Verification of avalanche forecasts depends on the spatial and temporal scale of the forecast, and the classes of informational entropy of data implicit in the forecast. First I present a classification system for avalanche forecasts based on these parameters. Verification of models in avalanche forecasting may consist of two stages. Often, the first stage is to ensure that the model matches the scales (space and time) and the classification of forecast and that redundant variables and parameters are eliminated. Once that is achieved, verification can proceed to the second stage, testing the model against relevant field data and situations. I provide an example based on the public-danger scale bulletin used for warnings in the back country in North America and Europe. Using data on deaths and accidents from Alpine Europe with Bayesian statistics, I conclude the danger scale has more classes than necessary for back-country applications. This could be a first stage prior to actual verification of this experience-based model.

The SNOWPACK model developed at the Swiss Federal Institute for Snow and Avalanche Research is a one-dimensional momentum, mass- and energy-balance model. Its current version includes important features such as a numerical solution of the instationary heat-transfer and creep/settlement equations, a complete surface-energy balance, phase changes, water transport and snow microstructure development (metamorphism). The microstructural parameters are linked to the thermal conductivity and the snow viscosity. The new snowdrift routine uses the modelled snow to determine a threshold friction velocity The drift model describes the local mass flux of snow, distinguishing between a saltation and suspension contribution. The snow-cover model adapts to erosion (or deposition) due to drifting and blowing snow. The drift formulation improves the seasonal snow-cover simulation considerably for stations that show a significant influence of snow transport. From the mass-flux calculation, a snowdrift index results that provides valuable information on local snowdrift for avalanche warning.

The 1997–98 Summit (Greenland) winter-over experiment was conducted to investigate the seasonal changes that might affect snow-air transfer processes and snow chemistry for polar ice-core interpretation This paper discusses meteorological measurements that were obtained during the experiment We use the measurements in energy-balance modeling to investigate seasonal differences in the snow-air energy exchange, and to investigate the timing of snow accumulation. We found that the surface energy exchange has distinct seasonal differences. The winter (November-February) has both the coldest average temperatures of the year and the largest temperature variations. The winter also has both the largest peak wind speeds and the longest periods of sustained high winds. Most of the water-vapor transport across the snow-air interface occurs in the summer, indicating that summer may be the primary season for near-surface snow metamorphism. Snow-depth sounder results indicate that snowfall occurs throughout the year at Summit, and thus that the ice-core record may not be affected by large seasonal gaps in the precipitation if accumulation patterns have not changed. The changes in air temperature, wind speed and radiation cause clear seasonal differences in the surface energy balance and snow-surface characteristics that are likely to cause seasonal changes in air-snow transfer processes and snow chemistry as well.

Time series of Earth observation (EO) data (Landsat Thematic Mapper (TM), U.S. National Oceanic and Atmospheric Administration Advanced Very High Resolution Radiometer (NOAA AVHRR) and European Remote-sensing Satellite synthetic-aperture radar (ERS SAR)) were obtained for a 2250 km2 mountainous basin in northern Sweden to validate snow-cover area (SCA) estimates produced by a conceptual model (HBV) during three melt seasons. SCA depletion curves derived for each image type, arid coincident images, reveal that the SCA estimate varies with the sensor. Discrepancies betweenTM and AVHRR appear to be an effect of spatial resolution. However, differences betweenTM and SAR are not simply related. Since more AVHRR thanTM data were available, a TM-equivalent SCA was derived from AVHRR by relating TM SCA to AVHRR channel 1 reflectance. The TM-equivalent SCA was used to test SCA simulated by HBV for the 1992 melt season. Although the modelled and TM-equivalent SCA were in reasonable agreement, the modelled SCA declined faster than the TM-equivalent SCA. Partial recalibration of model parameters controlling snowpack accumulation improved the match between the modelled and EO-derived SCA decline. The recalibrated parameters were verified using SCA maps generated for the 1996 and 1998 melt seasons. The adjusted parameter sets had little effect on the Nash-Sutcliffe R2 runoff fit but improved the volume fit in all three years.

Detailed knowledge of snowpack properties is crucial for the interpretation and modeling of thermal microwave radiation. Here we use two well-known snow models, Crocus and SNTHERM, to obtain snow profiles from meteorological data. These profiles are compared with pit profiles and used as input to the Microwave Emission Model of Layered Snowpacks (MEMLS) for the simulation of microwave radiation. The snow-profile data can be applied almost directly. Adaptation is needed only in the conversion of the grain-size used in the snow models to the correlation length used in the emission model; it is based on empirical fits. The resulting emissivities are compared with in situ microwave measurements. The computed snow depths are in good agreement with observations. Comparison of selected profiles shows that Crocus is in good agreement with the pit profile, but the density of simulated melt-freeze crusts is underestimated. The SNTHERM profiles show no such crusts, and the density deviates from the pit profiles. The computed temporal behavior of the snowpack emissivity is reasonable. Comparison of selected situations with in situ measurements indicates good agreement. However, the polarization difference tends to be underestimated because of inaccuracies in the simulation of density profiles. The results show the potential of combined snow-physical and microwave-emission models for understanding snow signatures and for developing snow algorithms for microwave remote sensing. Based on the frequency-selective penetration and on the high sensitivity to snow texture, density and wetness, microwave radiometry can offer a new dimension to snow physics. Potential applications are described.

Snowmelt lysimeters have been used occasionally to provide a physical measurement for testing models of snowpack energy balance and/or meltwater production. Despite the attractiveness of using records of snowpack outflow for comparison with model results, there are many difficulties with using such data for this purpose. The basic problem is poor correspondence between melt produced at the snow surface and water arriving at the base of the snowpack on a unit-area basis. Unenclosed snowmelt lysimeters allow lateral flow of water into and out of the column of snow overlying the collector. The well-known lateral flow of water in a snowpack allows the effective contributing area at the snowpack surface to be different from the surface area of the collector. Data from several years at two research stations in the Sierra Nevada, California, U.S.A., illustrate the great variability of water flux measured by several collectors. However, the mean of accumulated outflow for a melt season from all the collectors tended to be close to the water equivalence of the overlying snowpack at the onset of snowmelt. Therefore, there is some hope that a set of small snowmelt lysimeters or a few large collectors can adequately sample outflow from the base of the snowpack.

In this paper we discuss a physical model of frozen soil based on the systems approach and reflect contemporary knowledge about the constitution, structure and properties of this complicated medium. The component composition and specific spatial cryogenic coagulant-crystalline structure as well as physical subsystems of frozen soil conditioning its physical properties are considered. Examples of the use of a model for better comprehension and explanation of some electrical and mechanical property changes of sandy-clayey frozen soils are presented and discussed. The proposed model and its hierarchy is a useful tool for planning experiments and interpreting their results.

A mathematical model of snow-cover influence on soil freezing, taking into account the phase transition layer, water migration in soil, frost heave and ice-layer formation, has been developed. The modeled results are in good agreement with data observed in natural conditions. The influence of a possible delay between the time of negative temperature establishment in the air and the beginning of snow accumulation, and possible variations of the thermophysical properties of snow cover in the wide range previously reported were investigated by numerical experiments. It was found that the delay could change the frozen-soil depth up to 2–3 times, while different thermophysical characteristics of snow changed the resulting freezing depth 4–5 times.

To investigate the effects of steel snow-supporting structures on the thermal regime of the ground in typical Alpine permafrost avalanche terrain, ground temperatures were monitored and simulated on an avalanche slope equipped with experimental snow-supporting structures. Temperature measurements were effected in lm boreholes above and below a row of snow nets and in two 18 m boreholes located between the structures and in a reference location. The presence of the structures can induce modifications of the temporal and spatial snow-cover distribution, leading to differences in active-layer temperatures just below and above the structures: snow accumulates above the supporting surface of the structures, and frequently there is less snow below. The long-term thermal effect of these variations near a snow net was simulated using a two-dimensional finite-element program based on heat conduction. The material and thermal characteristics of the ground simulated are obtained from temperature measurements and from borehole-core information.

Non-uniformity of a temperature field in a 30 cm deep artificial snow cover in a wind tunnel was produced by keeping a selected cross-section, perpendicular to the wind direction, at a temperature different to that in the cold room. Quasi-steady-state temperature distributions in the snow around this cross-section were observed with and without wind, and were significantly different. The difference was attributed to the influence of an air flux inside the snow cover. The mechanism of this influence is discussed. Several temperature conditions and wind speeds over the snow surface were studied. It was concluded that the wind produced the air flux in the pore space of snow, and the air-flux velocity increases with wind speed. The calculated values of the horizontal air-flux velocity in the pore space of snow were of the order of l0–2 m s"1 and decreased with depth.

The paper discusses the verification of a previously developed structural dry-snow model based on the regular packing of isometric grains connected by rigid bonds. Using this model, we consider the probable snow-compaction mechanisms at different snow-density ranges (from new to dense snow), limited by critical densities corresponding to the real values of the structural indices of the model: texture looseness, bond rigidity and coordination number. We also obtain the analytic expression for longitudinal wive velocity and for bulk compressibility of snow as functions of density and structural indices. The calculation enables us for the first time to show the whole range of possible values of these important characteristics and to deduce the most probable configuration of the ice matrix in snow of various densities corresponding to the experimental data available on the snow-texture peculiarities and elastic-wave velocities. The model can be used to comprehend the changes in snow mechanical properties during compaction, as well as the steps by which it proceeds.

Snow-cover models are used in many applications in today’s snow and ice research. Although physically based models allow the evolution of the internal structure of the snow cover to be followed very closely a quantitative and objective description of the layer texture’s evolution in snow subjected to large temperature gradients is still required, in order to both improve and verify existing snow-cover models. Based on experiments done in the cold laboratory as well as on field observations on snow subjected to kinetic-growth metamorphism, we present new results on the quantification of texture-related parameters. Problems such as linking objective laboratory work to pragmatic field observations and finding a reproducible method to measure shape-related parameters are discussed. Finally a new shape parameter is proposed, zero curvature, which differentiates well between depth hoar, faceted crystals and snow types with rounded grains. It also shows a pronounced dependence on temperature gradient.

Large variations in values of the diffusion coefficient for snow have been reported in the literature. Some authors (Yosida and others, 1955; Yen, 1963) have claimed that the diffusion coefficient does not vary with density. Others (Colbeck, 1993; Arons and Colbeck, 1995) have reported that the diffusion coefficient decreases with an increase in mean pore length, and that it does not necessarily change with snow density. This appears to be inconsistent, since density and mean pore space are related for a given mass of snow and therefore these parameters cannot be taken independently. On the other hand, experimental results show an increase in grain-growth rate with decrease in snow density. In this paper, particulate and continuum approaches have been used to obtain the mass diffusivity Treating snow as a particulate medium, the one-dimensional model of grain growth from Satyawali (1994) has been extended. This approach has been integrated into the SNOWPACK model (Lehning and others, 1998) that predicts the rate of grain growth for a dry snowpack subject to a temperature gradient. The expression for effective vapor-diffusion coefficient resulting from the present study is

To test this equation, several experiments similar to those of Yosida and others (1955) have been conducted assuming that snow is a continuous medium. In this approach Fick’s law of diffusion is used to obtain direct experimental determinations of the diffusion coefficient. The experimental results have been compared to estimates of D∊ calculated from the above equation and it is shown that results are inconsistent at the upper and lower sample boundaries. This paper describes the features of snow metamorphism, in particular grain growth driven by an applied temperature gradient, and discusses the mass-diffusivity coefficient derived from the particle theory of Colbeck (1993).

Studying the structure inside an inhomogeneous stratified snowpack is very important for modelling of the snowpack stability on mountain slopes, and to approximate surfaces of weak zones, and boundaries with different properties These surfaces are often the sliding surfaces of avalanches. Weather conditions" windpumping, snow densification and mechanical and complex heat- and mass-transfer processes define the structural variations of snow and the strength characteristics. The main ventilation components in the snowpack during the snowstorm are the heat and mass exchange between the snow grains and bonds, vapor and heat transfer. The vapor diffusion due to windpumping through snowpack intensifies the metamorphic process We propose the current mathematical model using meteorological data to simulate the snowpack characteristics in order to clarify the changes of the structural and physical-mechanical properties in the stratified snowpack under changing weather conditions. The system of equations allows calculation of the temperature variation in the snowpack, as well as in melted or frozen soil, the snow density, the structural parameters and the snowpack strength on the mountain slope as a function of the heat- and mass-transfer parameters. A numerical finite-difference model for simulations has been used. This allows prediction of the disposition of the depth-hoar layers and the physical-mechanical snow properties. The model has potential to estimate the potential avalanche volume.

This paper describes a new triaxial testing apparatus designed to determine the creep (viscoelastic) behavior of snow. The device is deformation-controlled and can apply strain rates between 10–7 s–1 and 10–2s–1 in tension and compression. The sample volume change is determined by measuring the displaced pore-air volume. During winters 1997/98 and 1998/99, >100 compression and tension tests were carried out. It is shown that snow is a highly non-linear but ideal viscoelastic material with a strong strain-rate dependency. A selection of test results is provided. We show how snow viscosity varies with density and strain rate. In a final analysis we interpret our results with respect to snow microstructure in order to develop microstructure-based constitutive relations which can be implemented in finite-element programs. Our results clearly show that for snow densities and strain rates tested, straining of the grain bonds is the primary mechanism of deformation within the snow ice lattice.

To assess the safety against failure of rock slopes in cold regions, such as high mountain areas, where stability is potentially maintained by ice in rock discontinuities, the shear strength of ice-filled rock joints was investigated in a series of direct shear-box tests. To permit control and repeatability, the experiments were conducted using simulated rock specimens. These were cast in the laboratory using high-strength concrete. Laboratory measurements showed that at a constant rate of shearing, the interface shear strength between ice and a joint surface of repeatable roughness is a function of both temperature and normal stress.