I. M. Whillans

Force budget: I. Theory and numerical methods

A practical method is developed for calculating stresses and velocities at depth using field measurements of the geometry and surface velocity of glaciers. To do this, it is convenient to partition full stresses into lithostatic and resistive components. The horizontal gradient in vertically integrated lithostatic stress is the driving stress and it describes the horizontal action of gravity. The horizontal resistive stress gradients describe the reactions. Resistive stresses are simply related to deviatoric stresses and hence to strain-rates through a constitutive relation. A numerical scheme can be used to calculate stresses and velocities from surface velocities and slope, and from ice thickness. There is no mathematical requirement that the variations in these quantities be small.

Changes in the West Antarctic Ice Sheet

The portion of the West Antarctic ice sheet that flows into the Ross Sea is thinning in some places and thickening in others. These changes are not caused by any current climatic change, but by the combination of a delayed response to the end of the last global glacial cycle and an internal instability. The near-future impact of the ice sheet on global sea level is largely due to processes internal to the movement of the ice sheet, and not so much to the threat of a possible greenhouse warming. Thus the near-term future of the ice sheet is already determined. However, too little of the ice sheet has been surveyed to predict its overall future behavior.

Development of fabric in ice

Abstract A numerical model for the deformation and rotation of crystals in a polycrystalline ice mass produces crystal-orientation fabrics like those observed in glaciers. Major features of the model are that the stress on each crystal equals the bulk stress and that each crystal deforms by pure shear in a reference frame that rotates with the poly-crystalline aggregate. The single-maximum fabric in ice deforming under simple shear is correctly simulated if it is assumed that recrystallizing crystals are seeded by crystals that are already present in one of the optimum directions, rather than forming entirely new crystals. The strain rate of the aggregate reaches a minimum at about 10% bulk strain, later than observed in the laboratory, probably because effects dominating the initial stages of deformation in laboratory experiments are not included in the model. The various crystal-orientation fabrics exhibit enhancement factors that agree with those measured in the laboratory.

The role of lateral drag in the dynamics of Ice Stream B, Antarctica

The partitioning of resistive force between the bed and sides of Ice Stream B, Antarctica, is obtained for three large areas that have been measured using repeat aerial photogrammetry. Problems associated with data errors and local variations in ice strength and velocity are reduced by considering the areally averaged budget of forces for each photo block. Results indicate that the bed under Ice Stream B must be very weak and unable to provide muche resistance. Mechanical control on this ice stream emanates almost entirely from the lateral margins.

Catch a Falling Star: Meteorites and Old Ice

A model for the process of meteorite concentration in blue ice regions of the Antarctic ice sheet is proposed based on data from near the Allan Hills and the assumptions that both meteorite influx and glacial flow have been constant. The meteorite influx is calculated to be 60 x 10-6 kilogram per square kilometer per year, and the age of the exposed ice to be 0 to 600,000 years, varying with distance from the Allan Hills. These results are in line with other estimates of influx rate and with measurements of the terrestrial ages of the meteorites, providing support for the assumption of steady flow and meteorite influx. This may be the oldest sequence of ice in stratigraphic order yet discovered, and the results imply that this part of the east Antarctic ice sheet has been approximately steady during this time interval.

New and improved determinations of velocity of ice streams B and C, West Antarctica

Measurements of velocity have been made on and next to Ice Streams B and C, West Antarctica. The results are more precise than previous work and constitute a 93% increase in the number of values. These velocities are used to describe the confluence of flow into the ice streams and the development of fast ice- stream flow. The onset of fast-streaming flow occurs in many separate tributaries that coalesce down-glacier into the major ice streams. For those inter-stream ridges that have been studied, the flow is consistent with steady state. Along Ice Stream B, gradients in longitudinal stress offer little resistance to the ice flow. The transition from basal-drag control to ice-shelf flow is achieved through reduced drag at the glacier base and increased resistance associated with lateral drag. Velocities in the trunk of Ice Stream C are nearly zero but those at the up-glacial head are similar to those at the head of Ice Stream B.

Model experiments on the evolution and stability of ice streams

This is the publishers version, also available electronically from http://www.igsoc.org/annals/23/.

Polar Firn Densification and Grain Growth

A 50 m firn core from Dome C, East Antarctica, was found to consist of coarse firn, which comprised 90 to 95% of the core, and fine firn. Coarse firn was characterized by large crystals with a vertical shape orientation near the surface, connected to nearest neighbors by relatively large necks in a structure different from closest packing. Fine firn was of higher density and consisted of smaller, more spherical crystals connected by relatively narrow necks in a more nearly closest-packed configuration. Higher surface free energy in fine firn causes crystals and necks to grow more rapidly than in coarse firn. However, we find that coarse firn densifies more rapidly with time, contrary to the predictions of unconfined sintering models. Load-driven densification due to a power-law creep mechanism is found to account for the larger coarse-firn densification rate. However, if the exponent in the power law exceeds one, then densification rates are predicted to increase with depth due to increasing load, contrary to observed behavior. We speculate that different mechanisms may control the densification process in fine and coarse firn.

Erosion of Sognefjord, Norway

Sognefjord is formed by a combination of exploitation of rock structure and subaerial and subglacial processes. The fjord system follows zones of rock-structural weakness. Above sea level the landforms are due mainly to subaerial processes, and somewhat surprisingly not to glacial activity. Removal of erosive products and deepening of the fjord below sea level is due to glacial erosion.

Force budget: III, Application to three-dimensional flow of Byrd Glacier, Antarctica

Stresses at the surface and at depth are calculated for a stretch of Byrd Glacier, Antarctica. The calculations are based on photogrammetrically determined velocities and elevations, and on radio-echo-determined ice thicknesses. The results are maps of drags from each valley wall, of normal forces laterally and longitudinally. and of basal drag. Special challenges in the calculation are the numerical gridding of velocity, ensuring that unreasonable short-wavelength features do not develop in the calculation, and inference of ice thickness where there are no data. The results show important variations in basal drag. For the floating part, basal drag is near zero, as expected. Within the grounded part. longitudinal components of basal drag are very variable, reaching 300 kPa with a dominant wavelength of 13 km. Generally. these drag maxima correlate with maxima in driving stress. Usually the across-glacier component of basal drag is small. An important exception occurs in the center of the grounded part of the glacier where the flow shows major deviations from the axis of the valley. Other results are that side drag is roughly constant at 250 kPa along both margins of the glacier, tension from the ice shelf is about 100 kPa, and tension in the grounded part cycles between 250 and 150 kPa. Calculated deep velocities are too large and this is attributed to deficiencies in the conventional isotropic flow law used.