Fuzzy modelling of powder snow avalanches

This paper examines powder snow avalanches by introducing a predetermined degree of variation, or fuzziness, in model parameters. Given a value of vagueness in the parameters, fuzzy set theory makes it possible to evaluate the vagueness in the results. The use of a more complex stochastic analysis can be avoided. Six parameters of the model are taken to be affected by a certain amount of uncertainty; the response of the numerical model is calculated by solving the fuzzy equations. In this way, it is possible to evaluate how the results are affected by a given change in the model parameters.The paper first presents a well-known avalanche model and its solution considering the influence of friction. A brief introduction of the fuzzy set is given with regard to the avalanche model mentioned. Later, the fuzzy solution of the model in terms of velocity and average pressure is calculated for three different levels of imprecision in the data. At the end, the results are presented and commented.     

On forecasting large and infrequent snow avalanches

Snow avalanches that threaten a highway or a residential area are often large avalanches that have a return period > 1 year. Danger assessment strongly relies on precipitation data since these avalanches are typically triggered by major snow storms. Given the extensive protection work that is in place in the European Alps, the avalanche control service (also called avalanche commission) responsible for danger assessment will usually monitor the avalanche situation throughout the winter, but only become active in case of a major snow fall. Related safety concepts describing the procedures and measures to be taken in a given danger situation are therefore often based on threshold values for new snow. By analysing the avalanche occurrence of a major avalanche path, we show that forecasting based on new snow amounts involves high uncertainty. Whereas the return period of an avalanche to, for example, the road was about 5 years, the return period for the corresponding new snow depth was substantially smaller, in our case slightly less than 2 years. Similar proportions were found for a number of other avalanche paths with different snow climate. The return period of the critical new snow depth was about 2–5 times smaller than the return period of the avalanche. This proportion is expected to increase with increasing return period. Hence, based on the return period of an avalanche path a first estimate for the critical new snow depth can be made. With a return period of the critical new snow depth of 1–2 years, avalanche prediction for individual avalanche path becomes very challenging since the false alarm ratio is expected to be high.     

On forecasting large and infrequent snow avalanches

Snow avalanches that threaten a highway or a residential area are often large avalanches that have a return period > 1 year. Danger assessment strongly relies on precipitation data since these avalanches are typically triggered by major snow storms. Given the extensive protection work that is in place in the European Alps, the avalanche control service (also called avalanche commission) responsible for danger assessment will usually monitor the avalanche situation throughout the winter, but only become active in case of a major snow fall. Related safety concepts describing the procedures and measures to be taken in a given danger situation are therefore often based on threshold values for new snow. By analysing the avalanche occurrence of a major avalanche path, we show that forecasting based on new snow amounts involves high uncertainty. Whereas the return period of an avalanche to, for example, the road was about 5 years, the return period for the corresponding new snow depth was substantially smaller, in our case slightly less than 2 years. Similar proportions were found for a number of other avalanche paths with different snow climate. The return period of the critical new snow depth was about 2–5 times smaller than the return period of the avalanche. This proportion is expected to increase with increasing return period. Hence, based on the return period of an avalanche path a first estimate for the critical new snow depth can be made. With a return period of the critical new snow depth of 1–2 years, avalanche prediction for individual avalanche path becomes very challenging since the false alarm ratio is expected to be high.     

A field study on failure of storm snow slab avalanches

Storm snow often avalanches before crystals metamorphose into faceted or rounded shapes, which typically occurs within a few days. We call such crystals nonpersistent, to distinguish them from snow crystals that persist within the snowpack for weeks or even months. Nonpersistent crystals can form weak layers or interfaces that are common sources of failure for avalanches. The anticrack fracture model emphasizes collapse and predicts that triggering is almost independent of slope angle, but this prediction has only been tested on persistent weak layers. In this study, dozens of stability tests show that both nonpersistent and persistent crystals collapse during failure, and that slope angle does not affect triggering (although slope angle determines whether collapse leads to an avalanche). Our findings suggest that avalanches in storm snow and persistent weak layers share the same failure mechanism described by the anticrack model, with collapse providing the fracture energy. Manual hardness measurements and near-infrared measurements of grain size sometimes showed thin weak layers of softer and larger crystals in storm snow, but often showed failures at interfaces marked by softer layers above and harder layers below. We suggest collapse often occurs in crystals at the bottom of the slab. Planar crystals such as sectored plates were often found in failure layers, suggesting they are especially prone to collapse.     

Large mobility of dry snow avalanches: Insights from small-scale laboratory tests on granular avalanches of bidisperse materials

This paper reports small-scale laboratory tests on granular avalanches of bidisperse materials made of fine particles and larger ones. These experiments were motivated by a recent study on the rheology of dense flowing snow which provided evidence for relevant similarities in flow behavior between bidisperse granular materials and dry cold snow [Rognon and others, J. Rheol., 52, 3 ([32])]. The mass proportion of fine particles in the initial binary mixture was systematically varied at constant initial released volume, and we measured the resulting flow depth, the avalanche front velocity and the final avalanche runout. In particular, we show that the avalanche mobility is largely increased, about 40% in our tests, when the mass proportion in fine particles reaches a critical value, around 0.25 in our tests. The avalanche deposit is shallow and lengthened for this critical mass proportion in fine particles. The experimental results are interpreted by the existence of different avalanche mobility regimes on the basis of a heuristic model previously reported in literature. Finally, we discuss their possible implications for the dynamics of full-scale dry snow avalanches.     

Triggering of dry snow slab avalanches: stress versus fracture mechanical approach

This paper analyses the conditions for triggering of dry snow slab avalanches. As suggested by several Authors, we assume as a basic mechanism for avalanche triggering the mode II fracture of the weak layer lying beneath the stiff snow slab, i.e. we assume the presence of super-weak zones in the basal layer. By means of a linear elastic analysis, the shear stresses in the weak layer as well as the strain energy release rate caused by an increment of the super-weak zone are evaluated. Hence we introduce a stress failure criterion as well as an energy one. It is shown that the latter criterion can be seen as an extension of the criterion firstly proposed by McClung [McClung, D.M., 1979. Shear fracture precipitated by strain softening as a mechanism of dry slab avalanche release. Journal of Geophysical Research, 84(B7), 3519-3526.] for dry snow slab avalanche release. Finally we couple the two criteria, showing that the weak layer can fail only in a min–max band of thickness.     

Modelling soil removal from snow avalanches: A case study in the North-Western Italian Alps

Snow avalanches can exert considerable erosive forces on soils. If a snow avalanche flows directly over bare ground, basal shear forces may scrape away and entrain soil. Sediments mix up with the avalanche body and may be found within the run-out snow deposit. Based on a previous field campaign aiming to quantify the amount of sediments trapped within avalanche bodies for the study site of Lavancher, in the Aosta Valley, NW-Italy, we developed here a soil erosion model, which we preliminarily applied to that site. An already developed and tested 1-D avalanche dynamics model was modified to include soil erosion. Soil removal was triggered according to two different mechanisms, namely excess of shear and critical velocity. We used equations from the available literature to model the shear stress exerted by the avalanche flow upon the ground underneath. Critical threshold for soil removal of either shear or velocity were also retrieved from the available literature, possibly depending upon soil texture and geotechnical properties. The model performs well in reproducing soil removal for three wet-dense avalanches that occurred in the study site.Use of excess of shear mechanism to evaluate erosion seems more robust, as less dependent upon flow velocity, utmost uncertain. Albeit more accurately measured events of soil eroding avalanches seem necessary to test its performance, the model can be used henceforth as a basis for further refinement concerning geomorphologic contribution of avalanches.     

Snowpack properties associated with fracture initiation and propagation resulting in skier-triggered dry snow slab avalanches

This study investigates snowpack properties associated with skier-triggered dry slab avalanches, with a particular view on snowpack conditions favoring fracture propagation. This was done by analyzing a data set of over 500 snow profiles observed next to skier-triggered slabs (including remotely triggered slab avalanches and whumpfs) and on skier-tested slopes that did not release a slab avalanche. The relation of the snowpack variables with fracture initiation and fracture propagation, both of which are required for skier-triggering, was investigated. Specific snowpack characteristics, including hardness difference and difference in crystal size across the failure layer, associated with skier-triggered dry slab avalanches were identified and the frequency of skier-triggering was determined. In order to assess snowpack variables favouring fracture propagation, variables from failure layers associated with skier-triggered slabs that were not remotely triggered and relatively small were contrasted with snowpack variables from failure layers of remotely triggered slab avalanches, whumpfs and relatively large slab avalanches. The properties of the slab overlying the weak layer, as well as the layer above the weak layer, were found to affect fracture propagation. Stiffer slabs were associated with large avalanches as well as whumpfs and remotely triggered avalanches. Furthermore, a correlation analysis of snowpack variables with the size and width of the investigated slab avalanches further accentuated the importance of these slab properties with regards to fracture propagation.     

Explanation and limitations of study plot stability indices for forecasting dry snow slab avalanches in surrounding terrain

In the Columbia Mountains of western Canada, some snow avalanche forecasting programs use slab stability indices calculated from study plot measurements near tree-line and find these indices helpful for forecasting dry slab avalanching many kilometers from the study plot. Research in the same mountain range has confirmed the correlation between the indices and avalanche occurrence. Due to spatial variability and scale issues, the explanation for the correlation between the indices, which are based on measurements over a small area, and avalanching many kilometers away has been unclear. The stability indices for natural (spontaneous) avalanches are ratios of shear strength of a weak snowpack layer to the shear stress on the weak layer applied by the overlying slab. The denominator of these ratios is proportional to vertical overburden pressure (load). One time series of overburden and shear strength measurements shows that neither measurement can be extrapolated from one site to another. A second time series shows a substantial difference in the stability index between the two sites, which is likely due to different initial crystal sizes in the weak layer at the two sites. However, different sites exhibit concurrent decreases in the strength–load ratio during snowfall and concurrent increases in the ratio after snowfall. The increases after snowfall are explained by lagged densification of weak layers and pressure sintering between grains. Critical values of stability indices are shown to be less useful than their trends for forecasting natural dry slab avalanches. The potential correlation of study plot stability indices with avalanching in surrounding terrain is also limited by the spatial extent of the weather system that forms the weak snowpack layer.     

Explanation and limitations of study plot stability indices for forecasting dry snow slab avalanches in surrounding terrain

In the Columbia Mountains of western Canada, some snow avalanche forecasting programs use slab stability indices calculated from study plot measurements near tree-line and find these indices helpful for forecasting dry slab avalanching many kilometers from the study plot. Research in the same mountain range has confirmed the correlation between the indices and avalanche occurrence. Due to spatial variability and scale issues, the explanation for the correlation between the indices, which are based on measurements over a small area, and avalanching many kilometers away has been unclear. The stability indices for natural (spontaneous) avalanches are ratios of shear strength of a weak snowpack layer to the shear stress on the weak layer applied by the overlying slab. The denominator of these ratios is proportional to vertical overburden pressure (load). One time series of overburden and shear strength measurements shows that neither measurement can be extrapolated from one site to another. A second time series shows a substantial difference in the stability index between the two sites, which is likely due to different initial crystal sizes in the weak layer at the two sites. However, different sites exhibit concurrent decreases in the strength–load ratio during snowfall and concurrent increases in the ratio after snowfall. The increases after snowfall are explained by lagged densification of weak layers and pressure sintering between grains. Critical values of stability indices are shown to be less useful than their trends for forecasting natural dry slab avalanches. The potential correlation of study plot stability indices with avalanching in surrounding terrain is also limited by the spatial extent of the weather system that forms the weak snowpack layer.     

Triangular and uphill avalanches of a tilted sandpile

Recent experiments show that an avalanche initiated from a point source propagates downwards by invading a triangular shaped region. The opening angle of this triangle appears to reach 180° for a critical inclination of the pile, beyond which avalanches also propagate upwards. We propose a simple interpretation of these observations, based on an extension of a phenomenological model for surface flows.     

Motion resistance of avalanches on smooth paths

Dimensionless mathematical models are developed for the dynamics of mass-center avalanches on smooth and circular paths. Equations for velocity as a function of position are derived in terms of two dimensionless, spatially averaged resistance factors. A procedure is outlined to estimate the resistance factors and assess the relative effects of Coulomb friction and speed-dependent resistance on avalanche motion.     

Textile protection of snow and ice: Measured and simulated effects on the energy and mass balance

Measurements and simulations of the energy fluxes and mass changes of an artificially covered snow and ice surface (geotextile material) and an unaltered control plot in an Austrian glacier ski resort are presented and compared. A modified version of the snow cover model SNOWPACK is used to successfully reproduce the artificially compacted and the additionally covered snow cover in a physically based way. Supplementary measurements of crucial material properties of the 4.5 mm thin geotextile serve as model input as well. Results indicate that the shortwave reflectivity of the covers is responsible for 46% of the performance. Thermal insulation of the material (14%) and a negative latent heat flux due to evaporation of precipitation from the cover surface (10%) have almost the same contribution. A layer of air between the cover and the snow and ice surface (thickness 7.5 cm to 12 cm) adds the rest, which is at the upper limit of observations and may therefore also compensate for model errors. This generally explains the high performance of the method in glacier ski resorts and, most importantly, an altitude dependent application limit of the method: the method becomes less effective at lower altitudes, where sensible heat fluxes become more important compared to shortwave radiation.     

Erosive granular avalanches: a cross confrontation between theory and experiment

Results on two laboratory scale avalanches experiments taking place both in the air and under-water, are presented. In both cases a family of solitary erosion/deposition waves are observed. At higher inclination angles, we show the existence of a long wavelength transverse instability followed by a coarsening and the onset of a fingering pattern. While the experiments strongly differ by the spatial and time scales, the agreement between the stability diagram, the wavelengths selection and the avalanche morphology suggest a common erosion/deposition scenario. These experiments are studied theoretically in the framework of the “partial fluidization” model of dense granular flows. This model identifies a family of propagating solitary waves displaying a behavior similar to the experimental observation. A primary cause for the transverse instability is related to the dependence of avalanche velocity on the granular mass trapped by the flow.     

Whispering gallery modes of a curved antiresonant reflecting optical waveguide

The whispering gallery modes of a curved antiresonant reflecting optical waveguide are described and analyzed. We present a ray analysis method that can be used to derive an eigenmode equation and to analyze the loss characteristics of a waveguide in rectangular coordinates by using conformal transformation. With an optimized design of an antiresonant reflecting optical waveguide structure, the propagation loss of such a waveguide can be significantly reduced.     

Onset mechanism of granular avalanches in inclining layers using a continuum model

What is the onset mechanism of macro scale avalanches? How do macro scale avalanches happen in the granular layers in an inclining box? The answers to these questions are the main part of our article aims. Using 3-dimensional simulation method we show the stresses, the stress ratios and the packing fractions in the processes where the onset of macro scale avalanches takes place. Based on our results the critical conditions of the onset of avalanches are presented. The onset mechanism of granular avalanches is elucidated. The onset of macro scale avalanches occurs in the small area, about 2% of the whole area, in the inclining granular layers. These are the conditions for the onset of macro scale avalanches that the shear and normal stresses and the packing fraction reach the maximum values at the same inclining angle. Then the stress ratio should be larger than the static frictional coefficient of materials. Aggregates of stick-slip like event are formed in the longitudinal direction. The number of aggregates decreases and the physical quantities in the aggregates rapidly increase with increasing inclining angle in the small area in which the onset of macro scale avalanche occurs.     

The unacknowledged risk of Himalayan avalanches triggering

A “universal” model for avalanche triggering, as well as for collapse of suspended seracs, is presented based on Quantized Fracture Mechanics, considering fracture, friction, adhesion and cohesion. It unifies and extends the classical previous approaches reported in the literature, including the role of the slope curvature. A new size-effect, that on mountain height rather than the classical one on snow slab thickness, is also discussed and demonstrated thanks to glaciers data analysis from the World Glacier Inventory (http://nsidc.org/data/glacier_inventory/browse.html, 2014). The related most noteworthy result is that snow precipitation needed to trigger avalanches at 8,000 m could be up to 4 times, with a realistic value of 1.7 times, smaller than at 4,000 m. This super-strong size-effect may suggest that the risk of Himalayan avalanches is today still unacknowledged. A discussion on the recent Manaslu tragedy concludes the paper.     

Effect of the ellipticity of a dielectric resonator on the induced whispering gallery modes

The influence of ellipticity of a dielectric resonator on the whispering gallery (WG) oscillation modes induced by a lumped radiation source was studied. Dependence of the spectral characteristics of resonators and the spatial distributions of oscillation fields on the WG mode propagation direction is experimentally determined.     

The solar reflectance of a snow field

The radiative transfer equation has been solved using a modified Schuster-Schwartzschild approximation to obtain an expression for the solar reflectance of a snow field. The parameters in the reflectance formula are the single scattering albedo and the fraction of energy scattered in the backward direction. The single scattering albedo is calculated from the crystal size using a geometrical optics formula and the fraction of energy scattered in the backward direction is calculated from the Mie scattering theory. Numerical results for reflectance are obtained for visible and near infrared radiation for different snow conditions. Good agreement has been found with the whole spectral range. The calculation also shows the observed effect of aging on the snow reflectance.