The Holocene warmth is now affecting the flow of the central West Antarctic ice sheet. It is supposed that the ice sheet reached approximate steady-state during the Wisconsinan. A perturbation analysis of ice-sheet temperatures indicates that deep ice has warmed by one or two degrees since the Wisconsinan. Warmer ice deforms more rapidly and the ice sheet should now be flowing 10 to 30% faster than during the Wisconsinan.

This paper discusses the mass outflow and dynamics of a 3000 km long front of the Antarctic ice sheet—the coastline from Prinsesse Ragnhild Kyst to the Filchner Ice Shelf. Ice shelves, mostly 50–100 km wide, account for more than 95% of this coastline. Large mass losses by calving generally occur at intervals of several decades at any particular location, and usually involve shelf areas of 10-1000 km2. The mass loss by calving during the periods between the large calvings is insignificant, except where ice streams run directly into the sea without forming ice shelves. The latter sections account for 2% of the coastline in question and a similar part is made up of ice rises. Thus, with the exception of these short segments, the ice front advances systematically over time intervals of a few decades. Large calvings interrupting the advance can be recognized by significant change in shape and position of the ice front.

Although computer modelling using realistic flow parameters can simulate surging of the Antarctic ice sheet, the present model does not take into account certain factors that make surging less probable. Before discussing these factors, knowledge of the Antarctic ice sheet that might indicate the occurrence of former surging is reviewed. The following studies appear relevant

• (a) Observed temperature–depth profiles approximate to steady-state solutions, whereas a major surge within the last 10 000 to 20000 years would have produced markedly different temperature–depth profiles at Byrd and Vostok Stations.

• (b) Isotopic profiles are estimated for steady-state and for surging behaviour of the Antarctic ice sheet. When these are compared with observed profiles no convincing evidence of surging over the past 10 000 to 50 000 years is seen.

• (c) Studies of flow lines in and around the Ross Ice Shelf do not reveal any surging of discharge glaciers in the past I 000 to 2 000 years.

• (d) Although mass-balance calculations and balance-velocity calculations on the Antarctic ice sheet are not accurate, ice discharge is generally estimated to be within a factor of two of the total mass accumulation.

Three stabilizing factors that have not been included in computer models and need consideration are

• (1) It appears unlikely that a surge will be propagated up-stream of any substantial bedrock slope that opposes the ice motion.

• (2) The very high effective viscosity of great thicknesses of ice at very low temperatures adds considerable rigidity to the ice sheet at the lateral boundaries of any incipient surge.

• (3) Strong convergence of flow lines towards ice streams and major trunk glaciers apparently provides a stabilizing factor.

Tensile tests were carried out with core-ice samples obtained from various depths at Byrd Station, Antarctica in 1968, Specimens for the tests were so prepared as to have their long axes parallel (L specimen), perpendicular (T specimen), and inclined at 450 (I specimen) with respect to the axis of the core, or to the vertical direction of the ice sheet. Stress-strain relations for many specimens were obtained from tensile tests with different strain-rates and also at different temperatures between —10 and — 20°C.

The finite-element method is being used to simulate glacier flow problems, with particular emphasis on the surge behaviour of the Barnes Ice Cap, Baffin Island. Following an advanced feasibility study to determine the influence of major factors such as bed topography and flow relationships, a refined simulation model is being developed to incorporate realistically: the thermal regime of the ice mass; large deformations during flow and sliding; basal sliding zones; a temperature and stress dependent ice flow relationship; mass balance; and three-dimensional influences. The findings of the advanced feasibility study on isothermal, steady-state flow of the Barnes Ice Cap are presented in the paper before turning to a detailed discussion of the refined simulation model and its application to surging. It is clear that the finite-element method allows necessary refinements not available to analytical approaches.

A major question in ice-sheet dynamics is the state of balance between the net mass input and ice flow. Since an imbalance produces a change in surface elevation, the state of balance can be studied by monitoring the elevation, and this has been accomplished by surface-leveling techniques in a few locations. Due to the requirement for accurate and repetitive measurements over large areas, it is not practical to determine the status of balance of an entire ice sheet or even a major drainage basin by conventional techniques. Now, recent results from satellite-borne radar altimeter measurements over the Greenland ice sheet demonstrate the feasibility of accurately measuring and monitoring the topography of large ice masses. The application of this new technique offers the possibility of making a meaningful mass-balance determination and for detecting actual or potential ice-sheet surges.

Size, shape, and surface albedo of former ice sheets are needed in order to model atmospheric circulation for the CLIMAP 18000 years B.P. experiment. Both the size and shape of an ice sheet depend on the hardness of ice and its coupling to bedrock. Ice hardness is controlled by ice temperature and fabric, which are not adequately described by any ice flow law. Ice–bed coupling is controlled by bed roughness and basal melt water, which are not adequately described by any ice sliding law. With these inadequacies in mind, we assumed equilibrium ice-sheet conditions 18000 years ago and combined the standard steady-state flow and sliding laws of ice with the equation of mass balance to obtain separate basal shear-stress variations along ice-sheet flow lines for a frozen bed when the flow law dominates and for a melted bed when the sliding law dominates. Theoretical basal shear-stress variations were then derived for freezing and melting beds on the assumption that separate melted areas of the bed had water films of constant thickness which expanded and merged for a melting bed but contracted and separated for a freezing bed. Theoretical basal shear-stress variations were also derived for ice streams along marine ice-sheet margins and ice lobes along terrestrial ice-sheet margins on the assumption that the entire area of their bed was wet so that further melting increased the water-layer thickness, which would then be decreased by freezing. Melting was assumed to continue to the grounding line of an ice stream and the minimum-slope surface inflection line of an ice lobe, where freezing began and continued to the ice-lobe terminus. Ice–bed uncoupling is complete at an ice-stream grounding line and maximized at an ice-lobe minimum-slope inflection line, so ice velocity and consequent generation of frictional heat were assumed to reach maxima across these lines. Theoretical basal shear-stress variations were derived for the zone of converging flow at the heads of ice streams and ice lobes, and from domes to saddles along the ice divide for both frozen and melted beds.

Late-Wisconsin ice sheets were reconstructed for the CLIMAP 18000 years b.p. experiment. This experiment modeled the ice-age steady-state climate using boundary conditions that differed from present ones mainly in Earth-surface albedos, sea-surface areas, and land-surface topography. These required determinations of the area, volume, and elevation of Late Wisconsin ice sheets. An initial-value finite-difference numerical model for ice-sheet reconstruction was developed from a recursive formula which gave ice thickness for known variations of bed topography and theoretical variations of basal shear stress. Ice thicknesses were calculated in 50 km to 100 km steps along flow lines from margins to domes of late-Wisconsin ice sheets. We assumed that terrestrial margins were along the furthermost moraines, marine margins were along the present 500 m bathymetric contour, domes were centers of maximum post-glacial isostatic rebound, and flow lines were along glacial lineations (eskers, striations, drumlins, etc.) connecting margins to domes. At various locations ice-sheet margins were verified by dated moraines for terrestrial margins and Egga-type moraines for marine margins. Ice-sheet elevations and thicknesses were contoured from profiles reconstructed for 40 Antarctic flow lines and 137 Northern Hemisphere flow lines for a maximum ice-sheet extent, and 86 Northern Hemisphere flow lines for a minimum ice-sheet extent.

The CLIMAP 18000 years b.p. experiment required reconstructing late-Wisconsin-Weichselian ice sheets. In the Northern Hemisphere, the greatest uncertainty in these reconstructions is the area covered by ice sheets. Two schools of thought exist (Hughes and others, in press). The minimum-ice-sheet school holds that ice sheets originated from present ice caps in the High Arctic islands, but the northern seaward margins of these ice sheets retreated as the southern landward margins advanced. This occurred because northern margins became isolated from sources of precipitation as Arctic seas became permanently ice-covered and the advancing southern margin changed atmospheric circulation patterns. In this view, these ice sheets stay about the same size and migrate southward during an ice age. Northern margins rarely reach sea-level during the later stage of the ice age so no marine portions form and ablation is by melting or sublimation. Marine portions formed only when the ice sheets migrated across shallow seas between the High Arctic islands and the mainland. At the end of the ice age, huge amounts of heat had to be transferred from the tropics to the ice sheets in order to account for late-Wisconsin-Weichselian and Holocene retreat-rates by melting along ice-sheet margins.

Taking various retreat-rates for the presumed grounded ice sheet in the Ross embayment during Wisconsin time, as calculated by Thomas (Thomas and Bentley, 1978), and assuming a time constant of 4400 years for isostatic rebound, a sea-floor uplift of 100±50 m still to be expected in the grid western part of the Ross Ice Shelf can be calculated. The expected uplift diminishes from grid west to grid east, and is probably negligible in the eastern half of the shelf area. There are extensive areas near the present grounding line where the water depth beneath the shelf is less than 100 m, so that uplift would lead to grounding. As grounding occurred, the neighboring ice shelf would thicken, causing grounding to advance farther. This process would probably extend the grounding line to a position running grid north-eastward across the shelf from the seaward end of Roosevelt Island, deeply indented by the extensions of the present ice streams. Floating ice would remain in the grid south-eastern half of the shelf.

Several numerical simulations of the Arctic ice cover over a seasonal cycle are carried out. Two different types of constitutive laws are examined: rigid plastic and linear viscous. In both cases, the strength of the ice interaction is taken as a function of ice thickness and compactness. The thickness and compactness, in turn, evolve according to continuity equations which include thermodynamic source and sink terms. The simulations with the rigid-plastic law reproduce reasonable geographical ice-thickness variations, ice outflow, and ice-velocity characteristics. The viscous simulations (especially the Newtonian viscous case) produce less satisfactory geographical ice thickness variations, and near-shore velocity characteristics. In addition the Newtonian-viscous simulation produces highly unrealistic ice-edge effects in summer. The results are discussed in terms of the relative magnitudes of the shear and compressive strengths, and in terms of the non-linear versus linear dependence on deformation in the ice rheology. The portion of this study employing a plastic constitutive law is published in full in Journal of Physical Oceanography, Vol. 9, No. 4, 1979, p. 815–46.

Methods based on remotely-sensed data are needed to predict motions of drifting open pack ice and to determine sea-ice parameters associated with these motions. The method presented here is able:

• (a) to predict the motions of groups of wind-driven detached ice floes over periods of 12, 36, and 60 h;

• (b) to determine sea-ice thickness and the surface and sub-surface drag coefficients associated with these motions.

A glacier surge, according to most definitions, is a short-lived phase of unusually rapid glacier flow, after which the glacier returns to more normal behavior, with the surge–non-surge phases recurring on a regular or periodic basis. Recent interest is largely directed toward analyzing the effect of water at the bed on the periodic change in flow regime and on the rapid flow during a surge phase. For instance, study of a local depression of basal shear stress that dependson a “friction lubrication factor” which becomes important as the ice velocity increases, is one promising phenomenological approach. An important physical approach focuses on a water “collection zone” that occurs where and when the longitudinal pressure gradient in the subglacial wtaer film approaches zero. The data necessary for properly verifying these and other similar theories do not yet exist. Computer modeling of rapidly-surging glaciers based on a “friction lubrication factor” has been quite successful in duplicating their major features. Once rapid movement (102–103 m a–1) has begun, sufficient water is generated at the bed, from ice melted by heat dissipated in sliding, to produce some decoupling of the glacier from its bed and to maintain the surge, but only if this water is not lost by rapid drainage. Some glaciers exhibit periodic pulses in which the basal sliding velocity during the fastest part of the pulses appears to be in the range for “normal” glaciers (<102 m a–1). Some evidence suggests a continuum of behavior from steady (normal) glaciers through these “mini-surges” to classic surges. This continuum and the “mini-surges” seem to be difficult to explain quantitatively by existing theories. A few glaciers flow continuously at surging speeds (>103 m a–1) in certain reaches. The up-glacier transition reaches show speeds decreasing to “nonrmal” with no indication of intermediate surging regime, but the down-glacier transition reaches may be areas where surges are triggered.

An unstable situation can develop when a calving glacier (one that ends in water but is still grounded throughout) terminates on a shoal. This instability is largely a consequence of continuity and the extending flow which occurs up-glacier of the shoal. Whenever the calving-rate exceeds the ice velocity the ice front will start to retreat; the rate of retreat is accentuated by the extending flow and the front continues to retreat at an increasing rate.

Since late 1972, when the first Landsat images of Iceland became available, the ice caps of Iceland and their outlet glaciers have been under intensive study with Landsat images. The original emphasis of the Landsat research of Icelandic ice caps was to record and quantitatively measure dynamic change of glaciers and phenomena related to glaciers. A comparison of Landsat images with the best available topographic maps revealed a number of discrepancies in the planimetric shape and size of Icelandic ice caps and in the mapping of prominent surface features. Some of the surface features recorded on Landsat images turned out to be the subdued morphological expression of subglacial topography and geologic structure or the surficial response to subglacial volcanic and geothermal activity. Of particular interest was a winter image of Vatnajökull, acquired at a solar elevation angle of 7°, which revealed a number of surficial features not recorded before, including a large volcanic caldera in the Kverkfjöll area. A computer-enhanced early fall image of Vatnajökull revealed similar phenomena, and computer-enhancement techniques have also been applied to summer images of Hofsjökull, Langjökull, Mýrdalsjökull, and Eyjafjallajökull. In the case of Hofsjökull a subglacial volcanic edifice with the approximate dimensions of the Dyngjufjöll massif in north-central Iceland, and possibly with a caldera, may exist. Radio echo-sounding surveys have been carried out over some parts of Vatnajökull and Mýrdalsjökull to determine the precise nature of the subglacial topography, and it is of great interest to compare the results of these surveys of glacier bed topography with the surface features recorded on Landsat and other imagery. Landsat images are also being used to plan the optimum location of field traverses and as a navigational tool (map substitute) during field work.

For the first time field data from a temperate valley glacier, the Variegated Glacier, are used to investigate the behavior of longitudinal stress gradients predicted by the relation 1 where H is the local depth, and ys and yb are the surface and bed elevations respectively. This equation is similar to one derived by Budd (1970) for plane strain-rate, to evaluate the importance of longitudinal stress gradients, but a shape factor f is included to account approximately for lateral strain-rate gradients. Predictive numerical models of valley glaciers require the local base shear stress to be known as accurately as possible. It has been argued on theoretical grounds that when T is averaged over distances of more than five to ten times the depth, this term is negligible. At larger averaging scales, 2G can then be considered a correction to the simple geometric expression of base stress due to the presence of longitudinal stress gradients. Field data of velocity and geometry are used to evaluate the terms of Equation (1), where τb and 2G are estimated as and at intervals of 100 m, Us is the measured surface center-line velocity, A and n are the flow-law parameters, and is the surface longitudinal strain-rate. The expression for 2G is an approximation proposed by Budd (1970).

The recent glaciological literature contains a number of numerical simulations of ice-mass flow based on the mass conservation equation. Although rather complex ice masses have been modelled, there has been little discussion of the necessary tests for correct response time and amplitudes in the models. The analytical work of J. F. Nye (1960, 1963[a], 1963[b], 1965[a],1965[b]) on the response of a steady-state glacier to perturbations in its mass balance provides an excellent test of model dynamics. Only when properly verified can the numerical model be used to extend knowledge of glacier response to more general cases where analytical solutions are unavailable. The model in this paper is checked against Nye’s calculations of response to a step increase in mass balance. It is then used to extend Nye’s results by finding the time constants for diffusion parameters other than 0 and 1.

This paper presents a mathematical analysis of the steady-state motion of a large ice mass. The purpose of the study is to determine the parameters which govern the motion of the ice and to establish the relationships between these parameters and the observable features of the motion. The study considers both land-based glaciers and floating ice shelves as different cases of the same problem. The particular features of the motion which are considered in this study are the surface waves or ogives which appear on both glaciers and ice shelves.

Estimates have been made of the mass budget of the total drainage basin of Lambert Glacier. These show a small but significant positive state of balance for the interior basin (the accumulation area up-stream of the major ice streams) and strongly suggest a positive balance for the Lambert Glacier system (the region of major ice streams, between the Amery Ice Shelf and the interior basin). The total mass flux into the interior basin is estimated as 60 Gt a–1. Results are presented from a number of ice movement stations established between 1972 and 1974 around the perimeter of thesouthern Prince Charles Mountains. These results, together with ice thicknesses from radio echo-sounding in the area, give a total mass outflux through the 2000 m contour of 30 Gt a–1, implying a budget excess of a further 30 Gt a–1 over the whole interior basin. Results from velocity and ice-thickness measurements give a mass discharge through a section near the junction of Lambert Glacier and the Amery Ice Shelf of 11 Gt a–1. Losses within the Lambert Glacier system proper account for a further 7 Gt a–1 and an overall mass excess of 12 Gt a–1 is estimated for the Lambert Glacier system. This present positive state of balance contrasts with geomorphological evidence from the southern Prince Charles Mountains of a large drop in ice level in recent geological time, and the ice surface in the area may now be building up after a major recession.

This paper has been published in full in Journal of Glaciology, Vol. 22, No. 87,1979, p. 223—35.

The differential equation determining the elevations of a perfectly plastic three-dimensional steady-state ice sheet is set up. Analytical solutions of the equation are obtained in two simple cases, viz. (1) an ice sheet on a horizontal base with an arbitrary curve as edge and (2) an ice sheet ona plane but sloping bed, with an edge composed of straight-line segments. The solutions are discussed in particular with reference to the development of ice divides and ice streams.