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Snow avalanches are one of the most devastating natural hazards in the highlands that often cause human casualties and economic losses. The complex process of modeling terrain susceptibility requires the application of modern methods and software. The prediction of avalanches in this study is based on the use of geographic information systems (GIS), remote sensing, and multicriteria analysis—analytic hierarchy process (AHP) on the territory of the Šar Mountains (Serbia). Five indicators (lithological, geomorphological, hydrological, vegetation, and climatic) were processed, where 14 criteria were analyzed. The results showed that approximately 20% of the investigated area is highly susceptible to avalanches and that 24% of the area has a medium susceptibility. Based on the results, settlements where avalanche protection measures should be applied have been singled out. The obtained data can will help local self-governments, emergency management services, and mountaineering services to mitigate human and material losses from the snow avalanches. This is the first research in the Republic of Serbia that deals with GIS-AHP spatial modeling of snow avalanches, and methodology and criteria used in this study can be tested in other high mountainous regions.

Data on the disastrous snow avalanche that occurred on 18 January 2017 at the spa hotel Rigopiano, municipality of Farindola in the Abruzzo region of central Italy, are analyzed in different ways. The main results are the following. (i) The 2017 Rigopiano avalanche went beyond the run-out point predicted by the topographic-statistical α-β model with standard Norwegian calibration, while avalanches in neighboring paths appear to have run no farther than the β-point of their respective paths during the same period. (ii) The curvature and super-elevation of the trimline between 1500 and 1300 m a.s.l. indicate that the velocity of the front was around 40 m s−1. In contrast, the tail velocity of the avalanche can hardly have exceeded 25 m s−1 in the same segment. (iii) The deposits observed along all of the lower track and in the run-out zone suggest that the avalanche eroded essentially the entire snow cover, but fully entrained only a moderate amount of snow (and debris). The entrainment appears to have had a considerable decelerating effect on the flow front. (iv) Estimates of the degree to which different parts of the building were damaged is combined with information about the location of the persons in the building and their fates. This allows to refine a preliminary vulnerability curve for persons in buildings obtained from the 2015 Longyearbyen avalanche, Svalbard.

On 8th February 1996, in the north-western part of Andorra in the Pyrenees, the Les Fonts d’Arinsal (LFd’A) pure powder avalanche was triggered, descending some 1200 m to the bottom of the Arinsal valley and continuing up the opposite slope for about 200 m. This size 4–5 avalanche reached velocities of up to 80 ms−1, devastated 18 ha of forest, involved a minimum volume of up to 1.8 × 106 m−3 and caused major damage to eight buildings. Fortunately, no one was injured thanks to an evacuation, but 322 people lost their properties. This study describes the physical characteristics of the LFd’A avalanche path and provides data on earlier avalanches, the meteorological synoptic situation and snowpack conditions that generated the avalanche episode, the warning and preventive actions carried out, the effects and evidence of the large avalanche, and the defence system implemented afterwards. A discussion of the avalanche dynamics based on observations and damage, including the role of snow entrainment, the total lack of characteristic dense flow deposits, as well as the evidence of a two-phase flow (fluidisation and suspension), is presented. This case study is an example of a paradigmatic large, pure powder, dry-snow avalanche, which will be useful for model calibration.

This note first summarizes the history of the manuscript “On a Continuum Model for Avalanche Flow and Its Simplified Variants” by Grigorian and Ostroumov—published in this Special Issue—since the early 1990s and explains the guiding principles in editing it for publication. The changes are then detailed and some explanatory notes given for the benefit of readers who are not familiar with the early Russian work on snow avalanche dynamics. Finally, the editor’s personal views as to why he still considers this paper of relevance for avalanche dynamics research today are presented in brief essays on key aspects of the paper, namely the role of simple and complex models in avalanche research and mitigation work, the status and possible applications of Grigorian’s stress-limited friction law, and non-monotonicity of the dynamics of the Grigorian−Ostroumov model in the friction coefficient. A comparison of the erosion model proposed by those authors with two other models suggests to enhance it with an additional equation for the balance of tangential momentum across the shock front. A preliminary analysis indicates that continuous scouring entrainment is possible only in a restricted parameter range and that there is a second erosion regime with delayed entrainment.

The changes in the seismic signals generated by avalanches recorded at three sites along a path at the Vallée de la Sionne (VdlS) experimental site are presented. We discuss and correlate the differences in the duration, signal amplitudes, and frequency content of the sections (Signal ONset (ON), Signal Body (SBO), and Signal TAil and Signal ENd STA-SEN) of the spectrograms with the evolution of the powder, transitional and wet snow avalanches along a path. The development of the avalanche front was quantified using the exponential function in time F (t) = K’ exp (β t) fitted to the shape of the signal ONset (SON section of the spectrogram. The speed of the avalanche front is contained in β. To this end, a new method was developed. The three seismic components were converted into one seismic component (FS), when expressing the vector in polar coordinates. We linked the theoretical function of the shape of the FS-SON section of the spectrogram to the numerical coefficients of its shape after considering the spectrogram as an image. This allowed us to obtain the coefficients K’ and β. For this purpose, the Hough Transform (HT) was applied to the image. The values of the resulting coefficients K’ and β are included in different ranges in accordance with the three types of avalanche. Curves created with these coefficients enable us to estimate the development of the different avalanche types along the path. Our results show the feasibility of classifying the type of avalanche through these coefficients. Average speeds of the avalanches approaching the recording sites were estimated. The speed values of wet and transitional avalanches are consistent with those derived from GEODAR (GEOphysical Doppler radAR) measurements, when available. The absence of agreement in the speed values obtained from seismic signals and GEODAR measurements for powder snow avalanches indicates, for this type of avalanche, a different source of the measured signal. Hence, the use of the two measuring systems proves to be complementary.

The article is a review of mathematical models of snow avalanches that have been proposed since the middle of the 20th century and are still in use. The main attention is paid to the work of researchers from the Soviet Union and Russia, since many of their works were published only in Russian and are not widely available. Mathematical models of various levels of complexity for avalanches of various types—from dense to powder-snow avalanches—are discussed. Analytical solutions including formulas for the avalanche front speed are described. The results of simulations of the movement of avalanches are given that were used to create avalanche hazard maps. The last part of the article is devoted to constructing models of a new type, in which avalanches are considered as laminar or turbulent flows of non-Newtonian fluids, using the full (not depth-averaged) equations of continuum mechanics. The results of a numerical study of the effect of non-Newtonian rheology and mass entrainment on the avalanche dynamics are presented.

Mathematical models of different degrees of complexity, describing the motion of a snow avalanche along a path with given center line and spatially varying width, are formulated and compared. The most complete model integrates the balance equations for mass and momentum over the cross-section and achieves closure through an entrainment function based on shock theory and a modified Voellmy bed friction law where the Coulombic contribution to the bed shear stress is limited by the shear strength of the snow cover. A simplified model results from integrating these balance equations over the (time-dependent) length of the flow and postulating weak similarity of the evolving avalanche shape. On path segments of constant inclination, it can be solved for the flow depth and speed of the front in closed form in terms of the imaginary error function. Finally, the very simplest model assumes constant flow height and length. On an inclined plane, the evolution of flow depth and velocity predicted by the simplified model are close to those from the full model without entrainment and with corresponding parameters, but the simplest model with constant flow depth predicts much higher velocity values. If the friction coefficient is varied in the full model with entrainment, there can be non-monotonous behavior due to the non-linear interplay between entrainment and the limitation on the Coulomb friction.

Depth-integrated simulations of snow avalanches have become a central part of risk analysis and mitigation. However, the common practice of applying different model parameters to mimic different avalanches is unsatisfying. In here, we analyse this issue in terms of two differently sized avalanches from the full-scale avalanche test-site Vallée de la Sionne, Switzerland. We perform depth-integrated simulations with the toolkit OpenFOAM, simulating both events with the same set of model parameters. Simulation results are validated with high-resolution position data from the GEODAR radar. Rather than conducting extensive post-processing to match radar data to the output of the simulations, we generate synthetic flow signatures inside the flow model. The synthetic radar data can be directly compared with the GEODAR measurements. The comparison reveals weaknesses of the model, generally at the tail and specifically by overestimating the runout of the smaller event. Both issues are addressed by explicitly considering deposition processes in the depth-integrated model. The new deposition model significantly improves the simulation of the small avalanche, making it starve in the steep middle part of the slope. Furthermore, the deposition model enables more accurate simulations of deposition patterns and volumes and the simulation of avalanche series that are influenced by previous deposits.

In full-scale snow avalanche test sites, structures such as pylons, plates, or dams have been used to measure impact forces and pressures from avalanches. Impact pressures are of extreme importance when dealing with issues such as hazard mapping and the design of buildings exposed to avalanches. In this paper, we present the force measurements recorded for five selected avalanches that occurred at the Seehore test site in Aosta Valley (NW Italian Alps). The five avalanches were small to medium-sized and cover a wide range in terms of snow characteristics and flow dynamics. Our aim was to analyze the force and pressure measurements with respect to the avalanche characteristics. We measured pressures in the range of 2 to 30 kPa. Though without exhaustive measurements of the avalanche flows, we found indications of different flow regimes. For example, we could appreciate some differences in the vertical profile of the pressures recorded for wet dense avalanches and powder ones. Being aware of the fact that more complete measurements are necessary to fully describe the avalanche flows, we think that the data of the five avalanches triggered at the Seehore test site might add some useful information to the ongoing scientific discussion on avalanche flow regimes and impact pressure.