Identifying areas of low-profile ice sheet and
outcrop damming in the Antarctic Ice Sheet
by ERS-1 Satellite Altimetry


David G. Vaughan1 and Jonathan L. Bamber2,

1- British Antarctic Survey, Natural Environment Research Council, High Cross, Madingley
Road, Cambridge, CB3 0ET, UK.

2- Centre for Remote Sensing, Department of Geography, University of Bristol, Bristol, BS8 1SS,
UK.


Abstract

A Digital Elevation Model (DEM) of the surface of the Antarctic Ice Sheet is compared with a
simple two-dimensional ice flow model to illuminate gross distortions (> 500 m) of the ice
surface elevation. We use a DEM, derived from ERS-1 satellite altimetry, airborne data and
TWERLE balloon data. This is compared with an ice sheet elevation model generated by
applying theoretical surface elevations calculated for two-dimensional ice flow, to isolines of
distance from the grounding line (continentality). The model is scaled using only one parameter,
to match the measured surface elevation at Dome Argus. The model is far from rigorous,
violating continuity conditions, ignoring variations in surface mass balance and temperature, and
assuming uniform basal conditions. However, the comparison of model and observed surface
elevations is illuminating in terms of the behaviour of the ice sheet at a continental scale. Across
the ice sheet the RMS difference between modelled elevation and the DEM is around 300 m, but
much of this results from isolated areas of much greater disagreement. We ascribe these gross
differences to the effects of basal conditions. In four areas, the observed surface is more than 500
m higher than the modelled surface. Most of these are immediately upstream of substantial areas
of rock outcrop and are caused by the damming effect of these mountain ranges. In nine areas,
the measured surface is more than 500 m lower than predicted. Eight of these areas, in West
Antarctica and the Lambert Glacier basin, are associated with suspected areas of basal sliding.
The ninth is an area of 250 000 km2 in East Antarctica not previously noted to have unusual flow
characteristics, but for which very few data exist. We speculate that this area results from
unusual basal conditions resulting in a low-profile ice sheet. A low-profile ice sheet of this size
within the East Antarctic Ice Sheet indicates that basal conditions are perhaps more variable than
previously thought.
Introduction

Over the last couple of decades considerable effort has been expended to develop convincing ice
sheet models. These range from 2-dimensional, steady-state snap-shot models (for example:
Whillans and Johnsen, 1983; Waddington and Clarke, 1988, J”hannesson et al., 1989) to 3-dimensional time-evolving thermo-mechanical models (for example: Budd and Jensen, 1989;
Huybrechts, 1994; Fabre et al., 1995; Greve and Hutter, 1995). Together, these models form a
hierarchy of tools tuned to answer particular glaciological questions. While the trend is towards
more complex models that include more mechanisms and interactions, it is arguably true that we
have not yet fully exploited the simple models for the insight that they can provide into the
behaviour of the ice sheet.

In this study we use a model that is simple in concept and application to predict the surface
elevation of the ice sheet. While this model ignores many of the physical processes that would
be required to reproduce the details of the ice flow, most notably basal topography and drag
conditions, it can usefully be considered as a zero-order model of the ice sheet. We then compare
the predicted surface elevation with the best available continental DEM to highlight the grossest
model/observation differences. Finally, we attempt to ascribe these gross distortions of the ice
sheet surface to known areas of basal sliding and rock outcrop.

Antarctic digital elevation model - Observed DEM

This study arose from an attempt to assess a new digital elevation model (DEM) of Antarctica
(Figure 1.) previously presented and discussed by Bamber (1994) and Bamber and Huybrechts
(1996). For the majority of the continent, the DEM was derived from over 20,000,000
measurements of surface elevation retrieved from the eight 35-day repeat cycles of the ERS-1
satellite radar altimeter. Over areas where slopes are less than 0.5ø, the vertical accuracy is better
than ñ1 metre. In areas of higher surface slope accuracy of the altimeter is reduced. Around the
coast and in mountainous areas where the altimeter failed to maintain track on the ice sheet
surface, the altimeter measurements were supplemented with data taken from the Antarctic
Digital Database (SCAR, 1993).

Beyond the orbital limit of ERS-1, south of 81.5øS, data from the Scott Polar Research Institute
Folio Series (Drewry, 1983) and data from the original airborne radar sounding flights have been
used. In some areas the only data available was collected during the Tropical Wind Energy
Conversion Reference Level Experiment (TWERLE) 1975-76 (Levanon et al., 1977; Levanon,
1982).

All these data were gridded to 10 km resolution using methods described by Bamber and
Huybrechts (1996). Throughout the paper we shall refer to this DEM as the Observed DEM.
Figure 2. presents the Observed DEM as a series of images designed to highlight complementary
aspects of the topography. The two shaded-relief maps (Figure 2a and b) give an impression of
the overall shape of the ice sheet, while the map showing magnitude of surface slope (Figure 2c)
highlights flatter areas such as ridges, domes and lakes. Finally, Figure 2d shows the direction
of maximum slope and serves to highlight the exact position of the ice divides and ridges.

Ice sheet topography models - Modelled DEM

The model of ice sheet topography used in this study is the simple combination of two two-dimensional models.
A plan-view model based on a continentality argument yields the shape of
the predicted contours across the ice sheet. Elevations are then assigned to these contours using
a theoretical two-dimensional ice surface profile, to give a surface elevation contour map of the
predicted ice sheet. Interpolating the contours onto the same grid as Observed DEM gives the
Modelled DEM.

Continentality model

Martin (1976) gave a practical demonstration of the way that the positions of ice divides are
controlled by the shape of the margins of the ice sheet. As an analogue of ice he used sand, which
he poured onto a platform with a complex shape reminiscent of the bed beneath an ice rise. As
the addition of sand was gradual, a maximum load was eventually reached.
In this state of self-ordered criticality the maximum supportable surface slope was achieved everywhere, with the
exception of those areas very close to the crests of the ridges. The positions of the crests/divides
in this maximal system were easily observed under low angle illumination and shown to occur
midway between the edges of the platform. In this demonstration the sand behaves as a plastic
material - which can support only a certain maximum critical stress before failure making it a
reasonable first-order analogue of ice (Paterson, 1994, Chapter 5).

Reeh (1982) formalised and extended this analysis and showed analytically, assuming a plastic
rheology and without a strong bedrock slope, an ice divide should occur equidistant from the
margins. He went on to show that for the central Greenland Ice Sheet there are significant
departures from the idealised divide positions. He concluded that this was due to a strong trend
in bedrock elevation, the position of the ice divide being drawn towards bedrock ridges.

The experiment performed by Martin can now be simulated digitally. Given the shape of the
margin of an ice sheet, it is an easy procedure to draw "contours of continentality" - normals are
constructed inland from the grounding line and continentality is defined as the distance along that
normal to the grounding line. This was done for Berkner Island, Antarctica by Vaughan et al.
(1994) who showed that the pattern of the divides predicted in this way was indeed very similar
to that seen in reality. For the present study the margin is taken to be the grounding line extracted
from the Antarctic Digital Database (SCAR, 1993). In this case the contours of continentality
were drawn (Figure 3a) using the "buffering" algorithm available in the ARC/Info Geographical
Information System (GIS), but also in many similar products. Contours of continentality
correspond to the elevation contours predicted by Reeh's plastic ice sheet model, assuming a flat
ice sheet bed.

Figure 3b. shows a comparison of the drainage basins predicted by the continentality model
compared with those that have been derived from the Observed DEM (cf. Figure 2d). In many
areas the correspondence between the positions of Modelled and Observed DEMs is good, with
the largest areas of mismatch occur in Dronning Maud Land and West Antarctica.


Ice Sheet surface elevation profile model

A two-dimensional ice sheet profile model (Vialov, 1958) was used to assign predicted surface
elevations to the contours of continentality. Vialov (1958) showed that a model, based on a
power-law flow for ice yields a surface profile
where h is the ice sheet surface elevation, H is surface elevation at the ice sheet centre, x the
distance from the ice sheet margin and L is the distance from ice sheet centre to the margin. The
flow law parameter, n is taken to be 3. We tune the overall surface elevation by matching the
elevation at the Pole of Relative Inaccessibility (Figure 3a) to the elevation of Dome Argus (4050
m). Having applied this elevation profile to the contours of continentality we interpolated the
contour map onto a grid, to produce the Modelled DEM.

One inconsistency in the approach is that model assumes a zero ice sheet thickness at the ice
sheet margin, which is assumed to be the grounding line. Since ice thickness at the grounding
line is not generally zero there will be a model/observed mismatch near the grounding line.
However, the grounding line ice thicknesses are almost everywhere less than 2000 m, and around
1800 m of this are below sea level, so the mismatch due to this effect will only rarely exceed 200
m. We will see later that this is not significant compared to other sources of mismatch.

Below we shall present results for power-law flow. We have also produced a Modelled DEM
using a theoretical two-dimensional surface profile derived for plastic flow (Nye, 1953) with very
similar results. We therefore believe that our conclusions are largely insensitive to the choice
of flow law.

Comparison of Observed DEM and Modelled DEM

Figures 4a and 4b show the difference between the Observed DEM and Modelled DEM. Only
the areas of greatest mismatch (greater than ñ500 m) are shaded, together with areas of mapped
rock outcrop extracted from the Antarctic Digital Database (SCAR, 1993). The Modelled DEM
is on average only 300 m above the Observed DEM. It is likely that accounting for variations in
temperature and accumulation would have little effect on the model results and we conclude that
the gross areas of mismatch shown in Figures 4a and 4b are mainly the result of variations in
bedrock conditions.

Areas for which Observed DEM is higher than the Modelled DEM

Over much of the Antarctic Ice Sheet, the surface elevation does not closely reflect the
topography of the bed that lies beneath it. In other words, the bed topography is generally buried
so deeply that it fails to redirect the ice flow at the surface. This can be seen by comparing the
flowlines and bedrock topography given by Drewry, (1983) and Drewry and Jordan (1983). This
is, however, not the case where the bed protrudes through the ice sheet surface forming an
outcrop or nunatak, here the ice flow is necessarily diverted around the bed obstacle. Two effects
cause outcrops to dam the ice flow and raise the ice sheet surface upstream of outcrops. Firstly,
flow past the outcrop is genuinely obstructed and so the ice is at least partially dammed in the
interior. To drive the ice through gaps between the outcrops requires a large local surface slope.
Secondly, where ice flow is diverted around the outcrop, the actual distance which the ice must
travel to reach the grounding line is increased. Here continentality underestimates the distance
ice must flow to reach the grounding line. The ice surface is thus higher than would be predicted
by the model used here, which causes an apparent damming. Together these two effects are
largely responsible for the areas shown in Figures 4a, where the observed ice sheet surface
elevation is more than 500 m higher than the predicted surface elevations.

Areas H1,H3, H3 are directly upstream of extensive areas of rock outcrop associated with
extensive mountain ranges. The distributions of these areas shows up several noteworthy
points. The damming effect of mountain ranges in Dronning Maud Land (H1) appears to
reach back into the drainage basin and beyond the ice divide into the neighbouring basins.
The area of damming produced by the Transantarctic Mountains is not continuous and
the large glaciers that cut through the range (e.g. Byrd Glacier and David Glacier) appear
to be powerful enough to lower ice surface elevation on their hinterlands.

Areas H4 and some smaller unlabelled areas on coastal promontories are not so easily
interpreted as the result of damming by rock outcrops, rather they are probably associated
with elevated areas of bedrock.

Areas for which Observed DEM is lower than the Modelled DEM

Where basal conditions of an ice sheet reduce the maximum sustainable basal shear stress, the
ratio of ice velocity to surface slope is increased. This produces a low-profile ice sheet of the
type described by Boulton and Jones, (1979). Figures 4b shows the areas where the Observed
DEM is more than 500 m lower than the Modelled DEM. Most of these are associated with
reported areas of basal sliding.

Area L1 is an extensive area of low-profile ice sheet associated with the Siple Coast Ice
Streams (A-E) (Shabtaie et al., 1987).
Area L2 is the drainage basin associated with Pine Island Glacier and Thwaites Glacier,
which Lindstrom and Hughes (1984) have suggested suffers the "downdrawing" effect
of Pine Island Glacier
Area L3 is a low-profile portion of ice sheet occupying the area between Institute and
Foundation ice streams. This area was noted by Jankowski and Drewry (1981) as giving
unusual "ice-shelf-like" returns on airborne radar sounding records. They suggested that
this area might be some "intermediate" between ice sheet and ice shelf, resting on soft
water-saturated sediments and presumably suffering a large degree of basal sliding.
Area L4 covers some of Foundation Ice Stream and its drainage basin, which is known
to be flowing rapidly at more than 500 ma-1 (Riedel et al., 1995), and Patuxent Ice
Stream.
Area L5 is an area covering Lambert Glacier and its hinterland. It should be noted that
since the compilation of the Antarctic Digital Database the grounding line of Amery Ice
Shelf has been reinterpreted (Allison et al., in press) and the newly interpreted grounding
line is considerably further inland. Thus, while it is likely that some of the surface
anomaly in this area is real, it is also possible that the effect is the result of using an
incorrect grounding line.
Areas L6 and L7 are associated with Bailey and Slessor ice streams, respectively. Both
are highly active ice streams with considerable surface crevassing caused by the high
stresses associated with strainrates. Area L8 is fed by the Evans Ice Stream and includes
several tributary ice streams that converge and merge to form Evans Ice Stream (Jonas
and Vaughan, 1997).
Area L9 is not previously identified as being associated with basal sliding or having a
low-profile form.

L9 - A low-profile ice sheet in East Antarctica?

Almost all the areas of damming and areas of low-profile ice sheet identified in this exercise are
easily explained in terms of known outcrops and known or suspected basal lubrication. Only
Area L9, an extensive region (250 000 km2) of low-profile ice sheet within East Antarctica
remains unexplained. Such a large area of low-profile ice sheet has hitherto only been found in
West Antarctica where it is believed to be caused by massive ice stream activity and basal
lubrication. If L9 is the result of similar processes then it might cause us to rethink our ideas
about the stability of the East Antarctic Ice Sheet.

It should be noted that much of Area L9 lies beyond the limit of the ERS-1 altimeter data and so
the Observed DEM in this region is less precise than elsewhere. Over this area it is based largely
on TWERLE balloon data which, while being an order of magnitude less accurate than satellite
altimetry, still has a worst case error around of ñ 60 m (Levanon et al., 1977). Thus, while the
inaccuracy of the Observed DEM in this area may contribute to the surface elevation anomaly,
it is unlikely that it can account for the majority of the difference between Observed DEM and
the Modelled DEM ( > 500 m). In the event that L9 is the result of defective TWERLE balloon
data, then this is in itself constitutes a substantial result when we remember how many other
studies have directly or indirectly relied on this data.

We have found very few data of any type collected in this area which might confirm the
interpretation of Area L9. Only a few ice thickness measurements are available and so ice bed
elevation maps have been compiled from only a handful of points (e.g. Drewry and Jordan,1983).
Furthermore, no ice velocity measurements appear to be available. There does, however, appear
to be some corroborative evidence available from other modelling studies.

An area approximately corresponding to L9 was identified as having an unusually high sliding
fraction by the model fitting of Fastook and Prentice (1994). A similar effect can be seen in the
results of Huybrechts (1994, Figure 7) where it was interpreted as a region of anomalously high
basal temperature. In neither of these studies was the area explained or discussed in any particular
detail, or even noted as being contrary to current wisdom.

Budd and Warner (1996) used an ice surface DEM derived from Drewry, (1983) to calculate the
ice flux required to balance observed surface accumulation data over the entire ice sheet. Their
map of balance fluxes (Budd and Warner, 1996, Figure 1) does appear to show an area of high
ice flux roughly coinciding with Area L9. It is not, however, correct to simply interpret this high
flux as high velocity, when the ice thickness is so poorly known. Furthermore, since Budd and
Warner's DEM and the Observed DEM were derived largely from the same data in this area, the
two efforts cannot be seen as entirely independent results.

Clearly, Area L9 deserves the attention of field workers but would require a high logistical
commitment. Perhaps, the best hope for obtaining the required velocity data in the near future
will come from the Canadian satellite RADARSAT which carries a Synthetic Aperture Radar
(SAR). It has already been shown that fracture produced at ice stream margins is visible in SAR
imagery (Vaughan et al., 1994) and that ice stream velocities can be derived from SAR images
(Goldstein et al., 1993). RADARSAT is scheduled to be reconfigured to acquire complete
Antarctic coverage in September, 1997.

Conclusions

This study has shown the value of even simple models when used in conjunction with good
observational data, especially on a continental scale. In general, the results of the comparison
are confirmation of our intuitive expectations based on known regional flow characteristics. Rock
outcrops have a damming effect on the ice sheet which may dramatically shift the ice divide.
Conversely, areas of basal sliding lower the ice sheet surface and give rise to low-profile ice
sheets. The study has, however, been of further value, since it has identified an extensive region
of low-profile ice sheet reaching into the heart of the East Antarctic Ice Sheet (Area L9), whose
needs to be checked by some other method at the earliest possible date.

Acknowledgements

We wish to thank colleagues, especially CSM Doake, RCA Hindmarsh and AM Smith for
stimulating advice and APR Cooper for guidance in the use of the Arc/Info GIS. The comments
of three reviewers have also led to major improvements in the manuscript.

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Figures

Figure 1. Location map for Antarctica with areas of rock outcrop filled. 1. Institute Ice
Sheet, 2. Foundation Ice Stream, 3. Patuxent Ice Stream, 4. Amery Ice Shelf, 5.
Bailey Ice Stream, 6. Slessor Ice Stream, 7. Evans Ice Stream, 8. Lambert Glacier,
9. Dome Argus, 10. Transantarctic Mountains, 11. Byrd Glacier, 12. David
Glacier, 13. Siple Coast, 14. Pine Island Glacier, 15. Thwaites Glacier.

Figure 2. Digital elevation model of Antarctica - the Observed DEM. a. Shaded surface
relief with illumination from top of page. b. Shaded surface relief with
illumination from right side of page c. Shaded to show magnitude of surface
slope, with steeper slopes shaded darker. d. Shaded to show direction of surface
slope.

Figure 3. a. Contours of continentality used as elevation contours to produce the Modelled
DEM. Generated from Antarctic Digital Database grounding line, buffered at 50
km intervals. The figure shows graphically that the Pole of Relative
Inaccessibility for the contiguous continent is located at 82ø50' S 48ø20' E
(marked by triangle). This point is 1090 km away from that previously identified
(marked by a star, British Antarctic Survey, 1993).
b. Ice flow drainage basins derived from Observed DEM (full lines), and from
contours of continentality (grey lines).

Figure 4. Areas of difference between Observed DEM and Modelled DEM. a. Areas where
the Observed DEM is more than 500 m higher than Modelled DEM (grey) with
areas of rock outcrop (black) and extent of ERS-1 altimetry (circle) and drainage
basins (full lines). b. Areas where the Observed DEM is more than 500 m lower
than the Modelled DEM (grey) and extent of ERS-1 altimetry (circle) and
drainage basins (full lines). The labels identify areas discussed in the text.