The EISMINT II experiments revealed the tendency for idealized model ice sheets to produce spatially variable flow under certain uniform thermal, mass-balance and topographic boundary conditions. Warm, fast-flowing streams with enhanced creep were separated by zones of colder, slower flow. Similar but different spatial patterns of differentiated flow were produced by all authors. We present further experiments that explore the formation and function of such ice streams at higher modelled resolutions. These are explored by the use of flat, but stochastically rough (10 m amplitude) beds, idealized, parallel-sided model ice sheets and models of finer (12.5 and 5 km) resolutions. Ice streams self-organize irregularly, but with consistent typical spacings which vary with thermal and miss-balance boundary conditions. More radial features are produced at finer scales indicating a dependency on the grid resolution used although this is not linear; at finer resolutions streams occupy increasingly more gridcells. This variation in scale may be related to the finer resolution of the warm/cold streaming/non-streaming boundary. The numerical solution of the thermodynamic ice equation is also highly sensitive to the orthogonality of the model grid. A major deficiency is that the numerical solution appears to fail where the flow is parallel to the grid axes, suggesting that artificial diffusion in the numerical scheme helps to smooth streams lying across the axes directions. The inclusion of sliding produces fewer, more concentrated, flow features, but these also display a level of scale-dependent organization. The spatial arrangement of such streams adjusts in response to the global mass flux of the ice sheet between "warm" and "cold" flow end-member. The results point to a mechanism in which ice sheets respond to climate by altering the large-scale arrangement of their flow patterns.

Many glacier beds are anisotropic, by which is meant that the dominant wavelengths are different in the two map-plane directions. A largely unexplored consequence of Nye-Kamb sliding theory is the fact that an anisotropic bed can produce a sliding velocity not parallel to the tangential traction vector. This has important consequences, since observations of non-parallel flow are often taken as indications that the shallow-ice approximation has broken down, whereas this need not be the case with an anisotropic bed.

Mathematically, this effect can be incorporated through the use of a sliding tensor. The mathematical properties of this tensor are outlined, and the correct "invariant" for the sliding law, a quadratic form, is deduced. Nye-Kamb theory for anisotropic beds is discussed. Flow on the infinite plane and the properties of surface-topography diffusion are elucidated. The properties of kinematic waves and shock waves are discussed. Kinematic waves can have a lateral component. Numerical computations of ice-sheet flow on beds with anisotropic roughness are presented, with emphasis placed on how this affects divide-ridge structure It is suggested that cold-based ice sheets, which have an anisotropic bed affecting the shear layer, may also show non-parallelism of surface slope and velocity.

Classical theories of channelized subglacial drainage identify a melting vs creep balance at the channel-ice boundary that is crucial in determining its steady flow properties, but this consideration neglects the role of erodible-deformable basal sediments, especially in controlling channel morphology. Here we present a mathematical model for channel/underneath ice sheets, which incorporates the detailed mechanics of sediment transport over a mobile till-bed interface, and which allows a variable, wide channel cross section also. The resulting drainage conditions depend on the sediment flux (q) as well as the water flux (Q) through the channel - these quantities being controlled by the rates at which sediment and meltwater are captured by the flow. An approximate analytical solution indicates a "canal"-type drainage law (Walder and Fowler, 1994) of the form where N2 is thε effective channel pτessUτe, n is the exponent in Glen’s flow law for ice, and Ψ is the imposed hydraulic gradient (due to topography). By solving the downstream problem numerically, the canal characteristic has been confirmed and found to be insensitive to upstream conditions. Thus, low effective pressures can result from high basal water flux or melt rates. This supports the contention that canals may be a central component in fast ice flow over soft beds The proposed model also establishes a fundamental link between the plumbing system of a glacier and its sediment budget.

Two-dimensional steady isothermal flow of a marine ice stream is studied. Gases of different relations between shear stress and longitudinal deviatoric stress in the ice stream are considered. Analysis of the ice-stream-ice-shelf transition zone shows that even if the longitudinal stress deviator in the ice stream is much larger than the shear stress (as it is in the ice shelf), the ice-stream-ice-shelf transition zone if singular and the full system of Stokes equations must be solved in it. Scales of fields in the transition zone and the relation between the ice thickness and the horizontal mass flux at the grounding line are found.

State-of-the-art thermomechanical models of the modern Greenland ice sheet and the ancient Laurentide ice sheet that covered Canada at the Last Glacial Maximum (LGM) are not able to explain simultaneously the observed forms of these cryospheric structures when the same, anisotropy-enhanced, version of the conventional Glen flow law is employed to describe their rheology. The LGM Laurentide ice sheet, predicted to develop in response to orbital climate forcing, is such that the ratio of its thickness to its horizontal extent is extremely large compared to the aspect ratio inferred on the basis of surface-geomorphological and solid-earth-geophysical constraints. We show that if the Glen flow law representation of the rheology is replaced with a new rheology based upon very high quality laboratory measurements of the stress-strain-rate relation then the aspect ratios of both the modern Greenland ice sheet and the Laurentide ice sheet, that existed at the LGM, are simultaneously explained with little or no retuning of the flow law.

The problem of recovering the small aspect ratio of the ICE-4G reconstruction of the Last Glacial Maximum Laurentide ice sheet has proven to be a challenge for state-of-the-art thermomechanically-coupled three-dimensional ice-sheet models coupled to reduced climate models. Flow enhancements to Glen’s flow law, 20 to 30 times those required to adequately simulate the present-day Greenland ice sheet, have been found necessary in order to reproduce both the thickness and areal extent of the geophysical reconstruction. Within the confines of the Glen flow rheology, it is unclear what mechanism might explain the magnitude of this discrepancy in required flow enhancement for the Laurentide relative to the Greenland ice sheet We present a comparative analysis of three alternative explanations of such a questionable flow-law enhancement: radical changes to mass balance; radical changes to ice-sheet history; and strongly enhanced basal flows Based on this analysis, we argue that none of these alternatives provide a fully acceptable explanation for the small ICE-4G LGM aspect ratio of the Laurentide ice sheet, that has been inferred geophysically.

Numerical experiments, where a simple ice-sheet model was coupled with sediment-deformation models, were performed to investigate the transport of glacigenic material to the western Barents Shelf during the Late Weichselian. The ice-sheet model, and its environmental inputs, has been matched previously with a series of geological datasets relating to the maximum extent of the ice sheet (Howell and others, http://www.ggg.qub.ac.uk [rp05/1999]). Additional geological data on the volumes of sediment delivered to the Bear Island fan (Barents continental margin) are available for comparison. The experiments indicate the sensitivity of sediment transport and deposition to variations in (a) the ice-stream model and (b) a variety of model parameters. Two ice-stream models were used: (1) a height-above-buoyancy model, in which basal velocity is controlled by basal driving stress and a buoyancy-induced reduction in the normal load beneath a marine-based ice sheet; and (2) a modified version of the method presented by Alley (1990) in which basal velocity is related to pore-water pressure, sediment thickness, and driving basal stress. The results of the two different models were then compared. An extensive set of sensitivity tests was carried out to determine sediment-transport response to changes in the model’s parameters. Results indicate that, using physically realistic parameters for deforming subglacial sediment, both models reproduce the volume of Late Weichselian sediment measured on the Bear Island fan. Results from both models are sensitive to (1) cohesion of the sediment and (2) the thickness of deforming sediment beneath the ice sheet. The two models exhibited different degrees of sensitivity to the sediment parameters, with the height-above-buoyancy model proving to be less sensitive to variations in the thickness of the deforming sediment layer than the model proposed by Alley (1990). The differences between the two models examined here highlight the need for a comprehensive comparison of all the methodologies for calculating basal-ice motion currently in use.

For projecting future sea level, the mass-balance changes on Greenland and Antarctica are considered to be crucial. Promising tools for such estimates are general circulation models (GCM). Until recently, a major impediment was their coarse grid resolution (3°-6°) causing substantial uncertainties in the mass-balance calculations of the poorly resolved ice sheets. The present study is based on a new climate-change experiment of the highest resolution currently feasible (1.1 °) performed with the ECHAM4 T106 GCM, thereby increasing confidence in the projected mass-balance and sea-level changes. This new experiment, with doubled CO2 concentration, suggests that the mass gain in Antarctica due to increased accumulation exceeds the melt-induced mass loss in Greenland by a factor of three. The resulting mass-balance change on both ice sheets is equivalent to a net sea-level decrease of 0.6 mm a"1 under doubled CO2 conditions. This may compensate for a significant portion of the melt-induced sea-level rise from the smaller glaciers and ice caps, thus leaving thermal expansion as the dominant factor for sea-level rise over the next decades. This compensating effect, however, no longer applies should atmospheric CO2 concentration reach levels well above "doubled the present value". On the contrary, under these conditions, the greenhouse warming would become large enough to induce substantial melting also on the Antarctic ice sheet, thereby significantly accelerating global sea-level rise.

A series of ice-sheet-model intercomparison exercises have been organized as part of EISMINT. One such set of experiments investigated the implications of thermomechanical coupling on the flow of ice sheets with idealized geometry The results of these experiments are discussed by Payne and others (in press). They indicate that local concentrations of ice flow may develop as a consequence of interactions between ice flow, temperature and viscosity The nature of the intercomparison exercise meant that only a limited number of experiments could be performed by the ten contributing groups. Many of the implications arising from the results could not therefore be investigated. This paper focuses on four. They are the initiation of the patterning, its reversibility the influence of the relationship between ice temperature and viscosity and dependence on numerical time-step and horizontal grid size.

Balance velocities for the Greenland ice sheet have been calculated from a new digital-elevation model, accumulation-rates compilation and an existing ice-thickness grid, using a two-dimensional finite-difference scheme. The pattern of velocities over the ice sheet is presented and compared with velocities derived from synthetic-aperture-radar interferometry for part of northern Greenland and a limited number of global positioning system data. This comparison indicated that the balance-velocity scheme and boundary conditions used here provide a remarkably good representation of the dynamics of the ice sheet inland from the margins. It is suggested, therefore, that these balance-velocity data could provide a valuable method of constraining a numerical ice-sheet model. The balance velocities were compared with the diagnostic velocity field calculated from several different configurations of a numerical ice-sheet model. The general pattern of flow agrees well. The detail, however, is quite different. For example, the large (>300km) ice stream in the northeast is not generated by the numerical model and much of the detailed flow pattern is completely lost due to the limited model resolution and limitations in the model physics.

A model for the anisotropic behaviour of polar ice and the evolution of its strain-induced anisotropy is applied to the flowline between GRIP and GISP2. The linear constitutive law for polycrystalline ice is derived from the uniform-stress model under the assumptions of a linear transversely isotropic behaviour of the ice single crystal and of an orthotropic fabric described by a continuous parameterized orientation-distribution function (ODF). The velocities and fabrics obtained for the observed flowline and bedrock geometry assuming stationary flow, are compared to those measured at the ice-sheet surface and down the two boreholes.

Synthetic-aperture-radar (SAR) data are useful for the study of polar regions because of their independence of cloud cover and daylight, but their analysis is complicated by a lack of absolute reference in size and grey value. The geostatistical surface-classification approach provides a solution to this problem. Parameters extracted from variograms constitute a feature vector, which is characteristic of a surface morphological province. The goal is the classification of larger areas using the result of a characterization of prototype areas that are homogeneous with respect to ice-surface morphological types. This requires a feasibility study and comparison with ground-truth data. Both issues are investigated in this paper. Examples of 1995 ERS-1 and 1997 ERS-2 SAR data from Jakobshavn Isbræ serve to demonstrate that different ice-surface types can be distinguished automatically with geostatistical surface characterization. Ice-surface microtopography/roughness data collected during expedition MICROTOP 97 to the Jakobshavn Isbræ drainage basin provide the ground-truth data required to investigate whether areas that appear homogeneous on a SAR image are in fact homogeneous in ice-surface morphological properties An analysis of contemporaneous ERS-2 SAR data using geostatistical surface characterization is presented.

In most glaciological and hydrological models, surface roughness of snow and ice is an important parameter. However, roughness is generally used only as an estimated parameter for lack of available observations. In this paper, we present a method to collect and analyze ice-surface-roughness data using a specially designed instrument for survey and geostatistical methods for analysis. The glacier-roughness sensor (GRS), built at the University of Trier, records variations in microtopography at 0.2 m × 0.1 m resolution when pulled across an ice surface. Global positioning system data are used for location. After several processing steps, the data are analyzed using geostatistical methods. The mathematical tool used to achieve a morphological characterization of ice-surface types is the variogram. GRS data, variograms and surface roughness analysis are ideal matches for morphological characterization, because none of them requires or provides absolute elevation values. Morphology is described not by absolute elevation values, but by the change of elevation in space which is the derivative of elevation (surface-roughness values). The variogram is calculated from incremental values. Parameters extracted from variograms of GRS data serve to distinguish lake surfaces, wind structures, ridge-and- vaUey systems, melting structures and blue-ice areas. Examples are from Jakobshavn Isbræ drainage basin, West Greenland.

Crevasse patterns revealing mostly brittle deformation on glacier surfaces are analyzed based on video images collected during systematic overflights of Jakobshavn Isbræ, West Greenland, the Earths continuously fastest moving ice stream, in 1996 and 1997. Crevasse patterns on the surface of the central ice stream are distinct. All crevasses are closed, the surface appears rather smooth. Towards the margins, typical shear patterns with conjugate shears and still-closed crevasses prevail, curved patterns indicate the bending of crevasse lines into the flow direction. Outward from this zone different patterns of open crevasses occur. This suite of patterns is compared to similar data collected over Bering Glacier, Alaska, U.S.A., during its recent surge from 1993–95. There a number of patterns of mostly open crevasses is characteristic: parallel crevasses, two-directional orthogonal open crevasses, arrays of wavy crevasses, en-echelon crevasses. These patterns of the surging glacier are completely different from those of the fast-moving ice stream indicating different underlying kinematics and dynamics.