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Auxiliary Material
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Rapid dynamic activation of a marine-based Arctic ice cap
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Malcolm McMillan1*, Andrew Shepherd, Noel Gourmelen, Amaury Dehecq, Amber Leeson,
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Andrew Ridout, Thomas Flament, Anna Hogg, Lin Gilbert, Toby Benham, Michiel van den Broeke,
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Julian A. Dowdeswell, Xavier Fettweis, Brice Noël and Tazio Strozzi.
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1. Centre for Polar Observation and Modelling, School of Earth and Environment, University of Leeds,
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LS2 9JT, UK
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*Corresponding author: m.mcmillan@leeds.ac.uk
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1. Altimetry methods for estimating surface elevation change
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1.1 ICESat
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ICESat data from release 633, distributed by the National Snow and Ice Data Center
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(www.nsidc.org) and spanning the period 2003-2009, were processed along-track [Smith et al.,
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2009] to determine linear rates of elevation change. Data were selected from the GLAH12 v33
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data product, with all records from the poor quality campaign 2C removed. Measurements
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without valid saturation corrections were excluded, as were data flagged as not for use in
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elevation studies. The product elevation values were already corrected for all instrumental and
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atmospheric effects except for two, which were applied at this stage. These were the campaign
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bias, which was corrected using published values [Borsa et al., 2013], and the saturation, for
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which we applied the correction supplied with the product where appropriate. An accuracy of ±
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0.15m was assumed [Shuman et al., 2006].
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ICESat records from all campaigns were grouped within 700 m along-track segments, with each
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segment overlapping by 200 m and of sufficient width to encompass the across-track separation
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of repeated campaigns. For the reliable retrieval of model parameters, the data within each
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segment must be distributed in space and time. To remove instances where this may not be the
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case, we only processed segments that contained at least 3 single tracks, each consisting of at
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least 3 measurements, and collectively covering at least 3 years. For each segment we then
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iteratively solved for the spatial and temporal fluctuations in elevation, at each step removing
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records which deviated by more than 5 m from the model solution.
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1.2 Envisat
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Envisat elevations from product version 2.1 were processed along-track with the algorithm
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presented in Flament and Rémy [2012]. Elevation trends are only available in the upper
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catchment because, on tracks coming from the sea, the on-board tracker kept the lock on the
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brighter sea surface up to 20 km inland, thus not collecting any ice surface data closer to the
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coast. After processing, Envisat elevation trend estimates were relocated using the Point Of
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Closest Approach (POCA) method. We used a digital elevation model [Moholdt and Kääb, 2010]
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to locate the POCA and we limited the maximum displacement allowed for a given point to 6.3
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km, the radius of the Envisat radar altimeter microwave beam. After relocation, the
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measurements were gridded on a 50 m grid using weighted local averaging with a radius of 10
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km and weight defined by a squared cosine decreasing from 1 to 0 over the 10 km.
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1.3 CryoSat
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Between July 2010 and April 2014, CryoSat acquired a total of 125,000 interferometric mode
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elevation measurements over Austfonna. To estimate rates of surface elevation change, we used
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an along-track method [McMillan et al., 2014], which has been designed to utilise the long 369-
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day orbit repeat cycle of the satellite. Elevation records were grouped within either 2 km or 5 km
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square regions and within each region we solved, simultaneously, for spatial and temporal
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fluctuations in elevation. We modelled elevation ( z ) as a bilinear function of surface terrain (
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x, y ) and a linear function of time ( t ) within each region (equation 1).
z x, y, t   z  a0 x  a1 y  a2 t
(1)
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The larger (5 km) grid cell size was used when the full CryoSat record was split in to 2 separate
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time periods (2010-2012, 2012-2014), to increase data availability within each cell to constrain
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the model fit. As part of the processing, a correction was applied to account for temporal
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fluctuations in backscatter that cause spurious fluctuations in range [Davis and Ferguson, 2004;
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Khvorostovsky, 2012; Wingham et al., 1998]. To suit the scale of Austfonna, we adapted our
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previous method, which had been designed for application to the Antarctic Ice Sheet [McMillan
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et al., 2014], in two ways. Firstly, we modelled topography as a bilinear and not a quadratic
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surface. Secondly we did not solve for a surface anisotropy parameter [Armitage et al., 2013;
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McMillan et al., 2014], because Austfonna is located further from the latitudinal limit of the
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satellite, in comparison to the near Pole regions of Antarctica where this effect is most
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pronounced. These modifications led to a reduction in the number of parameters solved for in the
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model, and allowed us to group data within smaller (2 km square) regions, which are more
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appropriate given the size (8000 km2) of the ice cap.
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As part of the processing chain, several data editing steps were untaken. Firstly, we removed
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CryoSat records where the interferometer failed to compute an across track location, or where the
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deviation from a pre-existing digital elevation model [Moholdt and Kääb, 2012] was more than
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100 m. These criteria were applied in order to prevent poor quality measurements from entering
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the model fit. The latter threshold was chosen to be relatively large in order to avoid removing
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valid data, given that high thinning rates of up to 30 m/yr were observed. Secondly, during the
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elevation rate calculation outlying data were culled iteratively, using a 3-sigma clip, so as to
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minimise their impact on each solution. Finally, following the model fit, grid cells with poorly
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constrained model solutions were rejected based upon model residuals and parameter thresholds.
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To compute rates of ice volume change across basin 3 from CryoSat-2, we integrated all
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estimates of elevation change within the geographical region of interest, which was defined using
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data from an airborne topographic survey [Dowdeswell et al., 1986]. For the <5% of the region
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that remained unsurveyed, we assumed a basin-averaged elevation rate. Volume rates were
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converted to an estimate of mass imbalance by assuming an ice density of 917 kg m-3. 1-sigma
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elevation rate uncertainties were computed from each model fit. These uncertainties depend upon
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the distribution of elevation measurements accumulated within each grid cell, and provide a
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measure of the extent to which our prescribed model of linear elevation change through time fits
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these observations. This statistical measure does not formally account for all sources of
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uncertainty, but will include factors such as radar speckle, some errors in satellite location,
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retracker imprecision and unmodelled atmospheric attenuation [Wingham et al., 1998]. Volume
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rate uncertainties were calculated by summing elevation rate uncertainties, because we assume
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that errors may be correlated at the scale of ice cap basins, and then converted to mass using an
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ice density of 917 kg m-3.
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2. Velocity data and methods for estimating ice flow
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Ice velocity was calculated from measurements made by Synthetic Aperture Radar (SAR)
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satellite sensors. Displacement fields were calculated using the techniques of Synthetic Aperture
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Radar Interferometry (InSAR) when the time span between successive acquisitions was
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sufficiently short to preserve interferometric coherence [e.g. Goldstein et al., 1993], and feature
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tracking (FT) otherwise [e.g. Strozzi et al., 2002; Paul et al., 2013]. Table S1 summarises the data
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and techniques used. Prior to calculating displacement fields, SAR data were co-registered by
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masking the area of high displacement in basin 3. Displacement fields from InSAR or FT were
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then geocoded using a reference Digital Elevation Model [Moholdt and Kääb, 2012]. The value
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of the FT correlation window and the sampling step used for each dataset is summarized in Table
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S1.
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Table S1: List of data, dates and techniques used to map ice surface displacement.
Satellite
Date
Technique
Correlation
Sampling step
window size
ERS1
12/1995 - 01/1996
InSAR
-
-
ALOS
01/02/2008 -18/03/2008
FT
~ 1000x600m
~ 100 m
ERS2
07/04/2011 -10/04/2011
FT
~ 1300x1000m
~ 200 m
TerraSAR-X
19/04/2012-30/04/2012,
FT
256x256m
8m
FT
1280x1280m
100m
08/02/2014-19/02/2014
Sentinel1aTerraSAR-X
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19/02/2014-22/04/2014
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3. Supporting datasets
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We used several additional satellite and model datasets to supplement the ice thinning and
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velocity measurements. Calving front locations were manually delineated from geolocated ERS,
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TSX and S-1a SAR images, on an annual (1991-2010) or biannual (2011-2014) basis, subject to
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data availability, and used to chart ice terminus migration over this period. Daily maps of sea ice
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extent were computed between 1992 and 2013 using sea ice concentration (SIC) data provided by
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the National Snow and Ice Data Centre (www.nsidc.org) on a 25 by 25 km grid, where SIC was
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defined as the fraction of ocean area within each grid cell covered by sea ice. Annual surface
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mass balance and runoff estimates were compiled from daily MAR [Fettweis et al., 2013] and
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RACMO2 [van Angelen et al., 2013] simulations run on regular 10 km x 10 km and 11 km x 11
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km grids, respectively, and forced by Era-Interim reanalysis data for the period 1980-2013.
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4. Calving front location
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The migration of the calving front location at basin 3 was mapped between 1981 and 2014 using
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satellite optical and SAR imagery (Figure S1).
Figure S1. Calving front location of basin 3 between 1981 and 2014 overlaid on a SAR
backscatter intensity image from April 2014.
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5. Mass change from terminus advance
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To estimate the glacier mass retained due to terminus advance between 2010 and 2014, we
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combined area changes derived from calving front location maps (Figure S1), together with
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estimates of ice thickness from airborne radio echo sounding data [Dowdeswell et al., 1986].
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Specifically, we estimated ice thicknesses at the terminus in 1983, using all radio echo sounding
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data within 1 km of the calving front. We then adjusted these measurements to account for
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subsequent ice thinning using a comparison of near terminus ICESat and radio echo sounding
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data to estimate 1983-2003 surface elevation change, and our satellite derived rates of elevation
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change thereafter. The mean and standard deviation of these derived thickness estimates was 88
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m and 22 m, respectively, and we took these as estimates of the mean thickness and associated
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uncertainty of the advancing ice tongue. This approach uses the spatial variability in ice thickness
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as a measure of the true uncertainty, given the lack of spatially and temporally extensive
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measurements of ice surface and bed along the calving front.
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To compute area changes in ice extent caused by terminus migration we used the calving front
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location maps described in Section 3. For our estimate of 2010-2014 mass change we averaged
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the area changes apparent in the two closest pairs, that of 2007-2014 and 2011-2014, taking the
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uncertainty to be the standard deviation of these two estimates. We then computed the volume
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change associated with terminus migration from our estimates of mean ice thickness and area
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change, and converted these to ice mass by assuming a density of ice. Using this approach we
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estimate that between 2010 and 2014 ice front advance retained 3.7 ± 1.1 Gt of ice mass within
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the glacier system.
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6. Modelling terminus geometry
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The calving front geometry in 2012 was modelled at two locations which had experienced
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sustained ice thinning and acceleration in previous years, and more specifically along profiles
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where airborne radio sounding data had provided detailed surveys of the ice bed elevation (Figure
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S2). Our approach used rates of surface elevation change derived from altimetry to update the
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elevation recorded by the airborne survey in 1983. For the period 2003-2009, thinning rates were
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not sampled by ICESat acquisitions directly at the calving front of these two flow units. We
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therefore used estimates of surface elevation change located several kilometres upstream of the
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terminus, where the ICESat tracks crossed these flow units, based on an assumption that
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measurements at these upstream locations would be representative, as a minimum bound, of
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thinning at the calving front. We did not use ICESat elevation measurements that crossed the ice
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front because there are only two locations where this occurs and neither track intersects the centre
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of the flow units where ice acceleration and thinning were most pronounced (Figure S2). As a
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result, we believe that they are unlikely to be representative of the significant, but localised,
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changes occurring at the terminus in these regions. To estimate ice surface elevation change at
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the terminus between 1983 and 2003, prior to ICESat operation, we compared near terminus
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radio echo sounding and ICESat elevation measurements that were co-located within 50 m
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(Figure S4).
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Figure S2. Coverage of data across basin 3 that was used for estimation of terminus geometry evolution.
The colour scale indicates ice flow velocity (m/yr) mapped by ALOS in 2008. The pink lines mark ICESat
ground tracks acquired between 2003 and 2009, the blue lines locate airborne radio echo sounding lines
flown in 1983 and the black dots mark basin boundaries. N, N’ and S, S’ mark the radio echo sounding
flight lines along which the 2012 terminus geometry was estimated. I, I’ identifies the repeated ICESat
reference track shown in Figure S3.
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Figure S3. Repeated ICESat measurements of ice surface elevation along the transverse profile I, I’ shown
in Figure S2, as acquired over the full period of satellite operation from 2003–2009. Ice flow is broadly
orientated out of the page, towards the reader. Surface lowering in excess of 25 meters is apparent over the
period 2005-2009 at the location of the southern radio echo sounding transect, at approximately -1043 km
Northing, where ice acceleration was also observed. Across the northerly flow unit which also underwent
acceleration during this period, northwards from around -1035 km Northing, more moderate thinning is
evident. In contrast, across the central part of the basin, where velocities remained more stable, there is no
evidence of surface elevation change during this period.
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Figure S4. Ice surface elevation difference (m) between co-located airborne radio echo sounding (RES)
data acquired in in 1983 (black lines) and ICESat data acquired in 2003 (turquoise tracks). The pink dots
mark basin boundaries. RES elevation measurements acquired at higher elevation inland regions may be
affected by pressure anomalies across the ice cap [Moholdt et al., 2010] and are not used in this study.
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