the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Mar 2024
Glide-snow avalanches: A mechanical, threshold-based release area model
Abstract. Glide-snow avalanches release at the ground-snow interface due to a loss in basal friction. They pose a threat to infrastructure because of the combination of unreliable mitigation measures, limited forecasting capabilities, and a lack of understanding of the release process. The aim of this study was to investigate the influence of spatial variability in basal friction and snowpack properties on the avalanche release area distribution and the release location. We developed a pseudo-3D, mechanical, threshold-based model that consists of many interacting snow columns on a uniform slope. Parameterizations in the model are based on our current understanding of glide-snow avalanche release. The model can reproduce the power law glide-snow avalanche release area distribution as observed on Dorfberg (Davos, Switzerland). A sensitivity analysis of the input parameters showed that the avalanche release area distribution was mostly influenced by the homogeneity (correlation length and variance) of the basal friction and whether the basal friction was reduced suddenly or in small increments. Larger release areas were modeled for a sudden decrease and a more homogeneous basal friction. The spatial variability of the snowpack parameters had little influence on the release area distribution. Extending the model to a real-world slope showed that the modeled location of avalanche releases qualitatively matched the observed locations. The model can help narrow down the length- and time-scales for field investigations. Simultaneously, it can grow in complexity with our increasing knowledge on glide-snow avalanche release processes. Input parameters such as the basal friction or snowpack parameters could potentially all be connected to the liquid water content. This would allow for the use of meteorological measurements to drive the model. The model has the potential to help identify potentially dangerous conditions for large or numerous avalanches which would help improve glide-snow avalanche forecasting.
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Status: open (until 30 Apr 2024)
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RC1: 'Comment on nhess-2024-34', Jerome Faillettaz, 08 Apr 2024
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This paper investigates the mechanism of glide-snow avalanche through a threshold-based model. Despite its simplicity, such models have yielded compelling results by aiming to replicate the emergent behavior—specifically, the release of avalanches—by employing basic interacting elements. This approach seeks to minimize the number of parameters while capturing the statistical behavior of complex phenomena. Consequently, it allows for the examination of the relative impact of chosen parameters on the overall emergence of phenomena and enhances the qualitative understanding of the phenomenon under investigation.
Having already demonstrated success in modeling landslides, this threshold-based model is now extended to the domain of glide-snow avalanche release. Leveraging data from a specific field site, this study enables the comparison of numerical and field results and the testing of various hypotheses. The findings highlight the significance of heterogeneity and the evolution of basal friction properties in the dynamics of avalanche release. This study introduces a new framework that underscores the primary influence of friction on the triggering mechanisms of snow avalanches.
Furthermore, the initial attempt to apply this model to a real slope with realistic parameters shows promise and hints at further fruitful research.
This paper addresses relevant scientific questions with an original approach. The paper is well-written, logically organized, clear, and well-structured. I believe this excellent work deserves to be published in NHESS after clarifying some points:
General comments:
My primary concern revolves around the justification of the power law behavior observed in glide avalanche release areas. The entire framework of the paper is built upon the assumption that these release areas follow a power law distribution, serving as the fundamental basis for the overall approach and numerical model. However, it's worth noting that the field data utilized in the study were collected solely from a single site, which may not provide conclusive evidence of such behavior. While I am inclined to support this assumption, the authors should exercise caution in making such assertions. Although they acknowledge in the discussion section the necessity for additional data from different field sites to validate this behavior, it's crucial to emphasize this limitation. Universality class might change for different slopes, aspect, slope orientation…
Furthermore, while I am convinced of the relevance of employing Self-Organized Criticality (SOC) concepts to model avalanche release, I still have some doubts regarding the numerical findings. Specifically, the detection of power law behavior solely at the extreme tail of the distribution raises concerns, as it primarily affects only a few large avalanches over less than one order of magnitude. The authors mention the evaluation of the power law exponent using the maximum likelihood method and xmin using Clauset's method. However, to enhance the rigor of the analysis, it would be worth to compare different candidate distributions, such as lognormal and power law, and provide the p-value for a more comprehensive assessment. By doing so, this study would achieve a greater degree of robustness and credibility.
It could be worthwhile to mention in the introduction that other types of models, which address the interplay between sliding, friction, and tension cracking using the concepts of SOC, exist. These include spring-block model types such as the Olami–Feder–Christensen model, Burridge Knopoff model, and others. Additionally, various other models exist to study the fracture process, such as the Random Fuse Model, Fiber Bundle Model, percolation (Alava et al., 2006)…
Specific comments:
Line 44: I would suggest a more cautious formulation: "These heavy-tailed power law distributions may potentially be associated with SOC."
L.46: Other models utilizing these concepts can replicate such behavior, including the spring-block model (e.g., Burridge-Knopoff type), fiber bundle models, thermal fuse model, branching model, among others (Sornette, 2006). For statistical fracture models, please also refer to Alava et al., 2006.
L.70: Using a Gaussian random field with an exponential covariance function seems reasonable for reproducing the spatial fluctuations of the friction coefficient on a slope. Is there any evidence of such variation in spatial properties in nature? Could you provide any references? How does the initial distribution of friction affect your results? Would the results differ if the friction coefficient were initialized with a uniform random distribution?
Section 2.2: I'm not entirely certain about how bonds are handled. From what I understand, during the inspection of each cell, the failure of each bond is evaluated in shear, tension, and compression, and stress is redistributed according to those that remain intact. Is there any memory of bonds? In other words, if a bond between (q,r) and (q+1,r) failed in shear during the inspection of (q,r), will this failure be taken into account when inspecting (q+1,r)?
Section 2.5: The explanation of the weighting factor was clear. I was just wondering how the authors deal with the case where gamma = 0. Do they consider only one compressive bond, or three? Do they arbitrarily select two bonds among the three to be in compression?
Table 1: Why are there so few simulations, only 30? How long does a typical run last?
L.185: Figure 5b appears to depict a specific run where the outcome shows only one avalanche with an area of 848 m2 and four others of 3 m2 (which are not counted). Obtaining more than 500 avalanches with only 30 runs seems improbable based on this representation. It's possible that the figure is illustrating a particular case or scenario rather than a typical run. Further clarification from the authors may be necessary to reconcile this observation with the reported results of more than 500 avalanches from the 30 runs.
In Figure 8, the distributions look very similar despite the variation in alpha values from 2 to 5…
The emergence of a pure power-law (i.e. without cut-off) is theoretically possible only within a system of infinite size. In the case of a finite size system, the occurrence of the largest events is constrained by the size of the system. As a consequence, the power-law distribution is affected by an exponential tail (Amitrano, 2012). At first glance, the distributions displayed in Figures 6, 7, and 8 appear to follow a power-law distribution with some cutoff, possibly related to finite size effects. Have you attempted simulations with a higher number of cells? (104 cells may not be sufficient to capture the full range of behavior).
Figure 9a illustrates an almost power-law distributed release area for the model, even for small avalanches, a difference from the results observed in the baseline model. The authors may ponder the underlying reasons for this discrepancy. Could the mask used in the simulations have influenced this outcome? Alternatively, might it be due to the varying slope angles across the lattice in these simulations? Including a brief discussion of these factors in the discussion section would be beneficial.
The discussion section is quite interesting and raises important points. During my review of this paper, I noted a few additional remarks:
- Does the aspect ratio depend on the relative sharing magnitude (f) of 10:2:1? I suspect that higher shear would enlarge the avalanche ratio.
- The results presented in this paper are quite similar to those of Faillettaz et al. (2011). Although that study focused on instabilities in hanging glaciers, a similar investigation involving changes in friction coefficient was conducted, and similar effects were observed.
- Why not consider water basal discharge, such as drainage paths (computed with slope map), as a proxy for friction decrease? In this way, friction would decrease preferentially along flow paths (e.g., gullies), in relationship with intensity of melting.
Reference
Alava, M.J., Nukala, P.K.V.V., Zapperi, S., 2006. Statistical models of fracture. AP 55, 349–476. https://doi.org/10.1080/00018730300741518
Amitrano, D., 2012. Variability in the power-law distributions of rupture events. The European Physical Journal Special Topics 205, 199–215. https://doi.org/10.1140/epjst/e2012-01571-9
Faillettaz, J., Sornette, D., Funk, M., 2011. Numerical modeling of a gravity-driven instability of a cold hanging glacier: reanalysis of the 1895 break-off of Altelsgletscher, Switzerland. JG 57, 817–831. https://doi.org/10.3189/002214311798043852
Citation: https://doi.org/10.5194/nhess-2024-34-RC1
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