Introduction
The West Antarctic Ice Sheet (WAIS) contains about 10 %
of the Antarctic ice and is mainly marine based
. A partial collapse under the influence of
prospective warming scenarios could contribute to global eustatic
sea level rise by 3.3 m . Consequently,
a deeper understanding of the local ice dynamics and its drivers
concerning future developments is essential. In this study, we
focus on the West Antarctic Siple Coast, where the ice dynamics
are clearly dominated by five major ice streams, also called the
Ross Ice Streams: Mercer, Whillans, Kamb, Bindschadler and
MacAyeal Ice Stream (Fig. ). They are
responsible for the vast majority of the ice transport from the
interior of the WAIS towards the adjacent Ross Ice Shelf.
Observations reveal a high variability in the mass flux of the
Ross Ice Streams as well as a significant short-term variability
in ice stream shear margin and grounding line positions
. The best-known example is the Kamb Ice
Stream, measuring 745 km from the onset of the
northernmost tributary to the grounding line. It began to stagnate
∼150 years ago , whereby its former
position could be reconstructed from short-pulse radar profiles
. They show scatter from buried crevasses,
which were presumed at the surface when the ice stream was still
active. The thickness of the undisturbed ice layers over these
crevasses allows a back dating and reveals a sequential
stagnation. The stagnation wave had its initiation at the
grounding line of the ice stream 130±25 years ago,
followed by the slow-down of the middle part
100±30 years ago and finally ended at the upstream
part only ∼30 years ago
. Surface-based
ice-penetrating radar profiles show an undulating internal
stratigraphy and thus prove its former fast flow conditions with
pre-stagnation flow velocities exceeding 350 ma-1 in
the trunk of the ice stream . With the same
observation techniques evidence for a former ice stream crossing
the Kamb to the Bindschadler Ice Stream at the northeast flank of
the Siple Dome was found . But also the
currently existing Whillans Ice Stream was detected to
decelerate. Over the period 1974–1997
estimated a velocity loss of about 23 % with
a combination of conventional interferometry and speckle-tracking
methods applied to Radarsat-1 data. This was confirmed by
using full InSAR, revealing a velocity
change of -100 ma-1 (-25 %) for the
Whillans Ice Stream and -40 ma-1 (-17 %)
for the Mercer Ice Stream at their grounding lines between the
years 1997 and 2009.
Since the Ross Ice Streams are responsible for the majority of the
mass export from the inner ice sheet to the grounding line, their
evolution plays a key role for the future mass balance of the
Siple Coast. In order to understand or even predict their dynamic
behavior, we consider two of the most commonly controls on ice
stream locations defined by literature
e.g.,: subglacial geology and
subglacial melt water routing.
The prime control which creates the precondition for ice streams
to evolve in this area of investigation is clearly given by the
subglacial geology. Numerous seismic campaigns detected a layer of
till under the Ross Ice Streams
e.g.,. Beneath the Whillans Ice Stream this
unconsolidated layer of sediment was estimated to be
5–6 m thick on average and presumed to be glacial till
e.g.,. The ratio of till viscosity to
effective ice viscosity is small
. Consequently, the vertical shear associated
with horizontal flow is confined to the deforming bed alone and
thus the deformation of till can be regarded as the primary
mechanism by which the ice streams move
. Borehole measurements with a tethered stake apparatus by yielded a basal
sliding in the amount of 83–100 % of the total ice
motion. However, rigid bedrock substrata may contact the ice base
beside the deformable till in small areas and cause vorticity in
the velocity field. At these spots the ice surface appears
rumpled, visible, e.g., at Landsat images of the MacAyeal Ice
Stream . also observed
sedimentary basins in seismic reflections upstream of the Kamb and
Bindschadler Ice Streams, which are considered to control the
onsets of these ice streams. The inland termination of these
sediments suggests that a possible future migration of the latter
onsets is unlikely . At the grounding line of
the Whillans Ice Stream, discovered a till
delta tens of meters thick and tens of kilometers long. These
sediments originate from upstream locations and are transported
downstream by the moving ice. Beyond, this sedimentary wedge at
the grounding line is believed to stabilize the position of the
grounding line even despite moderate changes in sea level
.
The existence of subglacial till gives the precondition for the
development of ice streams at the Siple Coast. However, their
exact locations seem to be defined by the pathways of melt water
flow. The general prevalence of basal water at the Siple Coast is
confirmed by a range of radar sounding campaigns
e.g.,. They
found high reflection strengths at the trunks of the ice streams,
interpreted as wet bed, and lower reflections at the ice rises in
between, interpreted as dry bed. The transitions between the areas
with detected wet and dry beds show exact correlation with ice
stream margins. Boreholes drilled to the ice bottom confirm that
the ice base is at melting point inside the confines of the ice
streams and reveal a dry bed outside
e.g.,. In addition,
seismic investigations discovered a highly porous basal till layer
which is saturated by water e.g.,for the Whillans Ice
Stream.
Following the above considerations, the evolution of subglacial
melt water pathways due to changing basal pressure conditions is
most likely capable to explain the observed spatial and temporal
variability of the ice streams at the Siple Coast. In this study,
we use the hydrology module of the ice flow model
Rimbay in
combination with current ice geometry data
and observed ice surface elevation changes to simulate present-day and prognostic basal water
catchment areas and subglacial pathways of water
flow. Subsequently, their patterns are investigated with respect
to correlations with present-day ice velocity observations and
possible implications for future migrations and velocity changes
of the Ross Ice Streams are derived.
Methods
Basal melting
Observations of many (active) subglacial lakes at the Siple Coast
reveal a widespread, dynamic subglacial water system
e.g.,. However, the precise
local melt rates are barely known since they elude direct
measurements and model results partly contradict each
other. Analytical model results, e.g., for the Whillans Ice
Stream, indicate melt rates between 3–7 mma-1 for
the upstream and 20–50 mma-1 for the downstream
domain . In contrast, used
another modeling approach and found that most melting occurs
beneath the tributaries where larger basal shear stresses and
thicker ice favor higher melt rates in the order of
10–20 mma-1. The ice stream tributaries and the
inland ice are accounted for about 87 % of the total
melting generated beneath the Ross Ice Streams including their
catchments . Following ,
this melt water transports latent heat from beneath inland ice to
the base of the ice streams, while temperatures at the bottom of
the ice streams itself and accordingly the melt rates are low,
caused by the scarce internal ice deformation and the consequently
lacking internal frictional heating.
In all following simulations, the hydrology-module within the ice
model Rimbay is forced
with a constant basal melt rate for all grounded ice nodes. In
this way, the influence of the entire basal water catchment area
of the Siple Coast is equally represented and the fluxes can be
expressed as percentage of this total catchment area. Thus, the
above discussed uncertainties discussed above related to the
calculation of basal melt rates beneath the Ross Ice Streams are
avoided and the focus is set on catchment areas sizes and water
pathways.
Basal water routing
In general, melt water at the base of an ice sheet follows the
gradient of the hydraulic potential p
p=ρwgz+pw
with ρw the water density, g the gravitational
acceleration and pw the water pressure at the
considered point of elevation z. The effective pressure
peff. at the ice base is defined as the ice overburden
pressure pi minus water pressure pw.
At the ice base of the Siple Coast, borehole measurements and
seismic investigations reveal the prevalence of a meters-thick layer
of unconsolidated sediments (glacial till). This layer is highly
porous and locally saturated by water, whereby the water pressure
was determined to be within 0.5 to 1.5 bar of the overburden
ice pressure e.g.. For example, a column of
1000 m ice (a common ice thickness at the main trunk of the
Whillans Ice Stream) with an ice density of 910 kgm-3
applies a gravitational pressure of 89.27 bar to the
bed. The measured difference between basal water and ice pressure of
0.5 to 1.5 bar corresponds to a deviation of only 0.6 to
1.7 % for the above example. Hence, the water pressure at
these measuring sites is very close to the ice pressure and one can
assume a distributed water flow system with an effective pressure of
zero e.g.,. Sparse borehole
measurements show pw>0.95pi
e.g., and confirm this approximation.
Consequently, the hydraulic potential p can be approximated by
p=ρwgz+piorp=ρwgB+ρigH,
where B is the bedrock elevation and H the ice thickness.
The flow of basal melt water is assumed to follow the basal
hydraulic potential (Eq. ) and to be in
a steady state. Thus, it can be taken advantage of the balance flux
concept e.g., to calculate the melt water
pathways with scalar water flux Φ by solving
divΦ=Mb,
where Φ=Wv¯(w) with water layer thickness W, vertical averaged water velocity v¯(w) and basal melt rate Mb. Hereby, a preceding modification of the hydraulic potential guarantees flux conservation .
Model domain
Our study area encompasses parts of Marie Byrd Land and the Siple
Coast, being enclosed by ice divides in the north and in the east
(Fig. a). We assume that these ice
divides act as subglacial watersheds, whereby the area of interest
can be also considered as hydrologically enclosed at these
margins. Beyond the Transantarctic Mountains a small part of the
East Antarctic Ice Sheet is included, because it belongs to the
basal hydrological catchment area of the Siple Coast. In the west,
the area of investigation is bounded by the Ross Ice Shelf.
Ice sheet geometry
For present-day simulations of basal melt water pathways, the
basal hydraulic potential (Eq. ) is
calculated by using the bedrock elevation and ice thickness data
provided by the Bedmap2 data set
. For this purpose, the Bedmap2 data
set is resampled to resolutions of 5, 10 and 20 km for the
Siple Coast region.
In order to enable prognostic simulations of the subglacial
drainage system, satellite-derived surface elevation change rates
from the ICESat and the CryoSat-2
campaign are applied to the present-day ice
sheet geometry in all stated resolutions
with a time step of one year for the next 200 years. The
consequent dynamic changes of the basal hydraulic potential
subsequently allow assessments of the future basal water
pathways. The applied basal melt rates are not affecting the ice
thickness in these simulations, since all processes which have an
influence on the local mass balance are assumed to be included in
the observed surface elevation changes. They are exclusively used
for the calculation of the balance flux.
Results and discussion
Present-day subglacial water pathways
The simulated pathways of basal melt water for three different
model resolutions are shown in Fig. ,
with the color scale illustrating the local drainage in percent of
the total catchment area. The outflow concentrates towards six
embayments at the grounding line. This finding is consistent with
results from who investigated the variable
supply of subglacial melt water to the grounding line, using
a similar steady-state water model and estimates for lake volume
changes derived from ICESat data.
Our simulated water pathways correspond to the areas of fast ice
flow depicted in Fig. . That
significantly supports the assumption, that the locations of the
ice streams are controlled by subglacial water
routing. Furthermore, the flow patterns of the two coarser model
resolutions clearly show how upstream water tributaries of the
former Kamb Ice Stream (C) are partly draining into the Willans Ice
Stream (D). The 5 km model run reveals a more finely
branching flow system which also covers the trunks of all
present-day ice streams. However, there are still non-negligible
melt water contributions towards the downstream part of the
stagnated Kamb Ice Stream (C). This does not necessarily mean the
model results are wrong. Airborne radio echo sounding field
campaigns detected a wet bed derived from strong reflections for
the main trunk of the Whillans and the stagnated Kamb Ice
Stream e.g.,. The detected transitions
towards dry bed areas in the inter-ice stream regions match
precisely the margins of the Kamb Ice Stream, which already slowed
down 150–30 years ago. Within the former Kamb Ice Stream
margins low radar reflectivity was limited to so-called sticky
spots (small areas with high basal ice traction) and along the Kamb
margins . A borehole drilled to the ice bottom
at a sticky spot also found a dry bed there
. This supports the hypothesis that sticky
spots control the stagnation and possible reactivation of ice
streams, once the basal melting passes a certain threshold
. assumed that the
loss of lubrication on localized sticky spots at the ice bed
interface can cause a shutdown or redirection of an entire ice
stream. On the other hand sticky spots, often observed to be
located along the ice streams margins, act as water sources and
supply the ice stream with melt water. The ice sliding at high
basal traction in combination with strong internal deformation
provides a powerful heat source for basal melting from which the
adjacent, comparatively cold ice stream benefits by enhanced
lubrication. Additionally, the ice-thickness perturbations induced
by ice flow over variable traction create local hydraulic
minima. That explains the observed collocation of sticky spots and
subglacial lakes .
Present-day subglacial water catchments
The relative sizes of the water catchment areas for all Ross Ice
Streams are listed in Table . They refer
to the total upstream area of five defined cross sections of
approximately 140 km length, corresponding to the
locations of the main trunks of the five major ice streams
(Figs. and
).
Neglecting small variations, the calculated water catchment areas
agree very well for the different model resolutions. The Whillans
Ice Stream (B) overspreads the heaviest flow of water which is
draining 31.3±4.6 % of the upstream catchments. This
supports the fact, that Whillans Ice Stream is the fastest flowing
Ross Ice Stream with ice surface velocities up to about
700 ma-1. Beneath Bindschadler (D) and MacAyeal Ice
Stream (E) drain the comparable percentages of
22.2±0.5 and 24.0±0.8 % of the total
upstream catchment area, well-fitting to their similar velocities
of about 670 ma-1. Accordingly, the flow beneath the
smaller and slower Mercer Ice Stream (A) drains the smallest part
with 9.3±2.1 % of the total upstream
catchment. Despite the fact that the Kamb Ice Stream (C) stagnated
tens of years ago, the basal flow underneath drains the
considerable amount of 13.2±3.1 % of the total
upstream Siple Coast catchment. Here, complex and yet not fully
understood control mechanisms at the ice base appear to rule the
ice motion in the face of a observation-proved wet bed as already
discussed above.
Prognostic subglacial water pathways
The simulated basal water pathways after adding observed ICESat
and CryoSat-2 surface
elevation change rates to the present-day ice geometry
at the Siple Coast for a timespan of
200 years are shown in Fig.
for a model resolution of 5 km. Again, the color scale
illustrates the percentual drainage of the total catchment
area. Beneath the outer Mercer (A) and MacAyeal (E) Ice Streams,
the water flow patterns show no remarkable changes within the next
200 years. However, underneath the central three ice
streams the water pathways show a very dynamic behavior. Here, in
the middle part of the stagnated Kamb Ice Stream (C), the strongest
growth in ice thickness occurs following the satellite
observations. This area is marked with a red circle in all figures
(Figs. c and
). The arising and thickening ice
bulge increasingly diverts the basal melt water flow at this spot
and leads to a lateral separation of the flow patterns. At present,
a major upstream water tributary (tagged with a red star) is
feeding into the Kamb (C) and the Whillans Ice Stream (B) area
(Fig. c). Within the next
200 years this water influx will be entirely redirected
towards the Bindschadler Ice Stream (D). Consequently, the water
flow beneath the Kamb Ice Stream will be lacking this contributions
(Fig. ). This main characteristic of
the computed future water pathways is found consistently for both
satellite surface elevation change rate data sets at all three
applied model resolution (5, 10 and 20 km) emphasizing the
robustness of the result.
Prognostic subglacial water catchments
The basal water fluxes towards the grounding line through five
cross sections corresponding to the locations of the main trunks of
the Ross Ice Streams under the influence of the ICESat and
CryoSat-2 surface change rates are estimated for the next
200 years. Due to the prescribed constant melt rate, the
temporal evolution of the water catchment area upstream of every
cross section can be computed as a percentage of the total upstream
catchment area of all cross
sections. Figure a shows the
evolution of the catchment areas for the experiments with
5 km resolution at a time step of 1 year. The
graphs confirm the above analysis of the water pathways. The water
catchment areas feeding underneath Mercer (A) and MacAyeal Ice
Stream (E) remain stationary over the period of the next
200 years. The water catchment area of the Kamb Ice Stream
(C) first gains about 2 % in size from the Whillans (B)
catchment within the next 10 years. Thereafter, it
continuously loses area in favour of the Bindschadler Ice Stream
(D). Again the analogy of the influences of the two satellite
derived surface change rates on the evolution of the basal
hydraulic system is striking. Additionally, the black line in
Fig. a shows the development of the
total upstream catchment areas which reveal very slight variations
in size due to the shifting of water sheds by the applied ice
thickness changes. Remarkable features are the occurring steps
within all graphs. They indicate points in time when larger water
tributaries are linked to (or delinked from) a catchment due to the
dynamics of the basal water pathways.
The variations of all catchment areas at all model resolutions
after 200 years are summarized in
Fig. b and c. Both ICESat and
CryoSat-2 surface change rates indicate a future loss of about
12 % (at 5 km model resolution) of the water
catchment area feeding underneath the Kamb Ice Stream (C) while the
water catchment area of the Bindschadler Ice Stream (D) increases
by the same amount. In this way, the water catchment area of the
Bindschadler Ice Stream grows by roughly 50 % and the
lower part of the stagnated Kamb Ice Stream becomes almost
hydrologically separated from the upper regions of the Siple
Coast. Due to the revealed spatial correlations between simulated
basal water flow and observed ice surface velocities, this might
indicate a continuation of the processes which caused the
stagnation of the Kamb Ice Stream in the past and could lead to an
acceleration of the Bindschadler Ice Stream in the future. The
experiments with a resolution of 20 km show this
redirection to a lesser extent
(Fig. b and c). Obviously, this
resolution is too coarse to point out details within the evolution
of local water flow patterns.
Conclusion
At the Siple Coast, the recent stagnation of the Kamb Ice Stream
and the discovery of numerous relict ice-flow features indicate
a steady competition between several preferred ice-flow paths of
the Ross Ice Streams. While an observed basal layer of
unconsolidated sediments beneath the ice sheet enables high basal
sliding rates by sediment deformation e.g.,,
the subglacial melt water routing is considered to be the main
control on the current ice stream locations at the Siple Coast and
has the potential to explain their observed variability in the
past.
The application of a steady-state approach to simulate the basal
melt water pathways supports this assumption as all current ice
stream outlines are found to be clearly associated with areas of
enhanced modeled water flow. Furthermore, the ice velocities of the
ice streams are found to be related to the water catchment area
sizes draining underneath. Applying observed present-day surface
elevation changes of two different satellite campaigns
to the present-day ice sheet
surface for 200 years allows an estimation of future basal
drainage routes. According to this simulation, the basal water
pathways at the Siple Coast are highly sensitive to small ice
thickness changes due to the prevailing smooth bedrock. A major
hydraulic tributary of the Kamb and Whillans Ice Streams is
estimated to be redirected underneath the Bindschadler Ice Stream
within the next 200 years. Accordingly, the water catchment
area feeding underneath the Bindschadler Ice Stream is estimated to
grow by about 50 % while the lower part of the stagnated
Kamb Ice Stream becomes increasingly separated from the upper
hydraulic tributaries of the Siple Coast. This might be
a continuation of the subglacial hydraulic processes which caused
the past stagnation of the Kamb Ice Stream
e.g.,. Furthermore, this might explain the
observed deceleration of the Whillans Ice Stream
and might also lead to a future increase of
the ice velocity within the Bindschadler Ice Stream followed by an
increased ice drainage of the corresponding hinterland.