Significant submarine ice loss from the Getz Ice Shelf , Antarctica 1

We present the first direct measurements of changes taking place at the base of the Getz Ice Shelf 6 (GzIS) in West Antarctica. Our analysis is based on repeated airborne radio-echo sounding (RES) 7 survey lines gathered in 2010 and 2014. We reveal that while there is significant variability in ice 8 shelf behaviour, the vast majority of the ice shelf (where data is available) is undergoing basal 9 thinning at a mean rate of nearly 13 m a, which is several times greater than recent modelling 10 estimates. In regions of faster flowing ice close to where ice streams and outlet glaciers join the ice 11 shelf, significantly greater rates of mass loss occurred. Since thinning is more pronounced close to 12 faster-flowing ice, we propose that dynamic thinning processes may also contribute to mass loss 13 here. Intricate sub-ice circulation patterns exist beneath the GzIS because of its complex sub-ice 14 topography and the fact that it is fed by numerous ice streams and outlet glaciers. It is this 15 complexity which we suggest is also responsible for the spatially variable patterns of ice-shelf change 16 that we observe. The large changes observed here are also important when considering the 17 likelihood and timing of any potential future collapse of the ice shelf, and the impact this would have 18 on the flow rates of feeder ice streams and glaciers, that transmit ice from inland Antarctica to the 19 coast. We propose that as the ice shelf continues to thin in response to warming ocean waters and 20 climate, the response of the ice shelf will be spatially diverse. Given that these measurements 21 represent changes that are significantly greater than modelling outputs, it is also clear that we still 22 do not fully understand how ice shelves respond to warming ocean waters. As a result, ongoing 23 direct measurements of ice shelf change are vital for understanding the future response of ice 24 shelves under a warming climate. 25


Introduction
Warming ocean waters are a recognised consequence of global warming trends, and ice shelves which float in these warming waters are prone to significant melting activity.This is important because ice shelves are an interface between grounded ice and the oceans and are therefore sites where these key interactions occur (Berger et al., 2017).For example, past work has shown that many of the ice shelves found along the Antarctic Peninsula have, in recent years, undergone significant and rapid retreat, and in some cases collapse (e.g.Rott et al., 1998;Holt et al., 2013).There is evidence of a gradual southwards progression of these occurrences, suggesting that there is an underlying climatic cause (Schannwell, 2018).Such changes are significant because ice shelves have a crucial role to play in regulating the rate of grounded ice-loss to the oceans (e.g.Scambos et al., 2000Scambos et al., , 2004;;Dupont and Alley, 2005;Pritchard et al., 2012;De Rydt et al., 2015).Although the mechanisms behind these changes are complex, any thinning enhanced by basal melting is caused by variations in oceanic temperature and ocean circulation due to oceanic warming (e.g.Pritchard et al., 2012).
Of the order of 74% of Antarctica is bounded by these floating ice shelves (BIndschadler et al., 2011;Berger et al., 2017), and the Getz Ice Shelf (GzIS) is one of many regions of floating ice around the Antarctic Peninsula.It is approximately 650 km in length and covers an area of approximately 33,395 km 2 , occupying a portion of the Antarctic perimeter in the Amundsen Sea (Jacobs et al., 2013;Rignot et al., 2013).A recent modelling study also showed that of all the Antarctic ice shelves, it is those of the Amundsen Sea (including the GzIS) where greatest changes are forecast to happen in the decades to come, as a result of warming ocean waters (Naughten et al., 2018).Understanding the changes going on here are thus of great importance, and arguably greater importance than elsewhere.Amongst Antarctic ice shelves, the GzIS is unique because its large size and position means that it is exposed to a more varied ocean environment than other ice shelves (Jacobs et al., 2013).It also differs from other ice shelves because it is fed by numerous glaciers and ice-streams.Furthermore, it is characterised by a margin which is anchored by many small islands and inland grounded regions, and it is thought that these might have an impact on calving rates and on circulation of ocean waters in sub-ice cavities (e.g.Rignot et al., 2011;Jacobs et al., 2013).Previous work has suggested that Circumpolar Deep Water (CDW) beneath the GzIS may actually be cooler than that found elsewhere (Jacobs and Giulivi, 2010;Jacobs et al., 2012;Jacobs et al., 2013), and combined with the sheer size of the GzIS and its complex ocean-boundary, there may be highly variable rates of submarine melting here.Despite these suggestions, in reality, relatively little is known about general rates of submarine melting beneath floating ice-shelves (Horne et al., 1985;Walters et al., 1988;Motyka et al., 2003), let alone the nature of such complexity which may exist here in the GzIS.Wilson and Straneo (2015) do suggest that where ice tongues are thickest, and where ocean waters are warmer and deeper, submarine melt rates are at their greatest (cf.Seroussi et al., 2011), however, significant complexity around this basic rule is expected.Despite uncertainties, the importance of understanding the magnitude of ice shelf loss, as well as any spatial complexity and variability is significant, because of the potential for ice shelves to collapse with consequent implications for the flow of grounded ice to the oceans, and on overall ice-sheet stability (Dupont and Alley, 2005;2006;Kulessa et al., 2014).The GzIS is of particular importance because not only is it particularly vulnerable to warming ocean waters, but future predictions suggest warming-induced losses will be most pronounced of all the Antarctic ice shelves, and because of its complexity, there is likely to be considerable spatial variation in the response of the ice shelf to this oceanic warming.
In 2013, Jacobs et al. collected profiles at sub-ice cavity openings along the GzIS to measure water temperature, salinity and dissolved oxygen content.From satellite-derived measurements of ice flux, modelling and other observations they calculated that through the 2000s, there was marked variability in ice shelf mass balance, with a positive mass balance in 2000 but a negative mass balance in 2007.These observations are invaluable but do not represent absolute and direct measurements of sub-ice melting and to date there have been no direct measurements of such losses on the GzIS.There has, however, recently been an attempt to explore subglacial melting directly on Antarctic ice shelves elsewhere (Khazendar et al., 2016).Khazendar et al. (2016) directly quantified submarine melting of the Dotson and Crosson ice shelves in the Amundsen Sea Sector of West Antarctica from observation of repeat Operation IceBridge radio echo-sounding (RES) lines.Amongst their findings, they observed very significant ice loss from beneath -much larger than the rates identified in a recent modelling study by Bernales et al. (2017).Clearly then, there is much to be gained from direct observations and measurements, and with that in mind, here we extend the The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-163Manuscript under review for journal The Cryosphere Discussion started: 18 September 2018 c Author(s) 2018.CC BY 4.0 License.approach of Khazendar et al. (2016) to the GzIS and directly quantify spatially variable ice shelf change.

Methods
In order to explore submarine change of the floating GzIS, repeat measurements are required of the ice shelf surface and bottom.Such measurements are available from the Centre for Remote Sensing of Ice Sheets (CRESIS) at the University of Kansas (Gogineni, 2012), and the radio echo sounding (RES) data that they have gathered extensively across both Antarctica and Greenland using an airborne system.
Initially, it was the Level 2 (L2) data which we looked to utilise, which provides measurements of ice thickness as well as the elevations of the surface and bottom of the ice.However, we found a number of anomalous points and so elected to go back to the Level 1B data from the Multichannel Coherent Radar Depth Sounder (MCoRDS) -it is these data that are utilised and explored.The benefit of using data from a lower processing level is that it enables picks to be verified or modified first-hand.This RES system has been used to gather data since 1993 using funding from both NASA and the NSF, most recently as part of the Operation IceBridge field campaign (Leuschen and Allen, 2014).
In November 2010, as part of the Operation Icebridge survey for this year, a flight took place over the GzIS, closely following the linear ice-cliffs of the series of glaciers and ice-streams that drain into the ice-shelf.As part of the Icebridge campaign of 2014, a section of the same survey line was reflown, again in November of that year (Figure 1).The MCoRDS radar data has an along-track resolution of ~25 m and a depth resolution of ~ 18 m (Khazendar et al., 2016).Using the Level 1B data, each flight was re-examined for anomalous points (often associated with apparent incorrect picking of the bottom reflector, or with inaccurate picking of the reflector) and these were corrected.This was carried out using the Matlab code: 'image_browser_v1_4' available via the CRESIS ftp site: ftp://data.cresis.ku.edu/data/picker/ (CRESIS, 2016), and corrected picks were then compared.
Of course, despite these two flights covering effective repeat-tracks, individual sounding locations are not exactly replicated between these four years.In order to maximise the usefulness of these datasets, but also so as to not introduce artefacts, we followed the example of Khazendar et al. (2016) and their recent work, by comparing points which are closer than 200 m in the horizontal.Khazendar et al. (2016) imposed this limitation in order to reduce the effects of the slope of the ice bottom when exploring change.An identical approach is followed here.The result of this analysis of close overlap between the two survey flights (in 2010 and 2014) delineates the zone over which this study takes place (see Figure 2).This zone covers a large part of the floating Getz ice shelf, and it is this region on which the remainder of this paper is focussed (cf. Figure 1).Once comparable points had been derived, the difference between the elevation of the underside of the floating ice shelf was determined in each year, so as to explore the spatial variability in rates of change at the ice shelf bottom.
The use of the MCoRDS radar to determine the ice shelf bottom does introduce some uncertainty, not least because despite every effort to the contrary, flying repeated survey tracks four years apart inevitably results in slightly different flight tracks and thus lightly different regions of the bed are imaged.Figure 3 shows example radargrams from part of the repeated survey line in 2010 and 2014.The region of the domain explored here is shown in green in Figure 2. Examination of Figure 3 reveals that despite the limitations indicated, remarkably good repeat-surveying has been achieved.Only very slight differences are visible between these two sampled regions, as a result of slight offsets in the two survey lines Khanzendar et al. (2016) go into some detail discussing how they account for errors in the MCoRDS data.They suggest that based on system and environmental parameters, a conservative estimate of vertical measurement uncertainty is ±25 m, while the uncertainty in measurements of change between two years is ±35 m.However, they go on to say that when considering annual rates of change in the base elevation, uncertainty is calculated by dividing total change by the time between the two measurements (Khanzendar et al., 2016).As a result, uncertainty estimates when comparing ice bottom changes between 2010 and 2014 is ±8.75 m a -1 .(red).The focus of this study is located towards the bottom of the image, and can be identified by the green rectangle and superimposed surface velocities (Rignot et al., 2017;cf. Figure 3).The background image is the MODIS Mosaic of Antarctica (MOA; Scambos et al., 2007;Haran et al., 2013;2014).All data projected in polar stereographic coordinates.
In order to confidently identify 'real' changes at the ice-shelf base, it is important to assess if any measured changes may actually be attributable to other erroneous factors (e.g.differences in system parameters from one survey to the next; successfully picking the same basal reflector in both The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-163Manuscript under review for journal The Cryosphere Discussion started: 18 September 2018 c Author(s) 2018.CC BY 4.0 License.
surveys; resolution of the data).In order to do this, we firstly only utilise bed data where the pickconfidence is high (as defined in MCoRDS data description).Furthermore, we also investigated basal elevation change between the four years, focussing on grounded ice areas only.Here, there should be a mean basal height change of zero (as there should be no basal change in grounded ice over this timescale) with scatter around this representing the noise associated with slightly different flight tracks and thus measured positions, as well as differences at the picking stage.We excluded extreme outliers occurring due to gross errors (where differences exceeded 60 m, accounting for just 11.6% of measurement samples), and investigated the relationship between the bed elevations in 2010 and 2014 in the remaining data.However, we did not treat all data points as one whole, since this simple solution would assume a constant bias across the whole domain, taking no account of the potential for different biases in different parts of the domain (e.g. a sloping bias).To that end, we explored the differences in bed elevation in the four years in each of the five grounded zones independently.From this investigation we discovered that the domain can be grouped into two regions which show slightly different trends in bed elevation offsets between the two years.In the northern region, a strong, systematic relationship between the bed elevations in 2010 and 2014 exists (R 2 ~1), with a mean difference of +17.55 m, meaning that the 2014 bed is systematically higher than the 2010 bed.In the southern region, there is also a strong, systematic relationship (R 2 of ~1), with a mean difference of +28.73 m, again meaning that the 2014 bed is systematically higher than the 2010 bed here, but by a slightly greater amount.These very strong systematic discrepancies mean we used this information to correct all samples (not just grounded regions) to account for this bias, treating the northern and southern regions differently.
Once debiased, we spatially average the along-track height change over samples within a 100m along-track window size.We did this because we observed substantial variability in the bed topography and spatially averaging reduces noise and helps to identify any outliers.(Rignot et al., 2011;2014;2016).The background (grey-scale) image is a hill-shaded relief map derived from the BEDMAP-2 product (Fretwell et al., 2013).The red/white/blue shaded superimposed background displays surface velocities (Rignot et al., 2017).In addition to investigating changes in the ice shelf bottom, we also investigated changes at the ice surface.This was done using laser altimetry data that were collected on board the survey aircraft at the same time as the RES data (Studinger, 2018).Data were gathered by the IceBridge ATM (airborne topographic mapper) sensor at a spatial resolution of 80 m (sample width) and with a 40 m along-track sample-spacing (Studinger, 2018).However, simply ascertaining changes in surface altitude is not sufficient for understanding and assessing overall change at the surface in Antarctica, because variability is also partly a consequence of changes within the firn layer, which can vary widely (Ligtenberg et al., 2011).As a consequence, in addition to measuring ATM-surface changes, we also explore the role of changes in the firn layer using output from the Regional Atmospheric Climate Model (RACMO2; Ligtenberg et al., 2011).The model was run from January 1979 to December 2015, and over this time period, surface height change was assumed to be zero (in agreement with the model assumptions of steady state over the 35 years of the model run; Ligtenberg et al., 2011).Changes in the firn layer (dH/dt_firn) between November 2010 and November 2014 were extracted from the model output, and these were subtracted from observed surface changes from the ATM (dH/dt_obs).This final, resultant change in surface elevation (dH/dt_ice) is then attributable to a mass loss at the surface due to melt (or thickening due to accumulation).Dynamic processes are also not accounted for, and are discussed later.Any uncertainty in the firn model used to calculate surface change arises from uncertainties in determination of accumulation and snowmelt in the initial spin-up stages of the model (Ligtenberg, personal communication, 2017).Estimates of uncertainty in accumulation are 0.004 m yr -1 (% Acc) -1 , The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-163Manuscript under review for journal The Cryosphere Discussion started: 18 September 2018 c Author(s) 2018.CC BY 4.0 License.
whereas there is an estimated 20% uncertainty in snowmelt quantity.Taken in combination, the greatest uncertainties occur in areas of greater melt (e.g. up to 0.15 m yr -1 on the Antarctic Peninsula) while the smallest uncertainties are in cold interior regions (< 0.0001 m yr -1 ) (Ligtenberg, personal communication, 2017;cf. Pritchard et al. 2012) (Krabill et al., 2002), but that where ice is afloat the effects of tides adds additional uncertainty of 0.4-0.6 m (Padman et al., 2002).As a result, we take a conservative error uncertainty of 0.7 m over the four-year study period, neglecting all apparent measures of change that are less than this, but annually this equates to 0.175 m/yr.
We utilise all of the datasets outlined above to examine the change in ice shelf thickness of the GzIS between, 2010 and 2014 and thus provide the first direct quantification of change at this ice-shelf.

Changes at the ice-shelf surface
Before considering changes occurring at the base of the GzIS, it is important to recognise that total ice thinning can be considered as the sum of changes taking place at both the top and bottom of the ice-shelf.In order to extract thinning that is occurring as a consequence of basal melting, it is necessary to constrain the contributions that come from changes taking place at the surface (Khazendar et al., 2016).As described in the methodology, we constrained this by considering observed changes from repeat ATM measurements in the domain, and by considering modelled changes in the firn layer.The resultant changes therefore represent changes due to melting or accumulation.In order to constrain the importance of surface changes on overall mass loss, we focussed further attention only on slow moving areas which are grounded.The reason for this is that it is in such regions that it can be assumed that the contribution to overall thinning at the base is zero (because there is no basal melting where the ice is grounded) and the contribution to overall thinning from dynamic processes is minimal.Table 1 summarises the findings of this analysis.4).Surface elevation change (dH/dt_ice; m a -1 ) is derived from measurements of repeated ATM observations (dH/dt_obs) and changes in the firn layer (dh/dt_firn) from the RACMO2 model (Ligtenberg et al., 2011).Data are subdivided into regions where the ice surface is rising (positive change) or lowering (negative change).

Min
In this region, where changes are greater than uncertainties, 87.35% of point locations (746 of 854) experiences surface lowering, with just 12.65% of locations (108 of 854) experiencing thickening.In the small number of areas where thickening has occurred, the mean rate is nearly three times less than where thinning has occurred.However, overall, these values are small, particularly when compared with changes at the bed (cf. in rates of accumulation (or otherwise) and we suggest that this variation can be explained by altitudinal effects.The mean altitude where thinning takes place is 308.9 m whereas where thickening dominates it is 504.2 m.Khazendar et al. (2016), in their work on the Dotson and Crosson Ice Shelves, also found such altitudinal-controlled variability, suggesting that the relative role and importance of air temperature, accumulation rate, as well as other factors that are influenced by surface elevation change, might vary, and thus explain why mass loss or gain at the ice surface might be experienced across the domain.Where they identified surface lowering (our dominant signal), this was in the range of 0.4-0.7 m a -1 , and the values we record here are in very close agreement with these.

Changes at the ice-shelf bottom
We initially explored the annual rate of basal change along the whole survey-line from 2010 and 2014, but then subsequently subdivided the domain into those regions which we classify as being within a floating ice-shelf, and others classified as being grounded (Figure 5).Arndt et al., 2013).Areas with a green background are areas where floating ice-shelves are present.Areas with a yellow background are where ice is grounded (cf. Figure 2 for location of survey domain).Note the significant data-gap between ~75-120 km along track.Here, bed picks are of lower confidence in one or both of the two surveys, and so data here is not included to avoid introducing erroneous measurements of change.
In Figure 5, a positive change reflects a rising of the ice-base and thus thinning and mass loss.Conversely, a negative change reflects a lowering of the ice-base and thus a thickening or mass gain.
Perhaps the most important panel in Figure 5 is the middle panel because this indicates the overall amount of change at the ice-shelf bottom.Red symbols in this panel (in Figure 5) represent a rising ice-bottom, and where this change reaches beyond the margins of error (grey horizontal lines in these panels) then we consider this rising ice-bottom to be real.It can also be seen that in some locations (where blue symbols are visible) the ice-base has lowered.These locations are more sparsely distributed, but nevertheless it is important to consider where these areas of apparent icebottom lowering (and indeed rising) are located.
Of all the spatially-averaged sample points along this line (5357 in total), 71.46% are classified as being within floating ice shelves, while 7.62% are associated with grounded ice (the remaining 20.93% are generally associated with no data (due to the exclusion of low-confidence picks).Where The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-163Manuscript under review for journal The Cryosphere Discussion started: 18 September 2018 c Author(s) 2018.CC BY 4.0 License.
picks are high quality however, 90.37% ( 3828) are classified as being within floating ice shelves, while 9.63% ( 408) are associated with grounded ice.
Considering floating and grounded ice together, 4350 (81.20%) show a rising of the ice-base (and thus thinning) with just 299 (5.58%) indicating a lowering of the ice base (and thus thickening).However, many of these points are within the error margins of ±8.75 m discussed previously -only 48.04% of all points show any sort of change larger than the margins of uncertainty.Of these points alone, 82.75% are within floating ice shelves and just 10.86% are within grounded ice.Table 2 summarises the changes that have taken place where the observed change is greater than the uncertainty.Table 2 shows that it is on the floating ice-shelves where change at the base is of greatest significance, and apparent rising of the ice base is the dominant signal (81.97% of all points where change is greater than errors).On the ice-shelf alone, positive change (i.e.thinning of the base) is apparent in 99.05% of all ice-shelf measurements that are greater than errors.In just 0.95% of cases ice shelf thickening is apparent.Table 3 shows the magnitude of the changes taking place in these floating-ice regions.It is important to note that the changes at the base here are two orders of magnitude greater than those at the surface (cf.Table 1) rendering the changes and uncertainties at the surface almost irrelevant by comparison.Clearly then, while there is some spatial variability, significant thinning of floating ice is the dominant signal in the domain.Table 3: Summary statistics of the magnitude of change (m a -1 ) at the ice base in floating ice-shelves where change is greater than the measure of uncertainty (±8.75 m).Data are subdivided into regions where the ice-shelf base is thinning or rising (positive change) and where it is thickening or lowering (negative change).Note that although the magnitude of mean thickening is greater than the thinning, thickening takes place over a much smaller number of measurement locations.

Min 1st
With respect to the thickening regions of floating ice shelf (where greater than errors), although these regions are relatively sparse, close analysis of bathymetry data from the International Bathymetric Chart of the Southern Ocean (IBCSO v1.0; Arndt et al., 2013; cf.bottom panel of Figure 5) suggests that they may arguably be most prominent where the bed topography is most variable (e.g. at ~0-75 m along-track and ~420-430 m along-track).In such regions, slope-changes are larger, perhaps reflecting locations where floating ice abuts grounded ice, and thus inaccuracies in The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-163Manuscript under review for journal The Cryosphere Discussion started: 18 September 2018 c Author(s) 2018.CC BY 4.0 License.
delineating the boundary between these two are apparent.We consider this further in the discussions.
Figure 6 shows the distribution of the magnitude of ice-base thinning and thickening (where measurements are greater than uncertainty), while Figure 7 shows where the greatest amount of ice-bottom melting has taken place.Figure 6 clearly demonstrates that the greatest signal is one of ice-base thinning in floating ice, and that overall, an annual ice-base loss of ~10-20 m a -1 is most common, with a few areas experiencing losses of 2-3 times this.Figure 7 shows the locations where these losses are at their greatest and it can be seen that in general there is a tendency towards greater ice loss in locations where the ice is fastest flowing (lefthand panel).In slower-flowing regions, changes are perhaps smaller.This relationship suggests there may be a dynamic thinning component, in which some ice loss occurs due to dynamic processes.This is dealt with further in the Discussions.
The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-163Manuscript under review for journal The Cryosphere Discussion started: 18 September 2018 c Author(s) 2018.CC BY 4.0 License.Where changes are apparently occurring at the base of grounded ice, it is important to keep in mind that all change in grounded regions accounts for a relatively small proportion of those sampled locations (10.86% of all data; Figure 6; cf.Table 4).Nevertheless, it is important to note that the apparent changes here are not insignificant.Such change under grounded ice is somewhat surprising, since, at the ice base, it would be expected that there would be no such change -at this location, over the timescale being explored, the ice base should effectively be static.However, we propose that this apparent change is in fact not indicative of real change, but is in part a function of an uneven (or rough) subglacial topography in which correct identification of the bed reflector is not straightforward and is indeed prone to errors.Under scenarios where a complex bed topography dominates, both along-track and off-track, it is highly likely that the bed is incorrectly picked between consecutive years (cf.Lapazaran et al., 2016).Indeed, we encountered this in our own investigations and adapted our methodology to go some way towards incorporating this (see Methods).It is also highly likely that precisely the same track is not taken between surveys, further introducing errors.Finally, a relatively large component in the error is likely a result of uncertainties in the aircraft flying height during data collection.In some
locations however, such discrepancies may be due to real changes, which will be discussed further in the discussions.

Discussions and Conclusions
For a long time, the main cause of mass loss from the Antarctic Ice Sheet was considered to be iceberg calving (Depoorter et al., 2013).More recently, melting of floating ice due to a warming ocean has been shown to be significant, particularly close to the grounding line and near the calving front (Jenkins and Doake, 1991;Rignot and Jacobs, 2002;Joughin and Padman 2003).However, direct measurements of basal ice shelf change in Antarctica are sparse.While Khazendar et al. (2016) were the first to show direct evidence of ice-shelf thinning from repeat RES measurements, here we have presented the first direct measurements of ice shelf change on the large GzIS using repeated airborne RES surveys.Comparison of the recent modelling output from Bernales et al. (2017) with the measurements of Khazendar et al. (2016) shows that the models underestimate the amount of basal melting, and given that it is the Amundsen Sea (including the GzIS) where greatest changes are forecast to happen in the decades to come (Naughten et al., 2018), assessing whether such discrepancies exist here is of importance.As a result, we have investigated the magnitude and nature of change at both the surface and the base.When exploring surface changes, we found that these are small compared to those observed at the bed, by up to two orders of magnitude, and thus in this study over the GzIS, surface lowering can, to all intents and purposes, be ignored.The changes taking place at the ice base are far greater and far more significant, and so it is therefore this location where we focus the remains of this discussion.
In terms of basal changes, floating ice dominates the domain, and it is here that changes are of greatest magnitude, of greatest interest and also of greatest significance.Where ice is floating and where changes are significant, thinning was observed in nearly 82% of locations, at a mean rate of nearly 13 m a -1 , but up to a maximum of ~52 m a -1 .These values are (on average) slightly smaller than, but nevertheless comparable with, the 40-70 m a -1 recorded by Khazendar et al. (2016) the Dotson and Crosson ice shelves.Furthermore, the rates of change that are identified here are substantially greater than those reported by Bernales et al. (2017) in their extensive modelling study of basal changes around Antarctica.Their model suggests melting rates of 2.5 / 4.3 m w.e. a -1 (equilibrium/non-steady state values) which are several times lower than our measurements.The identification of substantially higher rates of loss is of great concern because it means it is losing mass more quickly than previously thought, with significance for the rates at which ice is transmitted through the glaciers which drain into the GzIS.While thinning occurred over most of the domain, the biggest rates of thinning occurred where ice flowed more quickly (cf. Figure 7) perhaps also indicating a role for dynamic processes in the observed thinning.Dynamic thinning is a loss of ice as a result of accelerated flow (Pritchard et al., 2009).While not a true measure of dynamic thinning itself, increasing ice flow may lead to the dynamic thinning of a glacier (Bevan et al., 2015), and so by assessing changes in ice velocity (as well as velocity itself), the relative likely importance of the dynamic thinning process can be ascertained.The observations we make are thus further reinforced by Chuter et al. (2017) who identified variable rates of grounding line velocity increases (2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014), but particularly a coincidence between the largest grounding-line velocity increases and regions of greatest ice-shelf thinning (Chuter et al., 2017;their Figure 4).We therefore suggest that some of The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-163Manuscript under review for journal The Cryosphere Discussion started: 18 September 2018 c Author(s) 2018.CC BY 4.0 License.
the observed thickness change on the GzIS may be attributable to dynamic processes rather than direct mass loss at the bottom (or indeed the surface) of the ice-shelf.
Changes greater than uncertainty over grounded ice accounts for approximately 10.86% of the survey domain.Where ice is grounded, the complex subglacial topography makes it difficult to accurately pick the terrain, and as a result, there is some uncertainty surrounding the basal variability.However, in ~13% of locations we observe apparent shelf thinning over grounded ice, and it is possible that some of this apparent thinning may be attributable to ice-shelf ungrounding between the two surveys.We have no evidence of this having occurred but Schaffer et al. (2016) propose the existence of continuous troughs that link the open ocean to the grounding line, and propose that high basal melt rates here support the existence of a routeway along which warm ocean waters may access the ice base.This proposal, though untested would perhaps allow melting of grounded ice at the grounding line, and thus a degree of ungrounding, as we propose.
Our work highlights firstly, and crucially, that thinning is both significant and widespread across much of the GzIS.Secondly, it highlights that despite this, there is significant variability in ice-shelf bottom change, reinforcing the point made in the Introduction that ice shelf complexity has an important role to play in controlling the way and rate by which an ice-shelf responds to oceanic warming.Finally, and perhaps most importantly, our work identifies substantially greater rates of thinning than those recently reported from forecasting modelling investigations (Bernales et al., 2017).While we accept that our work represents investigations along a single transect, the difference between predictions from models and direct historical measurements (c.f.Khazendar et al., 2016) is clearly of concern.This suggests that models may be underestimating changes going on in at least some parts of some ice shelves, and thus more and continuous direct measurements of change are required.This is firstly to help better constrain models, and secondly to better constrain the changes actually occurring in ice shelves.Depoorter et al. (2013) state that the significance of basal processes in overall ice shelf mass balance is highly variable, accounting for 10-90% of overall loss, depending on the specific ice shelf in question.Here, we have shown that basal melting is a significant contributor to mass loss of the GzIS, but also that the relative contribution of basal melting is highly variable across the ice shelf.This variability within a single ice shelf, coupled with the apparent variability between ice shelves (Depoorter et al., 2013) is significant.In the GzIS, the variability can perhaps be attributed to the combination of complex sub-ice topography and numerous contributory ice streams and outlet glaciers that result in intricate sub-ice water circulation is cavity systems.Although the accuracy of this interpretation requires further investigation, the importance of these processes in overall ice shelf mass balance is undeniable.It, it is therefore of paramount importance that quantifying basal mass loss from Antarctic ice shelves is carried out, because of its role and importance for predicting the likely vulnerability of ice shelves to future subglacial warming and melting.

Acknowledgements
We acknowledge the use of data and/or data products from CReSIS generated with support from the University of Kansas, NSF grant ANT-0424589, and NASA Operation IceBridge grant NNX16AH54G.

Figure 1 :
Figure 1: CRESIS flightlines across Antarctica in 2010 (blue) and 2014(red).The focus of this study is located towards the bottom of the image, and can be identified by the green rectangle and superimposed surface velocities(Rignot et al., 2017; cf.Figure3).The background image is the MODIS Mosaic of Antarctica (MOA;Scambos et al., 2007; Haran et al., 2013; 2014).All data projected in polar stereographic coordinates.

Figure 2 :
Figure 2: Close-up of area of interest over the Getz Ice Shelf.The thin blue and red lines indicate the IceBridge flightlines from 2010 and 2014 respectively.The thicker black line represents the area of overlap and the data on which this study is focussed.The portion of this black line that is coloured green represents the area covered by the sample radargrams in Figure 3.The thin black line represents the grounding line(Rignot et al., 2011; 2014;2016).The background (grey-scale) image is a hill-shaded relief map derived from the BEDMAP-2 product(Fretwell et al., 2013).The red/white/blue shaded superimposed background displays surface velocities(Rignot et al., 2017).

Figure 3 :
Figure 3: Example radargrams from the Operation Icebridge surveys of November 2010 (A) and November 2014 (B).These two sections represent repeat surveys over the area marked in green in Figure 2. It can been seen here that the two surveys achieved remarkably good repeated sampling locations, although subtle offsets and differences are visible, indicative of slight offsets in the two survey lines.The red dashed lines in both (A) and (B) represent the picked bed while the pink dashed lines represent the picked surface.In both cases, these are the picks provided by CRESIS, with small modifications and corrections made by the author (see main text).
. Again, for investigating change in the elevation of the ice shelf surface, we follow the example of Khanzendar et al. (2016) and only compare points in the different years that fall within the smaller distance of 25 m of each other.Khanzendar et al. (2016) state that the uncertainty inherent in these ATM measurements is <0.09 m

Figure 4 :
Figure 4: Annual change in ice-surface elevation (m a -1 ) between 2010 and 2014 along the entire survey domain.The upper panel shows rates of surface change as derived from the repeat ATM measurements.The middle panel shows rates of surface elevation change based on changes in the firn layer, as derived from the RACMO2 firn densification model (FDM).The lower panel shows the residual change in surface elevation after considering firn densification processes.These changes are attributable to a mass loss due to melt.In all panels, blue dots indicate a positive elevation change meaning a rising ice surface and thus a thickening, while red dots indicate a negative elevation change meaning a lowering ice surface and thus a thinning.The black horizontal line represents no change.Grey shaded areas indicate where ice is slow-moving and grounded and thus minimal change would be expected.With reference to Figure 2, zero along-track distance in the above panels is associated with the southern-most points in the transect.

Figure 5 :
Figure 5: Annual change in ice-base elevation between 2010 and 2014 along the entire survey domain, with the 2014 bed elevations debiased according to the methodology described.The upper panel shows how the ice-bottom has changed between 2010 and 2014.The black line represents the bottom in 2010 and the grey line in 2014 (debiased).Data shown here are raw bed elevations.In the second panel, rates of bottom elevation change (m a -1 ) are shown, with elevation change spatially averaged over 100m-long windows.In the middle panel, red dots indicate a positive elevation change meaning a rising ice bottom and thus ice-shelf thinning.Blue dots indicate a negative elevation change meaning a lowering ice bottom and thus ice-shelf thickening.The grey horizontal lines represent the bounds of uncertainty -values must indicate changes of magnitudes greater than these limits to be indicative of real change (see text).The lower panel indicates the bathymetry of the sea-bed at each point derived from the International Bathymetric Chart of the Southern Ocean (IBCSO v1.0;Arndt et al., 2013).Areas with a green background are areas where floating ice-shelves are present.Areas with a yellow background are where ice is grounded (cf.Figure2for location of survey domain).Note the significant data-gap between ~75-120 km along track.Here, bed picks are of lower confidence in one or both of the two surveys, and so data here is not included to avoid introducing erroneous measurements of change.

Figure 6 :
Figure6: Histograms showing the amount of ice-bottom change experienced where the ice is floating (left-hand panels) and where it is grounded (righthand panels), with thinning displayed in red in the top two panels, and thickening displayed in blue in the bottom two panels (only where greater than uncertainties).Where ice bottom loss is positive, this represents thinning between 2010 and 2014.Where ice bottom loss is negative, this represents thickening between 2010 and 2014.Note the markedly different y-axis scales.It is very clear that thinning dominates, and that this thinning is much more pronounced and widespread where the ice is afloat.

Figure 7 :
Figure7: Left-hand panel shows ice shelf thinning (red circles) and thickening (blue circles) where change is greater than the margins of uncertainty, and only where ice is floating.Ice loss (thinning) is greatest where ice velocities are higher.The black line represents the grounding line(Rignot et al., 2011;  2014;2016).The background (grey-scale) image shows bathymetry data from the International Bathymetric Chart of the Southern Ocean (IBCSO v1.0;Arndt et al., 2013).The red/white/blue shaded superimposed background displays surface velocities with red regions indicating fast flow and blue areas indicating slow flow.(Rignotet al., 2017).In the right-hand panel, changes in surface velocity are displayed, derived from the MEaSUREs Annual Antarctic Ice Velocity Maps 2005-2016(Mouginot et al. 2017).Here we display the difference between two datasets, one of velocities from 2010-2011 and another from 2014-2015.

Table 1 :
Summary statistics of the magnitude of annual change (m a -1 ) at the ice surface elevation between 2010 and 2014 in areas of slow-moving grounded ice (cf. Figure

Table 2 :
Summary of changes at the ice-base where spatially-averaged changes are greater than the suggested error of ±8.75 m.The table shows the number of points and also the relative dominance of each class as a proportion of the total number of sample points where change is larger than uncertainty.The data is split into areas of floating ice-shelves and grounded ice, as well as being further subdivided into areas where the apparent change is positive (i.e.meaning a rising ice base and thus thinning) or negative (i.e. a lowering ice base and thus thickening).

Table 4 :
Summary statistics of the magnitude of change (m a -1 ) at the ice base in regions of grounded ice where change is greater than the measure of uncertainty (±8.75 m).Data are subdivided into regions where the ice-shelf base is thinning or rising (positive change) and where it is thickening or lowering (negative change).