A brief description of the resistivity method is given, stressing the points which are of particular importance when working on glaciers. The literature is briefly reviewed.

Satellite imagery is used as a basis to review and critique the results of studies at the mouths of Ice Streams Β and C and Crary Ice Rise. In many cases, these past analyses are extended by taking advantage of the broad coverage within each image. New perspectives are provided by the image data and some longstanding controversies are resolved. The grounding line is easily delineated and mapped in areas covered by imagery. Extensive areas of grounded ice with complex patterns of flow stripes are identified on the flanks of Crary Ice Rise. The imagery also allows a corrected map of surface topography in the vicinity of the Downstream Β camp. New questions are posed by hitherto unseen features. Data from the IGY traverse of the Ross Ice Shelf in 1957 are included to demonstrate that large changes have occurred in the past almost 30 years in the area upstream of Crary Ice Rise. These changes include modifications in the surface topography, elimination of crevasses and increases in the ice thickness by approximately 60 m.

A linear two-level atmospheric model is employed to study the influence of ice-sheet topography on atmospheric stationary waves. In particular, the stationary-wave-induced temperature anomaly is considered locally over a single ice-sheet topography, which is computed using the plastic approximation. It is found that stationary waves induce a local cooling which increases linearly with the ice volume for ice sheets of horizontal extents smaller than ∼1400 km. Beyond this horizontal scale, the dependence of stationary-wave-induced cooling on the ice volume becomes gradually weaker. For a certain ice-sheet size, and for small changes of the surface zonal wind, it is further shown that the strength of the local stationary-wave-induced cooling is proportional to the basic state meridional temperature gradient multiplied by the vertical stratification in the atmosphere. These results are of importance for the nature of the feedback between ice sheets and stationary waves, and may also serve as a basis for parameterizing this feedback in ice-sheet model simulations (e.g. through the Pleistocene glacial/interglacial cycles).

Water-pressure fluctuations beneath glaciers may accelerate rock fracture by redistributing stresses on subglacial bedrock and changing the pressure of water in bedrock cracks. To study the potential influence of water-pressure fluctuations on the fracture of subglacial bedrock, ice flow over a small bedrock step with a water-filled cavity in its lee is numerically modeled, and stresses on the bedrock surface are calculated as a function of transient water pressures in the cavity. Stresses on the bed are then used to calculate principal stress differences within the step. Rapid reductions in cavity water pressure increase principal stress differences in the bed, increasing the likelihood of crack growth in the step and the formation of predominantly vertical fractures. Relatively impermeable bedrock may be most susceptible to fracturing during water-pressure reductions because high water pressure in cracks within the rock can be maintained, as water pressure decreases in cavities. These results, when considered in conjunction with the strong likelihood that increases in water pressure accelerate the removal of rock fragments loosened from the bed, suggest that in zones of ice-bed separation where water-pressure fluctuations typically are large, rates of quarrying may be higher than along other parts of glacier beds.

We address the usefulness of the unstable manifold correction (UMC) in a Picard iteration for the solution of the velocity field in higher-order ice-flow models. We explain under- and overshooting and how one can remedy them. We then discuss the rationale behind the UMC, initially developed to remedy overshooting, and how it was previously introduced in a Picard iteration to calculate the velocity field in higher-order models. Using a laminar-flow experiment with two higher-order model implementations, we demonstrate that it is not overshooting, but undershooting, that is the main problem when using a proper implementation for the calculation of the velocity field in higher-order models. We also consider a variant of the original UMC algorithm that often enables a relatively fast solution, but is theoretically less sound. Therefore, neither the variant nor the original algorithm is suited for these problems. We present a more appropriate, stable and simple relaxed Picard algorithm and demonstrate that, compared to the true Picard iteration and the variant of the original UMC algorithm, it results in a faster solution of the velocity field in higher-order models for problems with real data.

Kongsvegen is a 102 km2 sub-polar (polythermal) surge-type glacier in northwest Spitsbergen, Svalbard. It surged just before 1948 and is currently in its quiescent phase. Measurements of surface geometry since 1966 show a retreat of the front and strong thinning of up to 75 m in the ablation area, and a build-up of up to 32 m in the accumulation area. Present-day annual velocities along the glacier are low, from 1.4 up to 3.6 m a-1. The measured mean net balance for the period 1987-94 and the balance reconstructed back to 1967 show a weak positive balance of about 0.1 m w.e. The measured actual ice flux is low and the mass transfer down-glacier at the ELA is only about 3-20% of that required for steady state. Thus, the glacier is building up towards a new surge. The total thickening rate on Kongsvegen is somewhat higher than in other cases from Svalbard, but it is small compared with other well-studied surge-type glaciers in Alaska and the Pamirs. This relatively low rate of change is a function of the low accumulation rate and the relatively cold climate compared to other areas and is common for surge-type glaciers in Svalbard.

In a series of papers, Bartelt and co-workers developed novel snow-avalanche models in which random kinetic energy (RKE) RK (a.k.a. granular temperature) is a key concept. The earliest models were for a single, constant density layer, using a Voellmy model but with RK-dependent friction parameters. This was then extended to variable density, and finally a suspension layer (powder-snow cloud) was added. The physical basis and mathematical formulation of these models are critically reviewed here, with the following main findings: (i) Key assumptions in the original RKE model differ substantially from established results on dense granular flows; in particular, the effective friction coefficient decreases to zero with velocity in the RKE model. (ii) In the variable-density model, non-canonical interpretation of the energy balance leads to a third-order evolution equation for the flow depth or density, whereas the stated assumptions imply a first-order equation. (iii) The model for the suspension layer neglects gravity and disregards well-established theoretical and experimental results on particulate gravity currents. Some options for improving these aspects are discussed.

Arches in stratigraphic layers directly under a flow divide (Raymond bumps) are predicted by models of steady ice-sheet flow, and have been observed in several ice domes. Here, we model the evolution of these layers when a formerly stationary divide migrates rapidly to a new position, then again becomes stationary, leaving the arched layers in a flank position. As they are then carried downstream with the flow, these abandoned arches can develop into recumbent folds. These folds can occur over a wide range of divide migration speeds. The shearing flow that produces these recumbent folds also distributes the folded layers over a wide distance downstream from the original divide location. If the divide offset is abrupt, ‘pre-cores’, or material lines comprising core-relative isochrones, can be used to quickly identify portions of an abandoned Raymond bump that would be overturned at any future ice-core site downstream. If, as appears to be the case in Greenland, the divide is never stable long enough to produce a mature arch, folds of this type would not occur. The most likely place to find such folds might be the flank of an ice ridge bounded by unsteady ice streams.

A comprehensive multi-mechanism theory of pressure sintering has been applied to the densification of two polar ice sheets. The comparison, which is made using pressure-sintering mechanism maps, indicates that power-law creep is the controlling mechanism between 50% and 98% theoretical density. Lattice diffusion becomes dominant at low porosities. The densification rates predicted by the theory are in good agreement with the data, and suggest that a reasonable estimation of the densification behaviour of a polar ice sheet can be made using the theory, based on information obtained from a relatively shallow core.

A degree-day glacier mass-balance model is coupled to a dynamic glacier model for temperate glaciers. The model is calibrated for two outlet glaciers from the Hofsjökull ice cap in central Iceland. It is forced with a climate scenario that has recently been defined for the Nordic countries for the purpose of outlining the hydrological consequences of future greenhouse warming. The scenario for Iceland specifies a warming rate of 0.25°C per decade in mid-summer and 0.35°C per decade in mid-winter with a sinusoidal variation through the year. The volume of the glaciers is predicted to decrease by approximately 40% over the next century, and the glaciers essentially disappear during the next 200 years. Runoff from the area that is presently covered by the glaciers is predicted to increase by approximately 0.5 m a−1 30 years from now due to the reduction in the volume of the glaciers. The runoff increase reaches a flat maximum of 1.5–2.0 m a−1 100–150 years from now and levels off after that. The predicted runoff increase leads to a significant increase in the discharge of rivers fed by meltwater from the outlet glaciers of the ice cap and may have important consequences for the operation and planning of hydroelectric power plants in Iceland.

Temperatures from a bore hole through an active rock glacier in the eastern Swiss Alps are presented and thermal conditions within the slowly creeping permafrost are analyzed. Present mean annual temperature in the uppermost part of the permafrost is −3°C. Permafrost is 52 m thick and reaches heavily fissured bedrock. Thermal conductivity as determined in situ from seasonal temperature variations and measured in a cold laboratory using frozen samples is close to 2.5–3.0 W m−1 °C−1. Vertical heat flow is anomalously high (around 150 mW m-2), probably due to heat advection from circulating ground water or air within the fissured bedrock zone. Beneath this zone, which could in fact represent a non-frozen intra-permafrost layer or “talik”, relic permafrost from past centuries may possibly exist as indicated by a corresponding heat-flow inversion. Given the current temperature condition at the surface of the rock glacier and the fact that the twentieth century is among the warmest in post-glacial time, permafrost conditions may be assumed to have existed during the whole of the Holocene and, hence, during the entire time of rock-glacier formation.

A number of improvements have been made to an existing two-dimensional ice-flow model applied to an alpine glacier. Analysis of the results of the existing model revealed several shortcomings. The first concerns the lack of mass conservation of the applied alternating-direction-implicit (ADI) scheme. A semi-implicit (SI) scheme is therefore proposed and the effects on mass conservation assessed by a comparison with the ADI scheme. The comparison is first carried out with a simple theoretical glacier for which the improvement is significant. Concerning the real case of Glacier de Saint-Sorlin, France, the initial deviation in mass conservation was much less pronounced such that the new scheme, although improving mass conservation, does not significantly change the modelled dynamics. However, other shortcomings that have a more profound impact on the modelling of glacier behaviour have been identified. The ice thickness may become negative over some gridpoints, leading to an inconsistency. The problem is partly resolved by incorporating extra checks on critical gridpoints at the glacier border. Finally, with the help of ice particle tracking, unrealistic ice settlement above the bergschrund has been identified as the main reason for spurious dynamic effects and has been corrected.

We investigate the errors caused by neglecting the crystal-orientation fabric when inferring the basal friction coefficient field, and whether such errors can be alleviated by inferring an isotropic enhancement factor field to compensate for missing fabric information. We calculate the steady states that arise from ice flowing over a sticky spot and a bedrock bump using a vertical-slab numerical ice-flow model, consisting of a Weertman sliding law and the anisotropic Johnson flow law, coupled to a spectral fabric model of lattice rotation and dynamic recrystallisation. Given the steady or transient states as input for a canonical adjoint-based inversion, we find that Glen's isotropic flow law cannot necessarily be used to infer the true basal drag or friction coefficient field, which are obscured by the orientation fabric, thus potentially affecting vertically integrated mass fluxes. By inverting for an equivalent isotropic enhancement factor, a more accurate mass flux can be recovered, suggesting that joint inversions for basal friction and the isotropic flow-rate factor may be able to compensate for mechanical anisotropies caused by the fabric. Thus, in addition to other sources of rheological uncertainty, fabric might complicate attempts to relate subglacial conditions to basal properties inferred from an inversion relying on Glen's law.

Radio waves of fixed frequency, which had passed through ice and firn from a transmitting antenna lowered down a bore hole, were monitored on the surface. By mixing the received signal with the fixed frequency, the beats which were produced as the antenna was lowered gave a value for the wavelength in ice at the depth of the antenna. This was multiplied by the frequency to give the velocity of radio waves m ice. Measurements averaged over 10 m and longer intervals were related to density values from bore holes in the same location. Results above 50 m were difficult to interpret, but at greater depths the velocities fitted a linear relationship between refractive index and density. A small extrapolation gives a velocity of radio waves in pure ice of 167.7±0.3 /μs at — 20° C.

More than 8,000 ice crystals have been oriented and measured for crystal fabric studies from widely separated temperate and polar glaciers, using a large universal stage and thin-section techniques. Very strong fabrics have been found and a number of laboratory experiments on deformation and recrystallization of ice were conducted in an attempt to solve some of the perplexing problems raised concerning glacier flow.

In polar glaciers the c or optic axes of the ice crystals tend to be perpendicular to the foliation plane (alternating planar structures of bubbly and clear ice). In areas of high shearing stress the preferred orientation of the axes reached 39 per cent in 1 per cent of the area when plotted on a Schmidt equal-area projection. In temperate glaciers the optic axes tend to form three or four strong maxima which also appear related to the foliation.

Patterns from ice deformed in the laboratory resemble some of the fabric patterns found in polar glaciers. During deformation of laboratory specimens, large crystals have been observed recrystallizing into many smaller ones, while fine-grained ice, after completion of deformation (both glacier ice and laboratory deformed ice), has been annealed at melting temperature into a few large crystals with different orientations from the original pattern.

An attempt is made to obtain and quantify the mechanical properties of two common types of seasonal snow on the ground. Different samples of natural snow whose metamorphism had stabilized (such as would remain on a road throughout winter in a cold, snowy area) were gathered and tested using mesoscale indentation tests (metrics on the order of mm to cm). Results from the stress vs displacement curves from indentation indicated that (1) first peak strength decreased, according to a power law, with increasing indenter size and was not affected by snow average grain size, (2) plateau strength decreased with increasing indenter size, and snow compaction strength might be calculated from these data, and (3) mean energy absorption density during indentation was independent of indenter size in some size ranges, and decreased with increasing indenter size in other size ranges.

From 1974 to 1981, a total of 32 bore holes was drilled on White Glacier and vertical ice-temperature profiles measured. The data obtained allowed the construction of three longitudinal and four transverse profiles of the two-dimensional temperature distributions. Thus, an extensive layer of temperate or near-temperate ice was discovered close to the bedrock in the lowest part of the glacier tongue. It was also found that the temperature distribution cannot be in a steady state, since there is a temperature minimum 100–150 m below the glacier surface in the accumulation area. A simple numerical model calculation shows that this minimum can be mostly explained by the general climatic warming since 1880. The 10 m temperatures show diffuse relations to climatic conditions and balance zones. A simple scheme for extrapolating “surface temperatures” is discussed.

Water is present in glaciers in the form of veins at the three-grain junctions. This water remains unfrozen even many degrees below the normal freezing point, mainly because it contains much of the soluble impurity content of a glacier, but also because of the microscopic curvature of the ice–water interfaces. As the temperature is lowered and the veins shrink, the concentration of impurities in them increases, and the curvature effect also increases. The predicted relation between vein size and temperature has now been verified by laboratory experiments.

Because of the latent heat of the vein water, the ice behaves macroscopically as a continuum with an anomalous specific heat capacity that depends strongly on temperature. From this point of view, a polythermal glacier is a single medium with continuously varying properties, rather than consisting of distinct cold and temperate phases with sharp boundaries between them. The paper sets up differential equations for heat diffusion in such a continuum. To explain the local uniformity of the vein system seen under the microscope, it is found necessary to include the effect of diffusion of solutes along the veins.

Solutions are presented for a model in which two semi-infinite slabs, initially having different temperatures, impurity concentrations and vein sizes, are instantaneously brought into contact. In this way, transition thicknesses between cold and temperate ice are estimated, and also the velocities of various kinds of waves that are generated from the original discontinuity at the interface.