The flow of the Antarctic ice sheet near Byrd Station is modeled using surface net accumulation-rate data, surface strain-rate data, and core-hole tilting results. The model empirically allows for the progressive development of ice fabric and for values of the vertical strain-rate nearer to zero at depth, and adjusts the strain-rates according to the effect of the climatic warming at the beginning of the Holocene.

The validity of the model is supported by the agreements between calculated bed form and that measured by radar sounding, and between calculated and measured present-day ice-sheet thinning-rates. The ice was about 200 m thicker before thinning.

The depth-age relationship for the Byrd Station ice core shows that the climatic change represented by the oxygen isotopic ratio of the ice began some 5000 years sooner than in north Greenland (Hammer and others 1978), but ended at about the same time.

Although theories of glacier movement generally assume that glaciers flow over rigid rock beds, there are many places where glaciers rest on beds of deformable sediment, and the great Pleistocene ice sheets which extended from time to time over much of Northern Europe and North America were largely underlain by such beds. Observations show that a large proportion of the forward movement of a glacier lying on such a bed may be contributed by deformation of the bed rather than the glacier. A theory is developed in which the glacier surface profile is related to the hydraulic and strength properties of potentially deformable bed materials. If these have a high hydraulic transmissibility, melt water is readily discharged sub-glacially, the bed is stable, and the profile is a normal parabolic one, governed by the rhcological properties of ice. If bed transmissibility is low, water pressures build up, the bed begins to deform, and a lower equilibrium profile will develop, so that in an extreme case the glacier approximates to a thin flat sheet, similar to an ice shelf. It is suggested that such behaviour may have occurred at the margins of large Pleistocene ice sheets over North America and Europe, and evidence in support of this is drawn from the reconstructed shapes of these ice margins, anomalously small amounts of isostatic rebound, anomalously high retreat-rates, and the presence of glaciotcctonic structures. Reasons are suggested to explain why this behaviour should have been important for Pleistocene glaciers which penetrated into currently temperate latitudes but does not appear to be important in large modern glaciers.

Surveys of a triangulation chain 250 km in length were carried out in December 1969 and December 1973–January 1974 along the surface contour lines from 2250 m to 2600 m in Mizuho Plateau, East Antarctica. Horizontal velocities were obtained as small values near the Yamato Mountains, while they had maxima of more than 20 ± 0.7 m a –1 around long. 39° E., lat. 72° S. in the drainage of the Shirase Glacier. Submergence velocities showed large values, such as (0.7 to 1)± 0.25 m a–1, in the region along lat. 72° S. from long. 39° E. eastward to long. 43° E. The amount of snow accumulation there, of average thickness 0.2 m a–1, was not enough to compensate for the deficit of the ice mass caused by the submergence flow. It follows that the ice sheet was thinning there. It is suggested that the ice sheet of Mizuho Plateau is in an unstable condition as a whole.

The Japanese Antarctic Research Expedition observed the thinning of the ice sheet, about 70 cm/year, in Mizuho Plateau. The thinning observed is analysed using an equation of mass continuity. The result of the analysis indicates that the thinning is predominantly caused by the basal sliding and the basal sliding velocity is about 10 m/year. This sliding velocity is compared with the basal sliding velocity obtained by the calculation of the velocity due to internal deformation of ice sheet.

Extensive radio echo-sounding has mapped the part of West Antarctica between Byrd Station, the Whitmore Mountains, the Transantarctic Mountains, and the Ross Ice Shelf. The ice sheet in this area is dominated by five major sub-parallel ice streams (A–E), which are up to 100 km wide and extend inland from the grounding line of the Ross Ice Shelf for about 400 km. Their positions have been determined by crevassing seen on radio echo-sounding records, trimetrogon photographs, and Landsat imagery. The ice streams are characterized by their flat transverse cross-sections, while the intervening ice sheet exhibits domes and ridges. Ice flow lines are defined from the ice-surface contour pattern and the trend of the ice streams. It is apparent from this work that the flow line passing through Byrd Station joins ice stream D.

The bedrock of the area is relatively smooth near the Ross Ice Shelf, becoming rougher near Byrd Station and especially so near the Whitmore Mountains. Bedrock troughs, which control the positions of the ice streams, are believed to have a tectonic origin.

In this paper the role of the ice streams in the glaciological regime of West Antarctica is investigated from radio-echo data and estimates of balance velocity, basal shear stress, and basal temperatures.

Recent measurements of accumulation and ice velocity made in the interior of East Antarctica indicate that a large sector between longitudes 80° E. and 135° E. and north of latitude 80° S. has close to a zero net mass budget. This sector is within the study area for the International Antarctic Glaciological Project (I.A.G.P.) and covers a major portion of the area indicated for projects of special emphasis. Velocity measurements were made at a number of points on a traverse route from Mirny (lat. 66° 33′ S., long. 93°00′ E.) on the coast Dome “C” (lat. 74° 40′ S., long. 124° 00′ E.), in the interior. Accumulation measurements were made along this and other traverse routes, extending as far as Vostok (lat. 78° 28′ S., long. 106° 50′ E.), by a number of methods. These included stake, stratigraphic, isotopic, and total β-decay observations. The better accumulation data have allowed a review of the total mass input to be made. The true mass budget has been estimated by comparing velocities, calculated assuming a zero net mass budget with measured velocities along the traverse routes and on a number of the outlet glaciers. For this purpose the area was divided into a number of drainage basins according to outlet at the coast. The area of about 106 km2 and 150 Gt a−1 flux input is drained primarily by three glacier systems of which the Totten accounts for 40% of the flux from 55% of the area; the Vanderford 20% from 15%; and the Scott/Denman 20% from 20%.

In order to determine accurate velocities of the ice sheet in the interior of Antarctica, approximately along a flow line, a detailed trilateration net was established in 1973 from the summit of Law Dome (100 km inland) to about 250 km south near the 2000 m contour. The net consisted of a double line of markers approximately 10 km apart with all sides and diagonals of the quadrilaterals measured with telluro-meters. In addition, satellite doppler survey positions and astronomical azimuths were determined at about 50 km intervals to control the net on the large scale. Other measurements carried out en route included: continuous barometric levelling, radio echo-sounding, gravimetry, accumulation, and surface sampling. The route was close to an earlier traverse route which reached Vostok in 1962 and along which other data, including snow-surface temperatures and temperature–depth gradients, were determined.

The trilateration net was re-surveyed in 1975 allowing velocities and strain-rates to be determined. The results indicate that the ice sheet is close to balance in this region.

Therefore, the measured velocities were used together with “balance velocities”, further inland, to carry out a modelling study of a flow line, to derive particle trajectories, ages, temperature profiles, and “dynamics velocities”, from a flow law. The results provide further insight into the dynamics and flow properties of the ice sheet.

An ice core has been obtained to the bedrock about 300 m deep in Terre Adélie, 5 km inland from the coast. Stable isotopes and gas content have been measured over the length of the core. The results have been interpreted in terms of the temperature and elevation of origin of the ice further inland on the ice sheet from the data obtained along an 800 km traverse towards Dome “C”, and from Dome “C”, at an elevation of about 3 200 m. The flow of the ice from Dome “C“ to the coast has been modelled to determine the ages and particle trajectories of the ice for present conditions.

It has been found that the upper isotope and gas-content values in the core can be matched with the present regime using a base for ice flow above the present bed which is suggested by moraine in the ice core. The ice in the layer from the 200 m depth, where the age is apparently more than 5 000 years, to the 250 m depth, appears to have originated from conditions which differ substantially from those existing on the present inland ice-sheet surface. The results give an indication of a colder climate and greater ice-sheet thickness in the past.

A 345 m deep bore hole in ice about 385 m thick, near the edge of Law Dome, Antarctica, was drilled in 1974 about 3 km up-stream from the site of a previous bore hole, nearly reaching the bed, obtained in 1969. The core from this new bore hole has been studied comprehensively, particularly with regard to the ice-crystal orientation fabrics. Samples of the ice core were subjected to simple shear at temperatures and deviatoric stresses which match the in situ conditions of the ice sheet.

Similar studies of randomly-oriented laboratory-made polycrystalline ice were undertaken. Long-term tests, lasting for up to two years, were required to determine minimum strain-rates. The flow law for the anisotropic ice was thus determined as a function of that for the isotropic ice together with a measure of c-axis fabric strength perpendicular to the shear plane.

Core studies indicate that the upper part of the ice sheet has a polycrystalline structure appropriate to the surface longitudinal stress. Deeper in the core a strong concentration of near-vertical c-axes develops. Ice having very large crystals with multiple maxima fabrics was found in the lower quarter of the ice thickness.

Shear measurements in the bore hole indicate the existence of high strain-rates in the zone of vertical c-axes, and of lower shear-rates below that level. The low values of shear-rates in the basal region cannot be explained in terms of crystallographic changes alone, and therefore it is inferred that the shear stress decreases in this layer–a result which also provides a possible explanation for the development of the observed basal crystal structure.

Numerical methods based on quadrilateral finite elements have been developed for calculating distributions of velocity and temperature in polar ice sheets in which horizontal gradients transverse to the flow direction are negligible. The calculation of the velocity field is based on a variational principle equivalent to the differential equations governing incompressible creeping flow. Glen’s flow law relating effective strain-rate ε̇ and shear stress τ by ε̇ = (τ/B)n is assumed, with the flow law parameter B varying from element to element depending on temperature and structure. As boundary conditions, stress may be specified on part of the boundary, in practice usually the upper free surface, and velocity on the rest. For calculation of the steady-state temperature distribution we use Galerkin’s method to develop an integral condition from the differential equations. The calculation includes all contributions from vertical and horizontal conduction and advection and from internal heat generation. Imposed boundary conditions are the temperature distribution on the upper surface and the heat flux elsewhere

For certain simple geometries, the flow calculation has been tested against the analytical solution of Nye (1957), and the temperature calculation against analytical solutions of Robin (1955) and Budd (1969), with excellent results.

The programs have been used to calculate velocity and temperature distributions in parts of the Barnes Ice Cap where extensive surface and bore-hole surveys provide information on actual values. The predicted velocities are in good agreement with measured velocities if the flow-law parameter B is assumed to decrease down-glacier from the divide to a point about 2 km above the equilibrium line, and then remain constant nearly to the margin. These variations are consistent with observed and inferred changes in fabric from fine ice with random c-axis orientations to coarser ice with single- or multiple-maximum fabrics. In the wedge of fine-grained deformed superimposed ice at the margin, B increases again.

Calculated and measured temperature distributions do not agree well if measured velocities and surface temperatures are used in the model. The measured temperature profiles apparently reflect a recent climatic warming which is not incorporated into the finite-element model. These profiles also appear to be adjusted to a vertical velocity distribution which is more consistent with that required for a steady-state profile than the present vertical velocity distribution.

Deep cores from Byrd Station were used to calibrate an ultrasonic technique of evaluating crystal anisotropy in the Antarctic ice sheet. Velocities measured parallel (Vp ↓) and perpendicular (Vp →) to the vertical axis of the cores yielded data in excellent agreement with the observed c-axis fabric profile and with the in-situ P-wave velocity profile measured parallel to the bore-hole axis by Bentley. Velocity differences ΔV (ΔV = Vp ↓ – Vp→) in excess of 140 m s−1 for cores from below 1300 m attest to the tight clustering of c-axes of crystals about the vertical, especially in the zone 1 300-1800 m. A small but significant decline in Vp ↓ with ageing of the core, as deduced from Bentley’s down-hole data, is attributed to the formation of oriented cracks that occur in the ice cores as they relax from environmental stresses. This investigation of cores from the 2164 m thick ice sheet at Byrd Station establishes the ultrasonic technique as a viable method of monitoring relaxation characteristics of drilled cores and for determining the gross trends of c-axis orientation in ice sheets. The Byrd Station data, in conjunction with Barkov’s investigation of deep cores from Vostok, East Antarctica, also indicate that crystal anisotropy in the Antarctic ice sheet is dominated by a clustering of c-axes about a vertical symmetry axis.

Field studies at a particular place at the margin of the Greenland ice sheet have provided information about the ice sheet. Ice temperatures were measured in five drill holes, two of which reached the unfrozen area of basal melting. Surface water entered these two bore holes, reaching the base in one, but remaining 59 m above the base in the other. The existence of this water conduit or fracture at 240 m depth, the calculated temperature profiles, and the local bedrock configuration suggest an area of stationary ice overridden by the ice sheet. This situation suggests creep rupture at depth in the ice sheet. Ice-fabric analysis made above 240 m depth shows patterns similar to fabrics elsewhere near the margin in zones of low deviatoric stress. Unfortunately no cores were obtained below that depth where stationary ice may exist.

Marine ice sheets rest on land that, for the most part, is below sea-level. Ice that flows across the grounding line, where the ice sheet becomes afloat, either calves into icebergs or forms a floating ice shelf joined to the ice sheet. At the grounding line there is a transition from ice-sheet dynamics to ice-shelf dynamics, and the creep-thinning rate in this region is very sensitive to sea depth; rising sea-level causes increased thinning-rates and grounding-line retreat, falling sea-level has the reverse effect. If the bedrock slopes down towards the centre of the ice sheet there may be only two stable modes: a freely-floating ice shelf or a marine ice sheet that extends to the edge of the continental shelf. Once started, collapse of such an ice sheet to form an ice shelf may take place extremely rapidly. Ice shelves which form in embayments of a marine ice sheet, or which are partially grounded, have a stabilizing influence since ice flowing across the grounding line has to push the ice shelf past its sides. Retreat of the grounding line tends to enlarge the ice shelf, which ultimately may become large enough to prevent excessive outflow from the ice sheet so that a new equilibrium grounding line is established; removal of the ice shelf would allow retreat to continue. During the late-Wisconsin glacial maximum there may have been marine ice sheets in the northern hemisphere but the only current example is the West Antarctic ice sheet. This is buttressed by the Ross and Ronne Ice Shelves, and if climatic warming were to prohibit the existence of these ice shelves then the ice sheet would collapse. Field observations suggest that, at present, the ice sheet may be advancing into parts of the Ross Ice Shelf. Such advance, however, would not ensure the security of the ice sheet since ice streams that drain to the north appear to flow directly into the sea with little or no ice shelf to buttress them. If these ice streams do not flow over a sufficiently high bedrock sill then they provide the most likely avenues for ice-sheet retreat.

Steady-state creep-rates of polycrystalline ice were investigated as a function of temperature, grain-size, and inclusion concentration through uniaxial compression in the laboratory. Samples were run at a constant load with the temperature systematically varied between about —5°C and —40°C. The presence of inclusions inhibits dynamic recrystallization and grain growth; the average crystal size produced by recrystallization is inversely proportional to the inclusion concentration. At temperatures above —8°C, creep-rate is enhanced by about a factor of two. This appears to be the result of the combined effects of recrystallization with accompanying grain growth and grain-boundary sliding. Over the temperature range —10°C to —40°C, the apparent activation energy for creep increases with increasing volume fraction of inclusions. This is apparently due to a thermally activated process which is modified by internal stresses created by the inclusions.

Self-consistent, steady, one-dimensional, subsolidus creep models of temperature and velocity are calculated for constant-thickness ice sheets sliding down a bed of constant slope under their own weight. Surface velocities of meters per year together with ice thicknesses of hundreds of meters can be realized by models wherein no melting occurs only if the activation energy for shear deformation E* is relatively small; a value of E* of about 60.7 kJ/mol (14.5 kcal/mol) is satisfactory, but an activation energy twice as large is not. Models which satisfy these constraints always lie close to the critical point which separates subcritical solutions (surface velocity u0 and basal temperature Tb increase with ice thickness h) from supercritical ones (u0Tb decrease with h). All steady states, whether subcritical or supercritical, are stable to perturbations of infinitesimal amplitude. However these ice layers are vulnerable to finite-amplitude frictional-heating instability which may be caused, for example, by sudden increases of glacier thickness. The superexponential growth-rates of such finite-amplitude instabilities may be responsible for the disintegration of large ice sheets in short periods of time.

On a calculé pour la température et la vitesse des modèles de fluage cohérents, stables, uni-dimensionnels, quasi-solides pour une épaisseur constante de glace glissant sur un lit de pente constante sous l’effet de son propre poids. Des vitesses de surface de quelques mètres par an liées à des épaisscurs de glace de quelques centaines de mètres ne peuvent être réalisées par des modèles sans fusion que si l’énergie d’activation pour la déformation par cisaillement E* est relativement faible. Une valeur de E* d’environ 60,7 kJ/mol (14,5 kcal/mol) est satisfaisante mais une énergie d’activation double ne l’est pas. Les modéles qui satisfont à ces contraintes demeurent trés proches du point critique qui sépare les solutions sous-critiques (la vitesse de surface u0 et la température à la base Tb croissent avec l’épaisseur de glace h) des solutions sur-critiques (u0, Tb décroissent avec h). Tous les états d’équilibre, sous-critiques ou sur-critiques sont stables pour des perturbations d’amplitude infinitésimale. Cependant, ces niveaux de glace sont vulnérables à l’instabilité par réchauffement de frottement d’amplitude finie, qui peut provoquer, par exemple, un acroissement subit de l’épaisseur des glaciers. La vitesse de croissance superexponentielle de telles instabilités d’amplitude finie peut être responsable de la désintégration de grandes calottes glaciaires en de courtes périodes de temps.

Für Eisdecken mit konstanter Dicke, die über ein Bett mit konstanter Neigung unter ihrem eigenen Gewicht herabgleiten, werden in sich abgeschlossene, stetige, eindimensionale Kriechmodelle der Temperatur und Geschwindigkeit berechnet. Oberflächengeschwindigkeiten von einigen Metern pro Jahr zusammen mit Eisdicken von mehreren hundert Metern können durch Modelle erfasst werden, in denen keine Abschmelzung auftritt, wenn nur die Aktivationsenergie für die Scherdeformation E* relativ klein ist; ein Wert E* von etwa 60,7 kJ/mol (14,5 kcal/mol) erfüllt diese Bedingung, eine doppelt so grosse Aktivationsenergie dagegen nicht. Modelle, die solchen Einschränkungen genügen, liegen immer nahe dem kritischen Punkt, der unterkritische Lösungen (Oberflächengeschwindigkeit u0 und Temperatur am Untergrund Tb wachsen mit der Eisdicke h) von überkritischen (u0, Tb nehmen mit h ab) trennt. Alle stationären Zustände, gleichgültig ob unter- oder überkritisch, sind stabil gegenüber Störungen mit infinitesimaler Amplitude. Jedoch können diese Eisschichten von Instabilitäten infolge Reibungswärme mit finiter Amplitude betroffen werden, die zum Beispiel durch eine plötzliche Zunahme der Gletscherdicke verursacht werden können. Die überexponentiellen Anstiegsraten solcher Instabilitäten mit finiten Amplituden könnten der Grund für die Auflösung grosser Eisschilde in kurzen Zeitspannen sein.

The Antarctic ice sheet has been reconstructed at 18000 years b.p. by Hughes and others (in press) using an ice-flow model. The volume of the portion of this reconstruction which contributed to a rise of post-glacial eustatic sea-level has been calculated and found to be (9.8±1.5) × 106 km3. This volume is equivalent to 25±4 m of eustatic sea-level rise, defined as the volume of water added to the ocean divided by ocean area. The total volume of the reconstructed Antarctic ice sheet was found to be (37±6) × 106 km3. If the results of Hughes and others are correct, Antarctica was the second largest contributor to post-glacial eustatic sea-level rise after the Laurentide ice sheet. The Farrell and Clark (1976) model for computation of the relative sea-level changes caused by changes in ice and water loading on a visco-elastic Earth has been applied to the ice-sheet reconstruction, and the results have been combined with the changes in relative sea-level caused by Northern Hemisphere deglaciation as previously calculated by Clark and others (1978). Three families of curves have been compiled, showing calculated relative sea-level change at different times near the margin of the possibly unstable West Antarctic ice sheet in the Ross Sea, Pine Island Bay, and the Weddell Sea. The curves suggest that the West Antarctic ice sheet remained grounded to the edge of the continental shelf until c. 13000 years b.p., when the rate of sea-level rise due to northern ice disintegration became sufficient to dominate emergence near the margin predicted otherwise to have been caused by shrinkage of the Antarctic ice mass. In addition, the curves suggest that falling relative sea-levels played a significant role in slowing and, perhaps, reversing retreat when grounding lines approached their present positions in the Ross and Weddell Seas. A predicted fall of relative sea-level beneath the central Ross Ice Shelf of as much as 23 m during the past 2000 years is found to be compatible with recent field evidence that the ice shelf is thickening in the south-east quadrant.

If sea-level depression in the Ross Sea embayment were: (1) < 120–130 m, or (2) > 120–130 m but sustained for < 104 a, it is unlikely that the Ross Ice Shelf would have become fully grounded over the whole continental shelf during Wisconsin times. Sediments flooring the Ross Sea and recent estimates of sea-level lowering and post-glacial emergence yield little support for grounded ice but do provide some evidence for expanded ice-shelf conditions. A reconstruction is presented based on this premise. The model is compatible with glacial geologic results, especially those in the McMurdo Sound area.

A simple qualitative model of global ice cover is presented to account for the apparent catastrophic transitions between glacial and interglacial climates. Unlike the Budyko (1972) and Weertman (1976) models, the catastrophe model employs a second control parameter besides the oribtally induced insolation fluctuations to differentiate between fast and slow glaciological response mechanisms. It is conjectured that this second control parameter is linked to isostatic actions occurring beneath the continental crust which shift the dynamic emphasis from terrestrial to marine ice margins.

Ice shelves may develop either by continued thickening of sea ice that is held fast to the shore, or by the seaward extension of inland ice. For both processes, as well as for an understanding of ablation and of accumulation at the bottom surface of ice shelves, we need to understand melting and freezing processes in relation to salinity, temperature, and pressure. Consideration of these factors shows that basal melting beneath the thicker parts of ice shelves is much greater than is generally appreciated. This could be sufficient to bring the estimated mass balance of Antarctica into approximate equilibrium. It appears that most Antarctic ice shelves are dependent on the supply of inland ice for their continued existence. However the thick layer of sea ice beneath the Amery Ice Shelf is readily explained in terms of sub-ice water circulation.

Transport of heat and mass by water motion beneath ice shelves has the potential to change ice thicknesses by similar amounts to that caused by internal deformation of the ice shelf. Bottom freezing due to thermal conduction throughout the ice shelf is of minor importance.

While attention is drawn to the basic equations for flow of ice shelves, it is pointed out that they have yet to be applied satisfactorily to the problem of iceberg calving. This appears from field observations to be due primarily to creep failure of spreading ice shelves, possibly aided by impact from floating icebergs. Recent observations show the effectiveness and likely quantitative importance of this “big bang” theory of iceberg formation in Antarctica.

A brief discussion of the effects of climatic change on the disintegration of ice shelves is presented.