Dynamic thinning of Antarctic glaciers

1Dynamic
thinning of Antarctic glaciers from along-track repeat radar
2altimetry
3
4
5Thomas Flament, LEGOS, 14 Avenue E. Belin, 31400 Toulouse – France
6Frédérique Rémy, LEGOS, 14 Avenue E. Belin, 31400 Toulouse – France
7
8
9
10Abstract
11Since 2002, the Envisat radar altimeter measures the elevation of the Antarctic ice sheet with
12a repeat cycle of 35 days. This long and regular time series is processed using an along-track
13algorithm to depict in detail the spatial and temporal pattern of elevation change for the whole
14ice sheet. From this dataset, we examine the spatial and temporal pattern of Pine Island
15Glacier thinning and compare it to the neighbouring glaciers. We also examine additional
16areas especially in East Antarctica whose mass balance is poorly known. One advantage of
17the finer along-track spacing of measurements is that it reveals places of dynamic thinning in
18regions of rapid ice flow. We observe the acceleration of thinning on Pine Island Glacier.
19Over the entire basin, the volume loss increased from 7 km 3 a-1 during 2002-2006 to about 48
20km3 a-1 during 2006-2010. We also observe an acceleration of thinning on the lower tens of
21kilometres of Thwaites glacier with a mean thinning of 0.18 m a -1 over its entire basin during
22our observation period. We confirm the dynamic thinning of Totten Glacier but we do not
23detect significant acceleration of the thinning on any glacier elsewhere than on the coast of the
24Amundsen Sea.
25
26
27Introduction
28
29The mass balance of an ice sheet can be estimated by several different techniques one of
30which is altimetry (e.g., Allison and others, 2009). Repeated elevation measurements at the
31same locations provide volume variations that can be converted to mass variations by adding
32an assumption on the associated density.
33
34In several locations around Antarctica, changes in mass balance linked to changes in the ice
35flow (“dynamic changes”) have been identified (e.g., Pritchard and others, 2009). For
36instance, glaciers flowing into the former Larsen B ice-shelf accelerated immediately after the
37disintegration of the ice-shelf, in 2002. This increase in ice flow velocity caused rapid
38thinning because of faster drainage of ice (Shuman and others, 2011). However, the surface
39height evolution of these glaciers cannot be studied properly with classical radar altimetry
40because of the relief surrounding them.
41
42Pine Island Glacier (PIG) on the contrary is much more easily observable, because of its large
43drainage basin and high thinning rates. It has been identified to be massively out of balance
44since the 1990’s (Shepherd and others, 2001). Accumulation over its basin totals a little over
4560 Gt a-1 but the glacier discharged 77 Gt a-1 of ice in 1996 (Rignot and others, 2004), 85 Gt a 461 in 2000 (Rignot, 2008, table S1) and 103 Gt a-1 in 2006 (+34 % compared with 1996, Rignot,
472008). The onset of this large out-of-balance discharge is thought to have been provoked by
48ocean warming that thinned the ice shelf and ice-plain (Corr and others, 2001) leading to the
49ungrounding of this plain (Thomas and others 2004; Jenkins and others, 2010). With the help
50of ERS-2 and Envisat radar altimetry, Wingham and others (2009) observed an acceleration
51of thinning close to the grounding line.
52Other glaciers in the surroundings are exposed to the same conditions, namely Thwaites,
53Pope, Smith and Kohler glaciers. The latter three were reported to be accelerating whereas the
54Thwaites glacier region of fast flow seems to be widening (Rignot, 2008).
55Dynamic thinning of the ice sheets could play a prominent part in global sea level in the next
56century. It is therefore necessary to better understand this phenomenon.
57
58The aim of this paper is to complete and extend the temporal series with the whole Envisat
5935-day repeat orbit that started in Spring 2002 (with valid data from September 2002) and
60ended in November 2010. To make the most of this dataset, we introduce an along track
61processing that produces much denser coverage than the usual cross-over processing. The
62sampling is also more regular in time and the series longer than what can be obtained from
632003-2009 ICESat data acquired during 2 to 3 campaigns each year between 2003 and 2009
64(see Pritchard and others, 2009 who used 2003-2007 ICESat data).
65
66We first focus on PIG, taking advantage of previous work and of in situ measurements to
67validate our processing scheme. Then we examine whether dynamic thinning can also
68unambiguously be detected on other locations of the Antarctic Ice Sheet (AIS).
69
70
712. Data and Method
72
732.1 Along-track processing
74The along-track processing used in this study is widely inspired from the work of Legrésy and
75others (2006) but it is also similar to the method used by Zwally and others (2011) or method
76M3 by Sorensen and others (2011) (see also Howat and others (2008) or Smith and others
77(2009)). Unlike the usual crossover analysis that uses only data points where satellite tracks
78cross, this method considers all of the altimeter measurements, i.e. one point every 350 m
79along-track. The result is a large increase (by a factor 25) in the number of available data
80points (from 60,000 crossovers to over 1,500,000 along-track processed points for the whole
81AIS). Moreover, the tracker system can lose lock when the satellite is flying from the ocean
82toward steep terrain so that some coastal crossovers are missing whereas one track is
83available. Along-track processing is thus of particular interest near the coast of Antarctica, at
84lower latitudes, where the dynamic signal is assumed to be strong and data coverage is sparse.
85Each satellite track was flown over up to 83 times during the considered period (09/2002 to
8610/2010, cycles 9 to 94, the “35-day repeat Envisat period”). Here, we chose to compute the
87elevation trend every kilometre along track. All available measurements in a 500-m radius
88from a point on the mean ground track are selected and processed together. The 500-m radius
89is well suited for 2 reasons. First, it corresponds to the across-track scatter of the points flown
90over by the satellite, as provided by orbit control. Second, it is possible to model the
91topography at this scale using a simple quadratic form (of the along- and across-track92coordinates). When using the quadratic form we obtain elevation residuals with an R.M.S. of
9340 cm whereas the R.M.S. was 46 cm with a simple linear fit. The gain using the quadratic
94form instead of a plane is thus of 22 cm R.M.S.
95
96The processing includes corrections based on waveform parameters (computed by the ICE-2
97retracker (Legrésy and others, 2005) to account for varying electro-magnetic properties of the
98ice sheet surface. The overall processing in itself is a least square fit to the measured
99elevations (Rémy and Parouty, 2009).
100The least square model can be written:
H ( x,y,t ) =dBS∗( bs−bs ) +dLEW ∗( lew −lew )∗dTES∗( tes−tes )
+H 0 ( x , y ) +sx∗( x−x ) +sy∗( y− y ) +cx∗( x²− x² ) +cy∗( y² − y² ) +cxy∗ ( x²− x² )( y² − y² )
+dh / dt∗( t−t )
+res ( x,y,t )
101
102where dBS, dLEW and dTES are the parameters determined for the backscatter (bs), leading
103edge width (lew), and trailing edge slope (tes) adjustment variables; H 0 is the mean altitude,
104sx and sy are the parameters for adjustments variables x and y, i.e. the local slopes; cx, cy, cxy
105complete the quadratic modelling of the surface (corresponding to curvatures) and dh/dt is a
106linear time trend. The overbar represents the local mean and res(x,y,t) are the residuals.
107ICESat measurements only span 100 to 200 m across track and good results are achieved with
108slope only. Here, a quadratic surface model was used because of the wider scatter of points
109across track.
110
111The processing can be broken down into the following steps:
112
- choose a location along track
113
- select all measurements within a radius of 500 m
114
- fit the 10 parameters
115
- compute the standard deviation of residuals
116
- reject individual measurements whose corresponding residuals are larger in
117
absolute value than three times this standard deviation. (3-sigma editing)
118
- fit the 10 parameters only on the remaining measurements
119
- if less than 130 measurements are left for the second fit or if the standard deviation
120
of residuals after this second fit is larger than 5 m, reject the processed point
121
- go to the next location along track, 1 km farther and repeat the same process.
122
123In theory, with all passes available, each processed point should be computed from 200
124measurements but this number is reduced because of missing passes and 3-sigma editing. The
125threshold at 130 measurements was determined empirically from a histogram as we expect
126that a location with fewer measurements suffers from measurement quality problems (e.g. due
127to crevasses, very steep slopes, etc.). For the whole AIS, this criterion eliminates 4.8 % of
128points.
129
130The regularity and density of the temporal sampling allow us to reuse the residuals from the
131fit to compute surface height acceleration (second derivative with respect to time, d²h/dt²) or
132to take into account the seasonal signal. To determine the elevation acceleration, we fit the
133following least square model:
2
h ( t ) =h0 +a ( t −t ) +b ( t −t² )
134
,
135where t is the time, a is our estimate of dh/dt, b our estimate of d²h/dt² and the overbar
136represents the mean.
137
138In the following, interpolated maps rendered on a five-by-five km grid are built by averaging
139with Gaussian weights. All points within a 25-km radius are taken into account and weighted
140with a decorrelation radius of 10 km.
141
142The interpolated maps of dh/dt is given in Fig. 1. 95 % of elevation changes are within 15 cm
143a-1 of zero. These changes are small in amplitude and have a large spatial extension. Rémy
144and Parouty (2009) already showed that they could vary depending on the observation period
145(from a comparison of ERS-2 and Envisat elevation trends). They are attributed to variations
146in meteorological forcings. A persistent anomaly in accumulation lasting a few years could
147account for these changes (Helsen and others, 2008; Rémy and others, 2002).
148
149However, it has been recognised that the ice thickness in some locations does vary because of
150changes in ice dynamics (Fig. 1). This happens especially in West Antarctica with the well151documented acceleration of Pine Island Glacier resulting in a dramatic thinning of the glacier.
152The opposite effect is also clearly visible on the small upstream part of Ice stream C seen by
153Envisat (on the Siple coast, close to the southern limit of coverage at 81.5°S) which is
154growing thicker since it stopped flowing, around 1850 (Retzlaff and Bentley, 1993, Jacobel
155and others, 1996, Anandakrishnan and Alley, 1997).
156
157
1582.2. Accuracy of our measurements
159In order to validate the accuracy of our measurements, we compare them to the ones by Scott
160and others (2009) on Pine Island Glacier. They computed elevation change rates from ICESat
161data and velocities observed during two austral summer campaigns using GPS receivers at
162three locations (see Table 1 and Fig. 2.a).
163
164From the along-track elevation time series obtained as the residuals of the processing
165described in section 2.1, we derive elevation measurements to be compared to those of Scott
166and others (2009). First, we select the 4 points of our data set that are closest to the locations
167given in the legend of Table 1 and average them to reduce the noise in the series. Then we fit
168a second order polynomial and a sine with a 1-year period to account for elevation change
169rate, elevation change acceleration and seasonal variations. Time series and the corresponding
170fitted curves are given in Fig. 3. Values given in Table 1 are computed from the fitted curves
171over the observation periods used by Scott and others. The error is estimated by propagating
172uncertainty on the fitted parameters. This error depends on the statistical distribution of
173measurements and accounts only for the misfit of our 4-parameter model to the series (see
174Table 1).
175
176The only point where the 1-sigma error intervals do not overlap is for the farthest point
177upslope, 171 km from the grounding line during the 2007-2008 austral summer. Scott and
178others measured a slow down in thinning; the elevation trend at PC171 varied from -1.2 m a -1
179during GPS 1 to -1.05 m a-1 during GPS 2. There are too few degrees of freedom in our fit to
180account for this behaviour as we assume steady elevation acceleration; but the precision of
181our altimetry data over such short time scales is not sufficient to achieve better results.
182The difference in location between the field GPS measurements and the altimeter
183measurements could contribute a little to the difference. From the spatial gradient of the
184elevation trend we estimate that this location error adds less than 0.1 m a -1 if the distance
185between PC55 and the chosen satellite measurements is 10 km. The error is lower for the
186other points, respectively 3 cm a-1 and 2 cm a-1 at PC111 and PC171. These values are added
187to the error estimates described previously.
188
189Part of the seasonal signal in radar height measurements might come from badly corrected
190effects of the seasonal modification of the snow-pack properties as we only fit three
191waveform parameters to account for this effect. The contribution from this error is difficult to
192estimate. Further investigation is still needed for an independent validation of radar altimeter
193time series over ice sheets with respect to this phenomenon (Arthern and others, 2001; Rémy
194and Parouty, 2009). However, the overall good agreement between our values and those of
195Scott and others (2009) gives good confidence in the quality of our altimetry data.
196
1972.3. Errors in interpretation induced by inter-annual variability in accumulation rates
198
199The natural year to year variability of accumulation could produce height changes over the
200observation period that should not be interpreted as long term mass imbalance of the ice sheet.
201We assume that there is no significant trend in accumulation over the last decades (Monaghan
202and others, 2006) and that the spatial and temporal variability of accumulation were the same
203as now. The idea is that the stronger the accumulation, the larger the deviation from steady
204state could be.
205
206We used a simplistic model to estimate the contribution of the natural variability of
207accumulation to surface height change. We took into account the contribution of past and
208recent accumulation anomalies through the variation in firn compaction velocity they induce.
209To do this, we drew 3,000 values of accumulation with a standard deviation of 30 % around
210the local mean. Each value produces a height anomaly that evolves with time as the snow is
211compacted into ice. The firn compaction is simply modelled by a decreasing exponential as in
212Rémy and Parrenin (2004), where the density of snow evolves as:
ρ( t ) =ρi −( ρ i− ρ s ) exp (−kt )
213
214We ran the simulation 10,000 times for a range of accumulation values and for several values
215of the densification coefficient k (0.1, 0.01 and 0.001).
216
217From the accumulation map by Arthern and others (2006), we then estimated the potential
218contribution of accumulation variation to the elevation change on each 5 km by 5 km pixel on
219our map.
220
221Although this model is only first order, it provides a guess of where elevation changes are
222significantly dominant over natural variability. With this method, it is also possible to
223estimate the influence of accumulation variability on the second derivative of surface height.
224
225This accumulation contribution is then considered to be an error and is combined with the
226standard deviation of dh/dt and d²h/dt² as estimated during the least square fit. We assume that
227both errors are weakly linked so we sum their variances.
228
2293. Pine Island Glacier
230
231On PIG, we observe “channels” of thinning corresponding to channels of fast flow. Pritchard
232and others (2009) already observed intense dynamic thinning on the fast flowing trunk (see
233their Fig. 3). Here, thanks to the better spatial resolution, we demonstrate that thinning is also
234following the branches of the flow pattern (our Fig. 2 b).
235In order to better describe the temporal evolution of the whole basin, we plot the evolution
236with time of elevation rates along two profiles shown on Fig. 2.a (North-South transect and
237central flow line). Height measurements are plotted according to the method described at the
238end of section 2.1 and re-interpolated along the profiles. We chose to average in time over
239periods of 1 year from fall to fall to take all data into account. Both transects (Fig. 4 exhibit an
240increasing thinning with a break between 09/2005-09/2006 and 09/2007-09/2008 and the
241North-South transect also displays an impressive propagation of the thinning toward the
242South.
243
244In order to compute the volume change with respect to the first full cycle of Envisat radar
245altimeter observations in 10/2002, we integrate the elevation measurements over the whole
246PIG basin. We observe (Fig. 5) a clear increase of loss since the beginning. Moreover, we
247observe a break in the volume balance of the glacier around year 2006 as the volume loss rate
248increases from 7 to 48 km3 a-1 respectively during the first and second half of the period. Note
249that, especially with such a curve, the estimation depends on the fitting. Fitting a parabola
250would yield a loss of 22 km3 a-1 at the beginning of 2006 but the volume balance would then
251be slightly positive towards the end of 2002. These figures are consistent with estimates by
252Rignot (2008) who computed a mass loss of 24 Gt a-1 in 2000 and 46 Gt a-1 in 2007.
253
254We also observe that the highest part of the PIG basin (i.e. the southern lobe of the basin)
255seems to be thickening, which is probably due to higher than average accumulation. This
256thickening shows that accumulation plays a role in the evolution of surface height also in this
257sector and firn compaction modelling would be necessary to compute an accurate mass
258balance estimate (Helsen and others, 2008). This higher than average accumulation and the
259consideration of the entire basin, in contrast to former studies (Wingham and others, 2009),
260might explain that we observe little volume change at the beginning of the series in fall 2002
261(Fig. 5).
262
263The cause for the propagation far inland of this perturbation is still subject to debate. To
264investigate the propagation, we display on Fig. 6 the data shown on Fig. 4.a in another way
265where the residuals are averaged every quarter instead of every year. From this figure, the
266propagation speed can be estimated to some 30 km a -1 (a vertical tangent means no
267propagation, while a horizontal one means instantaneous propagation). The propagation
268seems to decrease at about 300 km from the grounding line, where the bed rises to -500 m. On
269the contrary, it reaches 75 km a-1 at the beginning of the profile but decreases during the
270period. The effect of seasonal accumulation is seen as undulations in the contour lines.
271Joughin and others (2003) and Scott and others (2009) suggested that it is driven by the
272increase of the driving stress. The driving stress (τ = ρ g α E, where ρ is the ice density, g the
273acceleration of gravity, α the surface slope and E the ice thickness) is proportional to slope
274and ice thickness so that thinning in the lowest part of the glacier being stronger, it increases
275the surface slope, thus increasing the driving stress.
276
Δα
=
Δt
( Δ dhdt )
D
277
278
279where t is the time, D is the distance between points where dh/dt is estimated, Δ is the
280operator for difference. At first order, this effect dominates the overall diminution of ice
281thickness (e.g. Scott and others 2009).
282Scott and others (2009) estimated a slope increase along the centreline of PIG of about 2 10 -5
283a-1 between 2006 and 2008. From our estimation of elevation changes, we find the same order
284of magnitude: 1.5 10-5 a-1 for the same period. On average, we find about 1.1 10 -5 a-1 over the
285Envisat period with a mean slope of 1.5 10 -3 along the centreline. This could mean that the
286slope change accelerated during these 8 years. Our estimates agree with those published by
287Joughin and others (2003), and as we saw before, values by Scott and others are larger than
288ours, probably because of the limited time span of their measurements over the summer
289season.
290
291Fig. 7 shows the evolution of the slope along the centreline profile shown in Fig. 2.a, for each
292half and for the full 8-year period. It is given in percent of the initial slope, as derived from
293the topography by Rémy and others (1999). The slope and its evolution are computed by
294fitting a plane to the surface within a disc with a radius of 20 km. Up to km 170, the increase
295in driving stress is around 1 % a -1 with peaks up to 1.3 % a-1 during the second half of the
296period. If we assume the Glen exponent to be n=3, the increase in speed is thus of 3-4.5 % a -1
297over this period which is consistent with values published by Scott and others (2009),
298(acceleration of 4.8 and 4.1 % a -1 respectively 111 and 171 km from the grounding line).
299Farther inland, 200-250 km from the groundling line, the increase is lesser but still significant,
300it increases from 0.3 % a-1 for the period 2002-2006 to 0.6 % a-1 for the period 2006-2010,
301suggesting a recent increase in speed of 1.5 % a-1.
302
303We computed the second derivative with time of the surface height (elevation acceleration,
304Fig. 8.b) because inspection of the time series reveals an increase in thinning (e.g. Fig. 3).
305Wingham and others (2009) described an increase in thinning at PIG grounding line. We
306extended the area to the whole Amundsen Sea Embayment that is examined in the next
307section, to investigate the hypothesis of a regional phenomenon such as increased ice–shelf
308melting driven by ocean-warming. (Fig. 2.a)
309
310Most of the height loss is happening to the south of the central flow line (i.e. to the right of
311this line on the figures). The acceleration map (Fig. 8.b) also shows that thinning is
312propagating southward. To the North, PIG is limited by high subglacial grounds (Jones
313Mountains) whereas the southern branches of the glacier reach the thicker centre of the
314WAIS, ice to the North is less than 1000 m thick while it is over 2000 m thick to the South
315(see the North-South transect of PIG on Fig. Fig. 4.c and 4.d). To the East, thinning is
316detected within a few tens of kilometres from the divide with the Ronne Ice Shelf drainage
317basin (Fig. 4.a and 4.b).
318
319On Fig. 4.c, we observe that the centreline is not the place with the largest thinning rates. On
320the North-South transect, the maximum thinning rate is reached about 50 km farther to the
321South (at this latitude, satellite ground tracks are spaced 25 km apart so we have the adequate
322resolution to conclude). From our data, we infer that the thinning pattern of PIG will spread to
323the South.
324
325In average, PIG basin is thinning and this thinning is accelerating at a pace of up to several
326tens of centimetres per year per year. To the West of PIG, Thwaites glacier and glaciers
327flowing into the Crosson ice-shelf (Pope, Kohler and Smith glaciers) are also losing height at
328an accelerating pace but the phenomenon is located within 100 km from the coast (Fig. 8.b
329and 9.b).
330The regional behaviour of glaciers of the ASE supports the hypothesis that PIG’s retreat was
331triggered by a regional cause. However, it is sustained and propagated by some phenomena
332specific to PIG (e.g. Joughin and others, 2010).
333
334From the map of elevation change acceleration (Fig. 8.b), we show that most of the PIG
335northern basin is undergoing acceleration (in terms of elevation) whereas neighbouring
336glaciers are only subject to acceleration close to the coast and up to 50-100km inland.
337
3384. Other glaciers
339
3404.1 West Antarctic Ice Sheet
341Most of the coast to the West of PIG exhibits thinning that cannot be attributed to
342accumulation variation (Fig. 8 and Fig. 9). In Ellsworth Land (part of the WAIS at the base of
343the Peninsula), several glaciers also exhibit thinning. These observations are detailed below.
344
345Thwaites glacier (TG) is a big contributor to WAIS ice discharge with an outflow estimated to
346109 ± 5 Gt a-1 in 2007 leading to an imbalance of -34 ± 16 Gt a -1 (Rignot, 2008). The bed
347under TG is also sloping downward inland (Holt and others, 2006) and in the future, TG could
348be subject to changes similar to those of PIG. However, it does not seem to be subject to the
349same dramatic inland acceleration as PIG for the moment.
350
351Thinning on TG is widespread and significant with respect to our error analysis but it is less
352intense than on PIG. From our gridded maps, the largest height variation on TG is -4.5 ± 0.7
353m a-1 whereas it reaches -6.2 ± 1.2 m a-1 on PIG on average during 2002-2010. Errors are
354derived from the difference between maps built on ascending tracks only and descending
355tracks only. They reflect the raw altimetric error and the different sampling.
356
357Our acceleration values are too close to the uncertainty margins for any interpretation, except
358on the first 50 km from the coast, where acceleration is significant within 2 standard
359deviations. Rignot (2008) observed a widening of the fast flowing zone. Close to the
360grounding line, we do not process the time series, because surface slope and footprint-scale
361(2-6 km) roughness induced large errors. This restriction is inherent to radar altimetry and
362makes measurements sparse and of lesser quality, precluding any spatially accurate
363interpretation. In other words, we cannot observe the widening reported by Rignot (2008) but
364this does not mean it has not happened.
365
366Glaciers flowing in the Crosson ice shelf are confined between mountain ranges to the South
367of their small basins (Mount Takahe and Kohler range) so that the strong thinning they
368undergo cannot propagate far inland. Smith Glacier in particular flows in a deep trench (Holt
369and others, 2006). In contrast to their small basins and small potential contribution to global
370sea level, these glaciers are losing height at a very fast pace. The largest height variation from
371our gridded map is -7.4 ± 1.6 m a-1 on average over the Envisat period.
372
373Farther west, glaciers flowing toward the Pacific Ocean (tributaries to the Getz ice shelf,
374Cordell Hull and Emory Land glaciers) also exhibit dynamic thinning. Along this coast, the
375Envisat record might be too short but no acceleration is observed beyond our uncertainty
376margins.
377
378In Fig. 9.a, the map associated with the elevation trend shows that the whole Pacific coast of
379the WAIS is losing height at a rate that cannot be explained by accumulation fluctuations. The
380growth of ice stream C at the limit of coverage also clearly stands out.
381
382Last, glaciers along the coast of the Bellingshausen Sea are also thinning, especially glaciers
383of the Eltanin Bay (Box d in Fig. 1, Fig. 10). Glaciers flowing in the Abbot ice-shelf (directly
384North of PIG) are too small and too close to the coast to be correctly observed. From the
385regional growth of the ice sheet at high altitude (over 1000m), we can infer that the
386accumulation rate was higher than average in Ellsworth Land (the north-eastern part of the
387WAIS). Fast thinning glaciers (up to -2.5 ± 1 m a -1) are thus probably losing mass even faster,
388as part of the height loss due to ice loss is compensated by snow gain, at lower density.
389
3904.2. East Antarctic Ice Sheet
391
392Totten glacier (Fig. 11) has the largest outflow in East Antarctica (Rignot, 2002) and it has
393previously been reported to be thinning (Rignot and Thomas, 2002; Zwally and others, 2005;
394Pritchard and others, 2009). Zwally and others (2005) suggested that this evolution could be
395driven by the same causes as PIG, i.e. the influence of atmospheric and ocean forcings and
396Pritchard and others (see their Supp. Fig. S8) emphasized that surrounding glaciers follow the
397same evolution, reinforcing this hypothesis.
398
399Not many altimetry data points pass the tests for acceptable quality over the last kilometres of
400Totten glacier, probably because of the steep and crevassed surface. However, the remaining
401ones that are closest to the grounding line exhibit negative elevation change (up to -1.2 ± 0.6
402m a-1 on average over the period). To reinforce the dynamic argument, a few measurement
403points are available on the “ridge” between the main tributary to Totten glacier (flowing to the
404North-East from “behind” Law Dome) and another tributary, slightly to the East, flowing
405north and visible on the MODIS Mosaic Of Antarctica, Scambos and others, 2007). This ridge
406is also losing height, but much less rapidly that the surrounding fast flowing areas. Fig. 11
407shows that variation in accumulation could explain height variation on this ridge but not on
408the faster flowing areas. However, we do not observe acceleration in thinning, and thus
409confirm previous results of Rignot (2006).
410
411Denman Glacier (Fig 12) is located along the Queen Mary Coast and flows into the
412Shackleton ice-shelf, between the Amery ice-shelf to the West and Law Dome to the East. It
413is bounded by mountains about 1500 m high and its path is easy to infer from the altitude
414contour lines (compare with Rignot, 2002). Despite a relatively rough topography, some
415points are available on the glacier itself. The higher terrain to the West gained height at a very
416fast pace over the observation period, up to about 0.35 m a -1 while the trunk of the glacier, in
417its “trench” lost height up to – 0.4 m a-1. The clearly delineated thinning pattern at the bottom
418of the trench would point toward a local meteorological phenomenon such as wind erosion
419(Scarchilli and others, 2009), or orographic effect on precipitation (van den Broeke and
420others, 2006). The altimetric backscatter decreases during the observed period, suggesting a
421change in snowpack characteristics. But the link between electromagnetic properties and
422height is not stronger in this region than in other coastal areas. The backscatter trend is -0.2
423dB a-1 on the fast flowing part of the glacier and dependency of height with backscatter is
424around -1 m dB-1 in the area which means that our correction adds another 20 cm a -1 of
425thinning. The observed signal of -0.4 m a-1 (after correction) is likely to reflect a real change
426in surface height, which is consistent with Pritchard and others (2009).
427
428In Dronning Maud Land (DML), we observe thickening, closely related to the topography
429(Fig. 1). On the plateau between Dome Fuji and the Weddell Sea, we observe thickening
430between 2 and 3 cm a -1 on average. This zone of growth is delineated by the ridge linking
431Dome A to Dome Fuji and going on to the Northwest. Other features are linked to the
432orientation of slopes closer to the northern shore of DML. We reckon that specific
433meteorological conditions occurred during the observations. From the comparison of our
434results with the ones from Pritchard and others (2009) and former ERS height trends (Rémy
435and Parouty, 2009), we suggest that the dynamic thickening reported by Pritchard and others
436(2009) in eastern DML might in fact come from underestimated variability in snowfall.
437
438Finer interpretation of these results would require more information about accumulation
439variability and compaction. Spatial scales considered here are smaller than in the usual
440altimetric observations and some effects such as the orographic forcing of precipitation and
441local wind erosion might need to be taken into consideration.
442The error associated with the variability in accumulation close to mountain ranges and sloping
443terrain is thus probably underestimated from the coarse resolution of the accumulation map
444we used.
445
4465. Conclusion
447
448From a recent and relatively long, homogenous and dense altimetric time series, we
449investigated the thinning of several glaciers in the WAIS and EAIS. A formal error analysis
450and the agreement with previous observations on Pine Island Glacier confirm the reliability of
451our ENVISAT-derived elevation changes. Moreover, the along-track analysis provides good
452space and time sampling leading to a precise description of the evolution pattern, even of
453smaller glaciers (such as Smith Glacier in the Amundsen Sea Embayment).
454
455First, we confirm that the thinning of Pine Island Glacier is accelerating. This thinning is also
456spreading to the South of the basin and the speed of propagation upslope along the centre is
457about 40 km a-1. The thinning pattern is well correlated with the flow speed pattern derived
458from InSAR (Rignot and others, 2011) and thinning is detected farther than 250 km from the
459grounding line.
460
461From the Envisat altimeter dataset we demonstrate that the whole Pacific coast of the WAIS is
462dynamically thinning. Thwaites glacier is losing up to 4.5 m a -1 and glaciers of the Crosson
463ice shelf up to 7.5 m a-1. To the West of PIG, glaciers of the Bellingshausen Sea are also
464losing height. Acceleration is observed on the coastal region of all glaciers of the Amundsen
465Sea, and Thwaites Glacier in particular should be given attention in the future.
466
467In East Antarctica, we observe thinning on glaciers such as Totten Glacier (up to 1.2 m a -1),
468but we did not detect any significant acceleration of their surface lowering during 2002-2010.
469
470The 8-year time series is still too short to compensate statistically for the inter-annual
471variation in accumulation so that changes in snow and firn thickness due to specific
472meteorological conditions dominate the elevation trend and could mask the signal from small
473dynamic changes in ice thickness. Further studies will extend this analysis to the complete 35474day repeat orbit of previous altimeters (mainly ERS-2 and Envisat). It will provide 15 years of
475uninterrupted data, doubling the length of the current time series and will greatly help to
476reduce uncertainties, smoothing the effect of accumulation variability on the surface height.
477
478Acknowledgements
479The authors wish to thank F. Blarel for pre-processing the data and E. Berthier for his
480insightful comments. This work was supported by the ADAGe project (ANR-09-SYSC-001)
481funded by the Agence National de la Recherche (ANR) and by the French Space Agency
482(CNES) through the TOSCA program. T. Flament acknowledges a PhD fellowship from
483CNES and the French National Research Center (CNRS).
484
485The authors are grateful for the pertinent comments from two anonymous referees which
486greatly improved our paper.
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644
2003-2007
Points name
Scott and
others
ICESat
-1.9±0.4
-1±0.4
-0.6±0.4
This study
Envisat
GPS 1
(austral summer 20062007)
This study
Scott and
Envisat
others
GPS
-3.5±0.65
-3.0±0.5
-2.0±0.4
-2.2±0.3
-1.2±0.2
-1.4±0.3
GPS 2
(austral summer 20072008)
This study
Scott and
Envisat
others
GPS
-3.65±0.7
-3.3±0.5
-2.8±0.6
-2.3±0.3
-1.05±0.2
-1.6±0.2
PC 55
-2.15±0.3
PC 111
-1.2±0.15
PC 171
-0.7±0.1
645
646Table 1: Elevation changes in m a-1 at Scott and others (2009) points and values estimated by
647fitting a quadratic dependency on time and a one year sine to our ENVISAT height residuals
648(see text) closest to PC 55: 97.86 °W,75.357 °S; PC 111: 95.88 °W, 75.406 °S; PC 171: 93.71
649°W, 75.455 °S
651Fig. 1: Map of surface elevation trend, dh/dt. Black boxes delineate areas referred to in
652following figures. Meridians are plotted in dotted line every 10° and parallels every 5°. The
653limit of coverage is at 81.5°S. DML stands for Dronning Maud Land.
655Fig. 2: 2.a. Enlargement on the Amundsen Sea Embayment (box a in Fig. 1) dh/dt in m a -1.
656PIG basin is delineated in dashed black line, grounding line from the MODIS mosaic of
657Antarctica is in red. Altitude contour lines every 250m are in thin black lines. Red crosses
658give the location of Scott and others GPS measurements and dotted black lines are the profiles
659(respectively North-South transect and roughly East-West central flow line) used in fig. 6.
660Meridians are every 10°, parallels every 2°. 2.b. Enlargement on Pine Island Glacier elevation
661trend. White lines are the speed contours from Rignot and others (2011), they are plotted at 50
662m a-1, 100 m a-1, 200 m a-1, 500 m a-1 and 1000 m a-1 (right).
663
664Fig. 3: Averaged surface elevation time series at the 4 points closest to Scott and others
665(2009) GPS location. Red: PC 55, green: PC111, blue: PC 171 (see table 1 and Fig. 3 for
666location). Each thin line is the result of the least square fit to the corresponding series, as
667described in the text.
668
670Fig. 4: Elevation trend along the profiles shown in Fig 2.a. Along the central flow line,
671directed West-East, i.e. going upslope from the grounding line (Fig. 4.a) and along the North672South profile (Fig. 4.c.) Bed elevation (grey line, from Holt and others, 2006) and surface
673elevation (black line) are given below (b and d).
674
675
677Fig. 5: Volume change of the PIG basin in km3. The blue line is the measurements, the black
678line is a fit of a quadratic dependency with time and a one-year sine and the red lines define
679the 1-sigma error around the blue line.
680
681
683Fig. 6: Contour plot of the evolution of elevation change along the PIG centreline shown in
684fig 3. X-axis is the distance in km from the bottom of the profile (on PIG shelf) toward the top
685of the profile; Y-axis is the time in years from the beginning of the series. The “slope” of the
686contours indicates the speed of propagation of the thinning.
687
688
690Fig. 7: Surface slope trend in % a-1 of initial slope along PIG centreline.
691
692
694Fig. 8: Rate of elevation (Fig. 8.a) and acceleration of elevation change (Fig. 8.b) over the
695West Antarctic Ice Sheet. Thin black lines are altitude contours every 250m (from RAMP
696topography (Liu and others, 2001).
697
698
700Fig. 9: Maps of the ratio of the absolute value of elevation trend (Fig. 9.a) and elevation
701acceleration (Fig. 9.b) to their respective errors (see text)
702
703
704
705Fig. 10: Enlargement of dh/dt maps; around Eltanin bay, WAIS (box d in Fig.1) Meridians
706every 5°, parallels every 2°, altitude contour lines every 250m.
707
709Fig 11: Enlargement of the dh/dt map on Law Dome and Totten Glacier, EAIS, defined by
710box b in Fig 1. Altitude contour lines every 250 m. (Fig. 11.a). Maps of the ratio of the
711absolute value of elevation trend to the corresponding error. (Fig. 11.b)
712
713
715Fig. 12: Enlargement of dh/dt maps; around Denman Glacier, EAIS (box c in Fig.1)
716Meridians every 5°, parallels every 2°, altitude contour lines every 250m.