Dynamics of the West Antarctic Ice Sheet

The cryosphere accomodates about 1.6% of the earth’s water, the bulk of which is stored in the world oceans (93.6%; groundwater is the third important water reservoir). Nevertheless, small changes in ice volume can have large effects on sea level. For instance, a 1% change in ice volume results in a sea-level rise or drop of some 70 cm. So although the large ice caps are located in remote areas of the world, their evolution leaves a clear mark upon the regions in which we live.

The forces or stresses in a glacier are separated into lithostatic and resistive components. The lithostatic component is the weight of ice and gradients in it cause glacial motion as described by the driving stress. The remaining stresses oppose the motion and in assessing glacial stability it is important to determine which of the several potential resistive forces are most important, Data relating to the stresses driving and resisting the flow of the West Antarctic Ice Sheet are discussed. The driving stress is readily calculated and it shows an almost exponential decrease from the inland ice, along Ice Stream B, and across the Ross Ice Shelf to the calving edge. Prior work shows that basal drag restrains inland ice and that the backstress on ice shelves originates at islands, shoals, and the sides. The restraints on ice streams are not at present known, but basal drag, side drag, and back-pressure from the interstream ridges where the inland ice funnels into ice streams, are potential controls.

The ice cap covering Antarctica does in general not terminate at the edge of the continent. In most regions the ice is pushed into the sea, taking the appearance of a floating ice shelf. At the edges of the shelves, huge parts break off and drift away as tabular icebergs, characteristic for the Antarctic. As a result, the edge of an ice shelf usually has the form of a straight, vertical wall. Although the major part of this ice wall is submerged, it rises some tens of meters out of the sea — hence the common name ‘barrier’. Under typical conditions the submerged part of the ice wall measures roughly 200 m, while the sub-ice sea depths range from a few tens to a few hundreds of meters. Because the ice wall does not reach to the sea bottom, the shelf edge forms (in oceanographic sense) a highly remarkable type of ‘coast’. The present paper addresses the oceanic circulation near the shelf-ice edge, and concentrates on two aspects, namely the large-scale flow driven by wind stresses in the open sea, and the smaller-scale circulation driven by melting of the ice wall.

Data on the positions of ice edges in the eastern and southern Weddell Sea for the years 1980 to 1984 are presented. These data allow determination of apparent ice movements for the period under consideration, i.e. apparent advance rates and azimuths of ice-edge alteration during particular time intervals. The near-ice-edge movements thus determined are in good agreement with the ice movement as derived from interpretation of Landsat images and West Antarctic ice-stream flow patterns. The apparent areal growth of individual ice shelves in the Weddell Sea region can also be assessed. Together with estimates of near-ice-edge ice thicknesses, an apparent annual discharge rate can be computed. Our results for the Filchner-Ronne and the Brunt ice shelves amount to apparent calving rates of 60x10¹², 91x10¹² and 24x10¹² kg/yr, respectively, which in the case of the Filchner-Ronne Ice Shelf is lower than previous estimates.

Most of the major ice shelves in the Weddell Sea region show steadily advancing ice fronts during the period of observation. This has the consequence that the source region for icebergs during this time should be limited mainly to ice fronts in the eastern Weddell Sea. The present results support earlier contentions that large ice shelves undergo episodic, major calving events with frequencies well in excess of a few years, while smaller ice shelves are subject to more frequent calving, thus keeping the ice fronts close to equilibrium.

A new ice-thickness map has been compiled for the Ronne Ice Shelf north of about 81 °S using airborne radio-echo data collected by the British Antarctic Survey since 1975. Comprehensive cover was obtained during the 1982/83 season with flight lines at approximately 50 km spacing. The major features described previously are confirmed, but additional information over the western half of the ice shelf where there were few data before, has revealed the strong identity of individual ice streams. Individual features on radio-echo records, such as abrupt changes in echo strength or prominent bottom crevasses, allow flowlines to be drawn over the western part of the ice shelf. These correspond well with surface features seen on Landsat images.

Ice-front positions measured by the West German expedition have given a velocity profile between Berkner Island and the Antarctic Pensinsula. The profile can be fitted reasonably well by making a number of simplifying assumptions. In addition, velocities are known at the grounding line of the Rutford Ice Stream and across the ice rumples between Korff and Henry ice rises. Velocity profiles can be deduced along the two relevant flowlines using the principle of mass balance. Detailed results are of course dependent on bottom melting assumptions, but for the Rutford flowline there must be an average of 1 m/yr of bottom ice melt, assuming a net surface accumulation of 0.3 m/yr. Towards the ice front the melt rate probably increases to several meters per year. Calculations suggest that if the retarding force acting along the flowline were to be reduced slightly by, for example, iceberg calving, then the strain rates would show a significant, if temporary, increase. Ice at the grounding line takes about 1000 years to reach the ice front.

Along the flowline from the rumples there is probably only a small amount of bottom melting, in the order of 0.1 m/yr. Although over most of its length there is a retarding force, close to the ice front the force becomes tensile. This can be explained by a reversal in sign of the transverse shear stress gradient. This is consistent with the existence of a curvilinear rift in the ice front just to the west of the rumple flowline.

The spreading of an unconfined ice shelf in two horizontal directions involves the variation of the two horizontal velocity components and the thickness in both directions. Exploiting the slow variation of physical quantities in both horizontal directions compared to vertical variation allows simple solution of the vertical momentum balance and the derivation of plane stress equilibrium equations for integrals of the horizontal stresses through the thickness, together with integrated traction conditions on a front contour defining the boundary of smooth flow. This contour, however, is not prescribed, but is part of the solution. Equilibrium of the region between this smooth contour and the sea margin determines the integrated front tractions in terms of the sea water pressure provided that restrictions on stresses in the margin region can be made. The resulting two-dimensional system of integropartial differential equations on the unknown domain is a complex problem.

The longitudinal velocity and thickness of an ice shelf in steady plane flow, when temperature is prescribed as a function of the spatial coordinates, are determined by simultaneous integro-differential equations. These are solved numerically to illustrate the effects of temperature distribution, depth and ice flux at the grounding line, and surface accumulation.

The corresponding integro-differential equations for axi-symmetric flow are derived, which involves a strain rate transverse to the radial direction and hence non-planar spreading. Numerical solutions for a grounding line at a mean Antarctic radius and a range of ice-flux values are presented. Comparisons with corresponding plane-flow solutions indicate that radial spreading has little influence.

The traditional concept of ice-shelf backpressure, defined as the stress deficit reducing ice-shelf spreading rates below the unconfined-expansion limit, is inadequate to predict the stress regime at an ice-stream grounding line when the ice-shelf flow geometry differs from ideal, rectangular channel flow. This inadequacy results from the action of glaciostatic stresses distributed around the margins of an ice shelf, which lead to a reaction force, termed form drag, at the grounding line of an ice stream. Here, I examine the stress regime at the grounding line of the West Antarctic Ice Sheet in terms of form drag and dynamic drag, the latter of which arises purely due to ice-shelf motion and viscous coupling at the ice-shelf shear margins. Finite-element simulations of the Ross Ice Shelf discussed here show that form drag dominates dynamic drag at the grounding line of ice streams B and C. As a demonstration of the consequence of this dominance, the future evolution of the Ross Ice Shelf, and of the stress regime at the grounding line of ice streams B and C are simulated to assess the response to impulsive removal of the Crary Ice Rise. This simulation shows that the forces restraining Ice Stream B do not change by a significant amount even after 1000 years of simulated adjustment. The forces restraining Ice Stream C, however, reduce by 40% over the 1000 year period, with an initial 25% change occuring within the first 250 years. This contrast between ice streams B and C is attributed to the dominance of form drag, its dependence on the ice-shelf thickness distribution, and the effect Crary Ice Rise has on the ice-shelf thickness at the grounding lines of the two ice streams.

Results are presented from two years of field data collected along the Siple Coast region of West Antarctica. Measurements were made in the vicinities of base camps which were established in the mouths of ice streams B and C and at the upstream edge of Crary Ice Rise. The annual rate of ice deformation in Ice Stream C is very small, generally less than 10⁻⁵ yr⁻¹. Reoccupation of an 11 year old stake network permitted ice motion (6.1 m/yr) and grounding-line retreat (41 m/yr) to be measured. Visable strand cracks were used to map the grounding line. Its location differed from the grounding-line position determined from radar soundings by Scott Polar Research Institute (SPRI) by as much as 10 km but these differences are not believed to have dynamic significance. In contrast, Ice Stream B has no obvious grounding line near the position mapped by SPRI. The surface topography exhibits elongated ridges instead of the smoother surface of Ice Stream C. Regions of Ice Stream B with a lower surface elevation move faster than higher elevation regions, presumably because the lower-elevation ice is thinner and experiences less basal friction. Surface strain rates at Ice Stream B vary on a scale similar to the topographic relief but transverse differences in downstream velocity are only 1 to 2% of the 527 ± 50 m/yr ice motion. This value is slightly higher than predictions of the balance velocity which range between 450 and 480 m/yr. Near Crary Ice Rise, surface strain rates show increasing compression of the ice as it approaches the ice rise. The upstream boundary of Crary Ice Rise has been accurately determined based on a combination of surface measurements, aerial photography and radar-sounding data.

We report here on some of the results of our first two seasons work along the Siple Coast. These results are all preliminary in nature and could be modified substantially with further analysis. Furthermore, we have selected from a much larger body of data only a few points that we believe will be of interest to this workshop.

The horizontal and vertical velocity components within the transition zone between ice sheet and ice shelf are computed on a plane perpendicular to the grounding line. The transition flow is found numerically by solving a non-linear elliptic differential equation with fixed boundary conditions. The transition zone is located around the grounding line and its width is of the order of the ice thickness. In the case of basal sliding the transition zone can be widened considerably.

The finite-element technique as applied to a 1-D flowband model of an ice sheet is described, as well as several modeling experiments to demonstrate the power of this technique.

Based on the time-dependent continuity equation with ice velocity specified by a combination of flow and sliding laws, this fully time-dependent flowline-oriented finite-element model is used to:

The main problems in understanding the dynamics of a marine-based ice sheet are (i) the role played by longitudinal deviatoric stresses, and (ii) basal sliding. Although several studies have been reported in which both processes are incorporated in an ice-sheet model (either a numerical or a theoretical model), it is not clear how they affect the model outcome.

Following the recent analysis presented by Alley and Whillans (1984), however without neglecting the longitudinal-stress gradient along a flowline, an equation for the deviatoric stress is derived from the flow law and the equilibrium of forces. Incorporating this in a numerical model, together with an appropriate sliding relation, allows one to study the effect of (i) and (ii) on the behavior of the model ice sheet. This flowline model is compared with the Alley and Whillans model and with the earlier model of Budd and Jenssen (1975). In the latter model, longitudinal deviatoric stresses play a minor role and have very little effect on the model results. The two other models yield virtually the same results. This means that indeed the gradient of the deviatoric stress along a flowline may be neglected. In fact, the results suggest that only the longitudinal stress at the grounding line is important. Further inland, this stress becomes small and may safely be neglected without affecting the model results.

As for basal sliding, two laws were applied to the models. The classical Weertman-type sliding relation, corrected for subglacial water pressure, has little effect on the shape of the model ice sheet; a similar decrease in ice-sheet size can be obtained by increasing the deformation constant in the flow law. On the other hand, the sliding relation as used by Budd et al. (1984) causes a large thinning near the grounding line which is greatly enhanced when longitudinal stresses are incorporated in the model. Together, these processes yield a concave surface profile as observed on West Antarctic ice streams.

A subglacial aquifer bed model and basal sliding relationship is constructed for Ice Stream B West Antarctica. The calculated subglacial water discharge is 3 to 18 m³/s at the grounding line. The inferred subglacial water pressure is greater than 90 % of the ice overburden pressure for the entire 300 km length of the ice stream, and greater than 96 % of the ice overburden pressure for 230 km upglacier from the grounding line. This suggests that the high pore-water pressure mechanism proposed as an explanation of overthrust faulting also facilitates the rapid motion of the ice stream through the slower-moving mass of the ice sheet; that is, the ice stream is effectively decoupled from its bed by high water pressure within the subglacial sediments. In addition, this result suggests that subglacial water pressure in excess of 86 % of the ice overburden pressure, which is within the range found to be the cause of the 1982–1983 surge of Variegated Glacier in Alaska, may be typical of the flow regime of this ice stream. The bed model and inferred subglacial water pressures are consistent with (1) the calculated subglacial water flux, (2) the thickness of a porous water-saturated subglacial layer at a location where it was measured recently by geophysicists from the University of Wisconsin, (3) Darcy’s law, which governs water flow through a porous medium, and (4) an equation relating the basal sliding velocity of the ice stream to the inverse effective normal pressure on the bed, as well as to an empirical bed-smoothness function and the driving stress. The inferred distribution of subglacial water pressure is not a unique solution, but it falls within the range of physically-possible solutions.

The ratio R of the inferred subglacial water pressure to the ice overburden pressure beneath Upstream B camp (about 190 km upglacier from the grounding line) is 0.91 ≤ R ≤ 0.97. The effective normal pressure within the subglacial layer at this location, calculated from seismic velocity measurements by the University of Wisconsin geophysicists, is equivalent to 0.986 ≤ R ≤ 0.998. Both of these results suggest that if surge velocity is defined as abnormally high velocity for an ice mass of given geometry, due to minimal coupling at the bed caused, in turn, by high subglacial water pressure, then Ice Stream B is moving at surge velocity. This implies that ice streams may be expressions of ice-sheet surges. If so, the question of whether the West Antarctic Ice Sheet can surge (in a conventional sense), in response to warming climate caused by increasing CO₂ and other “greenhouse” gases, should be replaced by the question of whether the ice streams can accelerate, such that the rate of discharge across grounding lines exceeds the rate of replenishment over catchment areas. This question is of similar significance, because if ice-stream acceleration causes the mass balance of the West Antarctic Ice Sheet to become negative, thinning will occur, grounding lines will retreat, and sea level will be affected.

Integration of the thermodynamic equation over an entire drainage basin yields a fairly simple expression for the steady-state heat balance. This stems from the fact that dissipative heating can be calculated directly from the release of gravitational energy. When mass balance, surface temperature and geothermal input are known, the mean ice temperature at the grounding line can be obtained as a residual.

The procedure is applied to the drainage basin feeding the Ross Ice Shelf. The resulting mean outlet temperature is −16.2 °C. The heating rates making the balance turn out to be (in 0.0001 K/yr): dissipation 8.2, advective flux divergence -13.5 and geothermal heating 5.3. The method also reveals how the mean outlet temperature depends on mass balance, surface elevation, etc.

The three-dimensional ice-sheet model of the West Antacrtic Ross Ice Shelf Basin, developed by Budd et al. (1984), has been used to compute basal temperatures and melt rates for a wide range of values of the geothermal flux. Steady state is assumed and ice “balance velocities” are computed from continuity and used in the heat-conduction equation. As the geothermal flux increases, the melt area increases and becomes connected to the water under the Ross Ice Shelf via the major ice streams.

The large-scale average surface and bed slopes are used to determine the broadscale pattern of flow of the basal meltwater on the assumption that it flows as a film at the ice-bedrock interface. The total water volume flux for steady state is determined from the basal melt rates and continuity, and the film assumption then allows the mean water film thickness and velocities to be computed. The resulting pattern of steady-state mean water-film thickness is then interpreted in terms of its possible relationships to the basal sliding rates and the basal shear stress particularly under the major ice streams.

Increasing carbon dioxide and other trace gases in the atmosphere over the next few centuries may lead to important consequences in regard to climatic change. One of the most severe consequences alluded to is the possibility of a rapid rise in sea level resulting primarily from increased melting of the Antarctic Ice Sheet — particularly from West Antarctica where much of the ice is currently grounded well below sea level.

The present generation of coupled atmosphere-ocean general circulation models still have problems in simulating the present situation, but nevertheless have provided useful information on the possible decrease in the Antarctic sea-ice cover and the increase in ocean temperatures over time as a result of the warming following the increased atmospheric carbon dioxide concentration. This information has been used to analyse the extreme likely increases in the melt rates of the Antarctic ice shelves and the resulting increased strain rates which could then occur near the grounding lines.

A hierarchy of ice-sheet modelling studies has been carried out covering the fast-flowing ice streams, the ice sheet thermal regime and the whole Antarctic at a coarser resolution. The range of consequences likely for ice loss and sea-level rise are computed in detail for the next 500 years, and in less detail for several thousand years hence.

It is concluded that the effects for sea-level change could be substantial but of a magnitude (up to 1 m in 500 years and 3.5 m in 1000 years) and a rate of change (maximum of 0.6 m/100 years) that could be manageable if adequate monitoring and planning are carried out.