It is believed that water-filled cavities on the scale of decimetres are present in a number of glaciers in Spitsbergen. The evidence for this hypothesis comes from airborne radio echo-sounding records collected by the Scott Polar Research Institute in 1983. The size of these cavities prevents the use of Rayleigh scattering theory and requires a more general analysis. Mie scattering theory is used to investigate the scattered power providing some unexpected results, the most significant of which is that for water bodies greater than approximately 0.25 m in radius the returned power from the volume illuminated is greater than that from a perfectly reflecting plane boundary.

Trace elements in ice samples taken from Law Dome, Antarctica, were analysed using an instrumental neutron-activation analysis technique. A Jupiter multichannel analyser-computer system coupled to a Ge(Li) detector was used for the acquisition of γ-spectra and for data reduction. “Blanks” in water and in nitric acid, which were used in pre-concentration and sample transfer, were also analysed. To check the validity of this analytical procedure, a U.S. Environment Protection Agency water standard for trace elements was also analysed. The observed values agreed with the certified values.

The results (in ppb) of eight elements are:

Na   209         Mn   0.42   Mg  26   Fe  14

Sc    0.0017   Co   0.028   Al   9.6   Se   0.02

The enrichment factors for these eight elements relative to the Earth’s crust were calculated. These elements can be subdivided into three groups or sources according to their enrichment factors. The variations of elemental concentrations with depth show no positive tendency towards a systematic increase or decrease over the past 5000 years.

The steady-state flow model of Reeh (1988) is applied to a flow line that starts at the highest point of the Devon Island ice cap, follows the surface crest for 7.6 km, and then runs down the slope for a further 3.7 km. The effects of bedrock undulations, divergence of the flow lines, the variation of temperature with depth, and a basal layer of “soft” ice-age ice are taken into account. A flow law with n = 3 and a value of A close to that of Paterson (1981) is used. Longitudinal stress variations are neglected so that shear stress is calculated by the usual formula. It is estimated that these calculated values may be in error by at most 30%. Depth profiles of effective shear stress, and of the components of velocity and normal strain-rate, are presented at selected points along the flow line. These illustrate the large variations that occur near an ice divide and over bedrock undulations of amplitude comparable with the mean ice thickness. The model gives good predictions of the surface profile and of longitudinal and transverse surface strain-rates measured at ten points along the flow line. Predicted depth profiles of horizontal and vertical velocity components are compared with those measured in a bore hole. Comparison is limited by the fact that the model works in ice equivalent, whereas about 20% of the ice column consists of firn with different rheological properties from ice. The vertical velocity prediction is good. However, the model does not reproduce well the shape of the horizontal velocity profile, although measured and calculated fluxes differ only slightly. Predicted annual-layer thicknesses are within 15% of the measured ones in the upper half of the ice column, which consists of ice deposited in the last 1000 years. Predicted thicknesses in older ice are too small and the discrepancy increases with depth. This might indicate increased precipitation or, more likely, a thinner ice cap in the climatic optimum. However, it could also result from the fact that the layer of “soft” ice has been thinning continuously since the end of the ice age, so that the ice cap has never been in a steady state.

Run-off data for two basins in south Greenland, one of which contains glaciers, are compared with precipitation at a nearby weather station and with ablation measured in the glacier basin. Seasonal variations of run-off for the two basins are broadly similar while run-off from the glacier basin has smaller year-to-year variations. A simple statistical model shows that this is the result of a negative correlation between ablation and precipitation, which has the effect of reducing run-off variations in basins with a moderate amount of glacier cover although run-off variations may become large again for highly glacierized basins. The model also predicts an increasing run-off with ablation correlation and a decreasing run-off with precipitation correlation as the amount of glacier cover increases. Although there are still too few data sets from other parts of Greenland for final conclusions, there are indications that the present findings may be applicable to other Greenland basins.

The mechanical behaviour for the geometrical properties of two-dimensional deformation has been investigated. The Mohr formulation of failure, which is based on the concept of slip at the plane of weakness, is used in this study. It is shown that alteration of the shear stress τn at the plane of weakness requires self-similarity of features in deformation patterns. A general relationship between the angle of internal friction and the breaking angle of deformation patterns is derived. Using imagery data, this relationship is used to find the angle of internal friction from selected sea-ice deformation patterns. The value obtained for this angle is Φ = 15° ± 2° for deformation on a scale from 100 m to 100 km.

An internally consistent data set of geometry and flow variables for the lower part of Columbia Glacier, south-central Alaska, is derived entirely from vertical aerial photography. The principle of mass conservation is imposed on the data in the form of a centered finite-difference approximation of the continuity equation. It is applied on a 120-node section of a square grid covering the 15 km long, high-velocity stretch ending at the grounded, heavily calving terminus of this large glacier.

Photography was obtained 22 times between June 1977 and September 1981. Surface altitudes on the dates of the flights and the displacement vectors between pairs of flights were determined photogrammetrically. Natural features on the glacier surface were sufficiently prominent and enduring to be followed from the date of one flight to the next.

Because both the altitude points and displacement vectors were irregularly positioned spatially, interpolation was necessary to get values on the grid nodes. The points had already been subjected to the method of optimum interpolation to get surface altitudes on the grid nodes. The displacement vectors are subjected here to a constrained–interpolation method to get velocity vectors at the grid nodes that are consistent, through the continuity equation, with the other variables.

The other variables needed to achieve closure of the variable set are bed topography and mass-balance distribution. The latter was taken to be a separate linear function of altitude for each time interval. Values for bed altitudes at 120 nodes and two coefficients of each 21 balance functions were inferred as the 162 model parameters in a non-linear minimization problem having 4305 observed velocity components as its data.

A theory of icicle growth is presented. It is shown that icicles elongate as hollow tubes of ice with liquid water trapped inside the tip. A time-dependent computer model based on the theory shows that the growth of an icicle is a complicated process, which is very sensitive to the atmospheric conditions and water flux. The shape and weight of icicles predicted by the model agree well with laboratory data.

Hobbs Pool is an area of thin ice shelf situated within George VI Ice Shelf, Antarctica. Thicker ice shelf surrounding Hobbs Pool isolates the upper 155 m of the water column from water lying at the same depth else-where under the ice shelf. Summer melt-water lakes drain through crevasses at Hobbs Pool forming a 155 m thick layer of low-salinity water close to its freezing point. Colder and more saline water in the lower part of this layer leads to in-situ freezing of fresher water lying above it. Below 155 m depth, the water temperature and salinity are linearly related by basal melting which is observed elsewhere under the ice shelf. The surface ice shows areas of deformation and deposits of subglacial rock debris which may result from upward particle paths in the area. The raising of subglacial rock debris on to the ice surface may provide a mechanism for the transport of erratics across the ice shelf to Alexander Island from the base of Palmer Land glaciers.

The isotopic composition of river water discharging from the Norwegian glacier, Austre Okstindbreen, in summer varies on both daily and longer-term scales. Most δ18o values of samples from the principal river are within the range −12.5 to −14.0‰). Because new snow tends to be relatively depleted of 8180, water leaving the glacier early in the summer has low δ18O values. Subsequently, values rise as contributions of old snow, glacier ice, and their melt waters, which are isotopically heavier (median δ18O values generally above −12.0‰) dilute the δ18O depleted base-flow component of discharge, a mixture of waters with different histories of formation, storage, and transit. Accumulation-area melting contributes significantly to river discharge. Towards the end of the summer, as surface melting declines, δ18O values tend to fall. Between-year differences of within-summer trends reflect differences of development of the glacier’s drainage systems. The drainage systems are affected by outbursts from a glacier-dammed lake. During fine weather, δ18o variations follow the diurnal cycle of surface melting: they are strongly correlated with, but lag behind, air temperatures. Perturbations during rainfall cannot be explained simply in terms of the isotopic composition of the precipitation, since low values may be associated with isotopically heavy rainfall. Displacement of water previously stored within or below the glacier may account for the anomaly. Contrasts of composition characterize different rivers leaving the glacier, because the relative contributions of various water sources differ.

During the 1984 and 1985 melt seasons, flow velocities and dispersive characteristics of the englacial and subglacial hydraulic system on Storglaciären, a small valley glacier in northern Sweden, were studied with the use of dye-trace tests. Similar tests conducted on one of the two principal pro-glacial streams provided a basis for comparison of the combined englacial-subglacial system with the pro-glacial one. Velocities in the two systems were broadly comparable after compensating for the effect of slope differences. However, velocities in the glacial conduits increased almost linearly with discharge. Analysis suggests that this can be explained by an increase in water pressure in the conduits, combined with a decrease in effective sinuosity, as discharge increases. Dispersivity (the ratio of the dispersion coefficient to the water velocity) in the glacial system is high early in the season but decreases progressively during July. This is believed to reflect a change from an extensively braided to a more integrated drainage system. Dispersivity is only slightly lower in the pro-glacial streams than in the late-season glacial conduits, suggesting similar degrees of braiding. However, retardation of dye due to temporary storage is greater in the glacial conduits. This suggests that the glacial streams have a larger number of stable eddies in which dye can be trapped for extended periods of time.

On 4 July 1986, dye was injected at a point slightly above the equilibrium line on Storglaciären, a small valley glacier in northern Sweden. Just below the equilibrium line, the glacier bed is over-deepened. The dye re-appeared in a stream at the glacier terminus over the next 35 d. This stream normally carries relatively little sediment, in constrast to the situation in another nearby stream that also emerges from the glacier. This suggests that the dye traveled in englacial rather than subglacial conduits. Tracer tests utilizing salt in bore holes in the overdeepening support this interpretation, as the bore holes were draining well above the bed. The dye appeared during three distinct events, suggesting that it became divided into at least three separate parcels shortly after injection. This probably occurred in the crevassed area in the vicinity of the injection point.

The englacial location of the drainage may be explained by the fact that, in order to remain at the pressure melting-point, water in subglacial conduits coming out of the overdeepening may have had to warm up faster than would be possible by viscous heating alone. Such conduits would thus tend to freeze closed.

Three components of the kinetic friction of snow are described but only the lubricated component of friction is treated in detail. This component depends upon the thickness of water films which support a slider on snow grains over a small fraction of its area. The thickness of the film decreases with ambient temperature in a manner which is sensitive to the thermal conductivity of the slider. The minimum value of friction at any temperature is reached at an intermediate value of speed because friction decreases as the slider first begins to move and the films form but then increases at higher speeds because of the shear resistance. At sub-freezing temperatures a small area in the front part of the slider is dry and the friction is high. Once the water film is formed it increases in thickness towards an equilibrium value which can be very sensitive to slider properties, speed, and temperature. It appears that the mechanisms may be very different for hydrophobic and hydrophilic sliders. From the equations derived here it is clear why friction decreases with repeated passes over the same snow.

During fast indentation tests on ice sheets at constant rates, crushing is commonly observed at appropriate combinations of speed and aspect ratio. An analysis is made of this mode of failure, using as a basis a recently conducted test on an ice sheet under controlled conditions. The variation of load with time is given special attention, and cyclic variation of load is associated with periodic crushing (pulverization) events, followed by clearing of the crushed ice particles. An analysis of the clearing process is summarized in the paper, treating the crushed ice as a viscous material. A detailed analysis of the energy exchanges during the indentation process is given. Elastic variations of stored energy in the indenter and in the ice sheet are calculated; these are relatively minor. The dissipation of energy during a typical load cycle (3 mm movement during 0.05 s) is about 8 J. The energy required to create surfaces of the crushed ice particles is small (0.006 J), as is the work of crushing based on mechanical testing (0.09 J). It is concluded that the process of viscous extrusion of crushed ice is the main seat of energy dissipation, basically as a frictional process. A relationship for the mean thickness of the crushed ice layer is developed, based on energy-balance considerations.

The relationship between the intensity of snow acoustic emission impulses and snow-cover stability is revealed by measuring the physical and mechanical properties of the snow cover in the starting zones of avalanches. This relationship is fundamental to the remote identification of an avalanche-hazard period.

In order to estimate the mechanical properties of a snow layer, a method of applying a rigid penetrometer equipped with a piezo-electric accelerometer is used. The viscosity coefficients of snow under destruction and the specific energy of destruction are determined. The overall effect of different elements of destruction is assessed using both structural investigations and acoustic methods (acoustic emissions).

Observations of the discharge, electrical conductivity, cationic content, and isotopic composition of glacier-river water indicate that drainage of the lake dammed at the margin of the glacier Austre Okstindbreen, Okstindan, Norway, is preceded by disruption of the glacier’s drainage system(s). Annual studies over a period of 12 years have demonstrated that intense storm precipitation, changes of ablation conditions, and the stage of development of drainage systems all may play a role in triggering drainage of the ice-dammed lake. Water temperature may influence the course of the outburst. The lake has drained on at least ten occasions in the last 12 years. Three of the events (1979, 1985, and 1986) occurred early in the summer, whilst melting of the winter’s snow cover was contributing substantially to glacier-river discharge: high basal water pressure and rapid sliding may have facilitated disruption of drainage conditions within the glacier. In 1982, the lake drained during a severe storm, in 1977 and 1984 shortly after a period of heavy rainfall. During the 1977 and 1984 events, water under pressure burst up through the glacier surface. The lake basin remained partly filled throughout one summer (1980): in-flow of water was balanced by out-flow into the glacier.

Glaciated valleys of the Dalton Range in the south-west Yukon Territory are dominated by rock glaciers identified as glacier ice-cored debris systems. The two rock glaciers studied have different amounts of deformation at present, resulting from post-formation mechanics.

The primary formation of lobes of the rock glaciers resulted from periods of glacier activity in the Neoglacial, although older lobes, probably late Pleistocene in age, occur below the Neoglacial lobes. The hydrological systems of the rock glaciers have played a major role in the post-formation deformation of the land forms and the present drainage system is entirely sub-surface. The explanation for the extensive occurrence of rock glaciers in the Dalton Range is lithological as a result of the high susceptibility of the Upper Jurassic/Lower Cretaceous sediments to frost action and glacier erosion.

Glacier variations during the last few centuries have shown a marked coherence over the globe. Characteristic features are the maximum stand somewhere in the middle of the nineteenth century, and the steady retreat afterwards (with some minor interruptions depending on the particular region). In many papers, qualitative statements have been made about the causes of these fluctuations. Lower temperatures associated with solar variability and/or volcanic activity are the most popular explanations. In particular, the statistical relation between glacier activity and major volcanic eruptions appears to be strong.

In this paper, an attempt is made to simulate recent glacier fluctations with a physics-based model. A simple climate model, calculating perturbations of surface-radiation balance and air temperature (not necessarily in phase!), is coupled to a schematic time-dependent glacier model. The climate model is forced by volcanic activity (Greenland acidity and/or Lamb’s dust-veil index) and greenhouse warming. Solar variability was not considered, because its effect on climate has still not been demonstrated in a convincing way. The output is translated into variations in equilibrium-line altitude, driving the glacier model.

The simulated variations in glacier length show good agreement with the observed record, but the amplitude is too small. This is improved when mass-balance gradients are assumed to be larger in warmer climates. Compared to recently published modelling studies of particular glaciers, in which series of local parameters (e.g. tree-ring width and temperature) were used as forcing, the present simulation is better. This suggests that the radiation balance is a decisive factor with regard to glacier variations on longer time-scales. The model experiments lend support to the results of Porter (1986), who concluded from a more qualitative study that a strong relation exists between periods of increased volcanic activity and glacier advances.

A comparison of some selected runs shows that, according to the present model, the greenhouse warming would be responsible for about 50% of the glacier retreat observed over the last 100 years.

A description of the reduction of two-dimensional equilibrium equations to one-dimensional form via the Kantorovich method is given. An appropriate interpolation function is obtained by relating basal shear stress to sliding velocity and integrating the constitutive model through the depth of ice. An example is presented which demonstrates the ability of the numerical model to effect solutions which are in good agreement with those obtained via full two-dimensional finite-element models; however, at a small fraction of computational and data input efforts. The technique described for the reduction of the equilibrium equations can also be used to convert three-dimensional stress equilibrium to two-dimensional form.

A jökulhlaup event of 6 months duration occurred near Casey Station, Law Dome, Antarctica, in late March (austral autumn) 1985. This was followed by sporadic outbursts during the austral autumn and winter of 1986. The event is the first recorded outburst of water from beneath a cold ice-cap terminus on Law Dome and, to the author’s knowledge, in Antarctica. From the results of oxygen-isotope and solute analysis, the water was found to have originated as basal melt water. It contained a high total solute load with a dominant enrichment in alkalis, indicting that it had been squeezed through subglacial sediments for an extensive time period. Evidence from the subglacial topography, basal ice exposures, and the sedimentology of nearby supraglacial moraines supports the presence of an ice-marginal subglacial water reservoir as the jökulhlaup source.

Scheuchzer’s dilatation theory and Altmann’s rigid sliding theory were the first glacier-flow theories to receive serious scientific attention. When Agassiz began a research program at Unteraargletscher in 1839, he held several incorrect notions about glacier flow. Forbes understood the difficulties with the existing theories, and in the early 1840s he and Agassiz acquired motion, temperature, and structural data that were incompatible with the dilation and sliding theories but were suggestive of flow analogous to that of a viscous fluid. How an apparently brittle rigid solid like ice could flow became the central paradox requiring explanation. Some of the most able physicists of the mid-nineteenth century went through contortions in their largely misguided efforts to explain the viscous behaviour in terms of the known physics of rigid solids. Personality and speculation played a far larger part in their debates than we see in scientific discussions today.