Accounting for isostasy in glaciological models has always been a necessity but these models mostly use very simple parameterizations (Le Meur and Huybrechts, 1996). The need for more realistic isostatic parameterizations rapidly became apparent, especially in the treatment of bedrock-sensitive issues such as the grounding-line migration (Huybrechts, 1990a, b). To this end, a rather sophisticated Earth model, avoiding most of the common assumptions, has been developed and is presented here. The two key groups of parameters, to which the model is most sensitive, are the Earth properties and the rheological law used for the mantle. The aim of this paper is first to justify the use of Maxwell rheology for the mantle and then to tune the most sensitive Earth parameter, namely the mantle viscosity, in order to match the numerous present-day uplift data over Fennoscandia. So, in the first instance, a short review of the different available rheologies is presented and discussed. The visco-elastic theory, as well as the mathematical background used in the present model, is also briefly sketched. Secondly, a glacial scenario over Fennoscandia served as an input for the model in a calibration test on the mantle-viscosity values. The degree of agreement of the model outputs with the present-day measurements gives a reference set of Green functions, to which one can reasonably refer when modelling the isostatic response over areas where such a control is not possible (Le Meur and Huybrechts, 1996). Finally, a closer look to the time-dependent surface displacements will confirm the ability for the model to reproduce correctly the main postglacial rebound characteristic features.

A crucial element of several leading theories of Laurentide ice-sheet instability (i.e. Heinrich events and advance/retreat cycles of the southern margin) is the evolution of melting conditions at the subglacial bed. Despite the great importance basal-temperature conditions play in these theories, relatively little has been done to test their physical plausibility. We therefore undertake a numerical model study of the ice-sheet temperature field along an important transect which extends from the lobate southern margin of the Laurentide ice sheet to the iceberg-calving from at the terminus of Hudson Strait. Our experiments illustrate the influence of important aspects of ice-sheet thermodynamics on ice-sheet instability, including horizontal advection and the development of an internal temperate-ice reservoir. Free oscillations of the basal temperature and ice thickness in Hudson Strait are possible under a restricted range of parameters elucidated by the model. These free oscillations may provide a basis for understanding ice-sheet instability, e.g. Heinrich events, with time-scales in the range of 103–104 a.

A continuum mixture model of coupled ice-sheet/ice-stream dynamics has been developed within a conventional three-dimensional finite-difference model framework. The ice mass is areally divided into sheet-ice and stream-ice components. Dynamic evolution of each component is solved with coupling terms to describe mass exchange between flows. In this way, ice-stream fluxes can be incorporated in a rigorous dynamical model with only a doubling of computational cost. This paper presents simple model tests using the EISMINT experimental ice block, a 1500 km × 1500 km ice sheet which rests on a flat bed. Ice-stream behaviour is investigated for a range of coupling rules and activation scenarios. In simple tests presented here, we find that the viscous response time of source ice feeding the ice stream may be a factor limiting ice-stream vigour and longevity.

A dynamical model governing the variations of ice-sheet volume, basal-water amount and ice-surge flux has been formulated in its simplest form, based on fundamental thermomechanical properties of ice sheets governing the basal-melting process. This model includes the effects of the geothermal flux, internal thermal advection and basal friction, the latter two factors being particularly important in regulating the bottom temperature and bringing it to the melting point, i.e. to a state vulnerable to catastrophic ice surges. It is shown that, for certain values of the unknown rate constants, such a model can exhibit oscillations on roughly the same scale as observed Heinrich events, even when external climatic changes are neglected, which would support the view that such events are an internal properly of ice sheets.

Results from a recent time-dependent ice-sheet modelling study of the late Weichselian Svalbard—Barents Sea ice sheet suggest that, under environmental conditions representative of those during the late Weichselian, ice derived solely from Svalbard may have occupied only the relatively shallow (<300 m water depth) northwestern Barents Sea, with other deeper regions remaining free of grounded ice (Siegert and Dowdeswell, 1995a). However, late Weichselian geological information from the 400 m deep Bjørnøyrenna (southern Barents Sea) indicates that grounded ice was present in an area modelled by Siegert and Dowdeswell (1995a) as free of ice (e.g. Laberg and Vorren, in press a). Isostatic uplift of the central Barents Sea may have reduced the relative sea level and hence provided a mechanism by which grounded ice could have migrated from relatively shallow regions of the Barents Sea into, previous to uplift, deeper water. We have used an isostatic Earth model to determine the geometry of an isostatic forebulge within the late Weichselian Barents Sea, caused by ice loads over Svalbard, Franz Josef Land, Novaya Zemlya and Fennoscandia. These data were then used as input to a time-dependent glaciological model, in order to predict further information about the magnitude of bedrock uplift required to allow grounded ice to flow from Svalbard into the central and southern Barents Sea. Our experiments suggest that grounded ice, originating from Svalbard, is able to form over Sentralbanken, providing that at least 60 m of uplift is achieved in the central Barents Sea. Grounded ice within Bjørnøyrenna was only predicted when the amplitude of the local forebulge exceeded 250 m.

Calculations have been conducted for the geometric evolution of the Greenland ice sheet through the last 250 000 years of its climate history. An extended version of Calov’s three-dimensional ice-sheet model is used, i.e. ice is modelled as a viscous thermomechanically coupled fluid with power-law rheology underlain by a heat-conducting lithosphere susceptible to bedrock sinking. The shallow-ice approximation is imposed and the simplified equations are numerically integrated by finite-difference approximation using a centred staggered Arakawa grid. This system is driven by data obtained from the European Greenland Ice Core Project (GRIP). The parameterization of the atmospheric temperature is based on data from Ohmura, precipitation data are taken from Ohmura and Reeh and implemented as shown by Calov. Topographic data for the present observed conditions are those of Letréguilly. The resultant 250 kyear model integrated topography is quite close to that obtained from a steady-state calculation under present conditions. For the calculations presented, Greenland’s north dome seems to be more sensitive to changes in precipitation than its south dome. While the height of the north dome is directly related to the atmospheric temperature, the height of the south dome is inversely related to this variable. In the south, changes in ice dynamics due to a change in ice temperature oppose changes in precipitation. The calculations are visualized in a short video clip that is kept on file with the authors.

This paper presents improved geometric boundary conditions (surface elevation and ice thickness) required as inputs to calculations of the surface-velocity field for the Antarctic ice sheet. A comparison of the two-dimensional horizontal velocity field obtained on the basis of conservation of mass (balance velocity) with the diagnostic velocity field calculated with an ice-sheet model (dynamic velocity) may yield information on shortcomings in the way the ice-sheet model describes the ice flow. Here, the surface-elevation grid is described in detail, as it has been generated specifically for such a study and represents a new standard in accuracy and resolution for calculating surface slopes. The digital-elevation model was generated on a 10 km grid size from over 20 000 000 height estimates obtained from eight 35 d repeat cycles of ERS-1 radar-altimeter data. For surface slopes less than 0.4°, the accuracy is better than 1.5 m. In areas of high surface slope (coastal and mountainous regions), the altimeter measurements have been supplemented with data taken from the Antarctic Digital Database. South of 81.5°, data from the SPRI folio map have been used. The ice-thickness grid was produced from a combination of a redigitization of the SPRI folio and the original radio-echo-sounding flight lines. For areas of grounded ice, the elevation of the bed was estimated from surface elevation and ice thickness. Significant differences (in excess of 25% of ice thickness) were obtained between an earlier digitization of the folio bed-elevation map and the data set derived here. Furthermore, a new value of 25.6 × 106 km3 was obtained for the total volume of the ice sheet and ice shelves, which is a reduction of 12% compared with the original estimate derived during the compilation of the SPRI folio. These differences will have an important influence on the results obtained by numerical ice-sheet models.

The ERS-1 satellite has delivered altimetric data since 1992, enabling us to map most of the Antarctic ice-sheet topography south to 82° S with better precision than all previous techniques. An algorithm has been developed such that the accuracy of the height data reaches the sub-metre level. As a first step, an inverse method has been designed to map the large-scale global topography, which is of interest to the study of the ice-sheet flow dynamics. As a second step, an adapted inverse algorithm displays precisely the short-scale undulations which are controlled by the bedrock below the ice. Finally, variations in the back-scattered altimetric signal allow us to map directly the kilometre-scale roughness that is related to the basal-flow conditions. Together, these maps constitute an important data base for modelling the ice sheet.

An approach to simulate the present Antarctic ice sheet with reaped to its thermomechanical behaviour and the resulting features is made with the three-dimensional polythermal ice-sheet model designed by Greve and Hutter. It treats zones of cold and temperate ice as different materials with their own properties and dynamics. This is important because an underlying layer of temperate ice can influence the ice sheet as a whole, e.g. the cold ice may slide upon the less viscous binary ice water mixture.

Measurements indicate that the geothermal heat flux below the Antarctic ice sheet appears to be remarkably higher than the standard value of 42 m W m−2 that is usually applied for Precambrian shields in ice-sheet modelling. Since the extent of temperate ice at the base is highly dependent on this heat input from the lithosphere, an adequate choice is crucial for realistic simulations. We shall present a series of steady-state results with varied geothermal heat flux and demonstrate that the real ice-sheet topography can be reproduced fairly well with a value in the range 50–60 m W m−2. Thus, the physical parameters of ice (especially the enhancement factor in Glen’s flow law) as used by Greve (1995) for polythermal Greenland ice-sheet simulations can be adopted without any change. The remaining disagreements may he explained by the neglected influence of the ice shelves, the rather coarse horizontal resolution (100 km), the steady-state assumption and possible shortcomings in the parameterization of the surface mass balance.

Ice-movement surveys in the Framnes Mountains from austral summers 1993–94 and 1994–95 are presented with complementary surface elevations and structural interpretations. Surface velocities of 21 m a−1 have been recorded in Ice Stream B and 31 ma−1 in Ice Stream C. The flow rate varied between 11.6 and 21.0 m a−1 over a lateral range of 2.1 km west of Rumdoodle Peak and between 17.1 and 31.5 m a−1 over 2 km west of Mount Parsons. Two ice streams of relative high flow between the central Masson and David Ranges and several zones of incremental increase in flow rate have been identified within Ice Stream B, using shear-sense criteria based as ice-fracture geometry and subsequent deformation of crevasse traces. These zones of localized strain correlate with ice-flow survey measurements.

A finite-element model was implemented that relates the computed flow to some field and fabric observations recorded on the Law Dome ice cap, East Antarctica. The results of the model suggest that the general ice flow is markedly affected by the bedrock topography. The zones of measured anomalous flow correlate with significant changes in the modelled stress within the ice mass. Stress increases of up to 50% above the reduced model shear stress were obtained in the models where the ice moved over a bedrock rise. Stress relaxation also occurs in the ice mass as the ice moves downward to a lee depression. There is a marked oscillation in the direction of principal stress and this is responsible for the progressive development of a set of high stress zones that are superimposed on the down-slope ice movement.