The behaviour of a floating sheet of lake ice was investigated for the case when it becomes loaded by a layer of fresh snow which is later soaked with water. This latter condition interferes with the traditional horse races of St Moritz, which are held on the lake each year. A piezometric precision gauge which measures accurately the vertical movements of the floating ice relative to the free surface of the lake is described. The level of the lake, in turn, oscillates, depending on the use of water by the local power company. Detailed measurements from the winter of 1978-79 are presented, showing that the piezometric level rises in direct response to precipitation, and that it rises further when the snow becomes soaked with water. With a simple model it is shown that the ultimate level is a function of the snow density, and it is concluded that immediate compaction of falling snow is an appropriate measure to reduce the amount of water entering the snow. It is very unlikely that the oscillations of the level of the lake caused by the demands of the power company have an influence on the slush problem.

The propagation of shock waves in unsaturated wet snow is investigated, both analytically and experimentally.

The experimental program was carried out in the laboratory with an electromagnetic stress-wave generator. During each test, impact velocity was measured at the base of the specimen by means of a contacting wire system. Also, pressure was measured at the opposite end with a piezo-resistive pressure transducer with a flat response from below 0.5 to above 100 kHz.

Densities of snow samples in the range from 200 to 500 kg m−3 were tested. Impact velocities at the base were varied from 20 to as high as 100 rns −1. Propagation distances (specimen lengths) were varied from 2 to 5 cm. Also, for each test, the free water moisture content in the test specimen was carefully measured so that the effect of this property could be evaluated. The test results are reported and the wave attenuation rates are characterized in terms of the parameters discussed above. In addition, these results are compared to test results for dry snow.

Finally, wave propagation theory is used to evaluate the material tangent modulus. The theory is also used to calculate particle velocity and density increases produced by the shock waves. The results are compared to those obtained earlier for dry snow.

In the austral winter of 1979-80, a German Antarctic expedition was sent by ship to the Filchner and Ronne ice shelves in order to find a suitable site for the establishment of a permanent Antarctic station. During this expedition, investigations were carried out on sea ice in the Weddell Sea in order to evaluate the accessibility of the site for icebreaking ships which are intended to convey construction materials to the site and, later on, to supply the station annually.

This paper covers the results of investigations on sea-ice conditions during the voyage along the ice shelves from Cape Fiske (at the base of the Antarctic Peninsula) to Atka Bay with emphasis on sea-ice conditions in the area about 100 km north-west of Berkner Island (Fig.1.). In addition to the drift conditions (speed, direction), a special feature of multi-year sea ice is described. The main part of the paper deals with mechanical properties such as flexural strength, uniaxial compressive strength and Young’s modulus of columnar-grained sea ice from the southern border of the Weddell Sea. Salinities and temperatures were measured over the depth of the ice and used for calculating the flexural strength and the Young’s modulus of the ice. The uniaxial compressive strength was investigated as a function of strain-rate, brine volume and temperature on a closed-loop testing machine on samples which were carried back from Antarctica to Hamburg.

A test program undertaken in April 1981 on the uniaxial compressive strength of freshly recovered first-year columnar-grained sea ice at a portable field laboratory floating on top of the ice cover in Eclipse Sound, Baffin Island, Canadian Arctic, is reported. Using a small battery-operated test machine, both vertical and horizontal samples were tested so that the load could be applied either parallel or perpendicular to the axis of the columns. Rate sensitivity of the observed strength is discussed in terms of measured average strain-rate and average stress-rate to upper yield or failure. Strain and time aspects of the test results are considered as well. Although vertical samples showed considerably greater strength than horizontal samples, no significant differences were detected in the failure strains. Examination of the interdependence of failure stress and failure time revealed certain anomalies in the results for vertical samples that could be linked to the performance characteristics of the test machine. As such problems could be common to any test system, methods of analysis are proposed for rational examination of the results.

Experiments were performed to determine the forces required to buckle a floating ice sheet pushing against structures of different widths. The characteristic length of each ice sheet was determined to enable a comparison to be made between the theoretical and experimental results.

Most of the experimental data points are within the range of the theoretical values of normalized buckling loads for frictionless and hinged boundary conditions, which represent the extreme situations for ice-structure contact. Thus, the agreement between the theoretical and experimental buckling loads is considered to be good. Photographs of the buckled ice sheets show a resemblance to the theoretical mode of buckling.

Ice pile-up and ride-up are common occurrences along beaches in the sub-Arctic and Arctic. An understanding of the factors which lead to pile-up is important for design of a defensive strategy to prevent damage to coastal installations.

Since ice action on a sloping beach is complex, an experimental model study was undertaken to determine the factors which promote ice pile-up. The factors varied in this study were the freeboard, slope, and roughness of the beach. One experiment was performed to observe the effectiveness of a shore defense structure against ice ride-up.

Analyses of several years of data show that acoustic emission activity is greater from unstable snowpacks than from stable snowpacks. Two types of signals have been identified: type I spikes and type II long-term elevation of the noise level. It is thought that the type I signals originate from macroscopic cracks. The type II signals may originate from differential movement on shearing surfaces, but this is less certain. Increased noise levels of both types correlate well with slope instability, when the slope stability is known. In some climates the limited range of signal detection might be a significant problem. A foam-mounted geophone set into the snow near active layers appears to be the best sensor available at present.

Results from a numerical model for the computation of ice-floe motions in ocean waves are presented and discussed for floes of various sectional shapes. It is shown that the beam-to-draft ratio is a crucial factor in determining the behaviour of each floe, and that ridges and keels can substantially affect the roll and sway characteristics, particularly for thick floes. Undercuts beneath floes appear to have little effect, but a protruding sill can lead to decreased motion at certain frequencies and a reduced capability for making waves. As the underwater character of an ice floe cannot easily be measured, it is necessary to infer draft from freeboard estimates using the method proposed by Ackley and others (1976). Although most of this paper is concerned with rigid body motions, a brief account is included of a modification to the model which allows each floe to bend on the passing wave. By this means, wave-induced flexure is discussed for floes of non-simple underwater shape.

The Seasat radar altimeter, which was designed to measure ranges to the sea surface, has also provided the most accurate available maps of ice-sheet elevation. Seasat operated for three months during the austral winter of 1978, when Antarctica was girdled by sea ice. As the satellite approached the continent from the ocean, the altimeter obtained very strong reflections from the sea ice, and it continued to measure ranges to the sea ice even for a short time after passing over the ice front. The measured ranges are oblique distances to the nearest portion of sea ice, and the sequence of oblique ranges gives the position of the sea ice along the ice front. After the satellite crossed the ice front travelling seaward, oblique ranges were measured to the nearest portion of ice shelf. Examples are given from Seasat orbits crossing the Amery and Fimbul ice shelves. The entire Seasat data set provides an opportunity for mapping most of the East Antarctic coastline to an absolute horizontal accuracy of ±(0.1 → 1) km. The resulting map would effectively be an instantaneous view of the ice margin, requiring no adjustment for ice movement during the survey period.

In order to interpret reliably the results of model tests which involve compressive (crushing) failures, the compressive strength of the model ice must be known. In this paper, the uniaxial and plane-strain compressive strengths of carbamide (urea) model ice are documented for scale factors of 40>λ>5. In addition, the influences of stress and strain-rates, platen materials and direction of loading are discussed. The results of the tests are interpreted in terms of the structure of the ice.

Prediction of the future retreat of Columbia Glacier, Alaska, required a calving law for the boundary condition at the terminus. Qualitative observations on the variations of all major iceberg-calving glaciers of Alaska suggest that calving is high whenever glaciers terminate in deep water, and greatly reduced whenever they terminate in shallow water. Calving relations were investigated based on calculations of calving speed, defined as the volume rate of iceberg discharge from the terminus divided by the cross-sectional area of the terminus. The calving speed was determined for 12 glaciers for which measurements of glacier speed, advance and retreat rates, and other variables were obtained. To extend the range of data, four additional periods of rapid retreat were examined. Values for the terminus characteristics of water depth, cliff height, and thickness of the terminus, averaged over the width of the glacier and over a year, were then examined in relation to the calculated speeds of calving. A statistical analysis to determine the form and coefficients of an empirical calving relation that approximates the data shows that calving speed is best fitted by a simple proportionality to average water depth at the terminus: 1 where vc is the calving speed and hw the water depth, both averaged over the width and over a year, and c a constant of proportionality. This gives a variance reduction fraction (similar to the coefficient of determination r2) of 0.90.

To investigate seasonal changes in calving, data based on shorter time intervals were obtained at the head of embayments from Columbia Glacier. At intervals of approximately two months, the following expression fits intra-yearly calving at Columbia Glacier: 2 where D is the meltwater discharge from the glacier, hj is the height of the ice column unsupported by water buoyancy, a, b, c are constants, and vc and hu are evaluated at the embayment head. D was determined by correlation with a nearby glacial stream, and hu = h _ hw PW/PJ, where h is glacier thickness and pi and pw the densities of ice and water. Best-fit values of b and c are approximately 0.5 and -2, respectively. This yields a variance reduction fraction r2 of 0.83.

Equation (2) does not fit data averaged over a year and over the width of the glacier and Equation (1) does not fit data obtained over shorter periods at the head of the embayment. Although the two equations are different in form, for similar or average values of D and h - hw (ice-cliff height), they give approximately similar results over the present range of the geometry of the terminus of Columbia Glacier. Whether this will be true after rapid retreat begins remains to be seen.

The behavior of Griesgletscher, Switzerland, is studied by application of a numerical model of temperate glacier flow. The analysis addresses the possible danger posed to a hydroelectric dam which is 600 m from the calving terminus of the glacier. Model parameters are adjusted to fit data collected over eleven years. A calving law relating the calving flux to the water depth at the front provides a good fit of the data. Assuming a continuation of the present climate, the terminus is predicted to retreat 200 m over the next forty years, followed by an advance of 150 m lasting several centuries. Numerous experimental climate alterations show that the dam will not be threatened by short-term climatic changes. A long-term mass-balance increase of 0.12 m of ice per year (or a drop of 0.2°C in mean annual air temperature) would be sufficient to fill the reservoir with ice. With an additional increase of 0.07 m of ice per year the terminus would reach the dam. Data from the 1923 and 1850 moraines are used to suggest lower-bound estimates of temperature changes (-0.4 and -0.6°C respectively) during these periods of glacial maxima.

Snow is a mixture of ice, air, water vapor, and liquid water, and as such is a mechanically and thermodynamically very active material. In an attempt to gain a better understanding of the process of meta-morphism and the interaction of mechanical and thermo-dynamic processes within mountain snowpack, modern mixture theory was used. Only dry snowpack was considered, so that the liquid phase could be neglected.

Each constituent (ice, vapor, and air) was assumed to have its own density ρα, temperature Θα, partial stress Ta, particle velocity ζα, internal energy εα, entropy ηα, free energy tα, and heat flux qα. Each constituent was considered to have the ability of reacting with the other constituents, so that mass supplies tα, energy supplies êα, and momentum supplies pα can be defined to characterize the manner in which each constituent receives mass, energy, and momentum from the other constituents due to chemical and mechanical interactions. In addition, a concentration cα was defined in order to specify the extent to which the solid and vapor phases have exchanged mass.

The mass balance, momentum balance, and energy balance principles were then developed for each constituent, thereby giving a set of nine differential equations to solve for θα, ζα, and ρα for each constituent. In addition the second law was defined for the mixture and used to place restrictions on the allowable forms for the constitutive equations for Tα, εα, ηα, Ψα, qα, Pα, εα, and ĉα for each constituent. In this way the forms for these variables under non-equilibrium thermodynamic conditions could be specified.

For example the restrictions imposed by the second law require that, under nonequilibrium conditions, the stress, mass exchange rate, heat flux, and momentum supply may have the forms: 1234 where Eα, ?Eα/?Z, Uα3, and ?θβ/?Z are respectively the strain, strain gradient, diffusion velocity relative to the air phase, and temperature gradient. An alternate form for ĉα which was also found to be consistent with the second law is 5 where ĉ2 is the rate of sublimation from the solid to vapor phase and μ1 and μ2 are the chemical potentials for the ice and vapor phases.

As a special example, densification due only to the presence of surface energy was calculated. In this case, the material is unloaded, and the free energy Ψ10 for ice is dominated by its surface energy. Therefore Ψ10 = σ1?1 where A1 is the surface area per unit volume and σ1 is the specific surface energy. If T1 and θ1 are set to zero and θ0, the solution to Equation (1) yields the result illustrated in Figure 1 for the density P1.C10 and γ10 _ are the initial elastic modulus and viscosity. This case corresponds to that of new, very fragile snow. Denser, stronger snows would densify much less, but cracking may still occur in the material if constrained froin densifying freely. Fig. 1.

Densification of low-density snow due to effect of surface free energy.

Next, the added effect of equitemperature meta-morphism on densification was considered. This involves the process of transfer of water molecules from small grains to large grains to produce a more efficient distribution of ice and hence some densification. The solution was found, and preliminary results indicate densification is enhanced by this process. However, final quantitative results must await a better means of relating density, grain size, and grain shape to specific surface area A1. Current formulations for finding ?1 are of questionable accuracy.

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.

We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

Intense deformation within an extensive englacial debris layer appears to be a dominant flow mechanism for glaciers on Mount St Helens, Washington. Observations of this phenomenon have been made on Shoestring Glacier and more recently on other glaciers on the volcano. Transverse velocity profiles on Shoestring Glacier have shown a marked plug flow behavior occurring between narrow marginal zones of crevassing. Both longitudinal and transverse velocity profiles on Shoestring Glacier were measured during the year before and the two years after the cataclysmic eruption of the volcano on 18 May 1980.

The geometry and regime of every glacier on Mount St Helens dramatically changed during the eruption. The entire accumulation area of Shoestring Glacier was removed by a volcanic landslide and blast, and the glacier surface was deeply incised through the action of pyroclastic flows and mudflows. Surface velocity measurements were supplemented by vertical profiles taken along the newly exposed ice cliffs. Large velocity gradients seen in the transverse, longitudinal and vertical profiles coincided with the mapped location of a recently exposed englacial debris layer. Further detailed measurements on the vertical profiles show that the intense shear occurs by deformation internal to the debris layer, A study of the properties of debris-laden ice was undertaken to determine the mechanism for localization of deformation to the debris layer and for the associated response of the glacier to a sudden change in stress.

We have reduced the time taken for measurement of snow water equivalent using cosmic radiation by two to four hours with an accuracy of 1 cm of water equivalent. When BF3 counters were used by Kodama in 1975, it took three days. For comparison we sometimes still have to make measurements manually or automatically in flat areas. These measurements can then be compared with measurements from avalanche starting zones where conditions can be quite different because of wind or ablation.

For avalanche forecasting, or in similar situations, when an accuracy of 1 cm is needed within a few hours, we suggest the use of scintillation counters with a doped plastic material. The greatest accuracy is obtained by using a separate site where values are recorded without snow. In this case 200 000 pulses per hour are obtained (absorption length of 400 cm) which after measurements of 2 h duration gives the desired error of 1 cm of water. After 8 h the error is 0.5 cm of water, and after 24 h it is 0.3 cm of water. At an altitude of 2 000 m at which most avalanches are released, the count rate is doubled and the measuring error is 0.7 of that at sea-level. At an altitude of 3 000 m the count rate is four times that at sea-level. In other regions at other latitudes and elevations other values would be found.

The necessary equipment can be built into the ground in autumn so that the surface is level with the ground. A slot antenna of frequency around 400 MHz is used for transmission of the data.

Blue Glacier was subject to 5 to 10% increase in thickness during the period 1958 to 1978. A surface velocity increase of 15 to 50% has accompanied this change in ice thickness. A non-uniform distribution of thickening over the glacier produced a general decrease in surface slope. The flow law parameters in a power-law relation for ice can be obtained from the resulting increase in velocity.

In 1957–58 the surface velocities and surface elevation along several transverse profiles were determined by others. During the period 1977 to 1980 similar measurements were made of surface velocity, elevation, and ice thickness along profiles spatially equivalent to those of the 1957–58 survey. Using these results a detailed study of the flow response has been made. Preliminary results indicate that the controlling surface slope a is one that is averaged over approximately ten times the glacier thickness and also indicate a relatively high stress exponent n = 4 to 5.

Blue Glacier flows in a complex channel and any detailed interpretation of the flow response requires the inclusion of this geometry in a model. For this reason multi-dimensional finite-element methods using a non-linear constitutive relation were employed. Various degrees of model sophistication allowed for the specification of different parameters governing the flow of the glacier. Variations in the flow law parameters and the curvature of the channel were found to have significant effects on the velocity and stress fields, as well as on the characteristics of the flow response to the thickness perturbation. Fully three-dimensional models of the flow of Blue Glacier and its response to the thickness increase were developed. Important effects such as those arising from longitudinal thickness and surface slope variations were included in three-dimensional modeling. The three-dimensional effects were seen to play an important role in flow of a rheologically non-linear fluid such as ice.

Lake ice often has inclusions of air bubbles and their presence affects the thermal, mechanical, optical and other physical properties of the ice cover. Vertical variation in the characteristics of the bubbles suggests that their characteristics should be related to the rate of ice growth at the time of formation and therefore reflect past meteorological conditions.

The laboratory studies of Carte (1961) and Bari and Hallett (1974) demonstrated that the rate of ice growth affects the size, shape and distribution of bubbles and the porosity of the ice. Their results were generally supported by the field study of Gow and Langston (1977), but Swinzow (1966) found no relationship between bubble characteristics and the rate of ice growth.

Freeze-up and initial ice growth were monitored at Small Lake, Resolute, NWT, Canada, in 1978 to determine what diagnostic information night he obtained fror,) the inclusion stratigraphy of the ice cover. Additional samples were collected from five other lakes in the Resolute area, a shallow lake near Hamilton, Ontario, and two lakes near Huntsville, Ontario. Daily ice samples were removed from the ice cover of Small Lake and the inclusion stratigraphy was mapped. A typical ice sample shows diurnal sequences of bubbly and bubble-free ice. The inclusion layers, 1 to 5 mm thick, were formed near midday and were separated by 10 to 15 mm of clear, bubble-free ice. All samples were missing at least one inclusion stratum. There was a wide variety of bubble types and sizes, and non-gaseous inclusions, believed to be algae, were noted in some of the bubble layers. The hourly rate of ice growth was calculated using a modified Stefan equation. No relationship between the bubble characteristics and the rate of ice growth was obtained. The influence of the algae and the absorption of solar radiation by the water are probably responsible for the diurnal cycle of bubble formation by influencing nucleation. The absorbed radiation will warm the water and decrease the amount of air that the water can dissolve, thus making more air available for bubble growth. The algae will also change the concentrations of dissolved gases and act as nucleating agents.

Cores taken from Small Lake in spring showed large cylindrical bubbles in the lower meter of the ice cover which had a thickness of 2.4 m. An inverse relationship between porosity and rate of ice growth was observed for these bubbles.

Ice samples taken from the other lakes in the Resolute area either showed no inclusions at all or exhibited fewer diurnal inclusion sequences. Using a general bubble stratigraphy obtained from Small Lake it is possible to correlate some inclusion layers in samples taken from lakes that are 15 km apart.

The samples from Hamilton also showed diurnal stratigraphie sequences except that the spacing between the bubble layers was more variable due to a larger range of daily growth rates. However, the two lakes near Huntsville had a detailed bubble stratigraphy, with little clear ice and no evidence of diurnal variation. The bubble layers in the ice from the two lakes could be easily matched, although they are 15 km apart.

This study shows that bubble layers formed in a growing ice cover may be used to reveal some aspects of the history of the growth of the ice cover, although the applicability depends greatly on local conditions. Additional studies are required to understand the mechanisms by which air bubbles and algae are incorporated into lake ice.

For the calculation of rates of closure of tunnels or bore holes in ice, the use of a flow law relation based on secondary or minimum creep rates necessarily underestimates closure rates, particularly for large strains where much higher tertiary creep rates develop. Long-term laboratory studies have shown that the change in strain-rate from primary to secondary or minimum and to an approximately constant tertiary stage is associated with recrystallization and the development of strong crystal-orientation fabrics which are dependent on the stress configuration, but not appreciably on crystal size. For bore holes, tunnels or cavities constructed in ice, initial rates of closure decrease, in primary creep, to a minimum value (at about 1% strain) dependent on stress and temperature. From this time, increasing strain-rates occur, analogous to the results obtained from the laboratory studies.

A 25-year record of closure of a tunnel at about 30 in depth at site S2 on Law Dome, Antarctica, illustrates the application of the laboratory-derived relations. Comparison between the results of deformation from bore holes, tunnels and laboratory tests, comprising various stress configurations, under similar conditions of stress and temperature, indicates that the strain-rates are compatible when considered as a function of total strain.

This study presents estimates of snow creep pressures from the centre section of an avalanche defence structure in western Norway. The structure is 15 in long and is erected on a 25° slope characterized by deep snow covers. Two methods of measurement are described: (1) direct estimates from earth pressure cells, and (2) construction of force, shear and moment diagrams from strains measured using vibrating wire strain gauges mounted on the steel beams of the structure.

In addition to the estimates of pressure, relevant snowpack data were measured, including snow depth, density, temperature and rammsonde hardness profiles as well as snow crystal stratigraphy. Snow gliding was also measured, and was found to be negligible. The snowpack measurements were made at approximately monthly intervals during each of the four winters which yielded useable data for the study.

Analysis of the pressure distributions along with the snowpack data yielded the following results: (1) the average pressure on the structure is linearly proportional to the product of average density times snow depth, (2) the average pressures are predicted fairly accurately by a linear, viscous creep model, (3) the maximum pressure depends strongly on the snowpack stiffness and decreases rapidly when warming and melt soften the snowpack, and (4) the maximum pressures are of the order of 254 higher than predicted by a linear, viscous creep model.