Mass, Volume and Velocity of the Antarctic Ice Sheet:Present-Day Changes and Error Effects

A. Groh • H. Ewert • R. Rosenau • E. Fagiolini • C. Gruber •

D. Floricioiu • W. Abdel Jaber • S. Linow • F. Flechtner •

M. Eineder • W. Dierking • R. Dietrich

Received: 19 July 2013 / Accepted: 19 February 2014� Springer Science+Business Media Dordrecht 2014

Abstract This study examines present-day changes of the Antarctic ice sheet (AIS) by

means of different data sets. We make use of monthly gravity field solutions acquired by

the Gravity Recovery and Climate Experiment (GRACE) to study mass changes of the AIS

for a 10-year period. In addition to ‘standard’ solutions of release 05, solutions based on

radial base functions were used. Both solutions reveal an increased mass loss in recent

years. For a 6-year period surface-height changes were inferred from laser altimetry data

provided by the Ice, Cloud, and land Elevation Satellite (ICESat). The basin-scale volume

trends were converted into mass changes and were compared with the GRACE estimates

for the same period. Focussing on the Thwaites Glacier, Landsat optical imagery was

utilised to determine ice-flow velocities for a period of more than two decades. This data

set was extended by means of high-resolution synthetic aperture radar (SAR) data from the

TerraSAR-X mission, revealing an accelerated ice flow of all parts of the glacier. ICESat

data over the Thwaites Glacier were complemented by digital elevation models inferred

from TanDEM-X data. This extended data set exhibits an increased surface lowering in

recent times. Passive microwave remote sensing data prove the long-term stability of the

accumulation rates in a low accumulation zone in East Antarctica over several decades.

Finally, we discuss the main error sources of present-day mass-balance estimates: the

A. Groh (&) � H. Ewert � R. Rosenau � R. DietrichInstitut fur Planetare Geodasie, Technische Universitat Dresden, 01062 Dresden, Germanye-mail: andreas.groh@tu-dresden.de

E. Fagiolini � C. Gruber � F. FlechtnerSection 1.2: Global Geomonitoring and Gravity Field, GFZ German Research Centre for Geosciences,c/o DLR Oberpfaffenhofen, 82234 Weßling, Germany

D. Floricioiu � W. Abdel Jaber � M. EinederRemote Sensing Technology Institute, German Aerospace Center (DLR), Oberpfaffenhofen,82234 Weßling, Germany

S. Linow � W. DierkingClimate Sciences Division, Alfred Wegener Institute for Polar and Marine Research,27570 Bremerhaven, Germany

123

Surv GeophysDOI 10.1007/s10712-014-9286-y

glacial isostatic adjustment effect for GRACE as well as the biases between laser opera-

tional periods and the volume–mass conversion for ICESat.

Keywords Antarctic ice sheet � Mass balance � Velocity � Accumulation

1 Introduction

The mass balance of the Antarctic ice sheet (AIS) is a key issue concerning the present-day

sea-level rise (e.g., Solomon et al. 2007). Over the last two decades an increased mass loss

has been observed (Rignot et al. 2011c). Although the surface mass balance (SMB) of the

AIS is decreasing over time (Rignot et al. 2011c) the accelerated mass loss is mainly driven

by a speed-up of the ice streams (e.g., Rignot 2008). The accelerated ice flow is triggered

by changes in the atmospheric and oceanic forcing. Temperature changes in the ocean

water cause an extensive thinning of floating ice shelves (e.g., Pritchard et al. 2012).

Hence, the decreasing buttress on the upstream glaciers increases flow velocities. However,

this accelerated mass loss is superimposed by large interannual variations in SMB (e.g.,

Horwath et al. 2012).

Various satellite methods have been utilised to observe different signals related to these

changes. The Gravity Recovery and Climate Experiment (GRACE; Tapley et al. 2004)

provides monthly snapshots of the Earth’s gravity field and allows to directly assess the

temporal variations in the ice sheet’s mass (e.g., King et al. 2012). Flow-induced

dynamical thinning of the coastal regions and variations in SMB cause changes in the

geometry of the AIS. Altimetry missions such as the Ice, Cloud, and land Elevation

Satellite (ICESat; Zwally et al. 2002) were used to observe these signals from repeated

height measurements (e.g., Pritchard et al. 2009). Observed ice-flow velocities, e.g., by

means of synthetic aperture radar (SAR) imagery, can be combined with modelled SMB

estimates in order to derive the mass balance of the ice sheet (e.g., Rignot et al. 2008).

However, all these methods exhibit individual strengths and weaknesses. For example,

GRACE observes the integrated mass signal and requires the correction of all non-cryo-

spheric mass changes. Solid earth mass changes caused by glacial isostatic adjustment

(GIA) can be as large as the present-day ice-mass changes (e.g., King et al. 2012). Since

available GIA models for Antarctica exhibit large uncertainties, these errors propagate into

the GRACE-derived mass-change estimates. Moreover, ICESat altimetry data need to be

corrected for instrumental offsets between different laser operational periods (e.g., Ewert

et al. 2012b). Ignoring these corrections can lead to non-negligible errors in the derived

height changes. Because of the large interannual signals, observations over short time

periods can result in misleading interpretations. Hence, long time series are required in

order to properly resolve temporal variations and to infer long-term changes.

This study makes use of different techniques in order to determine present-day changes

of the AIS. GRACE and ICESat are used to investigate changes in ice mass and ice-surface

height over the entire AIS. On basin scale ICESat-derived volume changes are converted

into mass changes and provide an independent estimate. Since the most dynamical region

of the AIS is located in the Amundsen Sea Sector, a more detailed data analysis focusses

on the Thwaites Glacier. We demonstrate the potential of Landsat optical imagery to

provide information on long-term changes in flow velocities. The data set is complemented

by ice-flow velocities in recent years derived from high-resolution TerraSAR-X SAR

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imagery. In addition to ICESat, height changes over Thwaites Glacier are derived from two

TanDEM-X digital elevation models (DEMs). In this way the period under investigation

can be extended and recent temporal changes can be studied. Furthermore, we investigate a

low accumulation zone (LAZ) in central East Antarctica with respect to long-term changes

in the accumulation rate. For this purpose passive microwave remote sensing data are used.

Table 1 summarises all utilised data sets, including the corresponding acquisition period,

the region under investigation and the derived quantities.

2 Data Sets and Methods

2.1 GRACE Satellite Gravimetry

Monthly release 05 (RL05) gravity field solutions generated within the frame of the

GRACE Science Data System exhibit correlated errors at short wavelength, which become

visible in terms of north–south ‘stripes’ in the spatial domain. These errors are caused by

an undersampling in longitudinal direction due to the mission geometry as well as by

limitations in the utilised background models. However, the correlated errors need to be

reduced by an appropriate filtering technique (e.g., Kusche 2007) before the monthly

solutions can be used to determine regional mass changes. Additionally, we make use of

spatially and temporally constrained monthly solutions based on radial base functions

(RBF). No post-filtering needs to be applied to this solutions.

RBF represent the gravity potential of a surface layer on the Earth’s sphere in an

arbitrary point in external space. The relation between this layer and the GRACE satellite

observations is given by Poisson’s kernel. In a first step, daily atmospheric and oceanic

mass anomalies as well as continental hydrological variations are estimated by an extended

Kalman filter approach that inverts observed relative acceleration differences between the

GRACE twin satellites (Gruber et al. 2013). The main difference to the standard solutions

is that the initial value for the time-varying gravity field has now been estimated during the

prediction step in the Kalman filter, whereas it is otherwise fixed to the time-varying

background modelling provided by the EIGEN-6C model (Forste et al. 2011).

Table 1 Overview of the observation methods, including the sensors and the acquisition periods, utilised inthe present study

Observation method Sensor Acquisition period Study area Quantity

Satellite gravimetry GRACE 2003/01–2012/12 AIS D _M

Laser altimetry ICESat 2003/10–2009/10 AIS, TG D _H; D _V ; D _M

Optical imagery Landsat 1988–2010 TG v

SAR imagery TerraSAR-X 2011/09–2011/11 TG v

SAR imagery TanDEM-X 2011/12, 2012/12 TG H; D _H

Laser altimetry ATM 2011/11, 2012/10 TG H

Passive microwave SSM/I 2007 LAZ A

In addition, the corresponding areas under investigation (the Antarctic ice sheet and its drainage basins—AIS; Thwaites Glacier—TG; a low accumulation zone in central East Antarctica—LAZ) and the derived

quantities (temporal height, volume and mass changes—D _H; D _V; D _M; ice-flow velocities—v; surfaceheights—H, accumulation rates—A) are given. The order is identical to those of the results presented inSect. 3

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Since the inverse formulation to obtain the daily gravity signal to the surface layer is ill-

posed due to an incomplete sampling coverage in space and time (ground track variations),

additional information is necessary to properly model the stochastic behaviour (correla-

tions of the time-varying continental, oceanic and atmospheric masses) as well as the error

characteristics of the remote sensor (i.e. the range-rate instrumentation). As external data

the WaterGAP Global Hydrology Model (WGHM; Doll et al. 2003) and the atmosphere

and ocean de-aliasing product (AOD1B; Flechtner 2007) have been used for the respective

time and area. In the second step these daily mass estimates are removed from the

observations leaving a residual of second kind that is further being analysed by monthly

accumulated normal equations and restored by the monthly average of the removed daily

mass equivalents along with the mean atmosphere and ocean de-aliasing product for the

respective period. Hence, the RBF solutions are spatially and temporally constrained to

empirical correlations stemming from external data, whereas the standard solutions are

temporally constrained to the initial value of the time-varying background model and

spatially constrained by the applied post-filtering. A detailed description of the processing

scheme is given by Gruber et al. (2013).

Monthly RL05 solutions provided by GeoForschungsZentrum Potsdam (GFZ; Dahle et al.

2012) and RBF solutions formed the basis to determine mass-change time series for the entire

AIS as well as for its major drainage basins (Fig. 3, inset). Our analysis was limited to

spherical harmonic (SH) coefficients with a maximum degree nmax = 60, corresponding to a

spatial resolution of about 333 km (half-wavelength) at the Earth’s surface. Since GRACE is

not sensitive to mass changes of degree n = 1 we utilised the estimates of Rietbroek et al.

(2012), which do not account for possible trends, to add the missing information. Monthly

solutions were analysed for the period January 2003 to December 2012 (115 months) as well

as for the period October 2003 to October 2009 (73 months). The latter period allows to

directly compare the inferred mass changes to ICESat-derived estimates.

In the following we address updates in the applied processing strategy which has

already been described by Ewert et al. (2012a) and Groh et al. (2012). Since we aim to

determine ice-mass changes superimposed mass signals were removed by means of geo-

physical models. Mass changes due to GIA were corrected using two up-to-date GIA

models, namely IJ05_R2 (Ivins et al. 2013) and W12a (Whitehouse et al. 2012; Fig. 1).

Due to the global nature of the monthly solutions and the limited spatial resolution pro-

vided by GRACE, mass signals outside Antarctica may leak into the regional Antarctic

estimates. Hence, mass changes originating from continental hydrology and ice-mass

changes of the Greenland ice sheet were reduced. The former correction is based on the

WGHM model (Doll et al. 2003), while the latter was derived from an updated ICESat

analysis presented by Ewert et al. (2012a).

The approximately decorrelating and non-isotropic smoothing filter of Kusche (2007)

was applied to the ‘standard’ RL05 solutions. Mass-change time series were calculated by

applying all five available filters (DDK1 to DDK5), which correspond to different degrees

of smoothing (weak to strong). For both GRACE solutions the temporal variations in the

mass-change time series were modelled using a linear and seasonal (annual and semi-

annual) model. Each monthly ‘standard’ solution was weighted according to its error

estimate based on the calibrated GRACE errors, while empirical errors (Horwath and

Dietrich 2009) were used for the RBF solutions. Finally, the most suitable filter for each

basin was chosen from an analysis of the resulting trend error estimates. We have chosen a

filter as the most suitable if both the GRACE error effect on the linear trend and the

leakage-out of AIS-induced mass changes, caused by the limited spatial resolution, are

minimised.

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2.2 ICESat/ATM Laser Altimetry

ICESat laser altimetry data of the Geoscience Laser Altimeter System (GLAS) 12 data

product (release 633; NSIDC 2012) were utilised for our investigations. For a detailed

description of our applied pre-analysis strategy and a summary of all applied corrections

the reader is referred to Ewert et al. (2012b).

Originally, a continuous operation of GLAS was indented. However, due to an unex-

pected fast decline of the laser’s energy and the failure of Laser 1 (Abshire et al. 2005) the

mission was replanned to a campaign-style schedule consisting of three 33 days periods

per year (Schutz et al. 2005). Nevertheless, the energy decline was still present and leads to

height offsets between the different laser operational periods (LOP). Ewert et al. (2012b)

inferred the correction from a regional crossover adjustment method using the ICESat

altimetry data over the subglacial Lake Vostok, East Antarctica. Since the updated

resulting offsets exhibit a non-negligible trend of -13.3 ± 3.6 mm/year (see Sect. 3.3)

they directly map into derived linear changes in the ice-surface height. Over the entire AIS

the inferred trend and the associated error correspond to an additional error in the linear

volume estimate of about 162 and 44 km3/year, respectively. Hence, a sound determination

and application of the LOP offsets are crucial prerequisites for the inference of reliable

height- and volume-change estimates.

In order to make use of the full potential of the high-resolution altimetry data provided

by ICESat, we apply a repeat-track analysis approach to the pre-analysed data set.

Therefore, all elevation measurements in an area of 1,000 m 9 500 m along the repeat

tracks (�172 m along-track spacing) were used to fit a mathematical model. This model

accounts for linear and annual ice-surface-height changes as well as for height differences

induced by the local ice-surface topography (Ewert et al. 2012a). Thus, temporal variations

in the ice-surface height can be separated from topographic height differences between the

tracks without using external data. Finally, a two-dimensional model with a spatial

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Fig. 1 Present-day GIA-induced vertical crustal deformation rates predicted by the models a IJ05_R2 (Ivinset al. 2013) and b W12a (Whitehouse et al. 2012). The red polygon indicates the generalised drainage basinsof Pine Island Glacier, Thwaites Glacier and Smith Glacier (PITS)

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resolution of 0.5� 9 0.25� was generated from the median of all derived linear height-

change rates within the corresponding grid cell. The median absolute deviation was used as

associated accuracy measure. These elevation-change rates were corrected for height

changes due to GIA as predicted by IJ05_R2 (Fig. 1a) and for elastic crustal deformations

caused by present-day ice-mass changes as described by Groh et al. (2012).

Furthermore, we used data from the Airborne Topographic Mapper (ATM) flown

aboard the NASA DC-8 aircraft during NASA’s Operation IceBridge (Studinger et al.

2010) over Thwaites Glacier in 2011 and 2012. ATM is a scanning LIDAR which mea-

sures topography to an accuracy of ten to twenty centimetres by incorporating measure-

ments from GPS (global positioning system) receivers and inertial navigation system (INS)

attitude sensors. The fundamental form of the ATM topography data is a sequence of laser

footprint locations acquired in a swath along the aircraft flight track. The IceBridge ATM

Level-2 Icessn Elevation, Slope and Roughness (ILATM2) data products (Krabill 2010)

contain resampled and smoothed elevation measurements and are available for download

at NSIDC. ATM data over Thwaites Glacier were acquired during Operation Icebridge

flights made on 4 November 2011 and 12 October 2012.

2.3 Landsat Optical Imagery

Freely available Landsat imagery was used to derive flow velocities in the area of Thwaites

Glacier. In this region flow velocities were obtained in the lower glacier area as well as in

parts of the floating ice tongue. Over 400 Landsat scenes covering the austral summer

between November and March each year in the period 1988–2010 were used. The majority

of the scenes were acquired by the Enhanced Thematic Mapper Plus (ETM?) sensor

aboard Landsat-7. To extend the time series further back in time, prior to the launch of

Landsat-7 in 1999, we utilised data from the Thematic Mapper (TM) on Landsat-4 and

Landsat-5. Due to an ETM? sensor failure in May 2003 all subsequent scenes exhibit a

loss of data of about 22 %, which appears as a prominent stripe pattern in across-track

direction (Loveland and Dwyer 2012).

The flow velocities were derived following the approach presented in Rosenau et al.

(2012). An area-wide flow velocity field with a horizontal spacing of 300 m was achieved by

applying a combined feature tracking approach on a regular spaced grid. At each grid node the

derived flow velocity vector is affected by several error sources. The most dominant error

results from an insufficient relative georeferencing between the image pairs. Because of the

lack of appropriate stable ground control points in the working area, which are not affected by

ice movements, residual displacements introduce systematic errors in the flow velocity

estimate. A further error source is the limited feature tracking accuracy. A representative

tracking error of 0.5–1.0 pixel in an image pair separated by 100 days translates into a

tracking accuracy of 0.03–0.06 km/year. The absolute georeferencing accuracy of Landsat-7

imagery is better than 50 m (Lee et al. 2004). To improve the absolute accuracy of the TM

data, all scenes were shifted relatively to a Landsat-7 reference image.

2.4 TerraSAR-X/TanDEM-X SAR Imagery

We used TerraSAR-X data to derive surface velocities and TanDEM-X data for surface

elevations on the Thwaites Glacier.

The surface velocity field of Thwaites Glacier in the austral spring 2011 was inferred

from X-band SAR data of the TerraSAR-X satellite mission (Werninghaus and Buckreuss

2010). The velocity maps are obtained from pairs of 11 days repeat pass data with 30 km

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swath width (stripmap mode). Two complete coverages were acquired between 24 Sep-

tember 2011 and 29 November 2011 (Table 2).

We applied the amplitude correlation (incoherent intensity tracking) technique to

enhanced ellipsoid corrected (EEC) spatially enhanced level 1b (SE L1b) geocoded pro-

ducts (pixel spacing 1.25 m; Breit et al. 2010). A total of 14 scene pairs, each covering

30 9 50 km2, were processed and mosaicked in a velocity map. Applying this method to

TerraSAR-X data robust results on the Antarctic ice streams and glaciers were presented

by Jezek et al. (2009).

The absolute accuracy of the velocity estimates is affected mainly by atmospheric path

delay and solid Earth tides variation between the two acquisitions, orbit estimation errors

and errors in the DEM used for geocoding, coupled with a baseline between the two passes.

The relative accuracy of the individual motion vector depends on the correlation coeffi-

cient, the patch size and the shape of the correlation function. It has been estimated through

simulations for speckle tracking under specific constraints (Bamler and Eineder 2005).

Mean accuracies of 0.03 m/day in ground range can be achieved while the accuracy of the

individual motion vector is determined by the magnitude of the correlation coefficient.

Data from the TanDEM-X mission (Krieger et al. 2007; DLR-HR 2010) were used to

derive surface elevations of the Thwaites Glacier in 2011 and 2012. In addition to oper-

ational data collected for the global SAR interferometric DEM, experimental TanDEM-X

data are acquired for scientific purpose at selected sites. For the present study we generated

DEMs from experimental acquisitions over Thwaites Glacier using the Integrated Tan-

DEM-X Processor (ITP; Rossi et al. 2012) at DLR. Currently, the final DEM’s absolute

vertical accuracy is below 3 m (Fritz et al. 2012), which is by far better than the initial

requirement of 10 m (DLR-HR 2010). This allowed to investigate possibilities to detect

annual elevation changes in glacier surfaces in the Pine Island Bay region from 2011

onwards and, thus, to extend the time series of ICESat elevations available between 2003

Table 2 TerraSAR-X data over Thwaites Glacier used for the ice velocity determination in late 2011

Date/time (UTC) Number of30 9 50 km2

scene pairs

Relative orbit nr. Beam Incidenceangle (�)

24.09.2011–05.10.2011 04:30 3 1 (asc) Strip_011R 39.32

25.09.2011–06.10.2011 04:13 3 16 (asc) Strip_011R 39.31

17.10.2011–28.10.2011 04:13 3 16 (asc) Strip_010R 37.33

23.10.2011–03.11.2011 04:05 2 107 (asc) Strip_010R 37.34

18.11.2011–29.11.2011 04:30 3 1 (asc) Strip_012R 41.10

The ground range resolution and the azimuth resolution of all scene pairs is 3.00 and 3.05 m, respectively

Table 3 Characteristics of the TanDEM-X bistatic acquisitions over Thwaites Glacier processed to infersurface elevations

TDMAcqID

Date/time(UTC)

Relativeorbit nr.

Beam Incidenceangle (�)

Beff

(m)HoA(m)

ATMacq. date

1048623 04.12.2011 04:39 77 (asc) strip_014R 44.6 81.94 97.62 04.11.2011

1109726 01.12.2012 04:39 77 (asc) strip_014R 44.6 107.6 73.85 12.10.2012

Beff—effective baseline, HoA—height of ambiguity. Last column: the dates ATM data are available overThwaites Glacier

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and 2009. The processed TanDEM-X DEMs (Table 3) cover an area of about 30 km by

110 km (Fig. 7). The horizontal grid spacing is 0.600 in latitude and 1.800 in longitude,

corresponding to distances of 18.6 and 14.0 m, respectively.

2.5 Passive Microwave Remote Sensing Data

Spaceborne sensors operating at microwave frequencies can be used to estimate snow

accumulation on the polar ice sheets. Under dry snow conditions, microwave radiation

interacts with the snow volume. The signal received by the sensor is, therefore, not only

integrated horizontally (over the extent of the antenna footprint) but also vertically. The

depth of signal penetration depends on wavelength and varies between a few centimetres at

85 GHz and �60 m at 7 GHz (Flach et al. 2005). There is a pronounced sensitivity of the

microwave signal to snow grain size (Wiesmann and Matzler 1998).

Climatological parameters, such as temperature and accumulation rate, influence snow

metamorphism processes and the microstructure of the firn (Domine et al. 2008). The

relationships between accumulation rate, temperature and grain size on the one hand and

grain size, firn layering and microwave signal on the other hand can be used to derive the

accumulation rate from passive microwave remote sensing data.

Two principal approaches are possible: firstly, formulating a purely empirical rela-

tionship between the microwave signal and the accumulation rate (Rotschky et al. 2006),

and secondly, modelling the interaction between polar firn and microwave radiation. We

chose the latter because it allows a more flexible treatment of the problem.

We will now give a brief description of our approach, which is described in more detail

in Dierking et al. (2012), Linow et al. (2012) and Linow (2011). The snow accumulation

retrieval technique consists of two steps:

1. An empirical parameterisation of polar firn stratigraphy as a function of accumulation

rate and mean annual air temperature is used to generate a set of firn profiles (depth,

density, age, temperature and effective radius) for a range of temperatures and

accumulation rates (Linow et al. 2012).

2. The microwave signal is calculated for each profile using dense medium radiative

transfer theory (Dierking et al. 2012).

The result is a lookup table containing microwave backscatter coefficients r0 or brightness

temperatures TB as functions of accumulation rate and mean annual air temperature. Using

snow temperature data, e.g., from the MODIS sensor, we can invert snow accumulation

rates from microwave satellite images. The resulting accumulation maps are validated by a

set of accumulation rate measurements from Dronning Maud Land, Antarctica, and are

found to be consistent for areas where the accumulation rate is lower than 0.2 m of water

equivalent (w.e.)/year.

3 Results

3.1 Mass and Volume Changes of the Entire AIS

3.1.1 Mass Changes from GRACE

Here, we present the ice-sheet-wide results from our GRACE analysis for the period

2003–2012. Firstly, we focus on the results derived from the RL05 solutions using the

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IJ05_R2 GIA prediction. Secondly, we present the inferred mass-change trends based on

the W12a model and discuss the impact of the applied GIA correction. Finally, results

inferred from ‘standard’ RL05 solutions and from solutions based on radial base functions

(RBF) are compared.

We applied the DDK3 filter for the entire AIS, East Antarctica (EAST), West Antarctica

(WEST) and all other basins under investigation with exception of basins 11, 12 and 13 (cf.

Fig. 3, inset). For the smaller basins in West Antarctica, where the major part of the mass

loss takes place, a less strong smoothing (DDK5) was required in order to reduce leakage-

out errors.

The spatial pattern of the GRACE-derived mass-change trend, given in terms of surface

density (mass per area), reveals distinct differences between EAST and WEST (Fig. 2a).

Central East Antarctica exhibits no significant mass changes over the period from January

2003 to December 2012. Only the coastal regions between Dronning Maud Land and En-

derby Land (20�W–60�E) exhibit a slight mass gain while a minor mass loss is observed

between Wilkes Land and Victoria Land (110�E–160�E). The transition to West Antarctica

is characterised by a pronounced positive pattern in the region of the Kamb Ice Stream, which

is accumulating mass since its shutdown about 165 years ago (e.g., Joughin and Tulaczyk

2002; Catania et al. 2012). Almost entire West Antarctica shows a clear mass loss. The

negative mass-change pattern spreads from the tip of the Antarctic Peninsula up to the coast

of Marie Byrd Land, with the largest loss signal located in the Amundsen Sea Sector. This

region comprises the drainage basins of Pine Island, Thwaites and Smith Glaciers (PITS).

These local differences are revealed both in the spatial pattern and in the inferred time

series (Fig. 3, green curves). The AIS time series shows a clear seasonal signal superim-

posed to a linear trend. However, the low-pass filtered time series (red line) exhibits

interannual variations, too. If the IJ05_R2 model is utilised, the estimated total mass loss is

109.3 ± 29.6 Gt/year, corresponding to a uniform global sea-level rise (SLR) of

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surface density trend [kg/m2/yr]

Fig. 2 GRACE-derived surface density trends for the period January 2003 to December 2012 based on‘standard’ RL05 solutions (a) and based on RBF solutions (b). The IJ05_R2 GIA correction was applied.The red polygon indicates the generalised drainage basins of Pine Island Glacier, Thwaites Glacier andSmith Glacier (PITS)

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0.30 ± 0.08 mm/year. The error estimate accounts for the a posteriori error of the linear

trend (GRACE errors and unmodelled temporal variations), errors in the applied model

corrections (atmosphere, ocean, continental hydrology and GIA) and leakage-out errors

caused by the limited spatial resolution and the applied filtering. Since the linear trend for

EAST is positive (34.0 ± 17.7 Gt/year), the mass loss in WEST (142.3 ± 13.3 Gt/year)

exceeds the mass decrease in the entire AIS. The EAST time series reveals that the mass

gain has clearly increased since 2009. According to the estimate for the period October

2003 to October 2009 (Table 4) the mass gain in EAST was clearly smaller

(13.2 ± 18.9 Gt/year) until 2009. Two exceptional large accumulation events took place in

Dronning Maud Land in 2009 and 2011 (Boening et al. 2012). Since no significant changes

in ice discharge were observed in this region the increased accumulation is solely

responsible for the observed mass gain (Lenaerts et al. 2013). Both events could be

observed by different sensors (e.g., radar altimetry) and are also visible in modelled surface

mass balance (SMB) data (e.g., Shepherd et al. 2012). Within West Antarctica the largest

mass loss of 87.6 ± 13.2 Gt/year is observed for basin 12 (PITS). Prior to 2005 the

observed mass loss was clearly lower and started to increase in 2009. By comparing the

linear trends for both time periods under consideration (Table 4) an increased mass loss

during the latest years becomes evident for all three basins in West Antarctica.

The amount of the inferred ice-mass changes strongly depends on the utilised GIA

model (Table 4). Figure 1 reveals that available GIA model predictions may differ sig-

nificantly. Among others, one remarkable difference between IJ05_R2 and W12a can be

mas

s ch

ange

[Gt]

2002 2004 2006 2008 2010 2012

time

−1500

−1250

−1000

−750

−500

−250

0

250

500

750

1000

1250

1500AIS: −109.3 ± 29.6 Gt/yr

−108.5 ± 30.2 Gt/yr

WEST: −142.3 ± 13.3 Gt/yr−123.2 ± 12.7 Gt/yr

−400

−200

0

200

400

EAST: 34.0 ± 17.7 Gt/yr14.5 ± 18.6 Gt/yr

2002 2004 2006 2008 2010 2012

time

−1000

−800

−600

−400

−200

0

200

400

600

800

1000

basin 11: −46.9 ± 8.8 Gt/yr−41.0 ± 6.3 Gt/yr

basin 12: −87.6 ± 13.2 Gt/yr−71.3 ± 07.5 Gt/yr

basin 13: −37.8 ± 10.8 Gt/yr−32.6 ± 09.6 Gt/yr

1 2 3

45

6

78

91011

12

1314

15

16

Fig. 3 GRACE-derived mass-change time series for the entire AIS, West Antarctica (WEST), EastAntarctica (EAST) and three basins in West Antarctica (note the different scales). Results based on‘standard’ RL05 solutions (green) and on RBF solutions (blue) are shown for each basin. The applied GIAcorrection is based on IJ05_R2. Additionally, the fitted linear and seasonal model (black) and a 13-monthmoving average (red) are given. Numbers indicate the linear trend and the corresponding error estimate. Theinset indicates the basin boundaries and the boundary between EAST and WEST (bold red line)

Surv Geophys

123

found for East Antarctica, where W12a predicts a clear GIA-induced mass loss (crustal

subsidence) due to increased accumulation since last glacial maximum. A detailed dis-

cussion on the two model approaches and their results is given by Shepherd et al. (2012,

supplement). However, the applied GIA corrections for the entire AIS of 73.4 ± 28.9 and

68.2 ± 29.3 Gt/year according to IJ05_R2 and W12a, respectively, are in good agreement.

The W12a error estimate was derived from the upper and lower bounds provided together

with W12a. Since IJ05_R2 does not provide an accuracy measure, we considered the single

standard deviation from the comparison with the prediction of the precursor model IJ05

(Ivins and James 2005). Obviously, the GIA uncertainties are still large and are by far the

largest error component in the overall ice-mass trend errors. Nevertheless, compared to the

GIA-induced mass changes predicted by previous models (IJ05: 114.2 Gt/year, ICE-

5G(VM2; Peltier 2004): 131.6 Gt/year) the predictions by these two up-to-date models are

clearly smaller, and hence, the GRACE-derived mass balance is less negative. Nearly all

mass-balance estimates, using IJ05_R2 and W12a, agree within the range of their accuracy

measures. However, clear differences exist for basins WEST and EAST (Table 4). The

W12a-based trend for EAST is more negative by 23.6 Gt/year. Due to the negative GIA-

induced mass change over central East Antarctica predicted by W12a, the corresponding

mass-balance estimate is positive and nearly twice as much as the IJ05_R2-based result

(62.9 ± 22.7 vs. 34.0 ± 17.7 Gt/year).

In general, the RL05-based results are comparable to those inferred from RBF solutions

(Table 4). Although the spatial mass-change patterns are in good agreement, Fig. 2 reveals

that the RBF solution exhibits less pronounced positive signals in East Antarctica. It is also

visible that the mass changes are more localised on the continent and do not leak that much

into the ocean. This is also supported by the somewhat smaller error estimates for the RBF

results, which are mainly due to a smaller leakage error since no additional filtering

(smoothing) was applied. Although the mass-balance estimates for the entire AIS agree

well, the mass decrease for basin WEST is about 19 Gt/year smaller than that derived from

the RL05 solutions. The difference for basin EAST is comparable. It is obvious, especially

from the time series of basin 12, that the RBF solutions are biased by spurious artefacts.

The maximum effect occurs for early 2009 and 2010 and can mainly be attributed to the

quality of the observations during these periods. Since these artefacts manifest in terms of

positive anomalies in the time series in West Antarctica the fitted models (Fig. 3, grey line)

are biased towards these anomalies, and hence, the estimated linear mass changes are less

negative. Moreover, these artefacts are also responsible for the underestimation of the

accumulation anomaly in Dronning Maud Land in late 2009, which leads to a smaller mass

gain for basin EAST.

A comparison of the GRACE-derived trends to those from other studies is not straight

forward. Differences in the analysis strategy, the utilised monthly solutions and the period

under investigation will lead to differing results. Shepherd et al. (2012) presented average

estimates from eight different groups for the period 2003–2010. These groups applied

different analysis strategies mostly on monthly RL04 solutions (using the oceanic cor-

rection of RL05) provided by the Center for Space Research, University of Texas using the

average of the IJ05_R2 and W12a GIA correction. Their average mass-balance estimate for

the AIS of -81 ± 33 Gt/year is about 30 Gt/year less negative than the average of our

RL05 estimates for the period 2003–2012 using IJ05_R2 and W12a (-106.7 ± 29.8 Gt/

year). While their trend for basin EAST (56 ± 38 Gt/year) is in good agreement with our

average estimate (48.5 ± 20.4 Gt/year), we have inferred a larger mass loss for basin

WEST (107 ± 27 vs. 154.1 ± 11.5 Gt/year).

Surv Geophys

123

Ta

ble

4L

inea

rh

eig

ht,

vo

lum

ean

dm

ass

chan

ges

for

dif

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nt

dra

inag

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asin

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dre

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of

the

AIS

(cf.

Fig

.3)

der

ived

fro

mIC

ES

at(I

)an

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(G)

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ion

D_ H

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ear)

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(km

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ear)

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ear)

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ear)

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05

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)D

_ MG

(Gt/

yea

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)D

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12

a)D

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(Gt/

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(W1

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11

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.7±

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.9-

20

.5±

06

.3-

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.4±

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.8-

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.4±

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.4-

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.9±

08

.8-

30

.7±

06

.4

-4

6.9

±0

8.8

-4

1.0

±0

6.3

-4

9.3

±0

8.8

-4

3.4

±0

6.4

12

-2

4.8

±0

.6-

10

0.8

±2

.5-

90

.7±

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.8-

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.7±

13

.2-

53

.6±

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.5-

75

.8±

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.2-

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.9±

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.5

-8

7.6

±1

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±0

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-7

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±0

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±0

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±0

8.8

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2.0

±0

7.0

-3

7.8

±1

0.8

-3

2.6

±0

9.6

-4

3.5

±0

8.3

-3

8.0

±0

6.6

EA

ST

-0

.5±

0.0

-5

0.8

±3

.9-

45

.8±

19

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8.9

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8.6

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3.3

±2

3.4

WE

ST

-4

.1±

0.2

-8

9.2

±4

.6-

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.2±

32

.7-

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7.5

±1

3.8

-9

1.0

±1

3.1

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31

.0±

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.1-

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-1

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8.2

AIS

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.0±

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-1

26

.0±

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.0-

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.9±

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.9-

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31

.3-

86

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.7

-1

09

.3±

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.6-

10

8.5

±3

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-1

04

.1±

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.0-

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3.0

±3

0.4

Th

eG

RA

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resu

lts

are

bas

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n‘s

tan

dar

d’

RL

05

and

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luti

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sas

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las

on

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corr

ecti

on

s(I

J05

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2an

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a).T

he

firs

tan

dth

ese

con

dro

wof

each

reg

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refe

rto

the

per

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Oct

ober

20

03

toO

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20

09

and

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ns

Surv Geophys

123

3.1.2 Volume and Mass Changes from ICESat

In general, the ICESat-derived pattern of ice-surface-height trends shown in Fig. 4a reveals

that the location of the local maxima and minima is comparable to those of the mass-change

pattern inferred from GRACE (Fig. 2). Due to the higher resolutions height changes can be

investigated in more detail. Central East Antarctica is nearly stable showing no significant

height changes. Only the coastal regions exhibit negative as well as positive changes in the

ice-surface height. Since ICESat ceased its operation in 2009 the positive anomaly in

Dronning Maud Land could not be observed. Over the Kamb Ice Stream a surface increase of

up to 0.6 m/year is revealed. This is in agreement with the results of Pritchard et al. (2009).

The largest decrease in surface height is inferred in the PITS basin with a maximum surface

lowering of 5.4 m/year located at the terminus of Smith Glacier (Fig. 4b).

For the entire AIS a mean surface-height change in -1.1 cm/year was derived. The

corresponding error estimate of ±1 mm/year was inferred by propagating the height error

of each individual grid cell. By far the largest mean height decrease is evident for basin 12

(PITS) and amounts to 24.8 ± 0.6 cm/year. Additional height-trend estimates as well as

the corresponding volume trends on basin scale are summarised in Table 4. Approxi-

mately, two-thirds of the entire AIS volume trend (-140.0 ± 6.0 km3/year) occur in the

PITS basin (-100.8 ± 2.5 km3/year).

As already mentioned, the elevation rates underlying the results discussed above were

corrected for height changes due to GIA as predicted by IJ05_R2 (Fig. 1a) as well as for

elastic crustal deformations caused by present-day ice-mass changes. Although both

quantities are small compared to the observed changes in the ice-surface height, they are

not negligible. Without correcting for both effects the volume-change estimate of the AIS

would be -128.6 ± 6.1 km3/year, only. The geometrical effect of GIA on the volume-

−180˚

−135˚

−90

˚

−45˚

0˚

45˚

90˚

135˚

(a)

−1.0 −0.5 0.0 0.5 1.0

Height change trend [m/yr]

−76˚

−74˚

−72˚

−70˚

−68˚

−130˚

−120˚

−110˚

−100˚

−90˚

−80˚

(b)

Pin

e Is

land

Gla

cier

Thwaites Glacier

Smith Glacier

−3.0 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0

Height change trend [m/yr]

Fig. 4 Height-change trend of the ice surface inferred from ICESat. a Overview of the entire AIS. b Focuson the Amundsen Sea Sector and the PITS basin (red polygon). Note the different scales. The blue boxindicates the region shown in Fig. 5

Surv Geophys

123

change estimates is much smaller than the corresponding gravitational effect on the

GRACE-derived mass-change estimates. Hence, the utilised GIA model has a minor

impact on the inferred volume changes. The largest difference in the volume trends using

the IJ05_R2 and the W12a GIA correction can be found for basin EAST (-50.8 ± 3.9 vs.

-45.1 ± 3.9 km3/year) where both model predictions exhibit the largest differences.

To infer independent mass-change estimates the volume-change rates have to be converted

into mass changes using an appropriate density assumption. In steady state, i.e. assuming

constant accumulation, temperature and melting, the depth-dependent density profile of a firn/

ice column does not change with time. Hence, the firn compaction rate is also constant over

time (Sorge’s Law; Cuffey and Paterson 2010). In this case, the density of pure ice is

appropriate for the volume–mass conversion. However, short-term (e.g., seasonal) variations

in accumulation and temperature will cause temporal changes in the density profile. If long-

term changes (e.g., over the period covered by the satellite missions) are investigated these

non-steady-state variations can be regarded as fluctuations in the statistical sense. Hence, they

average out to a great extent. Moreover, these variations are small compared to the long-term

changes if averages over larger regions (basins) are considered. In this case, a density of

900 kg/m3 can be used for the volume–mass conversion (Zwally et al. 2005).

Using this density assumption a mass loss of 126.0 ± 20.0 Gt/year was inferred for the

AIS which corresponds to a SLR of 0.35 ± 0.05 mm/year. Mass-change estimates for all

other basins are listed in Table 4. As described by Ewert et al. (2012a) the corresponding

accuracy measures account for errors in the volume trends, the error of the applied density

assumption and an additional error component due to possible volume changes caused by

trends in the firn compaction. The volume errors of each basin, as listed in Table 4, were

derived from the volume errors of all grid cells within the basin, which were inferred by

propagating the corresponding height-change errors. For the AIS the ICESat-derived

volume error translates into a mass-change error of ±5.4 Gt/year. Furthermore, we

assumed the error of the density assumption to be ±100 kg/m3. This error was propagated

using the basin-scale volume-change estimate and results in an additional density-induced

mass-change error of ±14.0 Gt/year. Zwally et al. (2005) report a height change of

-1.58 cm/year for WEST and ?0.21 cm/year for EAST, respectively, caused by tem-

perature-driven changes in firn compaction. Since these volume changes will not cause an

ice-mass change, we considered them as additional random volume errors for each indi-

vidual basin. For the AIS this results in a mass-change error of ±13.2 Gt/year. Altogether,

these three error components form the overall AIS mass-change error of ±20.0 Gt/year.

A comparison and discussion of the ICESat-derived mass changes with respect to the

GRACE results can be found in Sect. 4.

3.2 Rapidly Changing Regions of the AIS: the Amundsen Sea Sector

Both GRACE and ICESat revealed the largest changes in mass and geometry in the

Amundsen Sea Sector (PITS basin). In the following, we investigate the velocity and

height changes of the Thwaites Glacier, the second largest glacier in West Antarctica, as a

prominent example for the fast changing ice streams in this region.

3.2.1 Ice-flow velocities and temporal changes

Figure 5 compares two velocity fields from 2001 and 2011, which were derived from

Landsat-7 and TerraSAR-X acquisitions, respectively. At the grounded part of the glacier

Surv Geophys

123

both fields exhibit decreasing velocities with increasing distance from the grounding zone.

Obviously, very few velocity estimates were derived from the Landsat-7 data over the

grounded region. Since trackable surface features are sparse over this region the tracking

algorithm performed poorly.

Nevertheless, it becomes evident from both data sets that the floating ice tongue exhibits

much larger velocities of more than 3,000 m/year. Between 2001 and 2011 a significant

acceleration can be observed. Large differences in the ice-flow velocities are visible on

both sides of the large cracks, which are related to calving events in January 2002 (Rabus

et al. 2003) and 2010 (MacGregor et al. 2012). Showing the temporal evolutions of the

velocities along profile AB Fig. 6a also reveals these rapid changes. The complex mech-

anisms triggering the flow of the free floating tongue are influenced by changes in the

ocean currents and the wind regime (Rabus et al. 2003) and may explain the opposite

velocity gradients perpendicular to the cracks observed in 2001 and 2011.

Moreover, Fig. 6a reveals that the velocity of the grounded part of Thwaites Glacier was

only changing marginally until 2008/2009 and was slightly increasing at the floating

tongue. The larger increase observed in 2011 may be an indication for a starting accel-

eration of the ice stream. This acceleration is also evident in the flow velocities along the

grounding zone (profile CD) shown in Fig. 6b. After the velocity of the main trunk was

nearly constantly increasing until 2008/2009, a significantly larger speed-up of up to

800 m/year is evident in 2011. The observed acceleration can be driven by diverse forc-

ings. One explanation is the increased thinning of the grounded ice (Sect. 3.2.2) and the

progressive unpinning from both the eastern ice shelf and the offshore ridge (Tinto and

0 302010

−75˚30'

−75˚00'

(a)−74˚30'

km

−107˚ −106˚ −105˚−108˚ −107˚ −106˚ −105˚−108˚

0 302010

−75˚30'

−75˚00'

−74˚30'

(b)

km

0 20001000 3000 >50004000flow velocity [m/yr]

2001 2011

CD

B

A

Fig. 5 Velocity fields of Thwaites Glacier derived from a a Landsat-7 ETM? scene pair from January/November 2001 (327 days separation) and b TerraSAR-X acquisitions between September–Novem-ber 2011. The evolution of flow velocities along two profiles (AB and CD) is shown in Fig. 6. The purpleline indicates the grounding line from Rignot et al. (2011a). Visible large cracks in the ice shelf are shown asdotted blue lines in both images. For a general location map cf. Fig. 4

Surv Geophys

123

Bell 2011). Additionally, changes in the ice shelf geometry caused by calving events like in

2010 or by higher melt rates of the floating tongue close to the grounding line due to warm

seawater (Shepherd et al. 2004) can also control the upstream ice dynamics. In case of a

reversed bedrock topography, the following grounding-line retreat will expose formerly

grounded parts of the ice stream to warm ocean water and may lead to a further accel-

eration (Jenkins et al. 2010).

3.2.2 Ice-surface-height changes

Elevation changes for the frontal region of Thwaites Glacier were derived for different

periods using various data sets. TanDEM-X DEMs were used to obtain height changes

between 2011 and 2012, while height changes for the period 2003–2009 were inferred

from ICESat laser altimetry data. Hence, we can conclude on temporal variations in the

height changes between both periods. Moreover, the period under investigation could be

extended to the period 2003–2012 by combining ICESat and TanDEM-X data. This

requires the consideration of height biases due to the SAR X-band signal penetration at the

glacier’s surface. Coincident elevation data acquired by TanDEM-X and Operation Ice-

Bridge’s ATM were utilised to quantify the signal penetration.

The elevation-change rates for the period 2011–2012 (Fig. 7a) were obtained from the

two selected TanDEM-X DEMs (Table 3). Since the TanDEM-X scenes lack ice-free

features on land we validated the absolute elevation of the DEMs by comparing the sea-

level height and the freeboard height along ATM profiles crossing the front of the glacier.

Although the signals reflected by open water and ice melange at the front of the glacier

were noisy, the agreement between the TanDEM-X and ATM elevations referenced to the

WGS84 ellipsoid is in the order of the TanDEM-X absolute error.

At the homogeneous upper part of the glacier shown in Fig. 7a the mean elevation-

change rate is -4.30 ± 1.37 m/year. Some areas situated in the highly crevassed fast area

close to the front exhibit larger differences of up to -16 m/year. These artefacts are

probably due to horizontal displacement and formation of new crevasses during this period.

(b)(a)

5000

4000

3000

2000

1000

0

0 20 40 60 80 100 120 140

flo

w v

elo

city

[m

/yr]

2008/2009 (Landsat)

2004/2005 (Landsat)2001 (Landsat)1988/1989 (Landsat)

2008 (Rignot, 2011)

2011 (TerraSAR-X)2008/2009

2004/2005 2001 1988/1989

2008

2011

profile distance A-B [km]

0 20 40 60 80 100 120 140

profile distance C-D [km]

Fig. 6 Change in flow velocity for profiles along a the centre flow line (profile AB) and b the groundingline (profile CD). The red line shows the transition from grounded to floating ice. Abrupt velocity changesbecause of detached floating ice areas are marked by dotted lines. Velocity data of 2008 according to Rignotet al. (2011b)

Surv Geophys

123

Along the ICESat repeat tracks the mean height-change rate between 2011 and 2012 from

both TanDEM-X DEMs is -4.26 ± 0.82 m/year. In contrast, a mean height-change rate of

-1.07 ± 0.65 m/year was inferred from all ICESat repeat tracks overlapping the Tan-

DEM-X DEM (Fig. 7a) for the period 2003–2009. It is noteworthy that the maximum

ICESat-observed rate for the Thwaites drainage basin is larger than -3 m/year (Fig. 4b).

However, the comparison of the results from both periods clearly indicates an increased

surface lowering in recent years.

Rott et al. (1993) measured a signal penetration of about 10 m at X-band in the dry

snow zone in Dronning Maud Land while the scattering phase centre is located at about

50% of this depth (Forsberg et al. 2001). Since the snow conditions may differ in the area

under investigation we utilised two IceBridge ATM profiles acquired only several weeks

earlier than the TanDEM-X overflights (Table 3) to assess the penetration depth effects on

TanDEM-X elevations. Therefore, we assume changes in the snow structure during these

short periods to be negligible. According to the TanDEM-X backscattering coefficients no

melting occurred at the snow surface in this period. Although the height patterns shown in

Fig. 7b are very similar, for 2011 the ATM elevation is on average 3.7 m higher than

TanDEM-X, while for 2012 this difference is larger with about 5.7 m. The absolute

accuracy of the TanDEM-X measuring system as well as variations in the snow cover

structure may explain the different biases in 2011 and 2012. Nevertheless, both values

agree with the expected interferometric height bias at X-band of about 5 m.

After correcting the TanDEM-X elevations for this bias we calculated height changes

for the period 2003–2012 along the ICESat tracks by differencing the observed heights

from ICESat LOP 2A (2003/10) and the TanDEM-X DEM from 2012. The resulting height

trend for this 9-year period is -2.71 ± 1.71 m/year. Hence, the height change observed for

different periods exhibit an increased thinning of Thwaites Glacier since 2003. The

increased volume loss implies a more pronounced negative mass balance in the area during

the last decade. This result is also consistent with the acceleration in ice flow (leading to

higher calving rate) observed by Landsat and TerraSAR-X and the increased mass loss for

PITS basin derived from GRACE.

20

15

0

5

10

-5

-20

-15

-10

hei

gh

t ch

ang

e tr

end

[m/y

r]

(b)(a)

2011-11-04

2012-10-12

−107.0 −106.5 −106.0 −105.5

surf

ace

hei

gh

t [m

]

400

450

500

550ICEBRIDGE [04-01-2011] [12-10-2012]

TanDEM-X [04-12-2011]TanDEM-X [01-12-2012]

Longitude [degree]

−110.0

−75.5

−75.0

−109.0 −108.0 −107.0 −106.0 −105.0

Fig. 7 a Height-change rates over Thwaites Glacier derived from two TanDEM-X DEMs in 2011 and 2012.Additionally, ICESat-derived trends for the period October 2003 to October 2009 are given along theICESat tracks. While the black lines indicate the locations of two ATM profiles shown in panel b, the redline shows the grounding line according to Rignot et al. (2011a). b Surface elevations derived fromTanDEM-X and ATM along two ATM profiles in 2011 and 2012 located as shown in panel a

Surv Geophys

123

3.3 Low Accumulation Zones in Central East Antarctica

Although the major part of the Antarctic ice-mass change is located in basin WEST, mass

changes in the huge eastern part of the AIS are highly relevant for the entire AIS mass

balance. Hence, we investigate the changes in the low accumulation zone (LAZ) of central

East Antarctica, where we focus on two different regions with verified low SMB changes.

One region exhibits a SMB change smaller than 60 kg/m2/year (Vau60; Vaughan et al.

1999), excluding the polar gap of ICESat, while the SMB changes over the second region

do not exceed 45 kg/m2/year (Vau45; Fig. 9). For both regions the ICESat-observed mean

height changes are as low as 1.2 ± 0.1 and 0.5 ± 0.2 mm/year, respectively. The corre-

sponding mass changes of 3.3 ± 5.9 and 0.6 ± 2.7 Gt/year are in good agreement with

GRACE-derived mass-gain estimates of 3.1 ± 4.8 and 1.1 ± 2.5 Gt/year, respectively

(both using the IJ05_R2 correction). Since the mass-change time series inferred from

GRACE (not shown here) do not exhibit significant interannual variations over the period

October 2003 to October 2009 it is justified to assume the accumulation to be nearly

constant over this period. To verify if this assumption is also valid for longer periods we

extend our analysis further back in time.

For this, we used passive microwave (SSM/I) data measured at two different fre-

quencies (19.35 and 22.2 GHz) to derive maps of snow accumulation for the Vau60 region.

Here, we make use of the fact that the depth of signal penetration into the dry snow volume

is larger at lower frequencies. For any given firn profile a certain depth corresponds to a

certain age of the firn, and the relationship between depth and age depends mainly on the

accumulation rate. As a consequence, the snow accumulation rates derived from the

19 GHz SSM/I channel are averaged over a longer time period than the accumulation rates

obtained from the 22 GHz data. Figure 8 illustrates this effect. It shows the microwave

emission contribution for each layer of the n-layer emission model described in Linow

(2011) plotted versus firn age obtained from the firn microstructure model by Linow et al.

(2012). In this example, firn microstructure profiles were calculated for mean annual

temperatures of -50 �C and for accumulation rates A = {0.01, 0.05, 0.1} m w.e./year. The

maximum emission contribution (measured in terms of brightness temperature) originates

at different depths (and hence firn ages). For equal accumulation rates, the emission

maximum at 19 GHz comes from older firn than at a frequency of 22 GHz. At an

0 50 100 150 200 250 300

firn age (yr)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

T B c

ontr

ibut

ion

(K)

0.10

0.05

0.01

0.10

0.05

0.01

accumulationrate (m w.e./yr)

age of scattermaximum (yr)

11.5

17.5

39.0

23.5

26.5

55.0

22 GHz

19 GHz

Fig. 8 Modelled emissioncontribution from modelled firnlayers versus firn age for differentaccumulation rates and SSM/Isensor channels

Surv Geophys

123

accumulation rate of 0.1 m w.e./year, for instance, the emission maximum is found at firn

layers, which are 23.5 years (19 GHz) and 11.5 years (22 GHz) old.

In principle, a comparison of accumulation rates determined from emission data

recorded at two different frequencies can be used to detect changes in snow accumulation.

While it would be difficult to directly quantify accumulation rate variability, it can be used

as a qualitative indicator for the long-term stability of the accumulation rate. Figure 9

shows snow accumulation mapped using SSM/I data at 19 GHz (left panel) and 22 GHz

(centre panel). Both maps show a good agreement in both the spatial distribution and

absolute accumulation values. Over large parts of region Vau45 the observed accumulation

rates are below 0.03 m w.e./year, while slightly larger rates are evident towards the coast.

A comparison with field data published by Picciotto et al. (1971) shows an overall

agreement, with values derived from our approach being slightly lower. However, it has to

be kept in mind that the authors of the study state that their methods of measurement tend

to overestimate snow accumulation rates due to inconclusive stratigraphic features. The

accumulation rate difference DA ¼ A19 GHz � A22 GHz is shown in Fig. 9c being on the order

of ±0.01 m w.e./year. The spatial distribution of DA values indicates effects of the spatial

sampling of the SSM/I sensor. Another possible explanation for such a pattern distribution

can be found in discretisation errors from the lookup table.

Both our multi-frequency accumulation rate retrieval approach and our comparison to

historical ground truth indicate that conditions for the low accumulation region considered

here are stable for larger time periods.

4 Discussion

Both GRACE and ICESat reveal a negative mass balance of the AIS for the period October

2003 to October 2009. The IJ05_R2-corrected mass-loss rates (94.9 ± 30.9 vs.

126.0 ± 20.0 Gt/year) agree within the range of their accuracy measures. However, by

comparing the results for basin WEST and EAST large discrepancies become evident.

Although the mass changes for basin WEST do also agree within the uncertainty range (-

107.5 ± 13.8 vs. -80.2 ± 32.7 Gt/year) this is not the case if the W12a-corrected GRACE

results are considered (-131.0 ± 10.1 Gt/year). For the three western basins the largest

discrepancy is revealed for the Antarctic Peninsula (basin 13; -26.1 ± 11.2 vs.

?10.5 ± 8.9 Gt/year). Over the narrow basin 13 ICESat is heavily affected by dense clouds

along the coastal regions. Hence, a larger amount of missing data complicates the inference

70° S

30° W 30° E

150° E

0° W

(a) (b) (c)

<0.0200.021 - 0.0300.031 - 0.0400.041 - 0.0500.051 - 0.0600.061 - 0.0700.071 - 0.1000.101 - 0.170

A (m w.e./yr)<0.0200.021 - 0.0300.031 - 0.0400.041 - 0.0500.051 - 0.0600.061 - 0.0700.071 - 0.1000.101 - 0.170

A (m w.e./yr)

<-0.01-0.01 - 0.000.00 - 0.010.01 - 0.02

ΔA (m w.e./yr)

Fig. 9 Accumulation rate at 19 GHz (a) and at 22 GHz (b) and their difference DA (c). Circles show thelocations where field data are available (Picciotto et al. 1971). The light red and the dark red line indicatesthe Vau45 and the Vau60 basin, respectively

Surv Geophys

123

of reliable height-change estimates. Moreover, due to the narrow shape and the north–south

orientation of basin 13 reliable estimates are also difficult to derive from GRACE due to

increased leakage-out. The largest overall difference was inferred for basin EAST, where

GRACE depicts a small mass gain of 13:2� 18:9 Gt/year while ICESat observes a clear

mass loss of �45:8� 19:9 Gt/year. Considering the results based on W12a the discrepancy

is even larger.

Beside the limitations mentioned above, the observed discrepancies can be explained by

three potential error sources: (1) limitations in the density assumption used for the volume–

mass conversion, (2) the applied offsets between ICESat’s laser operational periods (LOP)

and (3) uncertainties in utilised GIA corrections.

Interannual variations in accumulation and/or temperature will cause interannual

changes in the firn compaction process. If these effects are present within the observational

period the density of the ongoing mass change will deviate from the density of pure ice

used in our study. Regional atmospheric climate models (e.g., Lenaerts et al. 2012)

revealed such variations with distinct spatial patterns over the AIS. Other studies corrected

the ICESat-derived volume changes for changes in firn compaction using a firn densifi-

cation model (Ligtenberg et al. 2011) before performing the volume–mass conversion.

Shepherd et al. (2012) presented averaged ICESat-derived mass and volume changes for

the period October 2003 to October 2008 inferred by different groups using different

methods and ICESat releases. For example, their average volume change for basin EAST is

78� 19 km3=year. After correcting for firn compaction the corresponding mass change is

109� 57 Gt/year. If the ice density would solely be used for the volume–mass conversion

the mass change would be only 70� 17 Gt/year. Hence, by considering firn compaction

our mass-change estimate for basin EAST would be less negative and consequently be in

better agreement with our GRACE result.

However, the ICESat-derived mass change of Shepherd et al. (2012) for basin EAST is

significantly larger than their GRACE estimate for the same period (35� 40 Gt/year). Com-

paring their underlying volume rate to our ICESat estimate (78� 19 vs. �50:8�3:9 km3=year) reveals an unsatisfactory discrepancy. Beside slight differences in the con-

sidered time period and the processing the most remarkable difference consists in the applied

LOP offsets. While our LOP-offset time series exhibits a trend of�13:3� 3:6 mm/year their

time series, determined over the open ocean, reveals a trend of �6:5 mm/year, only (no

uncertainty given). To be consistent to the offset definition used by Ewert et al. (2012b) the

trend sign was changed. The difference between both trends corresponds to a volume change

of 68� 36 km3=year and explains a large part of the revealed discrepancy.

Our LOPs were inferred over the ice surface in the area of the subglacial Lake Vostok.

GPS surveys proved that the lake surface is very stable in time (Richter et al. 2008) and is

suitable to be used as a reference surface for the offset determination. The resulting trend is

also in good agreement with the trend of �15:8� 0:8 mm/year inferred over an low

accumulation zone (LAZ) in East Antarctica using a firn densification correction (Gunter

et al. 2013). Because different trends were inferred over ice and ocean we conclude that it

is favourable that the monitored surface and the reference surface used for the LOP-offset

determination have comparable characteristics in terms of the existing signal backscatter.

Beside existing differences in the utilised GIA models both are equally suited to correct

GRACE observations. However, the uncertainties are still large and there is still room for

further improvements. GPS-observed uplift rates have been used to validate existing GIA

models (Thomas et al. 2011) and revealed that existing GIA models underestimate the

observed crustal deformation. Hence, both applied GIA models used the observed uplift

Surv Geophys

123

rates to adjust the underlying Earth model and/or the ice-load history. Riva et al. (2009)

demonstrated that empirical GIA estimates, derived from the combination of GRACE and

ICESat, provide improvements over existing GIA models. According to the updated results

presented by Gunter et al. (2013) the empirical derived GIA-induced crustal deformations

are in better agreement with the GPS-observed rates than the model predictions. In general,

the empirical GIA estimates exhibit features comparable to those predicted by the models,

but do also reveal regional differences.

The GIA results of Gunter et al. (2013) for the AIS are in the range of 53–100 Gt/year,

depending on the used GRACE solution, which comprises the model predictions used in

our study. For basin EAST their estimates (31–53 Gt/year) exceed the GIA prediction of

W12a (5 Gt/year). Hence, although the predicted crustal subsidence in central East Ant-

arctica could be confirmed, it is less strong than predicted by W12a. This is also confirmed

by comparing our GRACE and ICESat mass-change results in the LAZ. For basin Vau60

the IJ05_R2-based mass rates (3:1� 4:8 vs. 3:3� 5:9 Gt/year) agree well while the W12a-

based GRACE result (21:3� 8:0 Gt/year) exhibits a larger discrepancy. Although ice core

data support the increase in accumulation since last glacial maximum, leading to the large

subsidence predicted by W12a, the spatial distribution and the effect on ice dynamics are

still poorly known (King et al. 2012).

Furthermore, the empirical results reveal an exceptional large GIA-induced uplift over

the PITS basin not predicted by any model. Using a comparable approach Groh et al.

(2012) already identified this anomaly and could also validate it by means of GPS-

observed deformation rates. If we apply the same methodology to the updated data set

presented above, we derive a GIA-induced mass change of 32:0� 18:8 Gt/year. This is

significantly larger than the predictions by IJ05_R2 and W12a (4.8 and 7.9 Gt/year).

Correcting the GRACE result for PITS basin for this GIA estimate gives an ice-mass trend

of �99:9� 18:8 Gt/year. Compared to the model-based GRACE results this corresponds to

an increase in the observed mass loss by more than 30%. Applying the new GIA correction

to the volume trend observed by ICESat results in an updated estimate of �108:9�5:6 km3=year and a corresponding mass change of �98:0� 11:8 Gt/year. Due to the nature

of the approach both mass trends are in much better agreement after applying the empirical

inferred GIA correction.

5 Summary and Outlook

The present study confirms that the contribution of the AIS to the global sea-level rise

(SLR) has slightly increased over the last decade. For the period 1993–2003 an AIS-

induced SLR of 0:22� 0:35 mm/year was observed (Solomon et al. 2007). According to

our GRACE results (�94:9� 30:9 Gt/year), using the IJ05_R2 GIA correction the global

SLR caused by the AIS has increased to 0:26� 0:08 mm/year for the period October 2003

to October 2009. This increase, derived by utilising up-to-date GIA corrections, is clearly

smaller than suggested by previous GRACE estimates (Ivins et al. 2013; King et al. 2012).

Nevertheless, the investigation of an extended GRACE observation period (January 2003

to December 2012) indicates that the AIS contribution to global SLR is still increasing in

the recent years (0:30� 0:08 mm/year). Because of observed interannual changes in

accumulation and discharge the determination of reliable long-term trends is still chal-

lenging and requires to continue the GRACE time series. An impending gap between

GRACE and the GRACE follow-on mission, due for launch in 2017, needs to be filled by

Surv Geophys

123

alternative satellite data like those to be acquired by the recently launched SWARM

mission (Wang and Rummel 2012).

ICESat-derived surface-height changes over the entire AIS confirm the previously

observed thinning of the ice sheet’s coastal regions, especially in West Antarctica (Prit-

chard et al. 2009). Therefore, a sound determination and application of offsets between the

ICESat LOPs are crucial. The consistency of mass changes derived from ICESat and

GRACE strongly depends on the validity of the density assumption used for the volume–

mass conversion.

Changing ice-flow velocities indicate changes in the dynamic behaviour of the ice

streams. Utilising Landsat optical imagery the evolution of ice velocities over Thwaites

Glacier was derived over a period of more than two decades. We demonstrate that the

moderate velocity increase of the floating tongue (Rignot 2008) experienced a significant

acceleration during the last 5 years. In addition, TerraSAR-X SAR imagery was suc-

cessfully used to derive high-resolution flow velocity fields in 2011. This complementary

data set proves that even the grounded part of the ice stream is now accelerating.

In order to extend the ICESat time series of ice-surface heights beyond 2009, we

derived high-resolution interferometric DEMs from TanDEM-X data. In this way height

changes over Thwaites Glacier were inferred for the period 2003–2012 revealing an

increased surface lowering. Consequently, TanDEM-X can provide valuable spatially

distributed elevation data to bridge the gap between ICESat and ICESat-2 scheduled for

launch in 2016.

Also, in the low accumulation zone (LAZ) in central East Antarctica our analysis benefits

from the application of different data sets. ICESat and GRACE revealed only minor changes

in the ice-surface height and the mass, respectively, between October 2003 and October

2010. Because of the dry snow conditions in the LAZ passive microwave remote sensing

data were used to infer accumulation rates over several decades. The long-term stability of

the accumulation rates in the LAZ could be confirmed using two different frequencies.

Acknowledgments This work was supported by the German Research Foundation (DFG) within thePriority Programme SPP1257 ‘‘Mass Transport and Mass Distribution in the Earth System’’. TerraSAR-Xand TanDEM-X data were provided by DLR within science proposals HYD1303 and XTI_GLAC0538,respectively. We gratefully acknowledge the helpful comments provided by two anonymous reviewers.

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