The objective of this research is to model snow's response to dynamic, impact loading. Two constitutive relationships are considered: elastic and Maxwell-viscoelastic. These material models are applied to laboratory experiments consisting of 1000 individual impacts across 22 snow column configurations. The columns are 60 cm tall with a 30 cm by 30 cm cross-section. The snow ranges in density from 135 to 428 kg m−3 and is loaded with both short-duration (~1 ms) and long-duration (~10 ms) impacts. The Maxwell-viscoelastic model more accurately describes snow's response because it contains a mechanism for energy dissipation, which the elastic model does not. Furthermore, the ascertained model parameters show a clear dependence on impact duration; shorter duration impacts resulted in higher wave speeds and greater damping coefficients. The stress wave's magnitude is amplified when it hits a stiffer material because of the positive interference between incident and reflected waves. This phenomenon is observed in the laboratory and modeled with the governing equations.

In the course of an artificially triggered avalanche, a particle tracking procedure is combined with supplementary measurements, including Global Navigation Satellite System (GNSS) positioning, terrestrial laser scanning and Doppler radar measurements. Specifically, an intertial measurement unit is mounted inside a rigid sphere, which is placed in the avalanche track. The sphere is entrained by the moving snow, recording translational accelerations, angular velocities and the flux density of Earth's magnetic field. Based on the recorded data, we present a threefold analysis: (i) a qualitative data interpretation, identifying different particle motion phases which are associated with corresponding flow regimes, (ii) a quantitative time integration algorithm, determining the corresponding particle trajectory and associated velocities on the basis of standard sensor calibration, and (iii) an improved quantitative evaluation relying on a novel in situ sensor calibration technique, which is motivated by the limitations of the given dataset. The final results, i.e. the evolution of the angular orientation of the sensor unit, translational and rotational velocities and estimates of the sensor trajectory, are assessed with respect to their reliability and relevance for avalanche dynamics as well as for future design of experiments.

Spatial variability of snowpack properties adds uncertainty in the evaluation of avalanche hazard. We propose a combined mechanical–statistical approach to study how spatial variation of slab depth affects the skier-triggering probability and possible release size. First, we generate multiple slab depth maps on a plane fictional slope based on Gaussian Random Fields (GRF) for a specific set of mean, variance and correlation length. For each GRF, we derive analytically the Skier Propagation Index (SPI). We then simulate multiple skier tracks and computed the probability based on the number of skier hits where SPI is below 1. Finally, we use a depth-averaged material point method to evaluate the possible avalanche size for given slab depth variations. The results of this analysis show that large correlation lengths and small variances lead to a lower probability of skier-triggering as it reduces the size and the number of areas with low slab depth. Then, we show the effect of skiing style and skier group size on skier-triggering probability. Spatial variability also affects the possible avalanche size by adding stress fluctuation causing early or late tensile failure. Finally, we demonstrate with our models the well-known relationship between the probability and the size in avalanche forecasting.

The snow compression test is a snow stability test where an isolated column of snow is progressively loaded by tapping on it to induce failure in a possible weak layer. The test result provides valuable information about the propensity of failure initiation within the snowpack. However, different persons might tap with different force and thus reduce the reproducibility of the test results. The aim of this work was to quantify the influence of different test persons and different snowpacks on snow compression test results. We therefore let 62 persons tap on a stress measurement plate during a workshop of the European Avalanche Warning Services. Moreover, in the field, we performed stress measurements during 116 snow compression tests with 13 persons at eight different locations in the Alps. Data on persons’ body features and snow properties were also collected. Our results show that the stresses that reach a weak snow layer due to tapping are influenced by both the snowpack as well as different persons. Still, the data's scattering is surprisingly small for lower loading steps and decreases with depth. Therefore, we can deduce that, especially when avalanche conditions are particularly dangerous, snow compression test results are quite reproducible.

Wet-snow avalanches are triggered by the infiltration of liquid water which weakens the snowpack. Wet-snow avalanches are among the most destructive avalanches, yet their release mechanism is not sufficiently understood for a process-based prediction model. Therefore, we followed a data-driven approach and developed a random forest model, depending on slope aspect, to predict the local wet-snow avalanche activity at the locations of 124 automated weather stations distributed throughout the Swiss Alps. The input variables were the snow and weather data recorded by the stations over the past 20 years. The target variable was based on manual observations over the same 20-year period. To filter out erroneous reports, we defined the days with wet-snow avalanches in a stringent manner, selecting only the most extreme active or inactive days, which reduced the size of the dataset but increased the reliability of the target variable. The model was trained with weather variables and variables computed from simulated snow stratigraphy in 38$^\circ$ slopes facing the 4 cardinal directions. While model development and validation were done in nowcast mode, we also studied model performance in 24-hour forecast mode by using input variables computed from a numerical weather prediction (NWP) model. Overall, the performance was good in both nowcast and forecast mode (f1-score around 0.8). To assess model performance beyond the stringent definition of wet-snow avalanche days, we compared model predictions to wet-snow avalanche activity over the entire Swiss Alps, based on the raw data over 8 winters. We obtained a Spearman correlation coefficient of 0.71. Hence, our model represents a step toward the application of support tools in operational wet-snow avalanche forecasting.

Once fallen, snow settles due to the combined effects of metamorphism and deformation of the ice matrix under gravity. To understand how these coupled processes affect snow evolution, we performed oedometric compression tests and continuously monitored the snow microstructure with X-ray tomography. Centimetric samples with an initial density between 200 and 300 kg m−3 were followed during an initial sintering phase and under two different loads of 2.1 and 4.7 kPa at $-8^\circ$C for ~1 week. The microstructure captured at a voxel size of 8.5 μm was characterized by density, specific surface area (SSA) and two metrics related to bond network, namely the Euler characteristic and the minimum cut surface. Load-induced creep of the ice matrix was observed only for sufficiently low values of initial density (<290 kg m−3 in our tests), and was shown to be associated to a significant increase of the number of bonds. Application of the load, however, did not affect the individual bond size nor the SSA, which appeared to be mainly controlled by isothermal metamorphism. The uniaxial compression did not induce any creation of anisotropy on the microstructural characteristics. Overall, our results show that, for the considered conditions, the deformation of the ice matrix mainly leads to a reduction of the pore space and an increase of the coordination number, while metamorphism mainly affects the grain and bond sizes.

For the release of a slab avalanche, crack propagation within a weak snowpack layer below a cohesive snow slab is required. As crack speed measurements can give insight into underlying processes, we analysed three crack propagation events that occurred in similar snowpacks and covered all scales relevant for avalanche release. For the largest scale, up to 400 m, we estimated crack speed from an avalanche movie; for scales between 5 and 25 m, we used accelerometers placed on the snow surface and for scales below 5 m, we performed a propagation saw test. The mean crack speeds ranged from 36 ± 6 to 49 ± 5 m s−1, and did not exhibit scale dependence. Using the discrete element method and the material point method, we reproduced the measured crack speeds reasonably well, in particular the terminal crack speed observed at smaller scales. Finally, we used a finite element model to assess the speed of different elastic waves in a layered snowpack. Results suggest that the observed cracks propagated as mixed mode closing cracks and that the flexural wave of the slab is responsible for the energy transfer to the crack tip.

Assessing the avalanche danger level requires snow stratigraphy and instability data. As such data are usually sparse, we investigated whether distributed snow cover modeling can be used to provide information on spatial instability patterns relevant for regional avalanche forecasting. Using Alpine3D, we performed spatially distributed simulations to evaluate snow instability for the winter season 2016–17 in the region of Davos, Switzerland. Meteorological data from automatic weather stations were interpolated to 100 m horizontal resolution and precipitation was scaled with snow depth measurements from airborne laser scanning. Modeled snow instability metrics assessed for two different weak layers suggested that the weak layer closer to the snow surface was more variable. Initially, it was less stable than the weak layer closer to the ground, yet it stabilized faster as the winter progressed. In spring, the simulated snowpack on south-facing slopes stabilized faster than on north-facing slopes, in line with the regional avalanche forecast. In the winter months January to March 2017, simulated instability metrics did not suggest that the snowpack on south-facing slopes was more stable, as reported in the regional avalanche forecast. Although a validation with field data is lacking, these model results still show the potential and challenges of distributed modeling for supporting operational avalanche forecasting.

We use seismic refraction data to investigate the firn structure across a suture zone on the Amery Ice Shelf, East Antarctica, and the possible role of glacier dynamics in firn evolution. In the downstream direction, the data reveal decreasing compressional-wave velocities and increasing penetration depth of the propagating wave in the firn layer, consistent with $\sim$1 m firn thickening every 6 km. The boundary between the Lambert Glacier unit to the west and a major suture zone and the Mawson Escarpment Ice Stream unit to the east, is marked by differences in firn thicknesses, compressional-wave velocities and seismic anisotropy in the across-flow direction. The latter does not contradict the presence of a single-maximum crystal orientation fabric oriented 45–$90^{\circ }$ away from the flow direction. This is consistent with the presence of transverse simple shear governing the region's underlying ice flow regime, in association with elevated strain along the suture zone. The confirmation and quantification of the implied dynamic coupling between firn and the underlying ice requires integration of future seismic refraction, coring and modelling studies. Because firn is estimated to cover $\sim$98% of the Antarctic continent any such coupling may have widespread relevance to ice-sheet evolution and flow.

Snow appears as a granular material in most engineering applications. We examined the role of grain shape and cohesion in angle of repose experiments, which are a common means for the characterization of granular materials. The role of shape was examined by investigating diverse snow types with discernable shape and spherical ice beads. Two geometrical shape parameters were calculated from X-ray micro-computed-tomography images after a particle segmentation was performed with a watershed algorithm. Cohesion was examined by conducting experiments at six different temperatures between −40 and −2°C, assuming sintering as its cause, which accelerates with increasing temperature. As a cohesionless reference, experiments with glass beads were performed. We found that both shape and cohesion exerted about equally strong influence on the angle of repose. We utilized our results for an empirical model that describes the influence of shape and cohesion as additive corrections of the angle of repose of cohesionless spheres and explains all experiments with a correlation coefficient r2 = 0.95. With temperature and the chosen shape parameter as fitting variables, previous experiments with another snow type could be consistently included. The experiments highlight the relevance of these parameters in granular snow mechanics and can be used for model calibration.

From field observations, dry snow slab avalanche initiation is associated with fracture within relatively thin weak layers under stronger, cohesive slabs. For risk-based avalanche prediction, it is important to understand the fracture properties of alpine snow. Alpine snow is a quasi-brittle material with a fracture mechanical size effect on nominal shear strength meaning that strength decreases with increasing specimen size. A related size effect is the critical length required for rapid propagation of a shear fracture. In that case, the probability of fracture increases with increasing crack length. In this paper, 45 sets of field-measured critical lengths are presented based on 591 individual tests. From analysis, a probabilistic size effect law based on critical lengths is derived analogous to the deterministic size effect law for nominal shear strength related to fracture mechanics. The new size effect law may be useful in applications, particularly since the critical length is easily measured in the field and it is a principal component of weak layer fracture toughness.

Snow properties relevant to the fracture processes involved in dry-snow slab avalanche release include weak layer specific fracture energy, slab elastic modulus and density. Various techniques exist to determine these snow mechanical properties, but it is presently unclear how values determined with different methods compare. In the laboratory, the 3-D microstructure of cm-sized snow samples is reconstructed by micro-computed tomography (μCT) so that density and elastic modulus can be computed. In the field, fracture energy and modulus are estimated based on particle tracking velocimetry (PTV) of the displacement field observed during propagation saw tests. Snow stratigraphy is measured with the snow micro-penetrometer (SMP) in either, field or laboratory. We compared SMP-derived properties to corresponding μCT- and PTV-derived values. Values of snow density related well to μCT results and so were SMP-derived elastic moduli related to PTV-derived values. By taking into account snow anisotropy a good relation between SMP- and μCT-derived moduli resulted suggesting the SMP-derived modulus characterizes the components of the modulus perpendicular to the axis of penetration. SMP- and PTV-derived values of fracture energy were correlated. The SMP can provide a bridge between scales and techniques, yet further improvements in signal interpretation are still needed.

Snow slab avalanches are caused by cracks forming and propagating in a weak snow layer below a cohesive slab. The gradual damage process leading to the formation of the initial failure within the weak layer (WL) is still not entirely understood. To this end, we designed a novel test apparatus that allows performing loading experiments with large snow samples (0.25 m2) including a WL at different loading rates and simultaneously monitoring the acoustic emissions (AE) response. By analyzing the AE generated by micro-cracking, we studied the evolution of the damage process preceding snow failure. At fast loading rates, the exponent of the AE energy distribution (b-value) gradually changed, and both the energy rate and the inverse waiting time increased exponentially with increasing load. These changes in AE signature indicate a transition from small to large events and an acceleration of the damage processes leading to brittle failure. For the experiments at slow loading rate, these changes in the AE signature were not or only partially present, even if the sample failed, indicating a different evolution of the damage process. The observed characteristics in AE response provide new insights on how to model snow failure as a critical phenomenon.

The critique by Issler and other (2017) of our avalanche dynamics model maintains that we disregard well-established results of particulate gravity flows. Here we show that the arguments of Issler and others (1) violate Newton's laws of motion in the avalanche core and (2) ignore size-dependent drag forces on snow particles (Stokes law) that lead to the formation of avalanche suspension layers. We explain why we cannot amend our model equations to accommodate their suggestions. The goal of our approach is to describe highly non-stationary processes in the avalanche core that lead to a wide range of avalanche flow types and therefore different flow behavior. This is important for practical applications.

The cone penetration test has been successfully used to classify soil for ∼100 years. However, it has received only limited contemporary use in frozen geomaterials. The historical and contemporary use of the cone penetration test in various frozen geomaterials is considered here and contemporary data from recent work in polar snow are examined. It is probable that many material physical properties (e.g. density, strength and microstructure) can be obtained directly from cone penetration testing. It appears under-utilized as a contemporary scientific and engineering investigative tool in frozen geomaterials.

Snow metamorphism and settlement change the microstructure of a snowpack simultaneously. Past experiments investigated snow deformation under isothermal conditions. In nature, temperature gradient metamorphism and settlement often occur together. We investigated snow settlement in the first days after the onset of temperature-gradient metamorphism in laboratory experiments by means of in-situ time-lapse micro-computed tomography. We imposed temperature gradients of up to 95 K m−1 on samples of rounded snow with a density of ~230 kg m−3 and induced settlement by applying 1.7 kPa stress with a passive load on the samples simultaneously. We found that snow settled about half as fast when a temperature gradient was present, compared with isothermal conditions. The change in specific surface area after 4 days caused by temperature-gradient metamorphism was only a few percent. The viscosity evolution correlated with the amount of the temperature gradient. Finite element simulations of the snow samples revealed that stress-bearing chains had developed in the snow structure, causing the large increase in viscosity. We could show that a small change in microstructure caused a large change in the mechanical properties. This explains the difficulty of predicting snow mechanical properties in applications such as firn compaction or snow avalanche formation.

The microstructure and stratigraphy of a snowpack determine its physical behaviour. Weak layers or weak interfaces buried under a slab are prerequisites for the formation of dry-snow slab avalanches, and a precise characterization of weak layers or interfaces is essential to assess stability. Yet their exact geometry and micromechanical properties are poorly known. We cast weak layers and their adjacent layers in the field during two winters and reconstructed their three-dimensional microstructure using X-ray microcomputer tomography. The high resolution of 10–20 μm allowed us to study snow stratigraphy at the microstructural scale. We quantified the microstructural variability for 32 centimetre-sized layered samples and we calculated Young’s modulus and Poisson’s ratio by tomography-based finite-element simulations. Layers in a sample could therefore be differentiated not only by a change in morphology or microstructure, but also by a change in mechanical properties. We found a logarithmic correlation of Young’s modulus with density for two different density ranges, consistent with previous studies. By calculating the relative microstructural changes within our samples, we showed that a large change could indicate a potential weak layer, but only when the weak layer and both adjacent layers, i.e. the sandwich, were considered.

Snow avalanche simulation software is a commonly used tool for hazard estimation and mitigation planning. In this study a depth-averaged flow model, combining a simple entrainment and friction relation, is implemented in the software SamosAT. Computational results strongly depend on the simulation input, in particular on the employed model parameters. A long-standing problem is to quantify the influence of these parameters on the simulation results. We present a new multivariate optimization approach for avalanche simulation in three-dimensional terrain. The method takes into account the entire physically relevant range of the two friction parameters (Coulomb friction, turbulent drag) and one entrainment parameter. These three flow model parameters are scrutinized with respect to six optimization variables (runout, matched and exceeded affected area, maximum velocity, average deposition depth and mass growth). The approach is applied to a documented extreme avalanche event, recorded in St Anton, Austria. The final results provide adjusted parameter distributions optimizing the simulation–observation correspondence. At the same time, the degree of parameter–variable correspondence is determined. We show that the specification of optimal values for certain model parameters is near-impossible, if corresponding optimization variables are neglected or unavailable.

Commercial cone penetration testing (CPT) equipment was adapted to allow penetrative testing in hard polar firn to depths of 10 m. The apparatus is hydraulically driven, rate-controllable and able to penetrate firn with a resistance of 10 MPa. It can be mounted on many types of typical polar vehicles, requiring connection to only hydraulics and 12 V electricity. Data recorded include both cone tip resistance and sleeve friction, a parameter not previously examined through such testing. This paper describes the development and calibration of the equipment and examines factors including snow density, penetration rate and cone size and shape that are shown to affect CPT interpretation. CPT can be used efficiently in polar environments to potentially provide estimates of physical parameters in hard firn to substantial depth.

Flowing snow is a cohesive granular material. Snow temperature and moisture content control the strength of the cohesive bonding between granules and therefore the outcome of granular interactions. Strong, cohesive interactions reduce the free mechanical energy in the avalanche core and therefore play a significant role in defining the avalanche flow regime. We introduce cohesion into avalanche dynamics model calculations by (1) treating cohesion as an additional internal binding energy that must be overcome to expand the avalanche flow volume, (2) modifying the Coulomb stress function to account for the increase in shear because of cohesive interactions and (3) increasing the activation energy to control the onset of avalanche fluidization. The modified shear stress function is based on force measurements in chute experiments with flowing snow. Example calculations are performed on ideal and real terrain to demonstrate how snow cohesion modifies avalanche flow and runout behaviour.