Pine Island Glacier flow and dynamics

Pine Island Glacier flow and dynamics
Case for support
1. Introduction
The aim of this project is to develop a threedimensional, first-order numerical model of ice
flow and apply it to Pine Island Glacier, West
Antarctica (PIG, WAIS). The two principal
outcomes of the project will be an understanding
of the relationship between basal traction and slip
for the ice stream; and a predictive model of its
future evolution. The project will also see the
development of a generic ice-flow model suitable
for the analysis of many of the ‘meso-scale’
problems of contemporary glaciology (e.g., the
onset areas and margins of ice streams, and icedome flow).
The WAIS contains enough water to raise
global sea level by over 5 m [IPCC 1995]. PIG and
its neighbour Thwaites Glacier (TG) drain 40% of
the ice sheet. The marine termini of these glaciers
have been highlighted as potential sources of rapid
retreat because of their lack of significant ice
shelves and a bedrock topography which deepens
considerably inland [Hughes 1980; Bindschadler
et al. 1998; Oppenheimer 1998]. The grounding
line of PIG is known to have retreated between
1992 and 1994 at a rate of 1.2 km yr-1 [Rignot
1998]. There is therefore an urgent need to
understand the causes of this retreat, as well as its
future implications for the WAIS and global sea
level.
The project draws on several recent
developments made by the glaciology groups at
Southampton and University College London
(UCL). These include: the mapping of PIG’s
surface velocity using satellite radar interferometry
(SRI); the mapping of a dramatic ice-surface
lowering for PIG over the last seven years using
repeat satellite altimetry (RA, see Figure 1); the
development of a transect ice-flow model which
fully incorporates longitudinal stresses (i.e., is a
first-order approximation to ice flow).
The project has four main objectives, which are:
1. Apply existing transect model to PIG.
2. Extend existing data coverage to cover the
whole of the PIG drainage basin.
3. Develop three-dimensional (3-d) version of
the first-order model.
July 2000
Objective Two will be undertaken by a funded
postdoctoral research associate (PDRA) at UCL
(one year), while the remaining objectives will be
undertaken by the principle investigator (PI), co-PI
(SJC) and a second funded PDRA at Southampton
(two years). Objectives One and Four both have
two phases. The first is to apply the respective
models in a diagnostic fashion with a fixed ice
geometry and using SRI velocities to constrain the
parameterization of basal slip in the model. The
second phase is to allow ice geometry to evolve in
response to the calculated ice-flow field using the
basal parameterization determined in the first
phase.
Figure 1. Ice-surface elevation change (coloured
dots in m yr-1) superimposed upon ice-surface
velocity (greyscale in m yr-1) over the main
trunk of PIG [Shepherd et al., submitted],
showing the first-ever direct observation of
imbalance in a WAIS ice stream. These new
data indicate that the relatively unknown PIG
basin is undergoing change, in contrast to the
near stasis of the Siple coast and RonneFilchner regions.
4. Apply this model to PIG using additional
data generated by the project.
Pine Island Glacier
1
2. Scientific Background
2.1 The importance of WAIS ice streams
The evolution of the WAIS has been identified
by many authors as a key unknown in future sealevel change [Oppenheimer 1998; Bentley 1998;
Bindschadler et al. 1998]. The vast majority (>
90%) of mass lost from the ice sheet flows through
a relatively small number of ice streams [McIntyre
1985].
An understanding of the long-term
behaviour of these ice streams is therefore vital if
we are to predict future sea level accurately. PIG
has the largest discharge (66 Gt yr-1) of all WAIS
ice streams [Vaughan et al. submitted]. Despite its
importance in draining large areas of the ice sheet
(with TG 40%), relatively little is known about
PIG in comparison to other WAIS ice streams.
The exciting new findings summarized below
suggest that PIG is changing rapidly. These
changes may have far-reaching consequences for
the future of the WAIS because of PIG’s role as
the primary drainage portal of the ice sheet.
2.2 Previous PIG research
Observations of PIG change by Rignot [1998]
showed that the grounding line retreated 8 km
inland between 1992 and 1994. This implies ice
thinning at the grounding line of the order of 3.5 m
yr-1. In addition to these measurements, the UCL
group has recently shown [Shepherd et al.
submitted], through the combination of SRI and
RA data, that grounding-line retreat is due to a
widespread pattern of ice thinning that extends up
to 150 km inland, reaching the ice-stream head
(Figure 1). This thinning cannot be explained by
fluctuations in the surface mass budget, and is
likely to have resulted from a change in the
dynamics of the ice stream itself. However, the
source of the disturbance still remains uncertain.
One suggestion [Rignot 1998] is that the
disequilibrium may have resulted from the
disintegration of a large ice shelf in Pine Island
Bay at some stage in the recent past. However,
new thickness observations by British Antarctic
Survey [Vaughan et al. submitted] cast doubt on
this. PIG is shown to be lightly grounded for a
short distance inland of its marine terminus.
Immediately upstream of this area, there is a very
deep subglacial trough. Given this configuration,
it may be argued that the inland stream is insulated
from changes at or downstream of the grounding
line, and that the source of thinning must lie
elsewhere.
The grounding-line retreat observed by Rignot
[1998] and the surface-lowering shown by
Shepherd et al. [submitted] imply that PIG is
changing rapidly. This may be a consequence of
either external forcing or may be generated
internally (possibly cyclic). The mechanisms
driving this change will only be fully understood
by modelling of PIG and its drainage area. In this
way, internal variability within the ice-flow system
can be quantified [e.g., Payne 1998] and the
effects of external changes (for instance sea-level
rise or ice-shelf removal) assessed.
2.3 Modelling Ice Flow
Ice-sheet models can be divided into four
coupled components: ice-thickness evolution; icetemperature evolution; ice flow and stress regime;
and ancillary calculations (including isostasy and
mass balance calculations). In this proposal, we are
principally concerned with third component.
The
widely-accepted
Shallow
Ice
Approximations (SIA) [Hutter 1983] are based on
assumptions regarding the stress regime within ice
masses, and relate this regime to ice velocities (or
strain rates) using the non-linear flow law for ice
proposed by Glen [1955]. Depending on the
spatial scale of investigation (with respect to ice
thickness) and the nature of ice flow, varying
degrees of SIA are appropriate. Two sets of
approximations are widely used within the
glaciological literature. The first (the zero-order
approximation) is the basis for virtually all models
of grounded ice sheets [e.g., Huybrechts and de
Wolde 1999; Payne 1999]. This assumption is
strictly appropriate only at spatial scales 20 times
ice thickness [Paterson 1994] (i.e. 20 to 50 km for
the WAIS). It assumes that longitudinal stresses
are minimal and flow is dominated by vertical
shearing. This type of model is inappropriate for
studying PIG because of this scale limitation, as
well as the likelihood of high longitudinal stresses
within the ice stream.
The second commonly used model is
specifically designed to study ice-stream and iceshelf flows. It replaces the assumptions mentioned
above with an assumption that vertical shear is
negligible [MacAyeal 1989]. These first-order
models can be used down to spatial resolutions 4
times ice thickness [Paterson 1994] (5 to 10 km).
However, their use is only justified in situations
where basal traction is guaranteed to be low and
vertical shear can therefore be ignored [MacAyeal
1989]. This type of model may not be applicable
to PIG because it experiences high driving stresses
[Bentley 1987] and flows over steeply inclined
bedrock slopes [Vaughan et al. submitted].
Pine Island Glacier
2
Recently, significant progress has been made on
a class of model that is first order (i.e.,
incorporates longitudinal stresses) but does not
rely on the negligible vertical shear assumption
[Blatter et al. 1998; Gudmundsson 1997]. The
only assumptions made in these models are that
acceleration can be ignored; that the momentum
balance in the vertical is dominated by gravity; and
that the vertical shearing is simple.
These
assumptions are all valid away from icefalls and at
spatial scales similar to ice thickness. A secondorder model would avoid the latter two
assumptions [Blatter 1995] but would necessarily
be considerably more complex. It is believed that
first-order models of this class represent a natural
tool for the analysis of PIG flow.
The PI has recently developed a first-order
flowline model (FOFM, incorporating the vertical
and one horizontal dimension) of the type
described above. The numerical implementation is
based around that proposed by Herterich [1987].
Several innovations have improved the numerical
stability of the scheme in comparison with the
original. These include the use of finite-volume
discretizations [Patankar 1980]; a non-linear
iteration technique [Hindmarsh and Payne 1996];
and a stretched vertical coordinate system [Jenssen
1977]. Figure 2 illustrates results from this model
for the Arolla benchmark dataset [Blatter et al.
1998]. The scheme solves the momentum-balance
and flow-law equations in the form of a highly
non-linear elliptic equation.
The required
boundary
conditions
are
discussed
below.
Figure 2 Results from a newly developed firstorder model applied to the Glacier d'Arolla,
Switzerland. The variation of longditudinal
stress (in kPa) throughout the ice mass is
shown. Axes are in m.
3 Specific Objectives
3.1 Transect model of PIG
The aim of this objective is to test and refine the
methodology that will be used later in applying the
3-d first-order model to PIG.
The FOFM was developed by the PI while on
sabbatical at the University of British Columbia.
Its immediate use is to study the flow of the
Langjökull Ice Cap, Iceland under the NERC
thematic programme Arctic Ice and Environmental
Variability (ARCICE). This application is similar
in many respects to the proposed PIG work,
however Langjökull is isothermal so that
thermally-induced variations in the viscosity of ice
can be ignored. This is certainly not the case for
PIG and Payne [1995; 1999] has shown that the
coupling between temperature and flow may be
crucial in the long-term evolution of ice streams.
A certain amount of development work will
therefore be necessary before the existing model
can be applied to PIG. The use of an existing
flowline model ensures that the proposed
methodology can be tested rapidly and efficiently
rather than waiting to a later, more critical stage of
the project to discover potential flaws.
A flowline representation of PIG is not ideal for
two reasons. First, there are indications that PIG is
fed by a number of tributaries [Stenoien 1998] and
the geometry of its drainage basin is complex
[Bamber and Bindschadler 1997]. Second, the
incorporation of transverse shear at the ice-stream
margins is problematic in flowline models.
Nonetheless the FOFM should provide a useful
test bed for the project. Table 1 shows the data
that will used in this and the 3-d modelling.
The FOFM’s velocity model requires boundary
conditions at the upper and lower boundaries of the
ice mass. On the former, a zero-traction boundary
condition is appropriate. While the basal boundary
condition depends on the nature of the
ice/substrate interface. If ice is frozen to the
substrate then a zero-velocity condition is
appropriate.
However, if basal meltwater is
present a prescribed traction is most natural
[Herterich 1987].
MacAyeal et al. [1995]
parameterize this traction as a function of basal
slip velocity. Alternatively, a basal slip velocity
can be prescribed directly.
Application to PIG is likely to use a horizontal
grid of 5 km. The other components of the model
(ice thickness and temperature evolution and
ancillary calculations) already exist in a suitable
form.
The model application will be in two phases:
prognostic and diagnostic. First, the model will be
run in diagnostic mode with ice-mass geometry
held fixed. The aim of this phase will be to use
SRI-derived estimates of surface velocity to
constrain the parameterization of basal slip. A
Pine Island Glacier
3
number of alternative methods are available to do
this. MacAyeal et al. [1995] use control methods
to accomplish this task with a vertically-integrated
ice-stream model. A naïve approach to this
problem is as follows (we return in Objective Four
to a more sophisticated approach based on control
methods).
1. Determine velocity assuming a frozen bed.
2. Find anomaly between SRI and modelled
upper-surface velocities.
3. Repeat the calculation using this anomaly as
the prescribed slip velocity.
4. Iterate Steps 2 and 3 until anomaly between
SRI and modelled velocities falls below a
threshold value.
The inclusion of temperature calculations and
their coupling to ice flow will complicate this
proceedure slightly. The scheme is analogous to
the restoring boundary conditions used for seasurface temperatures and salinities in many general
ocean circulation models. The resultant basal
velocity and stress fields will be consistent with
the SRI data and the model’s physics. The
relationship between these two quantities can then
be used to identify a realistic parameterization that
can be used in the next, prognostic, stage of the
objective.
The precise details of this
parameterization will depend on the results,
however the separation of PIG into spatially
distinct regimes is a likely approach.
The
robustness of these parameterizations to
assumptions about ice viscosity, thermal regime
etc will be investigated in a sensitivity analysis.
The aim of the prognostic stage is to compare
modelled changes in ice thickness to those
available from RA assessments of surfaceelevation change [Shepherd et al. submitted] and
grounding-line migration [Rignot 1998].
In
particular, the modelling will attempt to determine
whether the observed changes imply long-term
collapse or internally-generated cyclic behaviour
[Payne 1995; 1999]. This work will be
complimented by a larger analysis of the effects of
changes in sea level, sub-shelf melt rates, air
temperatures, accumulation rates and basal traction
on PIG.
Objective One will therefore allow us to
develop an effective research methodology using
the computationally-efficient FOFM before
moving to the more cumbersome 3-d model of
Objectives Three and Four. In addition, it will
generate publishable results in its own right.
Table 1 Data required in the modelling. Likely
data sources are indicated as well as data’s use
in diagnostic (D), prognostic (P) or both (B).
Data
Surface topography
and surface change
Bed topography
Surface velocities
Air temperatures
Geothermal flux
Accumulation rates
Sub-shelf melt rates
Grounding line
D
Source
RA
B
D
B
B
P
P
B
BAS’ BEDMAP
SRI
Giovinetto et al. 1990
Assumed
Vaughan et al. 1999
Jenkins et al. 1997
Rignot 1998
3.2 Acquistion of new data
This objective aims to extend the existing data
coverage to include the majority of the Pine Island
basin. This is needed so that the 3-d modelling is
adequately contrained over the basin and can
therefore be used to study long-term evolution.
This objective will generate information of
unprecedented detail for an area which includes all
tributary flows to the PIG, as well as regions of
slow-flowing ice in the basin interior. Two
techniques will be used. First, the existing SRI
coverage of ice-surface velocity (Figure 1) will be
extended by a factor of four. Second, RA will be
used to measure changes in ice-surface elevation
over the same area.
The spatial distribution and temporal variability
of ice-surface velocity within the PIG drainage
basin will be determined using SRI from the ERS
satellites. The existing velocity mosaic will be
extended to cover the remainder of the basin
viewable by the synthetic aperture radar (SAR)
sensor using existing ERS data (Figure 3). This
task will lead to a fourfold increase in our existing
ice-surface velocity map. The substantial ERS
SAR data volumes that will be required are
available to us through the VECTRA programme.
In the slow-moving interior of the drainage basin,
tandem and 3-day ERS SAR repeat passes may be
insufficient to reveal the intricate nature of the ice
flow patterns. Fortunately, snow accumulation is
typically low in these regions, and 35-day repeat
pass data, which is frequently available, can also
be used to produce interferograms with good phase
coherence. The temporal spread of the ERS SAR
dataset, in conjunction with velocity estimates
from other sources (e.g. feature tracking using
historical satellite imagery), will be used to
identify possible velocity variations within the PIG
basin.
Pine Island Glacier
4
Part of the southern lobe of the PIG drainage
basin (Figure 3) falls beyond SAR coverage, and
other methods of velocity estimation will be
required to complete the velocity map.
Interferometric data from the RADARSAT sensor
(which covered this region during a dedicated
Antarctic mapping mission in 1997) has been used
to estimate the velocity of slow moving interior ice
(<100 m yr-1) [Joughin et al. 1999]. We will
endeavour to obtain similar data through existing
collaborations, but in the event that RADARSAT
data are unavailable to us, we will employ other
remote sensing techniques, such as feature tracking
using Landsat imagery, to obtain direct estimates
of ice speed within the southern lobe. The
RADARSAT data have been particularly useful in
identifying regions of flow imbalance [Bamber et
al., 2000] and, building upon these findings, we
aim to characterise the nature of the ice-sheet flow
within the southern lobe to determine any
departure from equilibrium. As an alternative to
the direct measurements of SRI, balance velocities
[Budd and Warner 1996] may be sufficiently
accurate in the slow-moving interior, and we will
investigate the utility of this technique.
Measurements of surface-elevation change will
be extended through a succession of satellite
altimeters (ERS, ENVISAT, and ICESAT).
ENVISAT will provide a seamless continuation of
the current ERS time series, and data from the
ICESAT laser altimeter will offer increased spatial
coverage over the Antarctic Ice Sheet. These
extended time series will yield higher accuracy. An
increasing amount of fine detail will therefore be
revealed in the pattern of thinning across PIG and
its drainage basin.
3.3 Development of 3-d model
The aim of this objective is to develop a 3-d
first-order model of ice flow suitable for
application to PIG.
The FOFM is not the perfect tool for the study
of PIG. The main reasons for this are the tributary
structure of the upper parts of the ice stream; the
complex shape of the Pine Island drainage basin;
and the incorporation of ice-stream shear margins.
The development of a 3-d version of the model
(3DFOM) is therefore necessary.
Equivalent numerical models for the other
components of a general 3-d ice-mass model
already exist (thickness and temperature evolution,
and ancillary calculations). They have been
developed within the NERC non-thematic grants
on ‘Coupling models of ice streams and ice sheets’
(GR3/11532) and ‘Stability of the Antarctic Ice
Sheet: a numerical analysis’ (GR3/12917). The
change in scale between those projects (20km
grids) and the proposed project (5 km grid) does
not affect the validity of these model components,
although it may lead to numerical complications.
The experience gained in developing the
velocity/stress regime component of FOFM should
prove very useful in developing 3DFOM. It is
hoped that the same approach can be taken to the
solution of the underlying non-linear elliptic
equation. There are, however, two complicating
factors. The first is that two coupled elliptic
equations will have to be solved (one for each
horizontal velocity component). Experience in
solving these equations was gained in the
completed GR3/11532. The main source of
additional complexity is correcting for the
stretched vertical coordinate system, which can
often quadruple the number of terms involved.
The second complicating factor is that the
FOFM code uses a preconditioned conjugategradient method to solve the linear parts of the
equation. This is acceptable in two dimensions
with typically 20 vertical layers and 100 horizontal
columns (2,000 points). However, it may become
impractical over an equivalent 3-d domain
(200,000 points). FOFM uses the sparse-array
package SLAP [Seager 1988]. There are several
ways of avoiding this problem. First, the larger
capacity of parallel computers could be employed
(as in the current GR3/12917). Second, FOFM
could be used to explore the potential for
dramatically reducing the number of layers (initial
impressions are that the vertical structure of the
stress fields is relatively simple).
The development of a 3-d, first-order model
which is fully coupled to both ice-thickness and
ice- temperature evolution would represent a major
methodological advance. The model would be the
natural tool for the analysis ‘meso-scale’ problems
in ice flow. Examples of this type of problem are
the onset of ice streaming [Joughin et al. 1999];
the transmission of stress between ice streams and
neighbouring sheet-flow areas [van der Veen and
Whillans 1996]; and the long-term evolution of ice
domes (with their potential as ice-coring
locations). These types of problem are key to our
understanding of the dynamics of large ice masses
but are not readily amenable to analysis using
existing classes of model. This is because their
fine spatial scales violate the assumptions behind
zero-order continental-scale models, while
Pine Island Glacier
5
vertically-integrated ice-stream models may not be
applicable because very low basal traction cannot
always be assumed.
The proposed methodology is equally
applicable to vertical-shear dominated (sheet) flow
and horizontal-stretching (stream/shelf) flow, as
well as transitions between these types of flow. Its
use therefore avoids the need for an a priori
classification of flow before the appropriate model
is applied. Another potential use of this type of
model would be in studying ice caps and valley
glaciers, which are simply to small for zero-order
models to be applicable [Hubbard et al., 1998].
Objective Three will therefore develop 3DFOM
using the experience gained in developing FOFM.
The end result should be a very generic model,
which would be appropriate to the study of the
‘meso-scale’ ice dynamics problems of PIG, as
well as other glaciological features in Antarctica.
More generally, it would also represent a better
tool for the study of small ice caps and glaciers
than currently exists.
predicted to have beds at melting point. Areas
predicted to be frozen to their beds should only
have residual amounts of basal slip.
3.4 Application of 3-d model to PIG
This objective aims to understand the flow
dynamics of PIG and its long-term evolution by
applying a 3-d first-order model of ice flow to the
whole drainage basin.
The strategy used in applying 3DFOM will be
similar to that of Objective One.
The
computational domain will cover the entire Pine
Island basin at 5 km resolution.
The four
glaciological regimes present in the area will
therefore all be incorporated: slow-flowing inland
ice; ice-stream tributaries; PIG itself; and the
grounding-line and ice-shelf area. The physics of
the model are appropriate to all four regimes,
without a priori classification. It is essential that
the whole drainage basin be modelled in this way
rather than restricting the analysis to PIG itself.
This is because the long-term evolution of the ice
stream is likely to be controlled by ice drainage
from the basin interior and its thermomechanics
[Payne 1998].
The diagnostic phase of this objective will use
the ice-surface velocities generated in Objective
Two to constrain the unknown basal slip field (as
explained in Objective One).
The proceedure
should be equally applicable in areas both with and
without basal slip.
A simple check on model
consistency will be to compare the predicted basal
slip and temperature fields. Areas predicted to
experience large amounts of slip should also be
Figure 3 Current (upper) and potential (lower)
SRI coverage for Pine Island basin. Hatch
orientation indicates ascending and descending
(both are required to estimate the 3-d icesurface velocity vector), while hatch density
indicates single and repeat pass coverage.
A detailed analysis of the relationship between
basal slip, basal traction and basal temperature will
yield the parameterizations used in the prognostic
phase of the objective. In this phase, ice thickness
will be allowed to respond to the changing patterns
of velocity predicted by the model. A series of
experiments will be undertaken which gradually
remove constraints on the ice mass. Examples
include allowing the grounding line to migrate
freely, and allowing the inland boundaries of the
drainage basin to migrate. This later topic also
addresses the influence of neighbouring ice
streams on the drainage basin of PIG and will
attempt to explain the latter’s peculiar shape (see
Figure 3).
The aims of these prognostic experiments are
twofold. First, to determine whether the observed
Pine Island Glacier
6
PIG changes are a consequence of external forcing
or internal dynamics. Second, to assess the
consequences of these changes for PIG’s long-term
evolution and the likelihood of its collapse.
In the event that the proceedure of Objective
One proves inapplicable, we will follow the
control method techniques proposed by MacAyeal
[1993]. The key extension will be to apply these
techniques to a model which allows for high
driving stresses and vertical variability. The misfit
between the observed velocity constraints and the
output from the model is minimised using
Lagrange multipliers and a gradient-descent
algorithm. To ensure that the data is not overfitted,
it is necessary that the minimisation incorporates a
measure of the error in the data: random
measurement error, interpolation error or mapdigitization error, and so we will minimise the chisquared between the data and the model. We have
successfully applied this methodology in the
context of electrical impedance tomography (EIT),
which is a widely studied non-linear inverse
problem in medical imaging [Blott et al., 2000].
There is also the potential, indeed likelihood, of
multiple minima: an effective procedure to address
this is outlined in MacAyeal [1993]. Furthermore,
our experience from EIT work has demonstrated
that the fully 3-d problem may be less susceptible
to such problems when constraints are placed on
its boundary, particularly if additional smoothness
constraints are imposed on the final solution.
4 Timetable and Expertise
The project will last for two years and will start
on 1st February 2001. The grant is required
principally to support two PDRAs. One PDRA
will be based in Southampton and will work on the
modelling objectives for the whole of the project.
The second PDRA will work on the remotesensing objective at UCL for one year. The named
reseacher for this post is Andrew Shepherd who
has extensive experience in the application of SRI
and RA in Antarctica.
The four objectives will be subdivided between
the PIs and PDRA as follows.
1. FOFM application during months 1 to 12
with AJP (support) and Southampton PDRA
(main).
2. Data acquistion in months 1 to 12 with
DJW (support) and UCL PDRA (main).
3. 3DFOM development in months 1 to 12
with AJP (main) and Southampton PDRA
(support).
4. 3DFOM application in months 12 to 24
with AJP (support), SJC (support) and
Southampton PDRA (main).
The project is timetabled so that the data
acquistion will be completed before the application
of the 3-d model starts (Year Two). During this
first year, the Southampton PDRA will gain
training in the application of higher-order
glaciological models and will help in the
development of the 3-d model. Year Two will see
the application of the 3-d model, however there is
likely to be continued input from AJP and SJC on
development and control methods, respectively.
The three PIs have contrasting skills which are
well suited to the proposed project. AJP has wide
experience in the application of numerical models
to ice-sheet and glacier flow. Southampton-based
PDRAs D.J. Baldwin and A.L. Takeda will offer
support, respectively, in the development of icestream models and the application of parallel
computing. SJC has considerable expertise in the
development of parallel algorithms and the
solution of inverse problems. His work on nonlinear inverse problems in medical imaging will be
particularly helpful in Objective Four. DJW and
his group are world-leaders in the application of
remote-sensing techniques to glaciology, with
expertise in SRI and RA which is unparalleled in
the UK.
5 Justification of Resources
Previous awards to the Southampton group
have led to the purchase of a Silicon Graphics
Origin 200 server with associated workstations and
peripherals. Other high-performance computing
resources are available in Southampton through
SJC. The group is therefore well resourced in
terms of computational power. The purchase of a
medium-specification personal computer is,
however, requested to allow the Southampton
PDRA unrestricted access to these resources. A
compact-disk writer is also requested to facilitate
the storage of the large volumes of data likely to be
generated by the project.
Funds to cover
consumables such as software licences and
magnetic tapes are also requested. The latter are
needed because repeat-pass interferometric
coverage of the PIG drainage basin will require
around 400 further SAR scenes. To archive this
data we will need a total of 27 35Gb DLT tapes
(400×0.33Gb raw data, 400×1.1Gb SLC data,
200×1.1Gb interferograms, 100×1.1Gb differential
Pine Island Glacier
7
interferograms). This is the only viable method of
data storage for long strips of SAR data.
Some travel funds have been requested to
facilitate bi-monthly visits between UCL and
Southampton. These will be essential in guiding
model development and the acquistion of
appropriate data to constrain the model. Regular
visits to the British Antarctic Survey (Cambridge)
are also anticipated for discussion on the bedrock
topography and glaciology of PIG. Results from
the project will be reported at the annual American
Geophysical Union (AGU) meeting in 2002
(modelling results), and the International
Symposium on Remote Sensing in Glaciology in
2001 (remote-sensing results). The latter meeting,
in particular, will be useful in exposing the
modelling methodology to criticism early in the
project. The AGU meeting will be combined with
a visit to Allied Researcher Rignot, who is a
world-leader in the application of SRI to the
WAIS.
All data generated by the project will be
submitted for archiving at the Antarctic
Environmental Data Centre, Cambridge.
6 References
Bamber, J.L., and R.A. Bindschadler, An improved elevation
dataset for climate and ice-sheet modelling: validation with satellite
imagery, Ann. Glaciol., 25, 1997.
Bamber, J.L., et al.,Widespread complex flow in the interior of the
Antarctic Ice Sheet, Science, 287, 1248-1250, 2000.
Bentley, C.R., Rapid sea-level rise from a West Antarctic ice-sheet
collapse: a short-term perspective, J. Glaciol., 44, 157-163, 1998.
Bentley, C.R., Antarctic ice streams: a review, J. Geophys. Res., 92,
8843-8858, 1987.
Bindschadler, R.A., et al., What is happening to the West Antarctic
Ice Sheet?, EOS Trans., 79, 257-265, 1998.
Blatter, H., Velocity and stress fields in grounded glaciers,: a simple
algorithm for including deviatoric stress gradients, J. Glaciol., 41,
333-344, 1995.
Blatter, H., et al., Stress and velocity fields in glaciers: Part II.
Sliding and basal stress distribution, J. Glaciol., 44, 457-468, 1998.
Blott, B.H., et al., High fidelity imaging and high performance
computing in nonlinear EIT. Physiol. Meas., 21, 7-13, 2000.
Budd, W.F., and R.C. Warner, A computer scheme for rapid
calculations of balance-flux distributions, Ann. Glaciol., 23, 21-27,
1996.
Giovinetto, M.B, et al., Dependence of Antarctic surface mass
balance on temperature, elevation, and distance to the open ocean,
J. Geophys. Res., 95, 3517-3531, 1990.
Glen, J.W., The creep of polycrystalline ice, Proc. R. Soc. London,
Ser. A, 228, 519-538, 1955.
Herterich, K., On the flow within the transition zone between ice
sheet and ice shelf}, in C. J. van der Veen and J. Oerlemans (eds.)
Dynamics of the West Antarctic Ice Sheet, D. Reidel, Dordrecht,
185-202, 1987.
Hindmarsh, R.C.A., and A.J. Payne, Time step limits for stable
solutions of the ice sheet equation, Ann. Glaciol., 23, 74-85, 1996.
Hubbard, A., et al., Comparison of a first-order approximation for
ice flow with field data: Haut Glacier d’Arolla, Switzerland, J.
Glaciol., 44, 368-378, 1998.
Hughes, T.J., The weak underbelly of the West Antarctic Ice Sheet,
J. Glaciol., 27, 518-525, 1980.
Hutter, K., Theoretical glaciology, D. Reidel, Dordrecht, 1983.
Huybrechts, P., and J. de Wolde, The dynamic response of the
Greenland and Antarctic ice sheets to multiple-century climatic
warming, J. Climate, 12, 2169-2188, 1999.
Gudmundsson, G.H., 1997, Basal flow characteristics of a nonlinear flow sliding frictionless over strongly undulating bedrock, J.
Glaciol., 43, 80-89, 1997.
IPCC, Climate change: the science of climate change, Cambridge
University Press, 1995.
Jenkins, A., et al., Glaciological and oceanographic evidence of
high melt rates beneath Pine Island Glacier, West, Antarctica, J.
Glaciol., 43, 114-121, 1997.
Jenssen, D., A three-dimensional polar ice-sheet model, J. Glaciol.,
18, 373-389, 1977.
Joughin, I., et al., Tributaries of West Antarctic ice streams revealed
by RADARSAT interferometry, Science, 286, 283-286, 1999.
MacAyeal, D.R., Large-scale flow over a viscous basal sediment:
Theory and application to Ice Stream B, Antarctica, J. Geophys.
Res., 94, 4071-4087, 1989.
MacAyeal, D.R., A tutorial on the use of control methods in icesheet modeling, J. Glaciol., 39, 91-98, 1993.
MacAyeal D.R., et al., Basal friction of Ice Stream E, West
Antarctica, J. Glaciol., 41, 247-262, 1995.
McIntyre, N.F., The dynamics of ice-sheet outlets, J. Glaciol., 31,
99-107, 1985.
Oppenheimer, M., Global warming and the stability of the West
Antarctic Ice Sheet, Nature, 393, 325-332, 1998.
Patankar, S.V., Numerical heat transfer and fluid flow, Hemisphere
Publishing, New York, 1980.
Paterson, W.S.B., The physics of glaciers, Elsevier, Oxford, 1994.
Payne, A.J., Limit cycles in the basal thermal regime of ice sheets,
J. Geophys. Res., 100, 4249-4263, 1995.
Payne, A.J., Dynamics of the Siple Coast ice streams, West
Antarctica: results from a thermomechanical ice sheet model,
Geophys. Res. Lett., 25, 3173-3176, 1998.
Payne, A.J., A thermomechanical model of ice flow in West
Antarctica, Clim. Dyn. 15, 115-125, 1999.
Rignot, E.J., Fast recession of a West Antarctic glacier, Science,
281, 549-551, 1998.
Seager, M., A SLAP for the masses, Lawrence Livermore Nat. Lab.
Technical Report, 1988.
Shepherd, A., et al., Inland thinning of Pine Island Glacier, Science,
submitted
Stenoien, M.D., Interferometric SAR observations of the Pine Island
Glacier catchment area, Ph.D. Thesis, Univ. Wisconsin-Madison,
1998.
van der Veen, C.J., and I.M. Whillans, Model experiments on the
evolution and stability of ice-streams, Ann. Glaciol., 23, 129-137,
1996.
Vaughan, D.G., et al., Reassessment of net surface mass balance in
Antarctica, J. Climate, 12, 933-946, 1999.
Vaughan, D.G., et al., A review of ice-sheet dynamics in the PIG
basin, West Antarctica: hypothesis of instability versus observations
of change, Ant. Res. Ser., submitted.
Pine Island Glacier
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