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Geophysical Research Letters
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Supporting Information for
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High basal melting forming a channel at the grounding line of Ross Ice Shelf,
Antarctica
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Oliver J. Marsh*1,2, Helen A. Fricker 1, Matthew R. Siegfried 1, Knut Christianson 3, Keith
W. Nicholls 4, Hugh F. J. Corr 4, Ginny Catania 5
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Institute for Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of
California – San Diego, La Jolla, California, USA
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Gateway Antarctica, University of Canterbury, Christchurch, New Zealand
Department of Earth and Space Science, University of Washington, Seattle, WA, USA
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British Antarctic Survey, High Cross, Madingley Road, Cambridge, UK
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Institute for Geophysics, University of Texas, Austin, TX, USA
*Correspondence to: oliver.marsh@canterbury.ac.nz
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Contents of this file
Text S1 to S8
Figures S2 and S3
Tables S1
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Introduction
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This supporting information contains a description of data processing steps and
supplementary figures to aid in understanding the results presented.
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Text S1 - MODIS Imagery.
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MODIS imagery highlights surface slopes as brighter or darker areas depending on
satellite look direction and solar incidence angle and is useful for mapping the location of
surface depressions [Scambos et al., 2007]. Channel features migrate with ice shelf
flow and are newly created at the upstream end.
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Figure S1 (separate .gif). Migration of channel A in the direction of ice-shelf flow,
mapped on the ice surface in MODIS imagery. The apparent channel initiation point
does not move over ten-years, while all other features delineating the channel advect
downstream with flow.
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Text S2 - GPR Data.
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We have used a custom-built, low-frequency (3 MHz), short-pulse radar system to image
the base of the ice sheet across the upper part of the channel. Flat reflectors are
present at the ice-sediment interface (left) and ice-ocean interface (right), with weaker
reflection over the sediment. The region of high melt, as identified using phase-sensitive
radar, has disrupted reflectors and suggests the possibility of corner reflectors and
channel terraces or some localised basal crevassing immediately downstream of the
grounding line. Terraces have been discovered elsewhere [Dutrieux et al., 2014] and are
linked to spatially uneven melting. Ice thicknesses (h) are calculated from two-way travel
times (T) using a constant velocity of radar in ice of 0.168 m ns-1 (v) with depth-density
adjustment to account for higher wave speeds near the surface [Catania et al., 2010]:
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𝒉=
𝑻𝒗
𝟐
2
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Figure S2. GPS profile across the upper part of channel A (CHX1 to CHX 9 – see
Figure 1) with locations of phase-sensitive radar melt measurements from 2014 and
unmigrated ground-penetrating radar from 2006 at the same horizontal scale and
position.
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Text S3 - TerraSAR-X Data.
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Grounding-line location and flexure-zone width were estimated from TerraSAR-X
differential interferograms, produced using six StripMap SAR scenes over consecutive
11-day time periods in two sets of three (Dates: 25/09/12, 06/10/12, 17/10/12; 02/09/12,
13/09/12, 24/09/12). X-band SAR at a satellite incidence angle of 44.6° produces
interferograms with good coherence in this area. Comparison of our 2012 TerraSAR-X
data with 1997 [Gray et al., 2002] and 2009 [Rignot et al., 2011] grounding line positions
derived from Radarsat suggests < 200 m grounding line movement in this area over this
period.
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Text S4 - ICESat Data.
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Surface elevations for 2003-2009 at 12 channel cross sections are calculated from
Release 33 of the GLA12 product from ICESat [Zwally et al., 2014]. Corrections have
been applied for the G-C elevation offset [Borsa et al., 2014] and signal saturation. The
ocean tide correction is removed and a new tide correction applied based on the
CATS2008a_opt modelled tide at a point 10km offshore (84.635 °S 163.5 °W). An
offshore location is used for the tide, as any tide model may be inaccurate close to the
grounding line. In the flexure zone downstream of the grounding line tide corrections are
applied using an elastic beam bending profile across the region identified as the flexure
zone in TerraSAR-X interferometry [Marsh et al., 2014; Holdsworth, 1969]:
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w(x) = ht (1 - e-πx/L [cos(πx/L) + sin(πx/L)])
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where x is distance from the grounding line, w(x) is the tidal correction at x, L is the width
of the grounding zone, and ht is the tidal height on the freely floating ice shelf from the
tide model. Cross-sectional area of the channel depression is calculated by integrating
the area beneath a straight line that bisects the ‘shoulders’ of the channel (Fig. 2).
ICESat orbits are repeated approximately every 91 days to with 200m and are close to
perpendicular to both the channel and surface flow. Surface elevations are measured in
an Eulerian frame of reference and new surface features move into the satellite footprint
with each repeat. As the tracks are perpendicular to the channel, an offset of the ground
track from the reference track is equivalent to a shift in acquisition time and introduces
an error in our measurements of channel cross-sectional area. The linear fit to all valid
orbits in an area with good ICESat coverage minimises this error in the overall thinning
trend.
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Text S5 - GPS Data.
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We deployed 12 Trimble NetR9 receivers with Zephyr Geodetic or Zephyr Geodetic II
antennas, collecting data at 15s intervals over a 14-day period . We processed the GPS
data using precise point positioning techniques in kinematic mode implemented by
Natural Resources Canada’s online tool Canadian Spatial Reference System-Precise
Point Positioning (CSRS-PPP). Vertical movement of the GPS receivers matched the
expected flexure relative to distance from the grounding line, consistent with TerraSARX interferometry. We identified episodic signals in horizontal movement linked to stickslip cycles [Bindschadler et al., 2003], with overall horizontal extensional strain and a
small amount of lateral shearing in the channel initiation zone. Ice flow is parallel to the
grounding line and the ice shelf is moving at ~300 m a-1 - more slowly than the grounded
ice. Shear stress is low and horizontal strain is extensional (1.2 x 10-3 +/- 0.1 x 10-3 a-1),
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and across flow (perpendicular to the grounding line), implying only a small component
of dynamic ice thinning in this area.
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Text S6 - Meltwater Plume Model.
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The approximate average melt rate in the grounding zone (ṁ) is given by the following
equation [Jenkins, 2011]:
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𝑿
𝒎̇ = (𝟏 + 𝟎. 𝟐 ) 𝑨𝑼
𝑨𝑻 𝑴 (𝒈𝑫𝑿𝒐 𝑼𝑿𝟎 ∆𝝆𝒊 )𝟏/𝟑 (𝑻𝒂 − 𝑻𝒂𝒇 )
𝑿𝟎
𝑳 𝟎 𝟎 𝟎
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where X is distance from the grounding line, L is a characteristic length scale, AU and AT
are geometrical factors for velocity and temperature respectively, M0 is a melt rate factor,
g is gravity, Δ𝜌i is the contrast in density, U the velocity of the plume, D the thickness of
the plume, Ta the ambient water temperature and Taf the ambient freezing point. Given
the uncertainty in oceanographic conditions, we fixed all parameters including ocean
temperature to those in Jenkins [2011] Table 4, Section: Whillans, except DX0 UX0
(freshwater discharge) and the geometrical factors which depend on the basal slope,
which can now be better estimated using our radar data (S2). With a value of basal
slope at the grounding line of 1.5 ° and discharge of 48 m3 s-1 spread over a 1 km wide
outflow, we estimate a potential melt rate of 24.3 m a-1. Ta - Taf is taken as 0.418 °C
[Jenkins, 2011]. Although this melt rate seems in agreement with the phase-sensitive
radar data, the geometry of the outflow and width over which the channel drains is very
poorly known and errors in any of the parameters could contribute to order of magnitude
differences in melt rate. The subglacial discharge during periods of no lake drainage is
also not well enough known to make inferences about whether high discharge events
are required to allow the observed melt rates to occur or whether steady background
flow is sufficient.
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Text S7 - Phase-sensitive radar.
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We used phase-sensitive FMCW radar to calculate basal melt rates by repeating shots
at weekly intervals at sites within and around the channel. Internal layers within the
upper part of the ice column (60 m to 100 m) were used to vertically align repeat
measurements, while cross-correlation between lower internal layers (100 m to 600 m)
with better than 95% phase coherence in returned power was used to calculate vertical
strain rates. Over this short-time period strain thinning is within the error bounds for our
melt rate measurements and is neglected. The first peak in return power below 600 m
was taken as the primary bed reflector. In general, reflections from sites in the centre of
the channel were specular. Uneven reflections and multiple strong basal reflectors were
evident at the channel sides in areas with steep gradients. Melt rates across the upper
channel (CHX_), lower channel (CHZ_) and channel centreline (CH__) are shown in
Table S1. The specified latitudes and longitudes are the location of the radar at the
middle of the acquisition period, as the ice shelf and therefore measurement point
migrates with ice flow. Thicknesses are calculated using the same conversion from twoway travel time as for the ground penetrating radar in section S2. Melt rates are
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calculated from the gradient of a robust linear fit through all thickness measurements
against time. Errors on melt rates are RMS values for thickness on the linear fit.
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Figure S3. Phase-sensitive radar data from site CH04 in the centre of the channel. (a)
Time series of point measurements of ice thickness and linear trend, (b) movement of a
strong bed reflector, (c) matching of deep internal layers.
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Text S8 - Hydropotential and Outflow Modelling.
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Hydropotential is calculated using the following equation:
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θh = g[𝜌wzs – (𝜌w – 𝜌i) h]
where θh is hydropotential, 𝜌w is freshwater density, 𝜌i is ice density, h is ice thickness
and zs is surface elevation from BEDMAP-2 [Fretwell et al., 2013]. Subglacial drainage
pathways follow the modelling of Carter and Fricker [2012] and adjustment of bed
topography has been made based on the hydraulic potential map to match the location
of the past and current channels visible in the ice shelf. This adjustment of outflow
pathways is justified due to the very flat nature of the ice surface across this region and
the uncertain bed topography, particularly close to the outlet of lakes 7 & 8. The suture
zone between the Mercer and Whillans Ice Streams may provide a preferable route for
subglacial drainage to that proposed by Carter and Fricker [2012].
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Name
Latitude
(°S)
Longitude
(°W)
Date of first
acquisition
CH01
CH02
CH03
CH04
CH05
CH06
CH07
CH08
CH09
CH10
CHX1
CHX2
CHX3
CHX4
CHX5
84.62389
84.61908
84.61628
84.61405
84.60650
84.59938
84.59446
84.58929
84.58199
84.57492
84.60954
84.61215
84.61424
84.61677
See
CH02
84.62173
84.62382
84.62668
84.62920
84.46958
84.47126
84.47436
84.42555
84.42823
84.43045
162.07596
162.16739
162.24455
162.31348
162.47038
162.61037
162.70678
162.85030
162.99959
163.21186
162.10045
162.11906
162.13347
162.15118
162.18600
162.20090
162.22230
162.23924
165.57705
165.58779
165.61180
166.21326
166.23921
166.26378
CHX6
CHX7
CHX8
CHX9
CHZ1
CHZ2
CHZ3
CHZ4
CHZ5
CHZ6
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
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N
Thickness
(m)
Melt Rate
(m/a)
04-Jan-15
19-Dec-14
03-Jan-15
18-Dec-14
03-Jan-15
18-Dec-14
18-Dec-14
18-Dec-14
18-Dec-14
18-Dec-14
11-Dec-14
15-Jan-15
15-Jan-15
17-Jan-15
Date of
last
acquisition
17-Jan-15
17-Jan-15
18-Jan-15
18-Jan-15
18-Jan-15
18-Jan-15
18-Jan-15
18-Jan-15
18-Jan-15
18-Jan-15
17-Jan-15
17-Jan-15
17-Jan-15
N/A
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2
1
870.99
763.87
780.28
734.14
810.61
745.12
719.37
716.03
732.69
745.50
901.18
908.49
905.57
N/A
16.33 ± 0.11
22.16 ± 0.18
15.94 ± 0.87
19.37 ± 0.11
11.78 ± 0.28
4.60 ± 0.20
4.54 ± 0.08
2.59 ± 0.08
3.49 ± 0.11
3.91 ± 0.16
0.03 ± 0.12
1.29
1.06
N/A
17-Jan-15
11-Dec-14
17-Jan-15
11-Dec-14
20-Dec-14
20-Dec-14
20-Dec-14
20-Dec-14
20-Dec-14
20-Dec-14
N/A
18-Jan-15
N/A
17-Jan-15
12-Jan-15
12-Jan-15
12-Jan-15
12-Jan-15
12-Jan-15
12-Jan-15
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1
9
10
7
8
8
7
7
879.79
833.48
N/A
901.16
805.68
787.80
718.18
736.36
710.40
726.54
N/A
16.42 ± 0.14
N/A
0.82 ± 0.07
1.02 ± 0.07
0.66 ± 0.05
2.35 ± 0.22
1.04 ± 0.27
3.37 ± 0.18
3.51 ± 0.35
Table S1: Phase-sensitive radar data from sites within the channel as shown in Fig. 1
(N = number of acquisitions)
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Bindschadler, R. A., M. A. King, R. B. Alley, S. Anandakrishnan, and L. Padman (2003),
Tidally controlled stick-slip discharge of a West Antarctic ice stream, Science, 301,
1087–1089.
Borsa, A. A., G. Moholdt, H. A. Fricker, and K. M. Brunt (2014), A range correction for
ICESat and its potential impact on ice-sheet mass balance studies, Cryosphere, 8, 345–
357, doi:10.5194/tc-8-345-2014.
Fretwell, P., et al. (2013), Bedmap2: Improved ice bed, surface and thickness datasets
for Antarctica, Cryosphere, 7, 375–393, doi:10.5194/tc-7-375-2013.
Gray, L., N. Short, B. Bindschadler, I. Joughin, L. Padman, P. Vornberger, and A.
Khananian (2002), RADARSAT interferometry for Antarctic grounding-zone mapping,
Ann. Glaciol., 34, 269–276.
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