The physical properties of eight ice cores recovered from along a flowline at Glacier de Tsanfleuron, Switzerland, have led to the identification of three distinctive internal zones. We use variations in the bulk ionic chemistry of these zones to approximate their relative liquid-water concentrations and ice viscosities. Results suggest that relative bulk water concentration and ice softness vary by over an order of magnitude between the zones. Implications of this variability for predictions of the glacier’s response to climate change are evaluated by incorporating these relative softnesses into a multi-layered (two-dimensional) model of ice flow. Model output is compared with that from an identical model constrained with a spatially uniform ice viscosity under advance and retreat modelling scenarios. The former scenario is used to tune viscosity by growing a glacier to its present long-section geometry, resulting in best-fit ice hardness values of 1.2 a1 bar–3 for the englacial ice in the multi-layered model and 7.0 a–1 bar–3 for all of the ice in the single-layered model. Both result in close approximations to the current long profile, yielding rms deviationsbetween measured and modelled ice thicknesses that are 5 5 m. In contrast, a single-layered model constrained with a hardness of 1.2 a–1 bar–3 overestimates the current measured long-section area by 31%, having a rms ice-thickness error of 15.0 m. Under the retreat modelling scenario, which gauges the response of the glacier to an imposed 75 m rise in equilibrium-line altitude (ELA), the multi-layered model predicts a long-section area reduction of 78%. This contrasts with a reduction of 64% for the single-layered model (hardness = 7.0 a–1 bar–3) and 85% for the single-layered model (hardness = 1.2 a–1 bar–3).

Layered ice has been used to investigate the initiation of fabrics in shear zones where there is preservation of a refolded layering The fabrics were measured using an apparatus that acquires pixel-based images that illustrate the variation of c-axis orientation within and between grains. In the centre of the shear zones there is dynamic recrystallization with the production of an asymmetric two-maxima fabric. The way dynamic recrystallization modifies the inherited folds and microstructure suggests that there is little effect of inheritance from a precursor grain microstructure or fabric No obvious evidence has been found for the occurrence of sub-grains, which implies that the role of sub-grain rotation is minimal or is obliterated by the recrystallization process. The final c-axis pattern is asymmetric with respect to the direction of shortening, with a strong maximum at ~5° to the pole of the shear zone, and a sense of asymmetry in the direction of the shear, and a secondary maximum inclined at ~45° to the plane of shearing. Distinct sets of nearest-neighbour c-axis distributions, namely, intermediate-angle (10–25°), high-angle (50–65°) and very high-angle (120–150°), suggest there may be special grain-boundary relationships.

The nature of the fall-off at lower stresses from power-law behavior to a lower-order stress dependency is of particular interest in glacier and ice-sheet modeling. Preliminary experiments show that the stress level at which the fall-off occurs is a function of the specimen’s dislocation density. The analysis employs a dislocation-based model of anelasticity that provides a quantitative relationship between the effective dislocation density and the area of hysteresis loops observed in cyclic loading experiments. Combining this technique with a staged creep experiment makes it possible to calculate the dislocation density as a function of strain, thereby supporting a quantitative dislocation analysis of the deformation process.Work on saline ice established that the threshold stress associated with power-law behavior increased as a result of prior straining, power-law behavior emerged when the effective dislocation density increased measurably during deformation, and approximately linear behavior was evident when the dislocation density remained relatively constant. Those findings motivated the experiments on fresh-water ice presented here. The preliminary experiments show that pre-straining increases the stress associated with the fall-off from power-law behavior, and the results are interpreted in the context of a dislocation-based constitutive model developed for sea ice.

A material model for the simulation of anisotropic behaviour due to texture development in polar ice is presented. Emphasis is laid on the strain-induced texture development and its relaxation due to rotation recrystallization and grain boundary migration in the low-velocity regime. The model is based on two scales (mesoscopic approach). Kinematics, balance equations and constitutive assumptions are defined with respect to the grain level (mesoscale). Slip-system behaviour is assumed to be Newtonian. Recrystallization and grain boundary migration are taken into account via a diffusion-type evolution of the crystallites orientation. Due to the inextensibility of the ice crystallites along their c axes, the Sachs–Reuss assumption is adopted. Volume averaging yields associated macroscopic relations, where the internal structure is represented by a second-order structure tensor. The proposed approach is illustrated by applying it to initially isotropic material under homogeneous deformation, giving results qualitatively in agreement with experimental evidence. Finally, it is shown that the proposed model is, under some simplifying conditions, directly related to phenomenological internal variable models (e.g. Morland and Staroszczyk, 1998).

In spite of the clear fact that annealing and recrystallization phenomena in ice sheets have their roots in the thermodynamics of polycrystalline media, most approaches seem to neglect it by proposing ad hoc theories which can eventually violate fundamental thermodynamic principles. The current work presents a useful fusion of modern concepts from the thermodynamics of mixtures with continuous diversity with recent developments in the modeling of induced anisotropy and recrystallization in ice sheets. The fabric (also called texture) of the medium is described by a continuous distribution of crystallographic c axes, while recrystallization processes are assumed to be essentially driven by an internal variable representing the density of dislocations within the material. Among other results of this coalition, a balance equation for the dislocation density is formulated, as well as additional terms in the balance equations of mass, momenta, energy and entropy, associated with specific microstructural processes. By picturing the polycrystal as a mixture with continuous diversity, we discuss how the modeling of recrystallization processes in ice sheets could profit from powerful notions of chemical kinetics, which are related to the so-called dynamics of continuous reactions. Additionally, further topics like homogenization, comparison with earlier work, and directives for the construction of constitutive theories are addressed.

Reorientation of individual crystal-glide planes as isotropic surface ice is deformed during its passage to depth in an ice sheet, lattice rotation, creates a fabric and associated anisotropy. A simple macroscopic description is that these material glide planes are rotated towards planes normal to an axis of compression, and away from planes normal to an axis of extension, inducing an instantaneous orthotropic viscous response with reflexional symmetries in the planes orthogonal to the current principal stretch axes. An orthotropic viscous law is presented for the strain rate expressed in terms of the deviatoric stress, the deformation, and three structure tensors based on the principal stretch axes. This anisotropic relation is expressed in terms of a single fabric response function in addition to the isotropic ice viscosity. The predicted responses in uniaxial compression and simple shear are determined. While the uniaxial response yields an explicit relation between the axial strain rate and stress, it is found that the shear response is governed by three, complicated, coupled relations between the shear strain rate and three deviatoricstress components. The new result derived here is the solution of this system: an explicit relation between the shear strain rate and shear stress. Correlation of these relations with idealized uniaxial and shear responses is then used to determine the required fabric function in the model law.

Along most particle paths in polar ice sheets, ice experiences a slowly changing local deviatoric-stress pattern, and develops a fabric characteristic of its current stress state, in which there is generally a correspondence between non-zero strain-rate components and non-zero deviatoric-stress components. Where the stress pattern changes rapidly in special transition zones, fabric may evolve more slowly than the local stress field, and unusual or unexpected deformation patterns can result. The degree to which fabric tracks the local stress is determined by the relative characteristic times for changes in stress, given by the transition-zone width and ice velocity, and for changes in crystal orientation, given, in the absence of recrystallization, by the inverse of the local strain rate due to the principal stress. Recrystallization can significantly reduce the time-scale of fabric adjustment. We examine transition zones where ice (a) enters ice-stream margins, (b) is overrun by a migrating divide, and (c) flows through a strong saddle. Stress and fabric tend to be significantly misaligned in ice-stream margins and in flow through a saddle. When stresses that are markedly different from in situ stresses are applied to ice specimens during creep tests, deformation may be difficult to interpret.

The effects of spatial and temporal variations in basal lubrication on the englacial strain rate and surface velocity distribution are investigated with a numerical ice-flow model. General aspects of the solutions are compared to measurements made on Lauteraargletscher, Switzerland, in 2001, that showed diurnal fluctuations in both surface velocity and englacial vertical strain. We find that spatial gradients in basal lubrication can set up variations in the deviatoric stress field that increases with distance to the bed and has a maximum value near the glacier surface. This stress field produces a significant strain rate near the surface. The temporal evolution of a slippery zone is identified as a possible cause of the observed diurnal variations in the vertical strain rate. Although general aspects of the measurements can be explained in this way, the calculated vertical strain rates are too small, suggesting that the modeled effective viscosity values using Glen’s flow law are too large near the surface.

The deformation of subglacial till is instrumental in causing certain glacier surges, the motion of rapid ice streams in ice sheets, and ice-sheet surges which are associated with Heinrich events, and consequent rapid climatic shifts, during the last ice age. It may also be the means whereby drumlins are formed, and these in turn may act as a brake on large-scale ice flow. It is therefore important in building models to understand the rate at which till deforms, and how this controls the basal ice velocity. In recent years, two paradigms have emerged. On the one hand, theoreticians have tended to use a viscous rheology, though this lacks quantitative support. On the other hand, field and laboratory studies suggest that till behaves plastically. In this paper I will examine some of the dynamic consequences of this latter assumption, and show how the dichotomy between viscous and plastic may be less clear-cut than previously thought.

Observations of crevasse and crevasse trace geometry recorded along marginal shear zones of Sørsdal Glacier, East Antarctica, are presented with fine-spatial-resolution measurements of ice flow collected at three selected study sites. Strain grids established at each site, comprising 254 points, were repeatedly surveyed during the summers 2000/01 and 2001/02 using a semi-kinematic global positioning system technique with relative coordinate precisions at the order of ±2 cm in horizontal and ±5 cm in vertical. The annual results show ice-flow velocities of 2–114 m a–1 across a 2.7 km section of the Sørsdal margin. Comparable ice-flow velocities were also obtained using a Doppler system DORIS. At one study site, covering a planar area of 0.04 km2, a preliminary comparison is made between the crevasse pattern and strain-rate tensors computed for 64 discrete points using the method developed by Nye (1959). The comparison indicates that the most recent crevasses are directly related to the principal strain rates in this zone of simple shear.

Recent surges of two outlet glaciers of the Vatnajökull ice cap, Iceland, were observed using European Remote-sensing Satellite (ERS) synthetic aperture radar (SAR) tandem interferograms from12 different dates between December 1995 and January 2000. ERS SAR interferometry provided new information on the temporal and spatial variations in surface velocity during surges, after fieldwork became impossible. The area affected by the surge and therefore by increased basal sliding was delineated. Themigration of flow divides on the ice cap during a surge was described. At Sylgjujökull, a western outlet glacier covering an area of 175 km2, the fully developed surge and its abating phase were studied. Over a period of 4 2 years after December 1995, the ice motion decreased steadily, with initially the highest velocities and subsequently the most pronounced decrease in velocity at the glacier terminus. The surge of Dyngjujökull, a northern outlet glacier covering an area of 1040 km2, reached its maximum in 1999/2000. Slow acceleration over an area of about 200 km2 was first observed between March 1996 and January 1997. The interferogram from January 1999 shows a well-developed surge area, covering 210 km2. This area more than doubled by January 2000, with maximum velocities reaching >7 md–1. Between January 1997 and January 2000, the flow divide between Dyngju- and Skeiðararjökull shifted 16 km to the south. The investigations indicate that a surge cycle on these glaciers spans several years, with slowly increasing motion over an extended area in the beginning, and more pronounced velocity changes during the active surge phase lasting 1–2 years.

Continuum damage mechanics describes the progressive deterioration of material subjected to loading. Jointly used with a level-set method, it proves to be a promising approach to computing the interface motion of a damaged material. For polycrystalline ice, a local isotropic damage evolution law (generalized Kachanow’s law) applied to Glen’s flow law allows the description of tertiary creep and facilitates the modeling of crevasse opening using a failure criterion based on damage accumulation. The use of a level-set method permits the description, in a continuum approach, of the motion of a fractured glacier surface. Using these methods, a model is developed. The ability of this model to describe phenomena connected to crevasse opening is presented. The rupture of a large ice block from a hanging glacier is computed and analyzed. The regular acceleration of such an unstable ice block prior to its collapse is calculated and compared to the acceleration function obtained from observations. A good agreement between the two acceleration functions was found.

In theoretical treatments of tidal bending of floating glaciers, the glacier is usually modelled as an elastic beam with uniform thickness, resting on an elastic foundation. With a few exceptions, values of the elastic (Young’s) modulus E of ice derived from tidal deflection records of floating glaciers are in the range 0.9–3 GPa. It has therefore been suggested that the elastic-beam model with a single value of E ≈ 1GPa adequately describes tidal bending of glaciers. In contrast, laboratory experiments with ice give E = 9.3 GPa, i.e. 3–10 times higher than the glacier-derived values. This suggests that ice creep may have a significant influence on tidal bending of glaciers. Moreover, detailed tidal-deflection and tilt data from Nioghalvfjerdsfjorden glacier, northeast Greenland, cannot be explained by elastic-beam theory. We present a theory of tidal bending of glaciers based on linear viscoelastic-beam theory. A four-element, linear viscoelastic model for glacier ice with a reasonable choice of model parameters can explain the observed tidal flexure data. Implications of the viscoelastic response of glaciers to tidal forcing are discussed briefly.

Glen’s law is commonly used to model the viscous deformation of polycrystalline ice. It is a power law that relates stress to viscous strain rate and contains three material parameters: n, a power-law exponent, Q, an activation energy, and A0, a material constant. Because polycrystalline ice is the constituent material of snow, it is to be expected that the viscous deformation mechanics of snow are related to the viscous behaviour of polycrystalline ice, especially under small strains and low strain rates when kinematic effects in the ice matrix like bond breakage, bond formation and grain sliding are of secondary importance. Based on 64 deformation-controlled compression tests on fine-grained snow in the density range 200–430kg m–3 and temperature range T = –20 to –2°C, we show that Glen’s law—with material parameters similar to those for polycrystalline ice—can be applied to model the viscous deformation of high-density snow However, the values of the ice material parameters are valid for densities above a relatively low density of 400 kg m–3; they are not valid for snow with densities below 360 kg m–3. We present the variation of n, Q and A for snow as a function of density and temperature. A possible explanation for this behaviour is that the ice grains in low-density snow are less constrained. Therefore, deformation mechanisms, such as grain-boundary sliding, increase in overall importance, leading to smaller n values and higher activation energies, Q. Although the material behaviour of low-density snow can be accurately modelled using a power law, the power-law parameters depart substantially from those of polycrystalline ice. The large variation of n and Q with temperature and density underscores the difficulty of predicting snow avalanches.

A study of c-axis orientations in the upper 1500m of the Dome C (East Antarctica) deep ice core has been carried out using an automatic ice-fabric analyzer (AIFA). Twenty-nine vertical and a few horizontal thin sections from different depths in the core have been analyzed. Several statistical parameters describing fabric strength and fabric shapes have been calculated from the c-axis orientation data. The fabric diagrams display a near-random c-axis orientation distribution in the uppermost parts of the ice sheet. A tendency of c-axis rotation towards a broad single-maximum fabric is observed in the lowest part of the studied interval. The fabric development at Dome C thus appears typical for ice-sheet summit and dome sites. The fabric development at Dome C is compared with the fabric evolution in the Dome F and GRIP ice cores, and data on crystal size obtained with image-analysis techniques are presented. Studies of misorientation angles between the c axes of neighbouring crystals reveal little evidence for polygonization, but microscopic observations show that sub-grain boundaries are present in half of the grains at any depth.

The micro-fabric of frozen sediment was studied using a triaxial deformation machine with computerized tomography (CT) to describe a quantitative relationship between microstructure and mechanical behaviour at different temperatures and confining pressures. Micro-fabric changes were described by CT images and CTvalues. Relationships between CT values and the stress–strain curves were analyzed. It was shown that CTvalues can describe the deformation quantitatively.

Ice-sheet basal ice is warmer than that above because of the heat from the Earth’s interior. The stresses acting on the basal ice are greatest. In addition, the basal ice often contains debris consisting of silt and small stones picked up from the rock over which the ice flows. Because the base is the warmest part of an ice sheet and the stress there is greatest, flow rates in the basal ice are large and often contribute most of the ice movement. It is therefore important, for accurate modelling of the ice sheets, to know whether the debris within the basal ice enhances or retards the flow of the ice. In this paper, we describe laboratory deformation tests in uniaxial compression and in simple shear, on sand-laden ice. We find no significant dependence of flow rate on sand content (up to 15% volume) in the stress range 0.13–0.5 MPa and temperature range –0.02 to –18.0°C. Further work needs to include laboratory tests on debris-laden ice extracted from the polar ice sheets. This work is underway.

Detailed measurements of crystal outlines and fabrics have been performed on 35 000 crystals in fifteen 10 × 20 cm2 vertical thin sections from the North Greenland Icecore Project (NorthGRIP) ice core, evenly distributed in the depth interval 115–880m. The crystals exhibit important changes over this period. As the ice gets older the mean crystal area increases towards a constant value, the shape of the crystals becomes increasingly irregular, and the area distribution of crystals develops from a single log-normal distribution into a bimodal lognormal distribution. The c-axis fabric of the ice shows a smooth development of an increasingly stronger vertical fabric with depth, and the formation of a weak vertical girdle. Already in the younger samples the fabric is rather strongly oriented towards vertical. The fabric and the area of individual crystals are found not to correlate. A simple model, which takes into account the vertical strain of the ice, is applied in an attempt to determine the crystal growth rate at NorthGRIP.

The aim of this case study is to quantify the seasonal variability in crystal properties and to discuss the reason for the variability. A continuous 1.10 m long vertical thin-section profile covering approximately five annual cycles has been obtained from the North Greenland Icecore Project (NorthGRIP) ice core at around 301 m depth. The crystal outline and the c-axis orientation of more than 13000 crystals in the profile have been measured on a new Australian automated ice-crystal analyzer. In 2.5 cm resolution we observe a strong seasonal variability in crystal areas of >30%deviation from the average value of 6.7 mm2. Each year, a band of smaller crystals is observed in ice deposited during spring. The area distribution function is found to be close to a lognormal distribution. The crystal areas are compared to the concentration of chemical impurities in the ice; at a 5 cm resolution, the best correlation is found with the concentration of Ca2+. Our results show no seasonal variability of the average c-axis orientation of ice crystals.

Vigorous flow of central regions of Ice Stream C, West Antarctica, near the UpC camp ended about the year 1830, based on analysis of a firn and ice core taken at the camp. Ice-stream flow was characterized by repeated fracturing and healing, probably subsurface, especially near the onset of streaming flow. High longitudinal stresses caused fracturing, recrystallization of the ice and elongation of bubbles, and enhanced densification rates of high-density firn indicating power-law-creep behavior.