www.sciencemag.org/cgi/content/full/science.aaa0940/DC1

Supplementary Material for

Volume loss from Antarctic ice shelves is accelerating

Fernando S. Paolo,* Helen A. Fricker, Laurie Padman

*Corresponding author. E-mail: fpaolo@ucsd.edu

Published 26 March 2015 on Science Express DOI: 10.1126/science.aaa0940

This PDF file includes: Materials and Methods Figs. S1 to S4 Table S1 and S2 Full Reference List Other Supplementary Material for this manuscript includes the following: (available at www.sciencemag.org/content/science.aaa0940/DC1)

Movie S1

Supplementary Materials:

Materials and Methods

Figures S1-S4

Table S1-S2

Movie S1

References (30-46)

Materials and Methods

Antarctic ice-shelf mask

To precisely define the ice-shelf boundaries (e.g., grounding lines, ice fronts) we used a 1-km-

resolution Antarctic mask (15), constructed using a composite of InSAR (30), ICESat (31,32),

MOA (33) and ASAID (34) products.

Raw radar altimeter data editing

Our satellite radar altimeter data are from NASA/GSFC’s Version 4 Level 2 Ice Data Records

(http://icesat4.gsfc.nasa.gov/radar_data/data_products.php). We rejected altimeter height

estimates in the following cases: i) The return altimeter waveform had no leading edge, meaning

that the part of the return corresponding to the surface was not captured; ii) The waveform had a

shape indicating specular reflection, which could indicate the presence of ponded surface water

(35); iii) One or more geophysical corrections were missing; iv) The point was located within

3 km of any ice-shelf boundary (grounding line or ice front); this removed across-boundary

measurements and minimized the impact of changes in ice-shelf perimeter.

Altimeter data corrections

All satellite radar altimeter data were retracked with the 5-parameter β-retracker algorithm (36).

We corrected for surface scattering variations for each satellite mission independently, similar to

Zwally et al. (13), Davis et al. (16), and Wingham et al. (17). We found that over the ice shelves

those methods provided more consistent results (i.e., similar performance over a wide range of

surface conditions) than accounting for short-time variability of surface properties as done by

Khvorostovsky (37). We corrected for tides using the Circum-Antarctic Tidal Simulation

CATS2008a (updated from 38), and load tide based on the TPXO7.2 ocean tide model (39). We

corrected for trends in atmospheric pressure (inverse barometer) using values from the ERA-

Interim (global atmospheric reanalysis) to estimate (mbar/year) for 1994-2012 (40). We

corrected for regional sea-level trends using the AVISO SSALTO/DUACS multi-mission

altimeter product (41), propagating and smoothing values for the unsurveyed regions underneath

ice shelves and persistent sea ice. Many of these corrections are small compared to the

magnitude of long-term thickness-change signals.

Radar-altimeter observations are relatively insensitive to fluctuations in the firn column due to

radar signal penetration into the firn layer (unlike laser pulses from laser altimeters that reflect

from the surface). We did not attempt to make a firn correction based on RACMO (42) as has

been adopted by some other researchers (e.g., 5), as we found no significant correlation between

the modeled firn-height trends and our observed height-change trends. Furthermore, we know

from work on the Amery Ice Shelf (43) that the radar extinction coefficient derived from the

return waveform (which is inversely proportional to penetration depth) is higher on the ice shelf

than it is on the drier parts of the ice-sheet interior (i.e., penetration is lower for the ice shelves

than for the ice-sheet interior). Additionally, in the vast majority of grid cells, densification of the

surface (a “competing” effect with penetration bias, i.e., opposite sign) is by far the dominant

effect, which we minimized by performing a backscatter correction.

In summary, our estimates of time-dependent ice-shelf height account for the lag of the satellite’s

leading-edge tracker, surface scattering variation, surface slope, dry atmospheric mass, water

vapor, the ionosphere, solid Earth tide, ocean tide and loading, atmospheric pressure and regional

sea-level variation.

Derivation of height-change time series

To estimate change in ice-shelf height at each location, we processed all satellite radar altimeter

data using crossover analysis where time-separated height estimates are differenced at satellite

orbit intersections (13,16,17). We only used height differences derived from the same mode of

altimeter operation, i.e., ocean-ocean or ice-ice (ERS-1 and 2) and fine-fine (Envisat). We

excluded any absolute height difference greater than 15 m and applied a 3-sigma filtering.

To enhance the signal-to-noise ratio we performed two key averaging procedures to construct

our time series of height differences. i) Averaging in time and space: we averaged the crossovers

derived from differencing pairs of height measurements taken from separate three-month bins

and spatial cells of 0.75° x 0.25° in longitude and latitude, respectively (~27 x 27 km at 71°S); ii)

Averaging time series: we extended the methods of Li and Davis (44) and Khvorostovsky (37),

where (in the previous step) all possible combinations between different height sets at each cell

location are differenced to form several time series referenced to different epochs. This two-

sided data matrix (one time series per row) is then referenced to a common time and weight-

averaged by number of observations to produce a mean time series per cell, with reduced

statistical error. We estimated average height-change per cell as

where is the mean height-change value between times and , and are height

changes formed by differencing ascending-descending and descending-ascending satellite

ground tracks, respectively, and are the number of crossovers of each type, and [] is

the median operator. The (weighted) average between ascending/descending and

descending/ascending crossovers is necessary to remove any time-invariant biases, such as those

introduced by the combination of satellite orientation, antenna polarization and ice surface

anisotropy.

In the mean time series on each grid cell we removed step changes greater than 3 m (e.g.,

resulting from anomalous backscatter), and also removed any peak greater than 3 standard

deviations from the polynomial trend (see below). We rejected any time series with data points

spanning less than 70% of the 18-year time interval, or showing evidence (to the eye) of poor-

quality data.

Estimating trends in ice-shelf height

To estimate acceleration terms present within the underlying trends of the height data, we fitted

polynomial models (using penalized least squares, see below) to the height-change time series

allowing for the degree to vary from m = 0 to 3, as

h(τ) = βm τ m +εm =0

3

∑

where is the polynomial model, , are the coefficients of the polynomial and

is the error term. We then calculated average and instantaneous rates of change as the slope of

the secant and tangent lines, respectively, to the fitted polynomial (by finite difference

approximation). The average rate of height change is then given by

where is the rate of change between and , is regional atmospheric-pressure trend

(inverse barometer effect), and is regional sea-level trend. In practice, the higher the

complexity of the model, the better the fit and the worse the generalization. To mitigate this, we

chose to use the lasso approach (21) and a 10-fold cross-validation for regularized regression and

model-parameter selection, respectively. In some cases the more robust polynomial-derived

trends show substantial differences with respect to trends derived from the ordinary straight-line

fit (Fig. S4).

Estimating thickness and volume changes from height time series

We converted our height-change time series and rates to thickness changes assuming that (i) the

ice shelf is in hydrostatic equilibrium and (ii) observed changes occur at the density of solid ice

βm

∆h /∆τ

(e.g., basal melting; 4,5,17). The latter assumption is justified since, as discussed above, radar-

altimeter measurements are relatively insensitive to changes in surface mass balance. We used an

ice density of 917 kg/m3 and ocean water density of 1028 kg/m3.

To map the spatial patterns of thickness changes, we fitted polynomials to the thickness-change

time series for each grid cell and derived averaged rates as described above. We then smoothed

and interpolated the rate-of-change spatial field using a Gaussian kernel with sigma equal to the

grid-cell size. To estimate full-ice-shelf and regional mean values we integrated the individual

time series, limited to the surveyed area only and weighted by grid-cell area (i.e., ice-shelf area

within each grid cell). The surveyed area is the fixed area of cells covered by the satellites’ orbits

for which data are available throughout 1994-2012, therefore excluding ice shelves south of

81.5ºS and regions of advancing and retreating ice fronts and grounding lines. Overall, we were

able to sampled about 86% of the ice-shelf area covered by the ERS/Envisat orbit. Our area-

average thickness-change time series are then

H(τ) = s wi hiobs(τ)

i∑

where

H(τ) is mean time series of thickness change, is the height-to-

thickness scaling factor, w are the weights for each cell

i in the area-weighted average, and

hobs(τ) is the observed height-change time series for each grid cell. To estimate the associated

total ice-volume change for each ice shelf, we multiplied the derived changes (from the

polynomial fits) on the surveyed area of each ice shelf by the full areas estimated using the 1-

km-resolution ice-shelf mask, as

∆V∆τ

= A s∆h∆τ

where is total ice-shelf/region area.

The extreme case for temporal changes in ice-shelf area is the addition of ~600 km2 to the area of

the Crosson and Dotson ice shelves due to grounding-line retreat during the period of 1992-2012

(25), corresponding roughly to 7% area increase. This area, which is excluded by our analysis, is

small compared to the area that we cannot survey due to other constraints such as missing data,

s = ρocean (ρocean − ρice )−1

narrow embayments, rough topography, proximity to ice-shelf margins, and grid resolution.

There are several ice shelves with more than 10% area unsurveyed (see Table S1). The error is

also small relative to the height-to-volume conversion uncertainty due to inability to partition

volume loss between basal melt, ice divergence and surface firn state. Uncertainties in the rate of

thickness/volume change for the surveyed minimum ice-shelf area are significantly larger than

any potential ice-shelf volume change by a retreating grounding line.

For calculating fractional change in ice-shelf volume we estimated the average thickness of each

ice shelf using the Bedmap2 dataset (45). To estimate average acceleration we calculated the

average rate of change (slope of the secant line) of the derivative of the fitted polynomial.

Estimation of uncertainties

Our averaging procedure facilitates the formal derivation of statistical error for individual

average-height values on every time series. Two factors contribute to lower the uncertainty in

our estimates: i) the large number of crossovers that contribute to the final estimate per location

per time step (typically 10-150); and ii) the long records (18 years), which makes the derivation

of long-term slopes robust to high-frequency fluctuations (e.g., seasonality).

Our uncertainties are meant to reflect (i) the sampling error (i.e., amount of information

available), and (ii) the relative variability in location. Hence, we derived the time-series error

bars as

where is the standard error, represents all height changes at time and grid-cell

location , and is the mean time series for each grid cell, backscatter corrected ( ) and

uncorrected ( ). The first term on the right hand side represents the noise at the grid-cell level.

The second term assesses the magnitude of the backscatter-to-height correlation; that is, we

assume that the true height lies between the uncorrected and backscatter-corrected values. Notice

that the first term is the standard error propagated in the time series averaging process, so that

both terms refer to the mean time series.

For the fitted trends we estimated the uncertainties based on the variance of the residuals, which

are generally higher than the uncertainty derived from the individual data points. This is because

the spread of the residuals arises from true natural variability in addition to observational

uncertainty (individual error bars). Furthermore, the spread of the residuals contain valuable

information on whether the fitted trend is a good statistical model for the data. We computed the

residuals as

ε = hobs − h

where are the residuals,

hobs is the observed time series of height changes and

h is the

polynomial fit. We then used the bootstrap approach to randomly subsample with replacement

the residuals of the polynomial fit (19). That is, every subsample of the residuals contains

original samples that can appear multiple times, so that the subsamples have the same number of

observations as the original set, but with less information about the noise (with respect to the fit)

in the data. We then added back each resampled residual to the original fitted model to construct

the bootstrap samples, i.e.

hboot = h + εboot

where is the bootstrap time series and are the resampled residuals. To each bootstrap

time series we then refitted the polynomial model and calculated the following: average rate of

change, the derivative of the polynomial and the average rate of change of the derivative

(average acceleration). By doing this repeatedly, we constructed an empirical distribution for

each parameter of interest. From this distribution we then estimated formal confidence intervals

and standard errors. We constructed 1000 bootstrap samples for each individual ice-shelf time

series, and 500 for each grid-cell time series (a total of 1,330,000 sets of calculations).

There is also a systematic component to the uncertainty in the estimated ice-shelf height rates,

which comes from the regional sea-level change. The error in the rate of change of ice-surface

height has an order of magnitude of millimeters-to-tens-of-centimeters per year, while the error

in the regional sea-level trend has an order of magnitude of a millimeter per year. The

uncertainty in the ice-shelf height rate is then given by

where is the uncertainty in the rate of height change at the 95% confidence level from the

bootstrap distribution, and is the uncertainty in regional sea-level trend (41). For thickness

and volume we scaled the uncertainties in height by the height-thickness conversion factor and

the full-ice-shelf area, respectively.

Estimating uncertainties using bootstrapping (top-down approach) has the advantage of not

relying on the assumption that characteristics of the noise are known (e.g., normally distributed),

or requiring that the relationships between the different sources of error are specified since an

algebraic solution of error propagation (bottom-up approach) is not required.

Limitations of our study

During the observation period, some ice shelves experienced significant grounding-line retreat

(25), meaning that the ice shelf increased in area. This ice-shelf migration could impact the

average value of volume loss if the new ice-shelf thickness is taken into account, although these

area changes are small relative to the total ice-shelf area (less than 7%). Since our objective is to

map and quantify the varying impacts of the ocean and atmosphere to ice loss around the

Antarctic ice shelves, we use a fixed area approach (i.e., Eulerian reference frame).

We are unable to sample near the ice-shelf grounding line. This data loss is most severe for small

ice shelves that have large melt rates in the grounding zone (e.g., Pine Island and Dotson). This

limitation is mainly due to: i) our grid-cell size (which is limited by the spatial distribution of the

satellite ground-track crossing points) and good-quality data availability near boundary

transitions. This imposes a limitation on sampling the grounding lines of small and narrow ice

shelves; (ii) our 3-km buffer for ice-shelf boundaries. Although this removes observations right

at the grounding line, it avoids biasing ice-shelf estimates with grounded-ice signal (an order of

magnitude larger) from the locations where grounded-ice changes are most accentuated. As a

result, our estimates for small and rapidly changing ice shelves can be regarded as a lower

bound, in particular those experiencing increased basal melting conditions where large changes

occur near the grounding line, e.g., Pine Island. This means that the ice-shelf loss could be even

higher, which should be considered when comparing estimates from different approaches.

A

B

Fig. S1. Time series of cumulative thickness change relative to series mean for individual

Antarctic ice shelves. Thickness change was averaged over the extent of each ice shelf (sampled

area only) for the period 1994-2012. (A) West Antarctic ice shelves, clock-wise from Ross-

WAIS to Ronne. (B) East Antarctic ice shelves, clock-wise from Filchner to Ross-EAIS.

Locations are shown in Figure 1. Black dots are 3-month-average thickness changes relative to

series mean, blue curve is the 18-year polynomial trend with the 95% confidence band, and red

line shows the regression line to the segment of our dataset that overlaps with the period used for

a prior ICESat-based analysis (2003-2008; 5). Average rates (in m/decade) are derived from the

end points of the polynomial models.

Fig. S2. Average rate and total thickness change for each Antarctic ice shelf from 1994 to 2012.

(left) Rate of thickness change (in m/decade) and (right) percentage thickness lost or gained in

18 years (values not significant at the 95% confidence level were set to 0%). Values are grouped

as: West Antarctic ice shelves (top), East Antarctic ice shelves (middle) and regions (bottom).

Red is thinning/loss and blue is thickening/gain. Locations are shown in Figure 1.

Fig. S3. Polynomial versus line fit to 18-year-long records. Examples of discrepancies between

polynomial regression (green) and straight-line fit (red) in representing long-term trends in

thickness-change time series (blue). Two examples showing (top) Pine Island Ice Shelf and

(bottom) Amery Ice Shelf, where the straight-line fit overestimates and underestimates,

respectively, the trend. The shaded region (light gray) represents the time interval used in a

previous ICESat-based study (5; 2003-2008).

Fig. S4. Error map for estimated rates of Antarctic ice-shelf thickness change. Map showing

estimated uncertainties for individual (grid cell) decade-averaged rates of thickness change (map

on Figure 1). Uncertainties are two standard errors (95% confidence level) estimated using the

bootstrap approach (19; see text).

Table S1. Average rates and total thickness change for Antarctic ice shelves from 1994 to 2012.

Table summarizing estimated area, decade-averaged ice-shelf-wide and local-minimum

thickness-change rates, volume-change rate and percentage-thickness change during 1994-2012,

for each Antarctic ice shelf and region. Uncertainties are stated at the 95% confidence level.

Total area refers to area under the satellite’s coverage (latitudinal limit of 81.5ºS). Percentages

have been rounded to the next integer or to ±0.5 when below 1% (only significant values have

been considered). Note: Small differences are due to values being computed independently

(subject to different constraints on the regression analysis from individual datasets), and use of

round-off values. All estimates are consistent within the formal errors.

Ice shelf

Area (Survey)

(km2)

Thickness rate

(m/decade)

Local minimum

(m/decade)

Volume rate

(km3/year)

%-Thickness

change 1994-2012

Ross WAIS 215,000 (97%) -2.3 ± 1.0 -35.0 ± 10.0 -48 ± 22 -1

Withrow 650 (82%) -19.2 ± 5.8 -19.2 ± 5.8 -2 ± 1 -10

Sulzberger 12,200 (78%) 0.1 ± 0.9 -6.8 ± 4.2 0 ± 1 --

Nickerson 6,600 (80%) 0.1 ± 1.3 -15.7 ± 3.0 0 ± 1 --

Getz 33,200 (85%) -16.1 ± 1.5 -66.5 ± 9.0 -54 ± 5 -6

Dotson 5,400 (80%) -26.0 ± 3.2 -64.5 ± 7.9 -14 ± 2 -10

Crosson 2,700 (78%) -31.1 ± 5.4 -31.4 ± 8.6 -8 ± 2 -18

Thwaites 4,600 (75%) -28.0 ± 4.1 -31.7 ± 4.4 -13 ± 2 -12

Pine Island 6,000 (60%) -23.0 ± 3.8 -34.7 ± 4.7 -14 ± 2 -9

Cosgrove 3,000 (65%) 1.6 ± 2.0 -29.2 ± 8.2 0 ± 1 --

Abbot 30,100 (80%) -1.5 ± 0.9 -19.2 ± 4.4 -4 ± 3 -1

Venable 3,100 (85%) -36.1 ± 4.4 -64.4 ± 4.9 -11 ± 1 -18

Stange 7,700 (80%) -7.8 ± 2.4 -15.1 ± 2.1 -6 ± 2 -5

Bach 4,600 (60%) -8.6 ± 1.0 -12.9 ± 1.3 -4 ± 1 -6

Wilkins 13,500 (82%) -6.2 ± 1.2 -19.9 ± 2.0 -8 ± 2 -5

George VI 23,200 (75%) -10.9 ± 1.1 -31.3 ± 6.7 -25 ± 3 -7

Larsen B 2,500 (50%) -3.5 ± 2.9 -5.5 ± 2.9 -1 ± 1 -2

Larsen C 46,500 (96%) -5.1 ± 0.8 -16.6 ± 8.1 -24 ± 4 -3

Larsen D 25,000 (70%) -1.5 ± 1.2 -22.5 ± 2.8 -4 ± 3 -1

Ronne 318,000 (98%) 0.1 ± 0.6 -10.0 ± 3.5 2 ± 19 --

Filchner 91,000 (95%) 1.5 ± 0.5 -12.7 ± 1.7 13 ± 4 0.5

Brunt 36,000 (78%) 2.6 ± 1.2 -24.5 ± 7.8 9 ± 4 2

Riiser 43,000 (90%) 0.8 ± 0.9 -3.7 ± 1.5 3 ± 4 --

Fimbul 40,500 (78%) 3.2 ± 1.1 -7.7 ± 2.5 13 ± 5 2

Lazarev 8,500 (75%) -0.1 ± 0.7 -1.6 ± 1.5 0 ± 1 --

Baudouin 33,000 (80%) 0.9 ± 0.8 -7.0 ± 8.5 3 ± 2 1

Prince Harald 5,000 (50%) 5.9 ± 3.8 -0.3 ± 2.1 3 ± 2 3

Amery 60,000 (88%) 1.6 ± 1.1 -18.3 ± 9.2 9 ± 6 1

West 15,500 (50%) -0.2 ± 1.7 -21.3 ± 5.7 0 ± 3 --

Shackleton 31,000 (48%) -0.9 ± 1.0 -9.3 ± 9.2 -3 ± 3 --

Totten 6,000 (50%) 2.0 ± 7.5 2.0 ± 7.5 1 ± 5 --

Moscow 5,600 (50%) 2.0 ± 5.6 -5.7 ± 4.2 1 ± 3 --

Holmes 2,000 (40%) -0.1 ± 7.0 -0.4 ± 7.4 0 ± 1 --

Dibble 1,500 (60%) -9.6 ± 4.6 -9.6 ± 4.6 -2 ± 1 -3

Mertz 2,800 (55%) 0.9 ± 1.5 0.9 ± 1.5 1 ± 2 --

Cook 3,200 (35%) -0.1 ± 3.9 -22.9 ± 4.0 0 ± 1 --

Rennick 3,200 (80%) -4.7 ± 1.4 -17.1 ± 2.2 -2 ± 1 -2

Mariner 2,600 (55%) 1.0 ± 2.1 1.0 ± 2.1 0 ± 1 --

Drygalski 2,500 (50%) -1.6 ± 4.3 -14.4 ± 11.2 0 ± 1 --

Ross EAIS 145,000 (98%) -0.9 ± 0.4 -32.9 ± 8.3 -13 ± 6 -1

Ross 360,000 (98%) -2.1 ± 0.5 -35.0 ± 10.0 -75 ± 19 -1

Amundsen 56,000 (80%) -19.4 ± 1.9 -66.5 ± 9.0 -109 ± 11 -8

Bellingshausen 86,000 (78%) -7.4 ± 0.9 -64.4 ± 4.9 -64 ± 8 -5

Larsen 75,000 (80%) -3.8 ± 1.1 -22.5 ± 2.8 -28 ± 8 -3

Filchner-Ronne 410,000 (97%) 0.2 ± 0.5 -12.7 ± 1.7 5 ± 22 --

Queen Maud 224,000 (78%) 2.0 ± 0.8 -24.5 ± 7.8 44 ± 18 1

Wilkes 87,000 (55%) 1.4 ± 1.5 -22.9 ± 4.0 12 ± 13 --

West Antarctica 650,000 (90%) -3.0 ± 0.5 -66.5 ± 9.0 -191 ± 32 -1

East Antarctica 600,000 (82%) 0.8 ± 0.5 -32.9 ± 8.3 45 ± 29 0.5

All Antarctica 1,250,000 (86%) -1.4 ± 0.4 -66.5 ± 9.0 -166 ± 48 -1

Table S2. Comparison of our estimated thickness-change rates (m/year) with previous studies.

Table comparing our estimates (Paolo et al.) with Pritchard et al. (5), Shepherd et al. 1 (46) and

Shepherd et al. 2 (4). Missing values correspond to either different ice-shelf boundary definition

or ice shelf not reported. When required, we converted all the estimates to thickness change (in

m/year) and rounded values to facilitate the comparison. Values not significantly different from

zero were set to 0.0. See text for explanation on potential differences.

Ice shelf Paolo et al.

18 years

(1994-2012)

Pritchard et al.

5 years

(2003-2008)

Shepherd et al. 1

9 years

(1992-2001)

Shepherd et al. 2

14 years

(1994-2008)

Sulzberger 0.0 0.3

Nickerson 0.0 0.0

Getz -1.6 -1.7 -1.6 -1.8

Dotson -2.6 -5.2 -3.3

Crosson -3.1 -3.3 -4.5

Thwaites -2.8 -5.6 -5.5 -8.3

Pine Island -2.3 -4.9 -3.9 -6.0

Cosgrove -0.2 -0.6 -0.7

Abbot -0.2 0.4 -0.6

Venable -3.6 -2.5 -16.0

Stange -0.8 -0.6

Bach -0.9 -0.7 8.8

Wilkins -0.6 -0.6

George VI -1.1 -0.9 -0.8

Larsen B -0.4 -2.3

Larsen C -0.5 -0.9 -0.8

Larsen D -0.2 0.4

Brunt 0.3 0.3 0.6

Riiser 0.1 0.3

Fimbul 0.3 0.0 -0.5

Lazarev 0.0 -0.6

Amery 0.2 -0.6 0.9

West 0.0 -1.1

Shackleton 0.0 -1.1

Totten 0.0 -3.8

Moscow 0.0 -1.0 5.4

Holmes 0.0 -2.8

Dibble -1.0 -2.2

Mertz 0.0 0.3

Cook 0.0 1.1

Rennick -0.5 -1.2

Mariner 0.0 0.2

Drygalski 0.0 -0.3

Ross -0.2 0.1 0.2

Filchner-Ronne 0.0 0.2 0.5

Movie S1. Animation of cumulative thinning for the West Antarctic ice shelves (1994 to 2012).

Each time step corresponds to a three-month average thickness centered at the midpoint of the

time interval. Each time step represents thickness loss with respect to 1994.

References and Notes 1. A. Shepherd, E. R. Ivins, G. A, V. R. Barletta, M. J. Bentley, S. Bettadpur, K. H. Briggs, D. H.

Bromwich, R. Forsberg, N. Galin, M. Horwath, S. Jacobs, I. Joughin, M. A. King, J. T. Lenaerts, J. Li, S. R. Ligtenberg, A. Luckman, S. B. Luthcke, M. McMillan, R. Meister, G. Milne, J. Mouginot, A. Muir, J. P. Nicolas, J. Paden, A. J. Payne, H. Pritchard, E. Rignot, H. Rott, L. S. Sørensen, T. A. Scambos, B. Scheuchl, E. J. Schrama, B. Smith, A. V. Sundal, J. H. van Angelen, W. J. van de Berg, M. R. van den Broeke, D. G. Vaughan, I. Velicogna, J. Wahr, P. L. Whitehouse, D. J. Wingham, D. Yi, D. Young, H. J. Zwally, A reconciled estimate of ice-sheet mass balance. Science 338, 1183–1189 (2012). Medline doi:10.1126/science.1228102

2. T. C. Sutterley, I. Velicogna, E. Rignot, J. Mouginot, T. Flament, M. R. van den Broeke, J. M.van Wessem, C. H. Reijmer, Mass loss of the Amundsen Sea embayment of West Antarctica from four independent techniques. Geophys. Res. Lett. 41, 8421–8428 (2014). doi:10.1002/2014GL061940

3. I. Joughin, R. B. Alley, Stability of the West Antarctic ice sheet in a warming world. Nat.Geosci. 4, 506–513 (2011). doi:10.1038/ngeo1194

4. A. Shepherd, D. Wingham, D. Wallis, K. Giles, S. Laxon, A. V. Sundal, Recent loss offloating ice and the consequent sea level contribution. Geophys. Res. Lett. 37, L13503 (2010). doi:10.1029/2010GL042496

5. H. D. Pritchard, S. R. Ligtenberg, H. A. Fricker, D. G. Vaughan, M. R. van den Broeke, L.Padman, Antarctic ice-sheet loss driven by basal melting of ice shelves. Nature 484, 502–505 (2012). Medline doi:10.1038/nature10968

6. T. A. Scambos, J. A. Bohlander, C. A. Shuman, P. Skvarca, Glacier acceleration and thinningafter ice shelf collapse in the Larsen B embayment, Antarctica. Geophys. Res. Lett. 31, L18402 (2004). doi:10.1029/2004GL020670

7. C. Schoof, Ice sheet grounding line dynamics: Steady states, stability, and hysteresis. J.Geophys. Res. 112 (F3), F03S28 (2007). doi:10.1029/2006JF000664

8. D. Goldberg, D. M. Holland, C. Schoof, Grounding line movement and ice shelf buttressing inmarine ice sheets. J. Geophys. Res. 114 (F4), F04026 (2009). doi:10.1029/2008JF001227

9. L. Favier, G. Durand, S. L. Cornford, G. H. Gudmundsson, O. Gagliardini, F. Gillet-Chaulet,T. Zwinger, A. J. Payne, A. M. Le Brocq, Retreat of Pine Island Glacier controlled by marine ice-sheet instability. Nat. Clim. Change 4, 117–121 (2014). doi:10.1038/nclimate2094

10. I. Joughin, B. E. Smith, B. Medley, Marine ice sheet collapse potentially under way for theThwaites Glacier Basin, West Antarctica. Science 344, 735–738 (2014). Medline doi:10.1126/science.1249055

11. T. Scambos, C. Hulbe, M. Fahnestock, in Antarctic Peninsula Climate Variability: Historicaland Paleoenvironmental Perspectives, E. Domack et al., Eds. (American Geophysical Union, Washington, D. C., 2003), vol. 79, pp. 79-92.

12. P. Dutrieux, J. De Rydt, A. Jenkins, P. R. Holland, H. K. Ha, S. H. Lee, E. J. Steig, Q. Ding, E. P. Abrahamsen, M. Schröder, Strong sensitivity of Pine Island ice-shelf melting to climatic variability. Science 343, 174–178 (2014). Medline doi:10.1126/science.1244341

13. H. J. Zwally, M. B. Giovinetto, J. Li, H. G. Cornejo, M. A. Beckley, A. C. Brenner, J. L. Saba, D. Yi, Mass changes of the Greenland and Antarctic ice sheets and shelves and contributions to sea-level rise: 1992-2002. J. Glaciol. 51, 509–527 (2005). doi:10.3189/172756505781829007

14. E. Rignot, S. Jacobs, J. Mouginot, B. Scheuchl, Ice-shelf melting around Antarctica. Science 341, 266–270 (2013). Medline doi:10.1126/science.1235798

15. M. A. Depoorter, J. L. Bamber, J. A. Griggs, J. T. Lenaerts, S. R. Ligtenberg, M. R. van den Broeke, G. Moholdt, Calving fluxes and basal melt rates of Antarctic ice shelves. Nature 502, 89–92 (2013). Medline doi:10.1038/nature12567

16. C. H. Davis, A. C. Ferguson, Elevation change of the Antarctic ice sheet, 1995-2000, from ERS-2 satellite radar altimetry. IEEE Trans. Geosci. Rem. Sens. 42, 2437–2445 (2004). doi:10.1109/TGRS.2004.836789

17. D. J. Wingham, D. W. Wallis, A. Shepherd, Spatial and temporal evolution of Pine Island Glacier thinning, 1995-2006. Geophys. Res. Lett. 36, L17501 (2009). doi:10.1029/2009GL039126

18. Information on materials and methods is available at the Science Web site.

19. B. Efron, R. J. Tibshirani, An Introduction to the Bootstrap, vol. 57 of Monographs on Statistics and Applied Probability (Chapman and Hall, New York, 1993).

20. Corrections include lag of the satellite’s leading-edge tracker (retracking), surface scattering variations, surface slope, dry atmospheric mass, water vapor, the ionosphere, solid Earth tide, ocean tide and loading, atmospheric pressure and regional sea-level variation (see Supplementary Materials, 18).

21. R. Tibshirani, Regression shrinkage and selection via the lasso. J. R. Stat. Soc., B 58, 267–288 (1996).

22. H. A. Fricker, L. Padman, Thirty years of elevation change on Antarctic Peninsula ice shelves from multi-mission satellite radar altimetry. J. Geophys. Res. 117 (C2), C02026 (2012). doi:10.1029/2011JC007126

23. S. S. Jacobs, A. Jenkins, C. F. Giulivi, P. Dutrieux, Stronger ocean circulation and increased melting under Pine Island Glacier ice shelf. Nat. Geosci. 4, 519–523 (2011). doi:10.1038/ngeo1188

24. M. Thoma, A. Jenkins, D. Holland, S. Jacobs, Modelling circumpolar deep water intrusions on the Amundsen Sea continental shelf, Antarctica. Geophys. Res. Lett. 35, L18602 (2008). doi:10.1029/2008GL034939

25. E. Rignot, J. Mouginot, M. Morlighem, H. Seroussi, B. Scheuchl, Widespread, rapid grounding line retreat of Pine Island, Thwaites, Smith, and Kohler glaciers, West Antarctica, from 1992 to 2011. Geophys. Res. Lett. 41, 3502–3509 (2014). doi:10.1002/2014GL060140

26. J. Weertman, Stability of the junction of an ice sheet and an ice shelf. J. Glaciol. 13, 3–11 (1974).

27. A. J. Cook, D. G. Vaughan, Overview of areal changes of the ice shelves on the Antarctic Peninsula over the past 50 years. Cryosphere 4, 77–98 (2010). doi:10.5194/tc-4-77-2010

28. P. R. Holland, A. Brisbourne, H. F. J. Corr, D. McGrath, K. Purdon, J. Paden, H. A. Fricker, F. S. Paolo, A. H. Fleming, Atmospheric and oceanic forcing of Larsen C Ice Shelf thinning. Cryosphere Discuss. 9, 251–299 (2015). doi:10.5194/tcd-9-251-2015

29. C. P. Borstad, E. Rignot, J. Mouginot, M. P. Schodlok, Creep deformation and buttressing capacity of damaged ice shelves: Theory and application to Larsen C Ice Shelf. Cryosphere 7, 1931–1947 (2013). doi:10.5194/tc-7-1931-2013

30. E. Rignot, J. Mouginot, B. Scheuchl, Antarctic grounding line mapping from differential satellite radar interferometry. Geophys. Res. Lett. 38, L10504 (2011). doi:10.1029/2011GL047109

31. H. A. Fricker, L. Padman, Ice shelf grounding zone structure from ICESat laser altimetry. Geophys. Res. Lett. 33, L15502 (2006). doi:10.1029/2006GL026907

32. K. M. Brunt, H. A. Fricker, L. Padman, T. A. Scambos, S. O'Neel, Mapping the grounding zone of the Ross Ice Shelf, Antarctica, using ICESat laser altimetry. Ann. Glaciol. 51, 71–79 (2010). doi:10.3189/172756410791392790

33. T. A. Scambos, T. M. Haran, M. A. Fahnestock, T. H. Painter, J. Bohlander, MODIS-based mosaic of Antarctica (MOA) data sets: Continent-wide surface morphology and snow grain size. Remote Sens. Environ. 111, 242–257 (2007). doi:10.1016/j.rse.2006.12.020

34. R. Bindschadler, H. Choi, A. Wichlacz, R. Bingham, J. Bohlander, K. Brunt, H. Corr, R. Drews, H. Fricker, M. Hall, R. Hindmarsh, J. Kohler, L. Padman, W. Rack, G. Rotschky, S. Urbini, P. Vornberger, N. Young, Getting around Antarctica: New high-resolution mappings of the grounded and freely-floating boundaries of the Antarctic ice sheet created for the International Polar Year. Cryosphere 5, 569–588 (2011). doi:10.5194/tc-5-569-2011

35. H. A. Phillips, Surface meltstreams on the Amery Ice Shelf, East Antarctica. Ann. Glaciol. 27, 177–181 (1998).

36. A. C. Brenner, R. A. Blndschadler, R. H. Thomas, H. J. Zwally, Slope-induced errors in radar altimetry over continental ice sheets. J. Geophys. Res. 88 (C3), 1617–1623 (1983). doi:10.1029/JC088iC03p01617

37. K. S. Khvorostovsky, Merging and analysis of elevation time series over Greenland Ice Sheet from satellite radar altimetry. IEEE Trans. Geosci. Rem. Sens. 50, 23–36 (2011). doi:10.1109/TGRS.2011.2160071

38. L. Padman, H. A. Fricker, R. Coleman, S. Howard, S. Y. Erofeeva, A new tidal model for the Antarctic ice shelves and seas. Ann. Glaciol. 34, 247–254 (2002). doi:10.3189/172756402781817752

39. G. D. Egbert, S. Y. Erofeeva, Efficient inverse modeling of barotropic ocean tides. J. Atmos. Ocean. Technol. 19, 183–204 (2002). doi:10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2

40. L. Padman, M. King, D. Goring, H. Corr, R. Coleman, Ice shelf elevation changes due to atmospheric pressure variations. J. Glaciol. 49, 521–526 (2003). doi:10.3189/172756503781830386

41. P. Y. Le Traon, F. Nadal, N. Ducet, An improved mapping method of multisatellite altimeter data. J. Atmos. Ocean. Technol. 15, 522–534 (1998). doi:10.1175/1520-0426(1998)015<0522:AIMMOM>2.0.CO;2

42. E. van Meijgaard et al., “The KNMI regional atmospheric model RACMO version 2.1” (Tech. Rep. 302, Royal Netherlands Meteorological Institute, 2008).

43. H. A. Phillips, thesis, Institute of Antarctic and Southern Ocean Studies, University of Tasmania (1999).

44. Y. Li, C. H. Davis, Improved methods for analysis of decadal elevation-change time series over Antarctica. IEEE Trans. Geosci. Rem. Sens. 44, 2687–2697 (2006). doi:10.1109/TGRS.2006.871894

45. P. Fretwell, H. D. Pritchard, D. G. Vaughan, J. L. Bamber, N. E. Barrand, R. Bell, C. Bianchi, R. G. Bingham, D. D. Blankenship, G. Casassa, G. Catania, D. Callens, H. Conway, A. J. Cook, H. F. J. Corr, D. Damaske, V. Damm, F. Ferraccioli, R. Forsberg, S. Fujita, Y. Gim, P. Gogineni, J. A. Griggs, R. C. A. Hindmarsh, P. Holmlund, J. W. Holt, R. W. Jacobel, A. Jenkins, W. Jokat, T. Jordan, E. C. King, J. Kohler, W. Krabill, M. Riger-Kusk, K. A. Langley, G. Leitchenkov, C. Leuschen, B. P. Luyendyk, K. Matsuoka, J. Mouginot, F. O. Nitsche, Y. Nogi, O. A. Nost, S. V. Popov, E. Rignot, D. M. Rippin, A. Rivera, J. Roberts, N. Ross, M. J. Siegert, A. M. Smith, D. Steinhage, M. Studinger, B. Sun, B. K. Tinto, B. C. Welch, D. Wilson, D. A. Young, C. Xiangbin, A. Zirizzotti, Bedmap2: Improved ice bed, surface and thickness datasets for Antarctica. Cryosphere 7, 375–393 (2013). doi:10.5194/tc-7-375-2013

46. A. Shepherd, D. Wingham, E. Rignot, Warm ocean is eroding West Antarctic Ice Sheet. Geophys. Res. Lett. 31, L23402 (2004). doi:10.1029/2004GL021106