In this paper, we present the summer-time energy balance for a site in the lower ablation zone of the West Greenland ice sheet. The summer climate of this part of Greenland is sunny and dry. The energy that is available for melting (on average 174 W m−2 or 4.5 cm w.e.d−1) is mainly provided by net global radiation two-thirds and sensible-heat flux (one-third). The contribution of the sub-surface heat flux, the latent-heat flux and the net longwave radiation to the energy balance are small. We tested some parameterizations to calculate energy-balance components that are currently used in general circulation models, energy-balance models and mesoscale meteorological models. For the area and time period under consideration, parameterizations that use screen-level temperature for the calculation of incoming longwave radiation systematically underestimate this quantity by 10 W m−2 owing to the proximity of the melting-ice surface that restricts temperature increase of the lowest air layers. The incoming global radiation was predicted correctly. Simple explicit schemes that calculate the stability corrections for turbulent fluxes as a function of the bulk Richardson number tend to underestimate the turbulent fluxes by 15 W m−2. The aerodynamic roughness length z0 derived from wind-speed profiles appears to be erroneously small, leading to underestimation of the fluxes by 30 W m−2. Probably, the wind profile is distorted by the rough terrain. An estimate of z0 biased on microtopographical survey yielded a more realistic result. Because all errors work in the same direction, the use of some of the parameterizations can cause serious underestimation of the melting energy.

General Circulation Models (GCMs) will be more and more used for coupled climatic simulations involving ice sheets. It is therefore of prime importance to evaluate the performance of these models in simulating the mass balance and climate over ice sheets. The Antarctic climate simulated with the U.K. Universities Global Atmospheric Modelling Programme General Circulation Model (UGAMP GCM, hereafter referred to as the UGCM) is in good agreement with the available observations. In particular, the accumulation pattern appears fairly reasonable. Some imperfections are related to the surface temperature and energy budget but without severe consequences for the atmosphere behaviour. Refining the snow-related parameterizations could improve the results of the model in high latitudes.

An energy-balance climate model designed for coupling to ice-sheet models is presented. Its independent variables are longitude, latitude and time of the year. The model is based on the vertically integrated equations of conservation of energy and humidity. It can predict the vertically averaged temperature. Since it includes a hydrological cycle, it can also diagnose the net fresh-water flux and hence the annual snow budget at the atmosphere–ice-sheet interface. To this end, the model does not require observed precipitation rates. The computational cost is reduced by using an analytically computed Fourier–Legendre representation of daily insolation. For a highly idealized test-case configuration, two simple sensitivity experiments are carried out.

In this paper the elevation model for the Greenland ice sheet based upon radio-echo-sounding flights of the Technical University of Denmark (TUD) (Letréguilly and others, 1991) are compared with the satellite-altimetry model (Tscherning and others, 1993) improved with airborne-laser and radar altimetry (IA model). Although the general hypsometry of both data sets is rather similar, differences seem to be large at individual points along the ice margin. Over the entire ice sheet, the difference between the IA model and the TUD model is 33 m with a root-mean-square error of 112 m. Differential GPS measurements collected in the ice-marginal zone near Søndre Strømfjord show that the IA model is more accurate than the TUD model. The latter data set underestimates the elevation by approximately 150 m in the ice-marginal zone near Søndre Strømfjord.

Calculation of the ablation with an energy-balance model and with a degree-day model points to a 20% decrease in the ablation if the IA model is used. Not only does this show the sensitivity of ablation calculations to the orographic input but it also indicates that the ablation calculated by the models used nowadays is relatively overestimated.

A high-resolution GCM ECHAM3 T106 was used to simulate the climates of the present and of the future under doubled CO2 The ECHAM3 T106 was integrated for an equivalent time of 5 years (1) with the observed SST of the 1980s and (2) with the SST for the 2 × CO2 climate generated from the ECHAM1 T21 coupled transient experiment. The main motivation for using the GCM to simulate the mass balance is the level of skill in simulating precipitation and accumulation recently achieved in the high-resolution GCM experiment. The ablation is computed, based on the GCM internal surface fluxes and the temperature/ablation relationship formulated on the Greenland field data. The two ice sheets show very different reactions towards doubling the CO2. As the decrease in accumulation and the increase in ablation in Greenland cause an annual mean specific mass balance of −225 mm (eq. −390 km3), the increase in accumulation and virtually non-melt conditions in Antarctica result in a mean annual specific mass balance of + 23 mm (eq. + 325 km3). The sum of the mass balance on both ice sheets is equivalent to the annual sea-level rise of 0.2 mm. This experiment shows that other mechanisms for sea-level change, such as the thermal expansion of the sea water and the melt of small mountain glaciers, will remain important in the coming century.

The preferred c-axes orientation (fabric) observed in cold polar ice is induced by intracrystalline slip only when the grain-boundary migration rate is low enough (i.e. corresponding to grain growth or rotation recrystallization regimes). Fabrics reflect the entire thermomechanical history of the ice and strongly influence its mechanical behaviour. Large viscoplastic anisotropy is always associated with pronounced fabrics. We use a viscoplastic self-consistent (VPSC) polycrystal deformation model to calculate fabric development. In this model, stress- and strain-rate fields are not uniform within the polycrystal and both equilibrium and compatibility conditions are fulfilled. We compare fabrics measured on thin sections along the GRIP ice core (central Greenland) with those calculated down to a depth of 2800 m. Behaviours predicted by uniform stress and uniform strain bounds are presented for comparison. Predictions of the VPSC model are in close agreement with measurements within the upper 650 m, which corresponds to the entire grain-growth zone. Deeper clown, the simulated fabric strength appears to be too high. A simple calculation shows that this discrepancy may be fully attributed to the effects of rotation recrystallization.

A new flow law for anisotropic polycrystalline ice is presented. The strain-rate tensor is related by a geometrical factor tensor (G) to the stress tensor. The G factor tensor can be obtained front the c-axis fabric data and stress condition. This new flow law describes well the direction-dependent mechanical properties of anisotropic ice which cannot be demonstrated by Glen’s flow law. For example, the new flow law can explain the fact that a strong single-maximum fabric ice, such as Dye 3 Wisconsin ice, can deform several times faster than isotropic ice under horizontal shear but can hardly deform under vertical or horizontal normal stress. We also show that at a deeper part of an ice sheet, where a single-maximum fabric develops, a positive vertical strain rate can be produced with only a horizontal shear stress.

The first topographic and ice-motion maps of the northwestern flank of Hielo Patagónico Norte (HPN, northern Patagonia Icefield), in Chile, were produced using satellite synthetic-aperture interferometric radar data acquired by NASA’s Spaceborne Imaging Radar C instrument in October 1994. The topographic map has a 10 m vertical precision with a 30 m horizontal spacing, which should be sufficient to serve as a reference for monitoring future mass changes of the icefield. The ice-motion map is accurate to within 4 mm d−1 (or 1 m a−1). The radar-derived surface topography and ice velocity are used to estimate the ice discharge from the accumulation area of four outlet glaciers, and the calving flux and mass balance of Glaciar San Rafael. The results demonstrate the use of SAR interferometry for monitoring glaciological parameters on a spatial and temporal scale unattainable by any other means.

A depth-averaged finite-difference numerical model has been used to make a preliminary study of the tides under the Filchner–Ronne Ice Shelf. Open boundary conditions were specified using the global ocean model of Schwiderski. Tidal constituents for the two principal semi-diurnal constituents M2 and S2, and the two principal diurnal constituents Ο1 and K1 were extracted from computed sea-surface elevations by harmonic analysis. Measured values near to the grounding line could only be reproduced satisfactorily by increasing the bottom friction coefficient under the ice to 50 times the open-ocean value. This destroys any agreement near the ice front or at pelagic sites. It is thought that a friction coefficient which varies with distance under the ice would be able to reproduce better all the available measurements. More tidal measurements are required to validate any model of the region with model experiments being used to help pinpoint possible sites for instrument deployment.

A high-resolution, three-dimensional thermomechanical ice-sheet model, which includes isostasy, the possibility of ice-sheet expansion on the continental shelf and refined climatic parameterizations, was used to investigate the basal thermal regime of the Greenland ice sheet. The thermodynamic calculations take into account the usual terms of heat flow within the ice, a thermally active bedrock layer and all of the effects associated with changes in ice thickness and flow pattern. Basal temperature conditions are documented with respect to glacial–interracial shifts in climatic boundary conditions, both in steady state as during simulations over the last two glacial cycles using the GRIP δ180 record. It is found that the basal temperature field shows a large sensitivity in steady-state experiments but that, during a glacial cycle, basal temperature variations are strongly damped, in particular in central areas. A comparison has been made with measured data from deep ice cores and the implications are discussed.

Recent observations in Shirase Drainage Basin. Enderby Land, Antarctica, show that the ice sheet is thinning at the considerable rate of 0.5–1.0 m a −1. Surface velocities in the stream area reach more than 2000 ma−1, making Shirase Glacier one of the fastest-flowing glaciers in East Antarctica. A numerical investigation of the present stress field in Shirase Glacier shows the existence of a large transition zone 200 km in length where both shearing and stretching are of equal importance, followed by a stream zone of approximately 50 km, where stretching is the major deformation process.

In order to improve insight into the present transient behaviour of the ice-sheet system, a two-dimensional time-dependent flowline model has been developed, taking into account the ice-stream mechanics. Both bedrock adjustment and ice temperature are taken into account and the temperature field is fully coupled to the ice-sheet velocity field.

Experiments were carried out with different basal motion conditions in order to understand their influence on the dynamic behaviour of the ice sheet and the stream area in particular. Results revealed that when basal motion becomes the dominant deformation process, (partial) disintegration of the ice sheet is counteracted by colder basal-ice temperatures due to higher advection rates. This gives rise to a cyclic behaviour in ice-sheets response and large changes in local imbalance values.

Laboratory-prepared fine-grained, initially isotropic polycrystalline ice samples were deformed under conditions of simple shear with simultaneous uniaxial compression at a constant temperature of −2.0°C. The aim was to investigate the effects of stress configuration on the flow rate of initially isotropic ice and on ice with subsequent stress and strain-induced anisotropy. Experiments were carried out for various combinations of shear and compression with shear stress ranging from 0 to 0.49 MPa and compressive stress ranging from 0 to 0.98 MPa, but such that for every experiment the octahedral shear stress was 0.4 MPa.

The strain curves resulting from the experiments clearly exhibit minimum strain rates while the ice is still isotropic, and steady-state tertiary strain rates along with the development of steady-state anisotropic fabric patterns. With constant octahedral stress (root-mean-square of the principal stress deviators), the minimum octahedral shear-strain rate has no dependence on stress configuration. This result supports the hypothesis that the flow of isotropic ice is dependent only on the second invariant of the stress tensor. This fundamental assumption has been used to provide a general description of ice-flow behaviour independent of the stress configuration (e.g. Nye, 1953; Glen, 1958; Budd, 1969).

For the tertiary flow of anisotropic ice, the octahedral strain rate is stress-state dependent as a consequence of the developed crystal-orientation fabric, which is also stress-state dependent, and which develops with strain and rotation. The present tests indicate that the enhancement factor for steady-state tertiary octahedral shear-strain rate depends on the shear or compression fraction and varies from about 10 for simple shear (with zero compression) to about 3 for uniaxial compression (with zero shear).

During the deformation of polar ice, a fabric develops which results in a macroscopically anisotropic behaviour. Since the plastic anisotropy of the ice single crystal is very high, the effect of a strong (single maximum) fabric on the macroscopic flow law cannot be neglected when simulating the flow of an ice sheet. As this is already a difficult task when using the familiar isotropic power law for ice, the fabric evolution and related macroscopic mechanical behaviour model, to be implemented in such a simulation, must be realistic yet simple enough to achieve results within a reasonable level of complexity, at least as a first step.

To this aim, we propose to model polar ice as a transversely isotropic medium; while simplifying the problem, this captures the essential features of the in-situ observed fabrics. The macroscopic mechanical behaviour of the ice polycrystal is obtained by using an orientation distribution function (ODF) for the c axes of the grains, which characterizes the fabric, and a self-consistent scheme, considering each single crystal as transversely isotropic. The evolution of the ODF is described by a conservation equation. In the first stage, this model was run in the simple cases of uniaxial compression and tension along the orthotropy symmetry axis.

This paper presents a formulation of a continuum model for so-called (stress or deformation) induced anisotropy in natural ice which, unlike computer-based Taylor-type models, can be incorporated in numerical simulations of large ice masses to account for the effects of this process on the flow of these bodies in a physical fashion. To do this, we treat natural ice as a rigid-elastic, non-linear inelastic material which can develop transverse isotropic behaviour (accounting for the simplest kind of induced anisotropy in natural ice masses), where the degree of such anisotropy at each point is controlled by the distribution of crystal glide-plane orientations there. This distribution is described by a so-called orientation-distribution function, for which an evolution relation can be derived. The central constitutive assumption of this formulation relates this distribution to the “structure” tensor representing the transverse isotropy of the material. On the basis of this relation, the model predicts in particular isotropic (e.g. classical Glen’s flow-law type) behaviour at a given point when the distribution of crystal glide-plane orientations is uniform there.

An understanding of the mechanical behaviour of the basal zone of an ice mass is fundamental to understanding the overall dynamics of that ice mass. Despite the fact that debris-laden ice is found in the basal zones of many glaciers and ice sheets, its mechanical behaviour is only poorly understood. This paper attempts to expand our knowledge of the mechanical behaviour of debris-laden ice by examining the uniaxial compressive strength of debris-laden basal ice sampled from the snout of the Taylor Glacier, Antarctica.

The mechanical behaviour of debris-laden ice (debris content 5–20% by volume) under uniaxial compression, and the relationship between the behaviours of debris-laden basal ice and ‘clean’ glacier ice, is complex and variable. At the relatively warm temperatures at which uniaxial compressive strength tests were conducted in the field, debris-laden ice was generally weaker than clean glacier ice. At these temperatures, between 0° and −5°C, pressure melting was the dominant deformation mechanism in the debris-laden ice and cracking the dominant deformation mechanism in clean ice. At −25°C, however, debris-laden ice reached higher strengths than lite clean glacier ice and cracking was the dominant deformation mechanism in both ice types. The change in relationship between the strengths of debris-laden and clean ice with temperature is inferred to be attributable to the temperature dependence of the rate of pressure melting.

These results suggest that the dynamic effects and significance of the presence of a debris-laden ice layer in the basal zone of an ice mass are likely to be highly variable in space and time.

For the first time high-quality coverage of the ERS-1 radar altimeter provides a very accurate surface topographic map covering 80% of the Antarctic ice sheet that can contribute significantly to glaciological studies such as ice-sheet flow modelling. The topography allows estimation of the ice-flow direction, the balance velocity and the basal shear stress. A relationship between shear stress, basal temperature and a parameter related to strain rate helps in mapping the behaviour anomalies of these parameters. Longitudinal stress, sliding, bedrock topography and variation in the pre-exponential factor of the flow law are found to play a major role in the ice-flow pattern. This relation can also be used to estimate rheological parameters: the Glen exponent n is found to be 1 for T < −10°C and 3–4 for higher temperatures, where Q is found to be 70 kJ mol−1.

An experimental study of the fracture mechanics and rheology of ice from the Ronne Ice Shelf, Antarctica, is currently being undertaken. The apparent critical stress-intensity factor (or apparent fracture toughness, KQ) for crack propagation has been measured using a three-point bend method for inducing crack growth perpendicular to the axis of cylindrical ice-core specimens. Tensile crack nucleation under applied uniaxial compressive stress has also been evaluated. Both methods have allowed a profile of ice elastic and fracture properties with depth through the ice shelf to be constructed. Preliminary results indicate that the measured elastic modulus increases with depth through the firn and upper meteoric ice before reaching a constant value in the deeper, dense meteoric and basal marine ice. The resistance to fracture, as measured by changes in apparent fracture toughness and crack-nucleation stress, increases with depth right through the firn and meteoric ice layers. A simple fracture mechanics model applied to the Ronne Ice Shelf indicates that crevasses form from small surface cracks, less than 40 cm deep, which quickly grow to depths of 40–60m and then remain stable.

Microstructural changes in three sets of experiments involving crystallographic slip in anisotropic polycrystalline ice are described and interpreted with the aid of computer models. The development of microstructure was followed using time-lapse photography and transmitted light observations with deformation undertaken in plane strain and at a temperature of approximately –1°C. The deformation within a grain aggregate that accompanies axial shortening is always heterogeneous on a grainscale. The extent of inhomogeneity varies depending on the pre-existing grain structure and the way it can accommodate intragranular slip. Grain interactions are extremely important in determining the bulk deformation and the degree of grain-boundary migration. A consequence of shortening of the aggregate is the formation of high stresses between neighbouring grains and under the appropriate conditions there may be either grain-boundary migration or melting at these sites. Where a sample undergoes translation and shear during deformation, anisotropic grains in the appropriate orientation undergo bending. A buckle instability may then develop and much of the strain is accommodated by grains in easy-glide orientations. In such situations, the ice undergoes extensive recrystallization and grain growth that is concentrated in the areas of greatest buckling.

Modelling studies of the tectonic evolution of the Transantarctic Mountains in Antarctica have drawn differing conclusions as to the primary mechanisms involved. None has considered the role of the East Antarctic ice sheet in detail. We use a denudation—flexural model to examine the isostatic response of the continental margin to glacial erosion to determine whether glacial processes have played a role in forcing mountain uplift.

The conclusion is that, although there are insufficient data formally to delimit the role of glacial erosion, available geophysical and geomorphological data are not inconsistent with the results of the differential denudation model, providing certain conditions are met. These results indicate that the current topography of the Transantarctic Mountains can be simulated, in part, from the isostatic response of the lithosphere to glacial erosion. The short wavelength and high amplitude of the Transantarctic Mountains do not require a low flexural rigidity in the unrated lithosphere, provided there is a fast escarpment retreat from the rift hinge, high escarpment denudation rates and a large differential in denudation between the coastal zone and the interior.

The bedrock isostatic response exerts a strong control on ice-sheet dynamics and is therefore always taken into account in ice-sheet models. This paper reviews the various methods normally used in the ice-sheet modelling community to deal with the bedrock response and compares these with a more sophisticated full-Earth model. Each of these bedrock treatments, five in total, is coupled with a three-dimensional thermomechanical ice-sheet model under the same forcing conditions to simulate the Antarctic ice sheet during the last glacial cycle. The outputs of the simulations are compared on the basis of the time-dependent behaviour for the total ice volume and the mean bedrock elevation during the cycle and of the present rate of uplift over Antarctica. This comparison confirms the necessity of accounting for the elastic bending of the lithosphere in order to yield realistic bedrock patterns. It furthermore demonstrates the deficiencies inherent to the diffusion equation in modelling the complex deformation within the mantle. Nevertheless, when characteristic parameters are varied within their range of uncertainty, differences within one single method are often of the same order as those between the various methods. This overview finally attempts to point out the main advantages and drawbacks of each of these methods and to determine which one is most appropriate depending on the specific modelling requirements.