Snow becomes patchy while melting, giving a heterogeneous surface with large contrasts in characteristics such as albedo. It is therefore necessary for surface schemes used in atmospheric and hydrological models to represent the influence of heterogeneities in snow cover on scales smaller than the model grid; this is typically done by introducing a snow-cover depletion (SCD) curve relating fractional snow cover to average depth. Here, ad hoc functional forms which have been used for this relationship are first compared with forms obtained for an assumed initial snow distribution undergoing homogeneous melt. The energy available for melt may be heterogeneous, however, and can be influenced by factors that also influence snow distribution, such as slope, aspect and vegetation cover. The modification of SCD curves by spatial variations in melt energy is investigated, and resulting curves are found to be similar to those which would be given by homogeneous melting of a snow cover with greater initial variance. This influence is increased by any negative correlation between snow depth and melt rate.

The snow-cover model SNOWPACK was applied to the wet-snow areas of Japan. Simulated variations of snow type, snow depth and weight, profiles of snow density, temperature and liquid-water content were compared with snow-pit measurements. The snow-depth simulation during early winter agreed with the measurements, but the differences between the simulation and the measurements increased during the course of the melt season. These differences were caused by underestimation of the energy balance at the snow surface, mainly that regarding sensible-heat flux during the melt season. The underestimation was caused by the implicit numerical treatment of the heat-transport equation. Consistent with the underestimation of snowmelt, simulated metamorphosis of compacted particles into melt forms was slower than the change shown by the measurements, and faceted snow particles, which constitute a snow type not actually found in the study area, sometimes appeared in the model. The inaccurate melt treatment also influenced simulated densities, which were larger than the measurements at small densities, while they were smaller than the measurements at large densities. Greater accuracy was achieved when an empirical compressive viscosity formulation for wet snows in Japan was introduced. A new version of SNOWPACK, with an accurate treatment of melt processes, is available.

A new in situ sensor for the simultaneous measurement of snow water equivalent, snow density and liquid-water content is presented in this paper. The system consists of radio frequency transmission lines of up to 25 m length cast in a flat PVC band, which can be set up either horizontally to monitor single snow-layer properties or sloping from a mast to the soil surface to determine vertical snowpack properties. The dielectric coefficient along the flat-band cable is measured with a time-domain reflectometer at high frequencies, and with a low-frequency impedance analyzer. The performance of the sensor system was tested during two winter seasons (2001–03) at the high-alpine test site Weissfluhjoch, Davos, Switzerland. The cable suspension and set-up of the sloping cable was shown to be critical with regard to stability and the formation of unwanted air gaps along the cable. Overall, the sensing system proved quite robust and produced results in agreement with manual snowpack observations.

Solar shortwave (SW) radiation is a primary energy source for the snow cover. Accurate measurements of the radiation energy balance in snow are not yet available over a broad spectral band. For accurate measurements in snow, sources of errors have to be eliminated such as the temperature dependence of some sensors, investigating a disturbed snow cover or neglecting the variation of the incoming radiation. The objective of our investigation is to measure the spectral SW energy balance in and above snow and to validate a radiation transfer model against the data. In July 2002 up- and down-welling fluxes at several heights in snow were measured on Summit, Greenland, with a spectrometer sensitive in the 340–1050 nm spectral band. Changing incoming solar radiation was accounted for by using two sensor heads. The resulting data are compared to the δ–Eddington model of radiative transfer in combination with Mie single-scattering calculations. Using as input the snow data obtained by weekly snow profiles, a good agreement between measured and modelled radiative fluxes was obtained when increasing the absorption in the snow grains which is justified by snow impurities. In the near-infrared a disagreement between model and measurements is obvious. This is most likely caused by non-sphericity of the snow grains.

Avalanche hazard is a threat to many residential areas in Iceland. In 1995 two avalanche accidents, causing a total of 34 fatalities in areas thought to be safe, prompted research on avalanche hazard assessment. A new method was developed, and in 2000 a new regulation on avalanche hazard zoning was issued. The method and regulation are based on individual risk, or annual probability of death due to avalanches. The major components of the method are the estimation of avalanche frequency, run-out distribution and vulnerability. The frequency is estimated locally for each path under consideration, but the run-out distribution is based on data from many locations, employing the concept of transferring avalanches between slopes. Finally the vulnerability is estimated using data from the 1995 avalanches. Under the new regulation, new hazard maps have been prepared for six of the most vulnerable villages in Iceland. Hazard zones are delineated using risk levels of 0.2×10–4, 0.7×10–4 and 2×10–4 a–1, with risk less than 0.2×10–4 a–1 considered acceptable. When explaining the new zoning to the public, a measure of annual individual risk that allows comparison with other risks in society has proven advantageous.

Results of acoustic emission tests on cylindrical specimens under compression are reported. Deformation-rate-controlled tests with strain rates ranging from 1.1 × 10-6 s-1 to 2.6 × 10-3 s-1 at temperatures between T = -11.2°Cand T = -1.7°C were performed. The investigated snow was fine-grained, with a density varying between 220 and 380 kgm-3. The acoustic emission was measured with two distinct piezoelectric sensors: a wide-band sensor (frequency 100–1000 kHz) and a resonant sensor (frequency 35–100 kHz). The relationship between the applied strain rate and the measured maximum acoustic-emission rate as a function of temperature and density was found to obey a power law, which is valid for the ductile behaviour range. The quantitative and qualitative effects produced on the acoustic emissions during the transition from ductile to brittle behaviour, occurring at strain rates of approximately 1 × 10-3 s-1, are reported. Finally, the influence of the load history on the acoustic emissions of snow is discussed on the basis of a cyclic test, including deformation-controlled loading steps and relaxation steps, performed at different strain rates and different relaxation times.

In heavy-snowfall areas facing the Sea of Japan, winter seasons with lower volumes of snow occurred from 1986/87 to 1999/2000. In this paper, the changes induced by these warmer winters in snowy areas in Japan are investigated using two datasets. One set was normalized for the period 1971–2000 from manned surface meteorological observations by the Japan Meteorological Agency, and the other set was for 1961– 90. Winter climatic monthly values for the first dataset were thought to be affected by the warmer winter seasons since almost half the relevant period coincides with them. By comparing each monthly climatic value in both datasets, the following results were obtained: (1) At each meteorological observation site the bimonthly average temperature fromJanuary to February increased and the amounts of increase were about 0.4°C on average. (2) The bimonthly maximum snow depth for the same period increased at a number of sites, but usually by only a few centimeters, the maximum increase being 0.05 m. (3) In contrast, the decreases in snow depth in heavy-snowfall areas facing the Japan Sea, which belong to a temperate climate zone, were large, ranging from about 0.05 to 0.22 m in climatic bimonthly maximum snow depth during January and February. The last result shows that snow covers in such warm snowy areas are very sensitive to climatic changes. An attempt is also made in this paper to estimate the amounts of decrease in snow depth from the increases in air temperature and the decreases in precipitation amounts.

Snow avalanches with failure layers including graupel are sometimes observed in Japan. A snow layer including graupel may be formed close to the melting point (0°C) after passage of a cold front with cumulus clouds. Graupel particles have a large diameter and a spherical shape, so they have a relatively small contact area per unit volume and may form weak layers within the snowpack. In this paper, characteristics of snow layers that include graupel are described by angle of repose, shear frame index (SFI), grain-size distribution, density and temperature. The mean value of the angle of repose was found to be 45°, independent of the grain-size. This suggests that a graupel layer near 0°C will not be formed on a slope exceeding 45°. SFI data for three different graupel layers were measured over 1–3 days for each layer, and were correlated with density. An exponential relationship between shear strength and density was found. The results indicate that the SFI of graupel layers is approximately one-third that of dry new snow with the same density.

Vapor-transfer theory is incorporated into a previous firn-densification model to investigate the effect of vapor-transfer processes on densification in firn within 10 m of the surface. The densification rate in the model is governed by the change of overburden pressure (determined by the accumulation rate), the firn temperature, and the temperature gradient. The time of exposure to temperature gradients at shallow depths is a critical factor determining the importance of vapor-transfer processes. In high-accumulation and high-temperature conditions such as for the Greenland ice sheet, the temperature gradient and vapor transfer are less important due to the shorter exposure times. The high summer temperatures dominate the rate of densification and annual variations in density. In low-accumulation and low-temperature conditions, such as for inland Antarctica, the vapor transfer driven by the temperature gradient has a stronger effect on the densification rate, and temperature-driven processes are less important. These factors determine both the rate of density increase with depth and the amplitudes of annual variations in density with depth.

Earlier studies have indicated that the soil on groomed ski slopes may be subjected to more pronounced cooling than the soil below a natural snowpack. We analyzed the thermal impacts of ski-slope preparation in a sub-alpine ski resort in central Switzerland (1100ma.s.l.) where artificial snow was produced. Physical snow properties and soil temperature measurements were carried out on the ski slope and off-piste during winter 1999/2000. The numerical soil–vegetation–atmosphere transfer model COUP was run for both locations, with a new option to simulate the snowpack development on a groomed ski slope. Snow density, snow hardness and thermal conductivity were significantly higher on the ski slope than in the natural snowpack. However, these differences did not affect the cooling of the soil, since no difference was observed between the ski slope and the natural snow cover. This might be because cold periods were rare and short and thus any snowpack could protect the soil from freezing. The major impact of the ski-slope grooming was a 4 week delay in snowmelt and soil warming at the end of the season. The newly implemented option proved to be a useful strategy for simulating the snowpack of a ski slope. However, snow density was underestimated by the model as it could not account adequately for compaction due to grooming traffic. Our study demonstrates that there is no site-independent answer as to whether a groomed snowpack affects the thermal conditions in the soil.

A system for predicting avalanche hazard in the windy climate of Vestfirðir, northwest Iceland, is presented. The system is based on (a) numerical simulations of the snowpack and evaluation of avalanche hazard due to overloading by the snow models SAFRAN–Crocus and MÉPRA, and (b) observations of wind speed in the mountains used as a proxy for snowdrift. The system was tested during two winter seasons and correctly predicts 30 out of 35 avalanche days. The 5 missing days feature either large spatial gradients in precipitation or very strong winds a few days before the avalanches, indicating much snowdrift. A comparison of the simulated avalanche hazard and observations of avalanches confirms that snowdrift is of primary importance not only for large avalanches, as already established, but also for small and medium-size avalanches in Vestfirðir. The system is a first step towards an objective evaluation of avalanche hazard in Iceland.

Avalanche defence structures such as retarding dams and breaking mounds are widely used to protect residential areas and other kinds of infrastructure. The effect of the defence structures depends largely on their effective height relative to the velocity, volume and flow depth of the avalanche. Snow depositions from earlier avalanches as well as from drifting snow can significantly alter the effective height of defence structures. Different designs of avalanche-breaking mounds and retarding dams were tested in the Cemagref (Grenoble, France) wind tunnel for their effect on drifting snow. Examples included dams and mounds of different sizes and heights. The models were tested in a wind tunnel with sand particles subjected to different wind directions. The resulting depositions were scanned with a laser system to obtain a three-dimensional picture of the accumulation pattern. The results show that the accumulated snow varies widely with the design of the structure for a given wind direction. Most snow is accumulated around narrow mounds, with least accumulation observed around mounds covering a smaller relative area of the avalanche path. The data obtained can be used to study the effect of the depositions on the retarding effect of the avalanche defence structures. However, because the similarity criteria for studying the interaction between structures and saltating particles in a wind tunnel cannot be met, the transfer of the results to reality must be performed with caution.

SNOWPACK has been in operational use for five consecutive winters on approximately 100 automatic weather stations in the Swiss Alps. It calculates snow precipitation, snowdrift and the layered structure of the snow cover. An analysis routine has been implemented that gives a stability estimation for a model profile. We distinguish between slab instability and direct action or deformation-rate instability. Slab instability relies on a static force balance within the snowpack (stability index) and may be used to assess stability for both natural and skier-triggered slab avalanches. We heuristically improve the slab index by adding a term of overload correction for all grain types and scaling the stability index with the bond size. Deformation-rate instability means that the load of the snow cover increases faster than the snow gains strength. An index is formulated based on the snow deformation rate. It may be associated with large snowfall events and wet-snow situations as they occur in catastrophic situations, or with the effect of a sudden increase in temperature. The results of both stability indices are compared to the fore-casted avalanche danger. The indices are able to recognize cases of avalanching. It is shown that the inclusion of several locations, for which the indices are calculated, improves the correlation between stability indices and avalanche danger. A sufficient number of profiles could bridge the gap between snow-cover characteristics at a point and avalanche danger.

The mechanical properties of snow depend on its microstructure. The fabric of snow was reconstructed in three dimensions using serial sections or X-ray microtomography. A voxel-based finite-element model, with the elements based on the microstructure and ice as the material, was used to calculate the stress distribution in the snow. A small elastic deformation was simulated and the bulk elastic moduli of these samples were determined. The simulated elastic modulus was 3–10 times or 10–100 times larger than previously published measurements. The deviation is possibly caused by the relatively slow deformation rates of the usual tests. This strain-rate effect is well known for pure ice. Locations of stress concentrations can be extracted and compared to the micro-structural location of bonds. By this method we are able to determine mechanical properties of thin or extremely brittle snow layers which are otherwise difficult or impossible to measure.

The time evolution of drifting snow under a steady wind is estimated using a new numerical model of drifting snow. In the model, Lagrangian stochastic theory is used to incorporate the effect of turbulence on the motion of drifting-snow particles. This method enables us to discuss both the saltation and the suspension process. Aerodynamic entrainment, grain/bed collision (splash process), wind modification and particle size distribution are also taken into account. The calculations show that the time needed by the total mass flux to reach a steady state appears to be 3–5 s. Vertical profiles of horizontal mass flux near the surface show a similar tendency. In contrast, it takes >50 s for the wind speed and the whole mass-flux profile to reach a steady state. This longer time depends on the time-scale of the turbulent diffusion, which is responsible for the mass flux extending to an order of a few meters in height. Applying Taylor’s hypothesis, the estimated length scale at which drifting snow reaches equilibrium is around 400 m. This result is comparable with previously reported field observations.

The statistical modelling of gravitational avalanche-type processes is carried out using the Monte Carlo method. The process of snow avalanche origin is described with the model of stress state and stability of snow cover on a slope. The statistical simulation of the stress state of a snow slab is performed for avalanche site No. 22 (Khibiny, Russia). The strength characteristics of the snow slab are considered as randomvariables.The influence of the first moments of the distributions of the slab-strength parameters on the probability of avalanche release is studied. Using a hydraulic model of a dense flow avalanche, the statistical modelling of avalanche dynamics for the avalanche site “Domestic” (Elbrus region, Russia) is carried out. The coefficients of dry and turbulent friction and snow entrainment are considered as random parameters of the model. The histograms and distribution functions of the run-out distance, thickness and volume of avalanche depositions are obtained. The model and empirical distribution functions of the avalanche run-out distance are compared. Statistical simulation of slushflow dynamics (basin of Bear brook, Khibiny, Russia) is performed. The two-layer deterministic model of slushflow is used. The random parameters of the model assumed are: the water inflow on the “tail”of the flow and the coefficient of dry friction for slush. The histograms and distribution functions of dynamic characteristics of flow are obtained. The model outcomes are compared with field data.

A continuum dynamical hydraulic model for the flow of a finite mass of cohesionless shallow granular material down an inclined plane was proposed by Savage and Hutter (SH) in 1989. This model consists of depth-averaged equations for the time and space evolution of the velocity profile and the avalanche depth. Their model was generalized to incorporate more complicated topography in which the coordinate lines in the downhill direction are curved but not twisted. We present recently developed model equations by Pudasaini and Hutter for free-surface geophysical gravity-driven flows (e.g. avalanches, debris and pyroclastic flows) down complicated realistic mountain terrain generated by arbitrary space curves with slowly varying curvature and torsion. These are very important extensions to the successful SH theory, which incorporate curvature and torsion effects of the sliding surface. Shock-capturing numerical schemes are used to integrate the hyperbolic conservation system of equations. The physical significance of the numerical solutions is discussed.

To develop avalanche runout models for short slopes, field measurements were made at 48 short-slope avalanche paths located in the Coast, Columbia and Rocky Mountains of western Canada, and at several paths in eastern Canada. Field studies included detailed topographic surveys and estimation of the extreme runout position in each path. A statistical runout model was developed using the runout ratio method, for which runout ratios from the four mountain ranges are well fit by an extreme-value type I (Gumbel) distribution when the β point is defined at the uppermost point where the slope is 24°. A second model was developed by regressing the α angle for the extreme runout position on numerous terrain variables. This regression model uses three predictor variables that can be easily measured in the field or on topographic maps. Length-scale effects were noted in both models, but are more pronounced in the runout ratio model. A comparison of models developed using the two methods shows that the runout ratio model estimates more conservative (longer) runout distances than the regression model for most threshold probabilities. Data from 13 additional paths from Switzerland and Québec, Canada, are used to test the models.

Passive protection structures reduce avalanche run-out distance and hence the potential damages brought about by an avalanche, by reducing its velocity and mass. This paper starts with a summary of the main existing results on interactions between snow avalanches and dams. In the case of dense avalanches, the effects of dams are re-examined and previous results are theoretically justified. For a powder-snow avalanche a dam has two primary effects. The momentum is reduced by the retarding force upstream of the dam and when the jet collides with the ground after the dam. Entrainment of air during the jet reduces its velocity since the mass increases. For a dense avalanche, there is a retarding force upstream of the dam and when the jet collides with the ground, but there is no significant effect of air entrainment. There is, however, deposition of snow which reduces the momentum of the avalanche without affecting the velocity. The reduction of the volume due to deposition reduces the spreading length and therefore the run-out distance of the avalanche. Downstream of the obstacle, the avalanche flow is regarded as an airborne jet. A comparative study shows that density and ambient-fluid entrainment effects are significant for gravity currents, powder and dense snow avalanches whereas they are negligible in granular flows.

In this paper, two-dimensional direct numerical simulations (DNS) of dense clouds moving down steep slopes are presented for the first time. The results obtained are in good agreement with the overall characteristics, i.e. the spatial growth rate and velocity variations, of clouds studied in the laboratory. In addition to the overall flow structure, DNS provide local density and velocity variations inside the cloud, not easily accessible in experiments. The validity of two-dimensional simulations as a first approach is confirmed by the dynamics of the flow and by comparison with experimental results. The interest of the results for powder-snow avalanches is discussed; it is concluded that two-dimensionality is acceptable and that large density differences need to be taken into account in future simulations.