A heat conduction equation for the determination of the temperature profile in a snowpack is developed. The magnitude of the temperature gradient tends to increase as the snow surface is approached, with local minima through layers of high snow density and local maxima above and below these layers. Calculations are made of the difference in vapor density in the pore and over the ice grain surfaces which border the pore. In the presence of sufficient temperature and temperature gradient, faceted crystals will develop near the top of the pore, as ice is sublimed away from the surfaces in the lower region. There will be a reduction in the percentage of rounded grains as the faceted form develops. The process is demonstrated to be enhanced at warm temperatures and large temperature gradients in low density snow.

Strain-rate measurements were carried out over eleven years on a firn pit 20 m deep in a temperate glacier. The stress strain-rate relation was applied in terms of invariants, because of the multiaxial state of stresses. The shear viscosity and the bulk viscosity were calculated as a function of depth and density. The result must be understood in terms of effective viscosities as the dependence of the viscosity from the state of stresses is unknown in this analysis.

A digital ice-concentration database spanning 20 years (1960 to 1979) was established for the Great Lakes of North America. Data on ice concentration, i.e. the percentage of a unit surface area of the lake that is ice-covered, were abstracted from over 2 800 historic ice charts produced by United States and Canadian government agencies. The database consists of ice concentrations ranging from zero to 100% in 10% increments for individual grid cells of size 5 × 5 km constituting the surface area of each Great Lake. The data set for each of the Great Lakes was divided into half-month periods for statistical analysis. Maxinium, minimum, median, mode, and average ice-concentrations statistics were calculated for each grid cell and half-month period. A lakewide average value was then calculated for each of the half-month ice-concentration statistics for all grid cells for a given lake. Ice-cover variability and the normal extent and progression of the ice cover is discussed within the context of the lakewide averaged value of the minimum and maximum ice concentrations and the lakewide averaged value of the median ice concentrations, respectively. Differences in ice-cover variability among the five Great Lakes are related to mean lake depth and accumulated freezing degree-days. A Great Lakes ice atlas presenting a series of ice charts which depict the maximum, minimum, and median icecover concentrations for each of the Great Lakes for nine half-monthly periods, starting the last half of December and continuing through the last half of April will be published in 1983 by the National Oceanic and Atmospheric Administration (NOAA). The database will be archived at the National Snow and Ice Data Center of the National Environmental Satellite Data and Information Service (NESDIS) in Boulder, Colorado, USA, also in 1983.

Icing measurements were carried out in natural winter clouds with an instrumented wind tunnel set up at the summit of Puy de Dome (1 500 m a.s.l.). The microphysical data (liquid water content, droplet spectra) were obtained by using the particle measuring system PMS ASSP 100. The ice density was measured on a rotating cylinder and the ice deposit of the cross-section was photographed on a fixed cylinder. The density measurements ranged from 300 to 900 kg m–3 during the experioment and are in agreement with Macklin’s results (1962). The profile of the ice deposit is comparedto the profile predicted by the model of Lozowski and others (19791, which considers a fixed density.

We propose to improve this model by talking into account the variation of ice density with the angle of impact on the cylinder. This calculation is based on Macklin’s results and on the determination of the local impact speed by using the result of Langrature, air speed, liquid wter content, and, especially, the droplet distribution. The improvement is not sufficiemuir and Blodgett (1960). The variation o fice density with the angle depends on various parameters: pressure, tempen to explain some observed profiles; this may be attributed to the fact that the model is not time-dependent.

Distance of maximum avalanche runout is calculated by four topographical factors. An empirical equation found by regression analysis of 206 avalanches is used to predict the maximum runout distance in terms of average gradient of the avalanche path (angle α). The correlation coefficient R = 0.92, and the standard deviation of the residuals SD = 2.3°.

The avalanche paths are further classified into different categories depending on confinement of the path, average inclination of the track 6, curvature of the path y", vertical displacement Y, and inclination of rupture zone Q. The degree of confinement is found to have no significant effect on the runout distance expressed by a. Best prediction of runout distance is found by a classification based on 5 and Y. For avalanches with β <30° and Y > 900 m, R = 0.90 and SD = 1.02°.

The population of avalanches is applied to a numerical/dynamical model presented by Perla and others (1980). Different values for the friction constants v and M/DY are computed, based on the observed extent of the avalanches. The computations are supplied by velocity measurements v from a test avalanche where Y = 1 000 m, and vmax = 60 m s−1. The best fitted values are μ = 0.25 and M/DY = 0.5, which gives R = 0.83 and SD = 3.5°.

The manner in which inelastic Shockwaves propagate through snow is evaluated. The volumetric material behavior of snow is represented as an inelastic rate sensitive relationship. The constitutive equation has incorporated into it such crystalline properties as grain size, bond length, bond radius, pore size, and average number of bonds per grain. As a consequence, this constitutive formulation can be used to describe how Shockwave behavior is affected by different physical properties. The governing equations, i.e. the momentum and continuity equations, are solved by integrating them to put these equations in terms of jumps in pressure, density, and particle velocity.

Results are obtained for a wide variety of snow properties. First, the effect of density is evaluated by considering densities ranging from 150 to 300 kg m−3. Then the effect of intergranular bonding is considered by varying the bond radius/grain radius ratio from 0.15 to 0.40. Finally, the Shockwave frequency is varied parametrically to determine the effect of these parameters on wave attenuation rates.

The results are then compared to experimental data. The theoretical results are shown to agree well with the test data. The degree of intergranular bonding was also found to have a very significant effect on attenuation rates.

Finally the importance of the air phase on the propagation of Shockwaves in snow is investigated. The governing equations for each phase are developed by using a mixture theory formulation. An order of magnitude analysis is made in order to assess the importance of the air phase on attenuation rates.

A theory based on classical fluid mechanics for an incompressible, chemically non-reacting, atmospheric mixture of air and entrained snow particles is derived. These continuum equations of motion are then expanded to include turbulent flow. The reduced, one-dimensional equations of this theory are further refined by order-of-magnitude analysis and correlation of the turbulent terms to mean flou parameters. The resulting one-dimensional, turbulent equations of motion for the snow contain apparent turbulent forces which enhance entrainment of snow where gradients of the air flow are high. These turbulent equations of motion are then solved numerically for snow particle velocity and concentration as a function of height above the surface. The results are similar to observed profiles of snow concentration and the superposition of the solution of this turbulent mixture theory for snow entrainment with an appropriate solution for the saltation layer will eventually lead to a working continuum theory for blowing snow.

A modified Bingham numerical model is developed and tested for the simulation of the motion of snow avalanches. This two-dimensional, incompressible model takes the form of a two-viscosity system in which a large viscosity is employed in the low stress regions of the flow and a smaller viscosity is used in the high stress regions. The model involves three parameters: the two viscosities, and the value of the stress for the transition between the two flow regimes. A simple no-slip boundary condition is used at the interface between the flowing snow and the stationary snow surface. Model parameters are evaluated by simulating the motion of the leading edge of the flowing snow, velocity versus depth information, and debris distribution of small snow test experiments.

The time-dependent vertical deformation and the variation of the cross-section of the Georg von Neumayer wintering station, built during the Antarctic summer of 1980-81, are investigated with regard to the rheological behaviour of the surrounding snow, firn, and ice. Computations are performed to determine the time-dependent settlement using the compactive ( compressée) viscosity nc as the viscoelastic parameter, being a function of the density, nc is derived from the depth-density curve down to to 73.6 m depth, the initial density p0, and the accumulation rate. The ground plan and the foundation pressures of the station, and the weight of snow-fill and accumulation, are employed in the analysis, using actual values.

These computations are compared with measurements for a period of 320 d. The described measurement systems include the possibility of finding a reference level in the continuously compressed ice shelf. The time-dependent deformation of experimental tubes is also presented on the basis of convergency data taken over a period of 480 d.

During several winters the positions and magnitudes of excess snow deposits or denudation zones caused by wind have been evaluated on the flanks of regular, elongated mountain ridges. The surveys were carried out by conventional measurements of mass balance. According to angle of slope (10 to 35°), shape of crest (hump- or wedge-shaped) and orientation to the wind, various patterns of snow deposition may be found. It is shown that, on ridges oriented perpendicularly to the main wind direction (north-west) during snow storms, near-periodic snow deposits may be expected on the lee slope. On the windward side, there is a denudation zone near the crest. The measurements indicate that lee slopes, of mean slope angle, are buried in mid-winter under twice as much snow as the adjacent windward slopes. However, the ridge system as a whole accumulates the same amounts of snow as do areas of flat terrain. Theoretical approximations based on theories of potential flow and semi-empi rical plume models are used to simulate the presumed dispersion of snow. The model calculations, intended as diagnostic tools, suggest that snow may be diffused and deposited on lee slopes in a plume-like manner similar to other particulate matter. Snowfall, together with low-level blowing snow as an additional source of suspended particles, appears to increase the snow deposits, mainly on the foot of steeper ridges.

Tests have been performed on fine-grained, columnar, freshwater ice sheets 40 to 70 mm thick grown in a refrigerated model basin. Cantilever beams of various geometries were tested for lengths ranging from 200 to 2 000 mm and widths of 50 to 250 mm. Analysis of the results in terms of simple elastic beam theory indicated that modulus increased with increasing beam length and decreasing bean width. An analytical model for beam deflection was developed, taking into account the effects of buoyancy, shear, and rotation and deflection at the root. This model satisfactorily explained the observed deflection behaviour and the apparent geometry dependence of the modulus. Flexura! strength was independent of beam length, but decreased with increasing beam width. Flexural strength was independent of loading rate, whereas modulus decreased with increased loading time.

In several experiments carried out in France, the Republic of the Ivory Coast, and Spain, icing clouds were penetrated at different heights by instrumented research aircraft. This paper describes the range and the frequencies of occurrence of the relevant icing parameters computed on the cloud scale and for different cloud types. Comparisons between micro-physical parameters and meteorolagical radar signatures show the limitations of these radars when used as a means of locating icing clouds.

An investigation was undertaken of the creep of columnar-grained ice under constant compressive stresses of 98 and 59 kPa in order to extend the observed relationship between strain-rate and stress further into the low-stress region. Stress was applied perpendicular to the long direction of the grains. Observations were made for temperatures between -5 and -40°C. The steady-state creep rate for secondary creep was not yet attained for strain of 1.4% and stress of 98 kPa. An initial yield was observed at that stress in the strain range of 0.2 to 0.3%, similar to that seen at higher stress. The observations showed that the strain-rate tended to a linear dependence on stress below 49 kPa and that more than one dislocation process with different values for the stress exponent may contribute to the strain at higher stresses. An activation energy of 63 kJ mol−1 was consistent with the observed temperature dependence of the strain-rate. Straining ice to a given strain under a stress of about 0.3 MPa and then reducing the load may be a convenient way to study the stress, strain and temperature dependence of the strain-rate at low stress.

The vertical concentration distribution of frazil-ice crystals in a stream during the formation and growth of frazil ice was discussed in a preliminary way by Gosink and Osterkamp (1981). This paper extends and completes the analysis of buoyant rise velocities of frazil-ice crystals and applies the results to an interpretation of measured velocity profiles in rivers during frazil-ice events. Additional experimental data are also presented. Two time scales are defined: the buoyant time scale TB, which represents the time required for a frazil crystal to rise, buoyantly, from the river bottom to the water surface, and the diffusive tine scale TD, which represents the time required for a frazil crystal to he transported by turbulence through the depth. It is shown that the ratio of the time scales TB/TD defines the nature of the layering processes; in particular, if TB/TD<1, then buoyant forces Till lift a frazil crystal faster than turbulent diffusion can redistribute it and the flow will be layered. Conversely, if TB./TD>1, turbulent mixing will proceed faster than buoyant lifting and the flow will be well-mixed. This ratio, for frazil particles of diameter 2 mm or more, corresponds to rule-of-thumb velocity criteria developed in Norway and Canada to distinguish layered frazil-ice/water flow from well-mixed flow.

The development of this theory depends in large part upon the determination of TB, which depends upon the rise velocity of frazil-ice crystals. A force balance .nodel was developed for the rise velocity of a frazil crystal. Field observations during frazil -ice formation in Goldstream Creek and in the Chatanika River north of Fairbanks are reported, including a series of measurements of the rise velocities of frazil-ice crystals. Typical particle size of frazil ice was about 2 mm with a rise velocity of about 10.0 mm s -1. The agreement of measured rise velocities with the theoretical model is good considering uncertainties in the drag coefficient and in the determination of frazil crystal sizes under field conditions.

Velocity profiles in the Chatanika River and in Goldstream Creek during frazil formation suggest that the time-scale ratio may serve as a transition criterion between layered frazil-ice/water flow and well-mixed flow. This ratio was calculated with the rise velocity of frazil-ice crystals arbitrarily chosen to be 0.01 m s−1.

Damage due to glacier floods in the Swiss Alps occurs about once every two years at present, despite the pronounced retreat of glaciers during the twentieth century and the installation of many water reservoirs, which act as flood retention basins. Over half (60 to 70%) of the observed floods are caused by outbursts of marginal glacier lakes or sudden breaks of ice dams, and 30 to 40% by ruptures of water pockets. In a glacierized mountain region as densely populated as the Swiss Alps, even debris flows triggered by outbursts of very small water masses may be dangerous. Historical information about glacier floods in the Swiss Alps, although incomplete and heterogeneous, is used as an empirical basis for an attempt to recognize potential hazards at an early stage by considering outburst processes, volumes of water involved, potential peak-discharge values, lithology and inclination within the reach of glacier streams.

Subglacial hydrology, sediment transport, pressure, and temperature have been studied beneath approximately 160 m of ice at Sondhusbreen, an outlet glacier from Folgefonni in south-western Norway.

The volume of the mean annual water discharge passing through the study area is about 60x106 m3. Most of this water is diverted into a tunnel system in the rock beneath the glacier and used for hydroelectric power generation. At the beginning of the melt season, this water flows in multiple small channels, but later it collects in one or two main channels. The discharge of eroded material is about 7 600 tonnes a−1. Of this, roughly 90% is transported by running water.

Pressure gauges and thermistors were installed at two sites under the glacier. Results from one of the sites indicated that ice can stagnate in some leeward positions, as almost no ice movement was recorded during most of the period of measurement and the pressure distribution was nearly hydrostatic. However, increased water pressure during the summer apparently resulted in the opening of subglacial cavities, adding a local up-glacier component to the flow at this site.

At another location, about 20 m up-glacier, non-hydrostatic differential pressures of up to 30 bar were recorded across an artificial dome-shaped obstacle. The flow at this location was more steady, in general, but rather dramatic effects were recorded when a boulder 0.3 m3 in size passed over the obstacle, destroying one of the pressure sensors. This sensor recorded a pressure of 90 bar before failing. The boulder was moving at a speed of about 40 mm d-1, whereas the sliding velocity of the ice was 80 mm d-1. Temperature measurements suggest that the difference in temperature across this obstacle was less than 0.03 deg, or an order of magnitude less than expected. This may mean that water was squeezed out of the ice on the stoss side of the obstacle as suggested by Robin (1976), and thus was not available to warm the lee-side ice by refreezing.

A reconnaissance program has been carried out to identify problems caused by glaciers in a large proposed hydroelectric development in the Susitna River basin of Alaska. Balance measurements on the major glaciers have been initiated, and long-term balance between 1949 and 1980 has been estimated from existing photo sets. From the latter it appears that shrinking of the glac!iers, which comprise 4% of the basin area, may have contributed appreciably to the measured basin runoff. A potential instability in the drainage of Eureka Glacier, on the edge of the basin, has been identified. The glaciers of the basin seem to be largely temperate, and most of them are surging or pulsing types. Velocity measurements show seasonal variations that suggest appreciable contribution to the motion from basal sliding. A study of the moraines of Susitna Glacier, which is a surging type, indicates that no surge is imminent. Glacier-dammed lakes exist in the basin; they are small but could be enlarged by surging or other mechanisms. Some general problems in the estimation of the transport of suspended sediment are noted.

Data obtained from tests of uniaxial and multi-axial compressive strength on saline ice have been used to determine the coefficients of the Smith yield function, which uses seven parameters, and of the Pariseau yield function, which uses five. Both functions describe orthotropic materials and have been reduced for transverse isotropy. The tests of compressive strength were carried out over the past few years in the ice laboratory of the Hamburgische Schiffbau-Versuchsanstalt (HSVA) on a closed-loop controlled triaxial loading frame with brush-type loading platens. The values for tensile strength have been obtained from data published by other researchers.

The ice-strength values computed by means of the two yield functions were compared with measured ice strengths; the seven-parameter Smith yield function provides reliable results over the whole stress space, while the simpler Pariseau yield function is only applicable within a restricted area of the stress space.

Due to the nonlinear nature of the ice interaction, sea-ice build-up against coasts and structures is a complex process. This build-up signifycantly affects mesoscale (10 to 100 km) ice motions over typical forecast time scales of several days. To examine the ramifications of assuming a non-linear ice interaction in ice forecast models, we have carried out a series of idealized simulations employing a viscous plastic sea-ice rheology (Hibler 1979). These simulations employ constant wind fields at a grid resolution of 18.5 km and allow the ice to build up and strengthen. With the plastic ice interaction the ice build-up is found to take place by means of a ridging front. Depending on the nature of the strength-thickness coupling, this build-up is accompanied by kinematic wave propagation effects. The nonlinear interaction can also result in fluctuating velocities in certain locations, even though the forcing is fixed. The build-up results are found to be consistent with the analytic solution of a one-dimensional rigid plastic model.