023-1586-RC2 - AC2: 'Reply on RC2', francis meloche, 18 Nov 2023
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2023-1586', Anonymous Referee #1, 18 Aug 2023
General comments
This paper explores slope-scale patterns in snowpack stability. Four field surveys were conducted at different locations where snowpack properties were measured with a snow microprenetrometer and terrain properties were measured with a UAV. Three snowpack properties (slab depth, slab density, weak layer strength) and three stability indices (skier crack length, critical crack length, skier stability index) were derived from the SMP measurements, and their spatial patterns were explored with variogram analyses. Trrrain properties (slope angle, convexity, etc.) were used to fit regression models to predict stability patterns across the slopes and explore which terrain factors were most influential. The results suggest slab properties were more variable than weak layer properties and recommend ways slab variability could be accounted for in mechanical models of avalanche release.
The study is well designed, relevant, and interesting; however, I think its presentation needs to be improved before publication in the Cryosphere. Some of the methods and concepts are not described in sufficient detail, the use of terminology and symbols should be more consistent and organized, and the overall contribution and relevance of the study should be clarified.
Specific comments
- Novelty of research methods. Line 105 states “no studies have linked snow stability and mechanical properties with microtopography indicators in spatial modeling”, but I would argue that Reuter et al. (2016) perform a similar study where SMP data was used to spatially predict a failure initialization criteria and critical crack length based on terrain and snowpack data. While the specific properties and terrain predictors differ, as do the type of regression models, the methods are conceptually quite similar. Sect 4.3 of that study specifically discusses spatial prediction of stability indices. I think the similarities and differences between this study and previous studies needs to be clearer in the Introduction (several distinctions are made throughout the section, but not presented in a complete succinct way that links to their objective), and any relevant comparisons with past studies should be added to the Discussion.
- Incomplete methods. Methods section 2.5 does not describe how the covariates were derived or how the GAM models were fit to the data in enough detail to reproduce the study. The technical comments below list some specific examples.
- Description of terrain variables. The microtopographic indicators (covariates) are not sufficiently described. The topographic position index and vector ruggedness measure are not common terms used to describe avalanche terrain and should be described with plain language interpretations. It’s difficult to interpret why these were significant explanatory variables without understanding what they represent. Similarly, some of the other terrain variables are not described in enough detail to understand how they were derived or how to interpret them (e.g., wind-exposure index).
- Relating results to terrain/snowpack influences. A strength of this study is that it was conducted at multiple sites with different terrain and snowpack characteristics. I think the results could be more impactful if the influence of these characteristics were discussed in more detail. For example, what were the main differences between the wind-exposed versus forested slopes and persistent versus non-persistent weak layer grains? Understanding how these factors influence slope-scale variability would be directly relevant to avalanche risk management.
- Consistency and organization of terms and symbols. In general, there were quite a few places where consistent and complete use of terminology and symbols needs to be improved. Many examples are provided below.
Technical comments
Abstract/Introduction
- Line 4: True in some contexts, but “can simulate with good accuracy” is better.
- Line 11: These were not “measured” on the slopes but estimated from SMP measurements.
- Lines 8-19: Some of these sentences are a little vague “models suggested significant covariates”) and would benefit with being a little more specific about what types of variables were included in various parts of the study (e.g., “covariance models and scaling properties”) and some plain language interpretations (e.g., what does it mean that “GAM models suggest significant covariates”?).
- Line 19: Winstral index as not defined in the abstract, so perhaps use wind-exposure index.
- Lines 26-27: Perhaps more general triggers such as “person” instead of “skier” and “stresses from snowfall or warming” instead of just “new snowfall”.
- Line 30: The conceptual model decomposes hazard into 4, not 2, factors (problem type, location, size, likelihood).
- Line 44: Is there a word like “depth” missing in “spatial pattern of snow”?
- Line 48: Can you describe what is meant by “roughness” in a way that links the concept to avalanche release? The interpretation of the fractal distances is unclear in the results.
- Line 52: Start new paragraph here?
- Line 110: Can you briefly describe this “knockdown effect”?
Methods
- Line 127: “receives” instead of “received”.
- Lines 131-136: Please provide consistent details for each site. For example, the text for the site in Quebec does not name it Arete de Roc or provide the abbreviation AR used later in the manuscript, no slope angle is provided for JBC, and shouldn’t “the other site” in line 131 be “the first site”?
- Fig 1: Very nice images to illustrate the study sites. Please add the word “survey” prior to green and red in the caption for consistency.
- Line 165: Provide a bit more detail about the weak layer criteria. It sounds like one weak layer was identified for each survey, was this the uppermost result in a compression test of any fracture character, the uppermost result with a sudden fracture character, an expert interpretation of the primary layer of concern, or something else?
- Line 167: Please clarify if the winter imagery was collected on the same day as the survey.
- Line 181: I would consider layer depth, thickness, and density to be structural rather than mechanical properties.
- Line 183: Missing “density” between slab and rho.
- Line 187: Out of curiosity, does this method of averaging the density of each slab layer account for the varying thicknesses of these layers so that it would be conceptually the same as a bulk density measurement made with a sampling tube, or is this a more abstract slab density?
- Line 191: State “… shear strength of the weak layer…” so it is clear this is in reference to how you will derive tau_p.
- Line 194: Macroscale strength is not defined or explained anywhere, so the justification for this assumption is unclear.
- Fig 2: This figure is helpful but could potentially be simplified with a bit less text (e.g., green boxes) and more consistent formatting (has a mix of serif and sans serif fonts and sizes, bold and non-bold font, why is some text red?).
- Line 201: You could consider just saying “the SPI is the ratio of two lengths” rather than “defined by”.
- Line 207: It’s not clear to me what “the surface beneath the skier” refers to in the definition of alpha.
- Eq 6: Missing right bracket at the end of the numerator.
- Lines 262-264: This sentence is confusing and perhaps belongs later in this section. Aren’t the microtopographic indicators defined by more than the second order derivates as listed in Table 1? And it’s not clear how these moving windows are applied or relevant to the analysis.
- Sect 2.4: The fitting of spherical and gaussian variogram models should be described here since they are discussed in the results. Also, the results suggest you pick the best fitting model.
- Sect 2.5.1 and Table 1: Some of the microtopographic indicators could be defined more clearly. Specifically, TPI and VRM should have plain language descriptions because they are not everyday terms used to characterize avalanche terrain with intuitive meanings. How should canopy height be interpreted if you masked areas with vegetation? How are the concepts of “potential of incoming solar radiation” and “Winstral index” quantified? How was prevailing wind direction determined? What is meant by moving windows represented with two values such as 5/15 and 25/50?
- Line 284: The symbol Sx has already been used to describe a slab layer (line 177).
- Sect 2.5.2: This section is not clear what data is used to fit GAM models. My interpretation is that Y is the 6 properties previously analyzed and the X are the ~13 covariates listed in Table 1. I also assume the model was fit (and cross-validated) using data from the 60-80 SMP profile locations, but this is not stated. While the concepts behind the statistical modelling are explained well, it should be clearer and more explicit how they were applied to this data.
- Eq 12: The asterisk for multiplication is not necessary.
Results
- Fig 3: It would help if the 4 surveys were presented in a consistent order throughout the paper (methods, table 2, figures, etc.). The y-axis is not labelled.
- Table 2: Based on the methods, 3 x 2 = 6 compression tests were done with each survey, so why is only a single test reported. Since the tests were performed following Canadian Avalanche Association (2016), they should also be reported following those standards: “CTM 15 (RP) down 25”. How was ac_PST derived from PST test results? These don’t seem like cut lengths from a 100 cm long column. The mix of words and symbols in the column headings is confusing, I suggest using words. Units can be specified in the column headings. Consider separate columns for slab depth and density. Dates should probably be in YYYY-mm-dd format.
- Line 311: Are the lengths reported for each weak layer the (average) observed grain size with a crystal screen and loupe or the thicknesses derived from SMP measurements?
- Line 315: What is meant by the slab is made up of one layer? Doesn’t the SMP identify very thin layers?
- Line 340: “slab thickness” used here but referred to as “slab depth” in other parts of the manuscript. Check manuscript for consistency.
- Line 340: Is there any relevant interpretation to gaussian versus spherical variogram models?
- Fig 3: Interesting that AR had some longer correlation lengths given it sounds like it was the most wind exposed site.
- Line 353: “surface roughness” could be misinterpreted to mean the physical texture of the snow surface, which is why I think the interpretation of fractal distances needs to be explained. What does a value of 2.7 mean?
- Line 360: Please be more specific about what variable or property the “variance” refers to.
- Fig 6/7: Please explain the grey vegetation in the caption. Consider presenting the RMSE and MAE as rounded values with units to improve interpretability. The prefix “CV” is unnecessary. In general, these are very interesting figures and I agree could be valuable teaching material.
- Line 368: “same” or “similar” variation?
- Line 370: This sentence is confusing and partly contradictory.
- Line 378: This could be the start of a new subsection on microtopographic indicators.
- Table 2 and 3 are not cited in the text. The asterisks next to covariates are not defined, but I assume refer to significance levels.
- Table 2/3: Interesting that the wind exposure index Sx was more frequent for the models at the Fidelity sites than the AR site which was apparently more wind exposed. This result could be better understood of the derivation of Sx was explained better.
- Fig 8: What is meant by “pondered” in the caption. Consider vertical gridlines to make it easier to align the labels with the upper chart.
Discussion
- Line 388: Again, “variance” of what variables?
- Line 395: Should this be “< 0.5”?
- Line 401: Consider “slope angle” instead of just “slope”.
- Lines 402-406: These interpretations of TPD and VRM are difficult to understand when these variables have not been described in plain language.
- Lines 408-434: These seem to be new results presented in the Discussion section, which is unconventional. Also, the relevance of these comparisons could be introduced initially (instead of lines 435-445) so it is clearer why estimating density and strength from slab depth/thickness is helpful for mechanical models.
- Results were not compared with the similar studies such as Reuter et al. (2016).
- Fig 9: It’s odd to present new datasets in the caption of a discussion figure (EP20, EP19). Also, caption should have plain text names for all symbols presented. The 2 subfigures should be labelled and cited as 9a and 9b. Consider using different colours for the McClung and Bazant curves, it initially appears they are from the same study.
Citation: https://doi.org/10.5194/egusphere-2023-1586-RC1 - AC1: 'Reply on RC1', francis meloche, 18 Nov 2023
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RC2: 'Comment on egusphere-2023-1586', Anonymous Referee #2, 18 Oct 2023
The paper "Snow mechanical properties variability at the slope scale, implication for snow mechanical modelling" present both experimental measurements and modelling results of the horizontal variability of mechanical properties and stability indicators at the slope scale, that is to say from 1 to 100m typically. The scientific question is of high importance as this variability can be of paramount importance for the avalanche hazard for two main reasons. Variability can lead to weaker areas compared to the mean properties of the slope. In case a skier (or other trigger) meet this area, it could trigger an avalanche that would not have been released elsewhere (the knock-down effect). Moreover, the variability of mechanical properties also influence the propagation of cracks in weak layer and could promote or arrest long propagations. The originality of this paper is to combine measurements and, from these measurements, a method to estimate the values anywhere in the slope by the inference of statistical relationships between some chosen predictors (terrain information, absolute position, snow depth, incoming solar radiations) and the mechanical and stability metrics. Both scientific question and used methods seems relevant and at the cutting edge of the avalanche hazard research field and adapted for the readership of EGU journals. However, the paper would benefit from additional efforts before publication as all elements are not provided to the reader to estimate the impact of such research and to reproduce the results. In particular, sections methods and discussion may be easily improved. I detail below my main concerns as well as some minor comments I identified while reading the paper.
Main comments
The main limitation to estimate the impact of this research is that the model transferability is not addressed in the paper. Being able to estimate the horizontal variability of mechanical properties in a slope is of very high interest for the community. However, the impact of the method depend on the minimal set of knowledge to be able to apply in a different situation. It would be interesting to discuss these requirements of the method in the discussion for better reuse of the results.
In relation with the first point, a 10-fold cross-validation is used to estimate the error. However, in the paper, you point out that mechanical properties are correlated in space (and measure a correlation length). Hence, a random draw of an evaluation group does not seem sufficient to be able to have an independent evaluation set. It would be necessary to ensure that points from evaluation and training sets are at least spatially separated by a correlation length (or more). This may introduce complexity in the method but ensure a stronger evaluation. In any case, a discussion of the impacts of chosen evaluation method would be welcome.
When studying correlation lengths of the values of mechanical properties and stability metrics, you used the R function to perform a fit. It would be interesting to know the model used (function that is used for the fit) and provide the fitted parameters to quantitatively compare the results. It would also strengthen the results. On Figure 3 and 4, it would be possible to plot a vertical line for correlation length. It would also be interesting to provide a reproducible table of fitted values (at least the correlation length) that is extensively used. On Figure 3 and 4 it may also be possible to provide a small insert on each graph to represent the log-log variogram and provide data for the fractal dimension.
The results are convincing for the mechanical properties but I wonder what could be the use of critical crack length and skier crack length with less interesting results. Could you comment it in the discussion? Moreover, it is possible to imagine two ways of inferring stability indices: it is possible to infer from mechanical variables or to use a statistical model to predict directly these final variables. Could you comment the choice you made ? There is good reasons to choose one or the other, and it could also be interesting to compare both methods.
The GAM model is evaluated on the basis of maps and scoring of Fig. 6 and 7. However, the choice of covariates and what do we learn from the frequency in GAM may be of interest for further use of such techniques. In particular, authors chose a set of covariates and perform different tests (e.g. with different moving windows for TPI and VMR). I would be interested in recommendations from the authors on choice of covariates for further use of similar methods.
The discussion is quite short and do not discuss the relative interest of the information provided by measurements and by the GAM modelling. The study gather a large amount of data and a brief summary of the main guidelines of the studies would help the reader at the beginning of the discussion (the start seem quite steep for me).
Additional minor comments are detailed below:
page 1, line 10-12: "snow mechanical properties [...] were measured". SMP does not provide a direct measurement of density or elastic modulus. Maybe it would be better to use the word "estimated" rather than "measured". Same remark for page 3, line 67.
page 1, line 16: I am unsure whether the mention to log-log variogram is useful in the abstract, especially as it is not shown in the article.
page 1, line 19: VRM is not defined in the text before page 24. It would be better to define at first occurrence and at least in the methods section. Moreover, an very short reminder of what are VRM and TPI variables would be welcome.
page 2, line 42: lacking space before parenthesis.
page 7, line 183: The method used to identify the weak layer and the influence of this expert identification on the results may be enhanced. We have very few information on how this have been done, how this choice can impact the results and what consequences do this manual interaction have on the transferability of the method.
page 7, equation 1: replace "+-" by "-".
Table 1: How is justified this choice of variables ? In particular, the use of variable xy limits the transferability. It would be interesting to understand what lead you to this presented set of variable.
Page 13, line 326: Isn't there also low correlation length for slab density?
Page 13, line 331: Please define in the methods clearly the method to compute the correlation length and show it on the plot as Figure 3 does not allow to clearly know the correlation length for slab density at JBC22-SH.
Figure 5: Could you provide the number of elements in each boxplot ? It may be interesting to provide a similar figure for correlation length.
Page 17, line 360: The percentage of deviance is not defined or presented in the methods section.
Figures 7: The computation of lsk and ac with the analytical equation suppose that the snowpack is sufficiently homogeneous on the horizontal axis. From what I see on the figure, the computed values are here relatively low compared to the scale the model is applied. However, such a check may be important to mention for further use of this method.
page 23 line 431: the usefulness of dataset EP20DF and EP19FC are not fully clear for me. Results are not shown, so we do not have an idea of the performance the method could have on such different areas.
Page 17, line 375-376: Could you identify the outliers and the two weak spots (I clearly see on the north side but I am unsure of the second one you identified).
Page 17, line 383-384 and page 19 line 401: How do you explain that snow depth is not an interesting predictor? Maybe the dataset is too homogeneous ?
Page 22: A lot of use of 'Our result' or 'this result'. It is not always perfectly clear to what you intent to refer. In the same idea, line 426 and 429 you refer to Fig.9, maybe precise the variable you are interested in and/or add a) and b) to the two subfigures to point more precisely the data you want.
Figure 9 : You introduce a new dataset and new results in the discussion which is quite unusual. This may be moved in methods and results section.
Citation: https://doi.org/10.5194/egusphere-2023-1586-RC2 - AC2: 'Reply on RC2', francis meloche, 18 Nov 2023
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