We use 3 years of Cryosat‐2 radar altimeter data to develop the first comprehensive assessment of Antarctic ice sheet elevation change. This new data set provides near‐continuous (96%) coverage of the entire continent, extending to within 215 km of the South Pole and leading to a fivefold increase in the sampling of coastal regions where the vast majority of all ice losses occur. Between 2010 and 2013, West Antarctica, East Antarctica, and the Antarctic Peninsula changed in mass by −134 ± 27, −3 ± 36, and −23 ± 18 Gt yr −1 , respectively. In West Antarctica, signals of imbalance are present in areas that were poorly surveyed by past missions, contributing additional losses that bring altimeter observations closer to estimates based on other geodetic techniques. However, the average rate of ice thinning in West Antarctica has also continued to rise, and mass losses from this sector are now 31% greater than over the period 2005–2010.

1 Introduction With a capacity to resolve detailed patterns of elevation change at the scale of glacier drainage basins [Shepherd et al., 2002; Davis and Ferguson, 2004; Pritchard et al., 2009; Remy and Parouty, 2009; Shepherd et al., 2004; Wingham et al., 2006; Zwally et al., 2005], repeat satellite altimetry has transformed our ability to study the polar ice sheets. Nevertheless, direct measurements of elevation change have been restricted by the latitudinal limits of satellite altimeter orbits (81.5° and 86.0° for conventional radar and laser systems, respectively), by the reduced performance of conventional radar altimeters over the steep terrain that is typical of ice sheet margins and by the irregular temporal sampling of satellite laser altimeter data due to the episodic nature of ICESat mission campaigns and due to the presence of clouds. These limitations have precluded, for example, comprehensive assessments of Antarctic Peninsula volume change, and altimeter data omission may also explain differences in mass balance estimates for other ice sheet regions [Shepherd et al., 2012]. CryoSat‐2 was designed to overcome several of the limiting factors that previous satellite altimeters faced, with an orbital limit extending to 88° and a novel synthetic aperture radar interferometry mode providing measurements of fine spatial resolution in areas of steep terrain [Wingham et al., 2006]. Here we use CryoSat‐2 data acquired between November 2010 and September 2013 to produce the first altimeter‐derived estimates of volume and mass change for the entire Antarctic ice sheet.

2 Data and Methods To compute changes in ice sheet elevation, we adapted a repeat‐track method [Flament and Remy, 2012; Moholdt et al., 2010; Smith et al., 2009] to suit the Cryosat‐2 data set, which provides high and low spatial and temporal sampling, respectively, relative to other altimeter missions (see supporting information). Altogether, Cryosat‐2 has acquired 159 million range measurements across inland and coastal sectors of Antarctica in pulse‐limited and synthetic aperture radar interferometry modes, and we process measurements from each mode in an identical manner. Ice sheet elevation is calculated as the difference between satellite locations and range measurements corrected for the lag of the leading edge tracker [Wingham et al., 2006], fluctuations in dry and wet atmospheric mass, the effects of the ionosphere, isostatic rebound [Ivins et al., 2013; Whitehouse et al., 2012], and for solid Earth and ocean tides. Elevation measurements are accumulated in 469,451 regularly spaced (5 by 5 km) geographical regions, and within each region, we solve, simultaneously, for spatial and temporal fluctuations in elevation and for a fixed contribution due to the impact of surface anisotropy on the tracked range (see supporting information). As part of this calculation, outlying data are culled, iteratively, to minimize their impact on each solution, and a correction is then applied to account for temporal fluctuations in backscatter that cause spurious fluctuations in range [Davis and Ferguson, 2004; Khvorostovsky, 2012; Wingham et al., 1998]. After editing the resulting trends to remove 14,098 poorly constrained solutions, we obtain 455,403 independent estimates of elevation change distributed across 96% of the grounded Antarctic ice sheet (Figure 1), with an effective average temporal resolution of 60 days. We compute the uncertainty of area‐averaged elevation trends from the root‐sum‐square of the uncertainties determined from contributing model fits (see supporting information), as errors associated with altimeter elevation measurements have been shown to rapidly decorrelate with increasing spatial separation [Wingham et al., 1998]. Figure 1 Open in figure viewer PowerPoint Zwally et al., 2012 Shepherd et al., 2002 2004 Wingham et al., 2009 Rate of elevation change of the Antarctic ice sheet between 2010 and 2013 determined from CryoSat‐2 repeat altimetry and smoothed with a 25 by 25 km median filter. Solid grey and white (inset) lines show the boundaries of 27 ice sheet drainage basins [.,]. The CryoSat measurements reach to within 215 km of the South Pole, as compared to 930 and 430 km for the ERS/Envisat and ICESat altimeters, respectively. Also shown (inset) are the numbers used to identify ice sheet drainage basins, with East Antarctica and the Antarctic Peninsula defined as basins 2 to 17 and 24 to 27, respectively, and West Antarctica defined as the remaining basins and the mask developed (see supporting information ) to identify elevation changes occurring at the density of ice (inset, black regions). Elsewhere, we assume that elevation changes are caused by fluctuations in surface mass balance alone, and we therefore applied a density of snow to these signals (inset, grey regions). Ice dynamical imbalance (IDI) is evident as thickening of the Kamb Ice Stream (basin 18) and as widespread thinning across the Amundsen Sea sector (basins 21 and 22), with the latter signal affecting a considerably larger area than at any time in the past two decades [.,.,]. We assessed the degree to which the CryoSat‐2 orbit pattern and interferometric mode of operation provide improved detection of ice sheet elevation changes relative to past altimeters. The data (Figure 1) show several geographically isolated regions of surface uplift and lowering interspersed with wide areas of no overall change, and, altogether, their extent is a significant improvement on that afforded by earlier missions [Pritchard et al., 2009; Wingham et al., 1998]. For example, the region of unsurveyed ice at the South Pole is now only 147,725 km2 in area −1.2% of the grounded ice sheet and 18 and 4 times smaller than that of the Envisat and ICESat missions, respectively. In addition, the rugged terrain of the continental margin—where the vast majority of known imbalance has occurred—is now densely surveyed, including the majority of the mountainous Antarctic Peninsula and the grounding zones of Totten Glacier (116°E) and of Marie Byrd Land (103° to 158°W). Altogether, CryoSat‐2 has surveyed 49% of the Antarctic coastal region on six or more occasions, 6 and 5 times more than the Envisat (8%) and ICESat (10%) altimeters, respectively (Figure 2). Moreover, CryoSat‐2 has surveyed 62% of the fastest‐flowing ice (>1500 m yr−1) where dynamic thinning is concentrated −10 times more than other missions. Although there is no obvious difference between the interferometric mode elevation rates and those determined in the traditional pulse‐limited altimeter mode (Figure 1), we nevertheless compared them to ~25,000 independent estimates derived from coincident repeat airborne laser altimetry (see supporting information) to assess their certainty. In the Amundsen Sea sector of West Antarctica where rates of ice thickness change are varied and large, elevation rates determined from ~85,000 CryoSat‐2 measurements are in close agreement with these airborne observations (Figure 3); after adjusting for bias introduced by the airborne sampling pattern (see supporting information), the mean difference (31 cm yr−1) is smaller than the expected elevation fluctuation due to snowfall variability. Figure 2 Open in figure viewer PowerPoint Rignot et al., 2011b British Antarctic Survey, Scott Polar Research Institute, and World Conservation Monitoring Centre, 1993 Rignot et al., 2011a Rignot et al., 2011b Shepherd and Wingham, 2007 Distribution of ice velocity [.,] at 55,440 regularly spaced locations around the margin of the Antarctic ice sheet (black) and the proportion of these locations surveyed on six or more occasions by the Envisat (blue), ICESat (green), and CryoSat (red) altimeters. The ice sheet margin was mapped from a digital database [] augmented with interferometric synthetic aperture radar observations [.,], and ice velocities were extracted where this boundary intersected a 900 m resolution gridded map of ice speed derived from synthetic aperture radar measurements [.,]. Although only a small fraction (2.5%) of the ice sheet margin flows at speeds in excess of 500 m/yr, these fast‐moving ice streams and outlet glaciers channel the majority of ice into the ocean and include the principal locations of contemporary dynamical imbalance []. The Envisat, ICESat, and CryoSat altimeters have surveyed 10, 8, and 49% of the coastal region with sufficient frequency to detect temporal changes in elevation, respectively. Figure 3 Open in figure viewer PowerPoint −1 and 110 cm yr−1 respectively; 21 cm yr−1 of the former can be explained by the airborne sampling bias, and the remainder can be explained by either a fluctuation in snow accumulation due to the 1 year mismatch in observation period (38cm yr−1, based on the data in Table −1, respectively). Surface elevation change of the Amundsen Sea sector, West Antarctica, determined from CryoSat‐2 (2010 to 2013) and, overlaid, from repeat airborne laser altimetry gridded at 5 km spacing (2009 to 2012) (see supporting information ). White boundaries delineate the drainage basins of the Pine Island Glacier (PIG), the Thwaites Glacier (THW), and the Pope/Smith/Kohler glaciers (PSK). (inset) Distribution of the difference (CryoSat minus airborne) between 495 coincident CryoSat and airborne elevation rates. The mean and standard deviation of the difference in the elevation rate determined using CryoSat and airborne measurements are 52 cm yrand 110 cm yrrespectively; 21 cm yrof the former can be explained by the airborne sampling bias, and the remainder can be explained by either a fluctuation in snow accumulation due to the 1 year mismatch in observation period (38cm yr, based on the data in Table 1 ) or the uncertainties of the airborne and satellite measurements themselves (17 and 16 cm yr, respectively). Table 1. The Area, Mean Accumulation Rate, Estimated Snowfall Variability, Average Elevation Rate, and Estimated Mass Imbalance of Antarctic Drainage Basins (Numbered 1–27) and of Regions of Ice Dynamical Imbalance (IDI) (see Figure ) From 2010 to 2013 Observed Areab Mean Ice Accumulation Ratec Snowfall Variabilityd Mean Elevation Rate Mass Imbalance Basin (km2) (cm/yr) (cm/yr) (cm/yr) (Gt/yr) 1 443,250 29.1 8.4 −4.9 ± 0.2 −8 ± 14 2 584,550 9.1 2.1 −1.4 ± 0.1 −4 ± 6 3 1,493,425 6.4 1.1 1.1 ± 0.1 6 ± 6 4 226,625 20.0 7.8 1.5 ± 0.5 1 ± 7 5 177,100 16.6 7.7 6.5 ± 0.5 4 ± 5 6 583,050 12.6 3.5 13.5 ± 0.2 28 ± 8 7 481,275 15.1 4.6 2.3 ± 0.2 4 ± 8 8 157,525 18.0 8.8 8.3 ± 0.4 5 ± 5 9 139,175 13.5 7.8 −0.3 ± 0.5 0 ± 4 10 886,950 5.9 1.2 −0.8 ± 0.1 −3 ± 4 11 248,275 7.1 2.8 0.8 ± 0.2 1 ± 3 12 714,475 22.9 6.3 −2.1 ± 0.1 −5 ± 16 13 1,101,250 22.0 5.0 −8.4 ± 0.1 −39 ± 20 Totten IDI 20,225 69.7 36.6 −52.2 ± 1.2 −10 ± 3 14 702,400 20.7 5.1 0.4 ± 0.1 1 ± 13 15 81,350 18.4 10.0 −5.7 ± 1.7 −2 ± 5 16 238,750 11.2 4.5 −1.9 ± 0.4 −2 ± 4 17 1,683,725 7.6 1.2 0.3 ± 0.1 2 ± 8 18 253,500 14.0 5.2 17.4 ± 0.2 29 ± 5 Kamb IDI 51,150 12.9 6.7 46.2 ± 0.4 22 ± 1 19 355,900 14.5 4.5 0.7 ± 0.2 1 ± 6 20 168,700 30.7 13.7 −15.9 ± 0.5 −23 ± 9 Getz IDI 33,200 37.5 19.4 −70.4 ± 1.1 −22 ± 3 21 205,650 37.2 15.1 −36.2 ± 0.4 −64 ± 12 Thwaites IDI 91,850 44.5 22.8 −37.5 ± 0.5 −32 ± 8 PSK IDI 20,950 37.9 19.6 −117.5 ± 1.3 −25 ± 2 22 207,325 42.9 17.5 −32.7 ± 0.3 −56 ± 13 Pine Island IDI 96,800 47.7 24.5 −59.4 ± 0.4 −53 ± 9 23 70,850 67.8 35.2 −30.6 ± 0.8 −12 ± 9 Ferrigno IDI 5,950 74.4 38.2 −123.7 ± 2.7 −7 ± 1 24 92,700 57.7 30.3 −32.2 ± 0.8 −11 ± 11 25 17,600 110.8 63.4 −52.3 ± 4.8 −9 ± 9 26 21,925 103.2 61.1 −24.6 ± 4.2 −4 ± 9 27 35,100 55.5 29.9 4.8 ± 2.9 1 ± 6 East Antarctica 9,499,900 11.6 1.0 0.1 ± 0.2 −3 ± 36 West Antarctica 1,705,175 26.0 4.4 −9.8 ± 0.3 −134 ± 27 Antarctic Peninsula 167,325 67.6 32.4 −25.6 ± 2.5 −23 ± 18 Antarctica 11,372,400 14.8 1.2 −1.9 ± 0.2 −159 ± 48

3 Results The CryoSat‐2 observations confirm the continuation of existing signals of elevation change [Pritchard et al., 2009; Shepherd et al., 2002, 2012; Wingham et al., 1998; Zwally et al., 2005], identify regions which have evolved since previous surveys, and allow investigations of new terrain. Between 2010 and 2013, the average elevation of the Antarctic ice sheet fell by 1.9 ± 0.2 cm yr−1. Although most of the observed changes are smaller than expected fluctuations in snowfall (Table 1), those that are not coincide with areas of known dynamical imbalance (basins 13, 18, and 20 to 22) or with episodes of anomalous snow accumulation (basin 6) [Lenaerts et al., 2013]. Overall, the pattern of elevation change is still dominated by widespread glacier thinning across the Amundsen and Bellingshausen Sea sectors (basins 20–24), with maximum rates of surface lowering reaching 9 m yr−1 at Smith Glacier. Ice catchments feeding this 3500 km stretch of coastline are now thinning at an average rate of 30 ± 0.5 cm yr−1. In the Ross Sea sector (basin 18), ice stream deceleration [Joughin et al., 2002] continues to drive widespread thickening of the Kamb Ice Stream and of faster flowing sections of the Whillans Ice Stream, at rates in excess of 50 cm yr−1. In East Antarctica, although there are mesoscale patterns of modest surface uplift (e.g., basin 6) and lowering (e.g., basin 13) that are typical of snowfall variability [Davis et al., 2005; Monaghan et al., 2006; Lenaerts et al., 2013], there is no significant change in elevation, overall, across the slow‐flowing interior (Figure 1). However, with detailed sampling of coastal regions, our data set does reveal, for the first time, that thinning of the Totten Glacier (basin 13) extends to its grounding line [Rignot et al., 2011a] and is everywhere correlated with fast ice flow. In contrast, the Cook glacier (basin 14), which thinned at modest rates during previous surveys [Shepherd et al., 2012], shows no significant change in elevation since 2010. We calculated rates of mass change within all Antarctic drainage basins [Zwally et al., 2012] using a surface‐density model (see Figure 1, inset) to discriminate between elevation fluctuations occurring at the densities of snow and ice. To delimit these regions, we updated an earlier classification scheme [Shepherd et al., 2012] to include additional information on ice flow (see supporting information). In calculating the mass imbalance, we treat both the elevation rate error and snowfall variability as sources of uncertainty (see supporting information). Between 2010 and 2013, we estimate that West Antarctica, East Antarctica, and the Antarctic Peninsula changed in mass by −134 ± 27, −3 ± 36, and −23 ± 18 Gt yr−1, respectively (Table 1). The largest signal of imbalance occurred in the Amundsen Sea sector (basins 21 and 22) which lost a total of 120 ± 18 Gt yr−1 over the course of our study period −90% of the entire West Antarctic mass loss. The Cryosat‐2 data set also reveals greater rates of mass loss from the main outlet glaciers of the Amundsen Sea sector, compared to observations acquired by ERS and Envisat between 1992 and 2010 [Shepherd et al., 2012] (Figure 4). While these differences are due to increases in the average rate of ice thinning, changes elsewhere—particularly in areas of steep coastal terrain—are in part due to the improved sampling of Cryosat‐2. For example, CryoSat‐2 now surveys 97% of glaciers flowing into the Getz Ice Shelf (basin 20), significantly more than either ERS (36%) or Envisat (72%), and the net effect is a threefold increase in the estimated volume change within the basin compared to a twofold increase in the coincident rate of thinning. Figure 4 Open in figure viewer PowerPoint Rate of mass change of areas of unbalanced ice flow (see Figure 1 ) within the Pine Island (red), Thwaites (blue), and Pope/Smith/Kohler (PSK) (green) glacier drainage basins (Figure 3 ), as well as the total area of dynamical imbalance within the Amundsen Sea sector (magenta). Trends are calculated over 6 year periods between 1992 and 2010 using a 19 year time series of ERS‐1, ERS‐2, and Envisat data (circles) and over a 3 year period using CryoSat‐2 data acquired between 2010 and 2013 (diamonds).

4 Discussion Our measurements of Antarctic ice sheet volume change extend the record of ice sheet mass balance to the present day. In the Amundsen Sea sector, where ice losses have tripled over the past two decades [Medley et al., 2014; Rignot et al., 2008; Wingham et al., 2009], our estimates of imbalance are in close agreement with those determined using independent methods. For example, according to mass budget estimates, the Pine Island Glacier—which remains the largest individual source of global ocean mass—lost 44 ± 7 Gt of ice in the year 2011 [Medley et al., 2014], a value that is consistent with our estimate (56 ± 13 Gt yr−1) derived over the period 2010 to 2013 and over an 11% larger area. Similarly, our estimate of the specific rate of mass loss from the wider, 419,000 km2 Amundsen Sea sector (286 ± 42 kg m−2 yr−1) is comparable to that derived for 89% of the same area using the mass budget approach (260 ± 35 kg m−2 yr−1 in Medley et al. [2014]). Although ice discharge from the Pine Island Glacier has remained stable since 2010 [Medley et al., 2014] following a notable decrease in the rate of ocean melting at the glacier terminus [Dutrieux et al., 2014], the period of the CryoSat‐2 measurements is too short to establish whether the inland progression of ice thinning has abated. At the continental scale, the most recent estimates of Antarctic ice sheet mass balance are based solely on satellite gravimetry surveys [Barletta and Bordoni, 2013; Velicogna and Wahr, 2013; Williams et al., 2014]. According to these studies, the rate of ice mass loss from Antarctica has increased progressively over the past decade and, between 2010 and 2012, fell in the approximate central range 105 to 130 Gt yr−1. Our survey puts the contemporary rate of Antarctic ice sheet mass loss at 159 ± 48 Gt yr−1, a value that, although larger, is nevertheless consistent given the spread of the gravimetry‐based uncertainties (16 to 80 Gt yr−1). A possible explanation for the discrepancy is the exceptional snowfall event of 2009, which saw an additional ~200 Gt of mass deposited in East Antarctica [Boening et al., 2012; Lenaerts et al., 2013; Shepherd et al., 2012] that, although absent from the CryoSat‐2 record, does factor in the gravimetry‐based estimates of imbalance. It is also worth noting that gravimetry‐based estimates of Antarctic ice sheet mass balance remain sensitive to the choice of model used to correct for glacial isostatic adjustment, with differences of up to 64 Gt yr−1 arising when alternative models are employed [Velicogna and Wahr, 2013], reinforcing the need for contemporaneous estimates of ice mass loss derived from independent techniques [Shepherd et al., 2012].

5 Conclusions We estimate that, since 2010, the average Antarctic ice sheet contribution to global sea level rise has been 0.45 ± 0.14 mm yr−1. This value, which is more than twice as large as the 20 year mean determined from an ensemble of geodetic techniques (0.19 ± 0.15 mm yr−1 in Shepherd et al. [2012]), reflects both the improved capability of CryoSat‐2 to observe regions of ice dynamical imbalance and the impact of short‐ and intermediate‐term changes in ice sheet mass. In West Antarctica, there is now little doubt that the rate of ice loss has continued to rise and that with over 97% sampling of this region, this increase is now well resolved. However, in East Antarctica and at the Antarctic Peninsula, the average change in ice sheet mass remains small in comparison to expected fluctuations in snow accumulation (Table 1), which present an observational challenge to all geodetic techniques. Although the CryoSat‐2 measurements allow an improved understanding of the drivers and timescales of ice sheet imbalance in these sectors, longer‐period data sets are required to separate the effects of meteorological and ice dynamical imbalance [Wouters et al., 2013]. Nevertheless, the fine spatial and temporal resolution of ice sheet elevation changes afforded by interferometric synthetic aperture radar altimetry represents a remarkable advance on the capability of past missions and provides greater confidence in assessments of ice sheet mass imbalance.

Acknowledgments This work was supported by the UK Natural Environment Research Council. The CryoSat‐2 and airborne altimetry data used in this study are available from the European Space Agency and the National Snow and Ice Data Center, respectively. We are grateful to the Editor and to two reviewers for their comments, which helped improve the manuscript. The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.

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