Journal of Glaciology, Vol. 00, No. 000, 0000 1
Interannual Changes of the Floating Ice Shelf of
Petermann Gletscher, North Greenland from 2000 to 2012
Andreas M ¨
UNCHOW,1Laurie PADMAN,2Helen A. FRICKER,3
1College of Earth, Ocean and Environment, University of Delaware, Newark, Delaware, USA
2Earth & Space Research, Corvallis, OR, USA
3Scripps Institution of Oceanography, University of California, San Diego, CA, USA
ABSTRACT. Petermann Gletscher, NW Greenland, drains 4% of the Greenland Ice Sheet
into Nares Strait. Its ﬂoating ice shelf retreated from 81 km to 46 km length during two
large calving events in 2010 and 2012. We document changes in the three-dimensional ice
shelf structure from 2000 to 2012 using repeated tracks of airborne laser altimetry and ice
radio-echo sounding, ICESat laser altimetry, and MODIS visible imagery. The recent ice-shelf
velocity, measured by tracking surface features between ﬂights in 2010 and 2011, is ∼1.25 km
a−1, about 15-30% faster than estimates made before 2010. The steady-state along-ﬂow ice
divergence represents 6.3 Gt a−1mass loss through basal melting (∼5 Gt a−1) and surface
melting and sublimation (∼1.0 Gt a−1). Airborne laser altimeter data reveal thinning both
along a thin central channel and on the thicker ambient ice shelf. From 2007 to 2010 the ice
shelf thinned by ∼5 m a−1, which represents a non-steady mass loss of about 4.1 Gt a−1.
We suggest that thinning in the basal channels structurally weakened the ice shelf and may
have played a role in the recent calving events.
Greenland’s tidewater glaciers are losing mass, through thin-
ning and retreat, at an increasing rate (Joughin et al., 2010b;
Howat et al., 2011; Bjork et al., 2012). Over the last decade
there has been a general clockwise progression of mass loss
(Khan et al., 2010; Chen et al., 2011), with initial retreat in
south-eastern Greenland (Luckman et al., 2006; Howat et al.,
2008) followed by loss in the south-west (Joughin et al., 2004)
and, most recently, in north-west Greenland (Khan et al.,
2010). In addition to this general trend, there is signiﬁcant
spatial and temporal variability of glacier mass budgets that
do not always correlate with readily observed surface forcing
(Howat et al., 2011; Moon et al., 2012). These observations
support the view that the mass balance of tidewater glaciers
is sensitive to the delivery of ocean heat to the submarine
portion of the glacier (Straneo and Heimbach, 2013).
Many marine-terminating glaciers in Greenland north of
78◦N terminate in ice shelves, ﬂoating extensions of the
glaciers extending up to several tens of km into the adjacent
fjords (Rignot et al., 2001). While most North Greenland ice
shelves have been relatively stable, Academy Glacier and C.H.
Ostenfeld Gletscher lost their ﬂoating ice shelves in the 1950s
(Higgins, 1991) and in 2001 (Joughin et al., 2010a), respec-
tively. Zachariæ Isstrøm separated from its slow-moving ice
shelf in 2012/2013 after two decades of retreat. Petermann
Gletscher lost more than 40% of its ice shelf area during two
major calving events in 2010 and 2012 (Johnson et al., 2011;
Nick et al., 2013). What remains of Greenland’s ice shelves
is threatened by a changing climate, because both regional
air (Chylek et al., 2009) and ocean temperatures (Zweng and
M¨unchow, 2006; Polyakov et al., 2010; M¨unchow et al., 2011)
continue to increase while Arctic sea ice cover continues to
decline (Stroeve et al., 2012). Based on recent observations
in Antarctica and Greenland, we expect that reduction in
size due to thinning and/or calving of these ice shelves could
cause accelerated dynamic loss of adjacent grounded ice and
consequent sea level rise (Scambos et al., 2004; Holland et al.,
2008; Nick et al., 2013).
In this paper we describe changes in Petermann Gletscher
(hereafter denoted PG) in Northwest Greenland from 2000
to 2012, after the second large calving event (Figure 1) us-
ing a range of remotely sensing ice surface and bottom mea-
surements. Opportunistic ocean surveys of Petermann Fjord
in 2009 (Johnson et al., 2011) and 2012 motivated studies
to determine whether the calvings were historically unusual
(Falkner et al., 2011), if it could be related to ocean variabil-
ity, and if loss of this portion of the ice shelf could lead to ac-
celerated discharge of grounded ice from Petermann Glacier.
BACKGROUND ON PETERMANN
Petermann Gletscher drains about 69,000 km2(Rignot et al.,
2001) of the 1,710,000 km2Greenland Ice Sheet, i.e., about
∼4%, into Petermann Fjord, which is ∼15-20 km wide and
extends ∼90 km from PG’s present grounding line (Figure
1). The PG terminates in an ice shelf that, over the historical
record since 1876, has been ∼70-80 km long (Falkner et al.,
2011). The average ice thickness, based on satellite altimetry
and ice-penetrating radio-echo sounding, is ∼300 m, and the
glacier is grounded at ∼600 m depth below sea level (Rignot
and Steﬀen, 2008). The glacier bed deepens for another 20 km
2M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012
upstream and is below sea level for another ∼60 km inland
(Bamber et al., 2013; Rignot, 1998).
The PG moves steadily seaward at a reported average rate
of between 0.95 km a−1(Higgins, 1991) and 1.1 km a−1(Rig-
not and Steﬀen, 2008), with a seasonal modulation of about
0.1 km a−1(Nick et al., 2012). The total annual discharge
at the grounding line is 12 ±1 Gt a−1(Rignot and Steﬀen,
2008). Higgins (1991) estimated the long-term mean calv-
ing rate at ∼0.6 Gt a−1or about 5% of the ﬂux across the
grounding line. Annual precipitation is small, and the ice shelf
surface undergoes net mass loss of 1.2 m a−1(1.3 Gt a−1for a
mean ice shelf area of 1300 km2) through winter sublimation
and summer melting (Rignot and Steﬀen, 2008; Rignot et al.,
2001). If the glacier is in a steady state, then about ∼85% of
the mass loss must occur via basal melting. Suﬃcient ocean
heat is available inside the fjord to melt the entire ﬂoating ice
shelf, if the heat can ﬂow into the sub-ice-shelf cavity (John-
son et al., 2011; Rignot et al., 2012). Hydrographic proﬁles
below the ice shelf about 10 km seaward of the grounding
line revealed water with temperature T > 0◦C (Rignot and
Steﬀen, 2008) at 600 m depth. This relatively warm ocean
water originates from adjacent Nares Strait, which receives
Arctic Atlantic Layer water from the Lincoln Sea in the Arc-
tic Ocean (M¨unchow et al., 2007). Rignot and Steﬀen (2008)
mapped the steady-state basal melt rate for the PG ice shelf,
using satellite-derived divergence of ice ﬂux. Values ranged
from ∼30 m a−1near the grounding line to ∼10 m a−1closer
to the ice front. Gladish et al. (2012) developed a model of
ice-ocean interactions that generated basal melt rates that
ranged from 25 m a−1at the grounding line to zero at the
The large calving events at PG in 2010 and 2012 reduced
the ice-shelf length from 81 km to 46 km (Figures 1 and 2).
While PG has experienced large calving events in the past
(Falkner et al., 2011), its terminus (ice front) has now re-
treated farther back than has been observed since the ﬁrst
reported measurements in 1876 (Nares, 1876). By analogy
with Jakobshavn Isbrae (Motyka et al., 2011; Holland et al.,
2008), we hypothesize that the observed slow warming of
Atlantic-sourced waters in Nares Strait during the last decade
(M¨unchow et al., 2011) could lead to increased basal melting
of the PG ice shelf. We presently cannot determine if ocean
warming in Nares Strait will continue, and modeling studies
suggest that even complete loss of the PG ice shelf would not
lead to accelerated loss of grounded ice (Nick et al., 2012,
2013). However, estimates of the PG ice-shelf mass budget
provide a case study of the relationship between basal melt-
ing and ice-shelf retreat through calving that is valuable for
testing models used to describe coupling between ocean vari-
ability and glaciological response. It is now straightforward
to track the areal extent of PG on short time scales (Johan-
nessen et al., 2013). However, here we extend that description
to include how the ice thickness of PG has evolved over the
last decade using repeat-track satellite and airborne altime-
try and direct measurements of ice thickness change using
ice-penetrating radio-echo sounding.
DATA AND METHODS
Aircraft ﬂight data
The NASA conducted overﬂights of PG using DC-8 (2010)
and P-3 (2002, 2003, 2007, and 2011) aircraft, the 2010 and
2011 ﬂights being part of Operation IceBridge. The aircraft
carried a multi-channel ice-sounding radar (hereafter denoted
ISR) operated by the University of Kansas to estimate the lo-
cation of the air-ice and ice-ocean or ice-bedrock interfaces to
determine ice thickness at about 100-m horizontal resolution
(Gogineni et al., 2001). They also carried a scanning laser
altimeter, the airborne topographic mapper (ATM) (Krabill
et al., 2002). We used level 1B ATM data (Krabill , 2010)
with spatial resolution of ∼1 m. We applied a Lanczos low-
pass ﬁlter to longitude, latitude, and elevation to generate an
along-track series to represent features at scales greater than
∼300 m, oversampled at ∼30 m spacing. Two lines, separated
across-fjord by ∼1.5 km (Figure 1), were repeated in multi-
ple years. The western line followed a narrow surface channel
while the eastern line was over thicker ice that is more typical
of the ice shelf.
Ice and land satellite (ICESat) data
We obtained elevation data from the Geoscience Laser Al-
timeter System (GLAS) on NASA’s ICESat which operated
in campaign mode from October 2003 to November 2009
(Shuman et al., 2006). ICESat acquired elevation estimates
every ∼170 m along-track, with a footprint diameter of ∼50-
100 m (Abshire et al., 2005). Four ICESat tracks cross the Pe-
termann fjord (Figure 1) and, for each track, up to ten cloud-
free repeats were acquired. Data processing followed protocols
described by Padman et al. (2008) and Fricker et al. (2009).
We used Release 633 of the GLA12 altimetry product, which
we converted from the TOPEX/Poseidon reference ellipsoid
to the WGS84 ellipsoid. We applied the GLA12 saturation
correction (Fricker et al., 2005) and retided the elevations by
adding back the GLA12 ocean tide corrections. Borsa et al.
(2013) reported a range error in the ICESat data, known
as the Gaussian-Centroid oﬀset. We did not make this cor-
rection, however, since the amplitude of this oﬀset is much
smaller than our signal.
Ice-sounding radar (ISR) data
For the ice surface and bottom data from ISR, we removed an
unknown platform bias by assuming hydrostatic equilibrium
of a 30 km ﬂoating section of the ice shelf. The bias is assumed
to be constant for each ﬂight. Using an approach similar to
Bindschadler et al. (2011), we ﬁtted estimates of ice thickness
Hfrom the ISR to
Z=offset +ratio ×H(1)
where Zis the ISR surface elevation above the geoid. The
regression coeﬃcients ”oﬀset” and ”ratio” were determined
via least-squares and represent, respectively, the unknown
(constant per ﬂight) platform oﬀset and a buoyancy ratio.
If the ice shelf is ﬂoating in hydrostatic equilibrium, then
ratio = (1−ρice /ρwater ) = 0.106 for an ice density ρice =917
kg m−3and an ocean density ρice=1026 kg m−3. The oﬀset
includes an unknown ﬁrn-air correction (Bindschadler et al.,
2011); however, this correction should be negligible for PG
M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012 3
because annual snowfall is small compared with surface mass
loss through melting and sublimation (see next section). Ta-
ble 1 lists these regression coeﬃcients along with pertinent
details of aircraft surveys conducted over PG since 2002. The
buoyancy ratio is close to the expected value for the ambient
ice shelf, but deviates somewhat for the central channel.
The ISR-based ice thickness estimates were accurate to
within 10 m (Gogineni et al., 2001), and the concurrent ATM
estimates of the location of the ice surface (elevation) were
accurate to ∼0.2 m (Krabill et al., 2002). We converted the
ATM elevations to ice thickness assuming hydrostatic equi-
librium to estimate the location of the grounding line and
to detect deviations from hydrostatic equilibrium, e.g., Bind-
schadler et al. (2011) and Fricker et al. (2002).
No ice-penetrating ISR data are available concurrent with
ICESat data; therefore, we cannot test the hydrostatic as-
sumption for these data.
Geoid and tidal corrections
We converted all ice elevation and draft data from the WGS-
84 ellipsoid to the EGM2008 geoid (Pavlis et al., 2012) to esti-
mate ice freeboard from surface elevation measurements. The
freeboard allows us to estimate ice draft using the hydrostatic
balance of the ﬂoating section of PG’s ice shelf. We corrected
all elevation data for tides using predictions from the AO-
TIM5 tide model (Padman and Erofeeva, 2004). This model
does not resolve Petermann Fjord; therefore, we used a model
grid point at the entrance to the fjord rather than actual lo-
cations of elevation measurements. We speculate that tidal
variability inside the fjord is small, because the barotropic
tidal wave propagates in and out of the fjord within 10 min-
utes. Frictional forces under the ﬂoating ice shelf will change
both tidal amplitude and propagation, but these are diﬃcult
to assess without a dynamical model or without knowledge
of ocean current, bottom depth, or ice shelf topography. Reeh
et al. (2000) found tidal amplitudes under the 60-km long ice
shelf of Nioghalvfjerdsfjorden oﬀ north-eastern Greenland to
vary less than 20% near the grounding line relative to the
forcing open ocean tide: at PG, this variability would corre-
spond to a tidal uncertainty of <0.1 m.
Moderate resolution imaging
spectroradiometer (MODIS) data
The MODIS ﬂown aboard the Terra satellite provides ra-
diation measurements starting in February 2000 at spatial
resolution of 250 at nadir for the 865 nm spectral band.
The polar orbiting, sun-synchronous satellite has a repeat
period of 16 days and provides about 8-12 scenes each day
of northern Greenland. We used the raw Level-0 data dis-
tributed by NASA’s Ocean Color Group along with altitude
and ephemeris data. Following Luo et al. (2008) and Tr-
ishchenko et al. (2009), we converted these data to calibrated
and geo-referenced 865 nm reﬂectance data. The subsequent
gridding preserved the 250 m spatial resolution using a Green’s
function approach (Wessel, 2009) that also facilitated auto-
mated estimation of the reﬂectance gradient vector at each
pixel. We constructed a time series of reﬂectance gradients
from one cloud-free MODIS Terra image per year from 2000
to 2012, acquired within 135 minutes of 20:50 UTC between
April 30 and May 20 of each year.
We made estimates of areal ice shelf loss by manually count-
ing MODIS pixels on paper, although there is uncertainty due
to partial pixels and semi-detached areas of the ice island
(Wang and Shi, 2009).
Changes in ice shelf extent
The surface evolution of PG and the ice islands it calved
are recorded by MODIS imagery from the summers of 2003,
2010, and 2012 (Figure 1). During the 2003-2010 period the
glacier’s terminus advanced about 6 km (to y≈80 km; see
Figure 1) even though, in 2008, two smaller calving events
removed 30 km2of ice shelf (not shown). The calving front
shed 253±17 km2on August 4, 2010; a further 130±10 km2
calved on July 16, 2012.
Figure 3 shows surface elevation from ATM and bottom to-
pography from ISR for repeat airborne survey in the springs
of 2010 (March 24) and 2011 (May 7), δt=408 days apart. The
proﬁle from 2010 has been shifted seaward by δx=1.4 km rela-
tive to the 2011 proﬁle to achieve the largest spatially-lagged
correlation between the two proﬁles for both surface eleva-
tion and ice thickness. This shift corresponds to an average
ice ﬂow rate of V=δx/δt = 1.25±0.09 km a−1. The uncer-
tainty is a 95% conﬁdence limit or 1.96 times the standard
error ǫ= 2∆/√Nwhere ∆=300 m and N= 150 represent,
respectively, data spacing and degrees of freedom for the 45
km section of ﬂoating ice shelf used in the correlation. Our
estimate of ice ﬂow speed for the ﬂoating ice shelf is ∼30%
higher than estimates by Higgins (1991) for the late 20th
century and Rignot and Steﬀen (2008) for 2002-03, but it
falls within the range of values given by Nick et al. (2012)
and Johannessen et al. (2013) for the 2006-11 period.
The segments of the ice shelf that calved in 2010 and 2012
were, on average, 76 m and 182 m thick (Figure 3) with stan-
dard deviations of 6 m and 16 m, respectively. Using these
along-shelf proﬁles and assuming a realistic ice thickness pro-
ﬁle across the glacier (discussed below), we ﬁnd that the mass
was similar during each of the two calving events in 2010 and
2012: the mass los was about 18±2 Gt for each event.
After the 2012 calving event the terminus was at the most
landward location of all locations in the historical record,
which begins in 1876; see Figure 1b in Falkner et al. (2011)
and updated to the end of 2012 in our Figure 2.
The elevation of PG ice shelf varies substantially on scales
of order 1 km and less both along (Figure 3, from ATM)
and across the ice shelf (Figure 4, from ICESat). The ICE-
Sat tracks also reveal a deep channel near the middle of the
ice shelf (Figure 4). This channel coincides with the western
track ﬂown by aircraft surveys and is most pronounced in
ICESat Track 220, ∼15 km seaward of the grounding line
(Figure 4). The elevation of this channel varies from a max-
imum of 18 m in November 2003 to minima of 6 and 8 m in
March 2004 and March 2007, respectively (Figures 4 and 5).
Linear trends from point measurements of elevation change
over time are generally not signiﬁcantly diﬀerent from zero;
however, the along-track (approximately across-shelf) aver-
age over the central section of the surface elevation of the ice
4M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012
shelf decreased at a rate of 0.33 ±0.26 m a−1(Figure 5); the
uncertainty represents a 95% conﬁdence limit in linear regres-
sion (Fofonoﬀ and Bryden, 1975). This section includes both
the central channel and the ambient ice shelf to its east and
The elevation of the ambient ice shelf on either side of the
central channel is markedly diﬀerent: the western ambient
ice shelf stands 10-25% higher than the ambient ice shelf to
the east. Along ICESat Track 220, the time-mean, spatially
averaged elevation are 33 m and 31 m to the west and east
of the central channel with standard deviations of 6.0 m and
11.7 m, respectively (Table 3). The elevation of the central
channel is always less than half of that of the nearby ambient
ice shelf; cf. Rignot and Steﬀen (2008).
We can trace the central channel seaward in ICESat tracks
101 and 1336 even though it becomes broader and its am-
plitude diminishes (Figure 4, Table 3). The channel is also
visible near the grounding line in ICESat Track 399, and in
MODIS imagery (Figure 1). This observation allows us to use
MODIS data (2000-2012) to test whether the channel changes
its lateral position during this period, which is longer than the
ICESat period. Gradients of surface elevations cause varia-
tions in surface reﬂectance in remotely-sensed optical MODIS
imagery (Figure 1). For similar sun and satellite angles the
spatial gradients of reﬂectance fall at similar locations (Bind-
schadler et al., 2010; Scambos et al., 2007). Figure 6 shows the
absolute magnitude of the reﬂectance gradient vector for an
across-shelf section located 15 km seaward from the ground-
ing line near ICESat Track 220. The central channel appears
as a feature that does not move laterally by more than one
pixel (250 m) throughout the 12-year record. It also reveals
a distinct secondary peak gradient to the east of the central
channel (x∼83 km), coincident with a shallower channel vis-
ible in ICESat elevation data (Figure 4) about 4-5 km to the
east of the central channel.
We further investigated elevation and ice thickness change
along ice ﬂowlines using proﬁles from repeat ATM surveys
along the fjord with two ﬂight lines spaced 1.5 km apart.
The ATM-derived elevation proﬁle acquired in 2002 (Figure
7) shows that the central (west) channel extends from the
grounding line at least 50 km seaward and remains approxi-
mately half the thickness of the ambient ice shelf (east tran-
sect) for much of this range.
Ice draft and thickness proﬁles
We estimated along-ice-shelf draft from the ATM-derived el-
evations assuming hydrostatic equilibrium, and compare this
with that estimated by ISR. For the ambient ice shelf, these
two estimates show excellent agreement with a correlation
coeﬃcient r2=0.993. Figures 3 and 7 show these high corre-
lations which give conﬁdence in the ice surface (ATM) and
bottom (ISR) measurements as well as the validity of the
hydrostatic assumption and the constant oﬀset bias in Eq.-1.
Deviations from hydrostatic equilibrium near the grounding
zone indicate the location where the glacier sits on bedrock
rather than being aﬂoat (Bindschadler et al., 2011; Fricker
et al., 2002). Figure 7 suggests that the grounding zone is
near 2 km in our coordinate system, consistent with Rignot
and Steﬀen (2008) based on 2002 and 2003 surface ground
penetrating radar data.
The same analysis applied to the 2002 transect along the
central channel (Figure 7, bottom panel) shows similar agree-
ment along most of the ﬂight line; the exception is a ∼5 km
long region where the ISR-derived ice draft is much deeper
than that derived from the ATM elevations assuming hydro-
static equlibirum. Based on ICESat Track 220 across this re-
gion (Figure 4), the minimum elevation in the central channel
varies rapidly, from ∼18 m in 2002 to ∼6 m in 2004 (Figure
5b). This rapid change is consistent with advection of basal
crevasses seen in the along-ﬂowline transects of ice draft (Fig-
ure 3). The ISR-estimated ice thickness is comparable to ice
thickness of the ambient ice shelf at the same distance along
the fjord; therefore, we tentatively interpret this region as
a narrow basal channel that cannot be resolved by the ISR
data, so that the return echos come from the ice base on
either side of the channel. Given that the ice thickness in the
channel (∼150 m) is comparable to the width of the channel,
it is also likely that the force balance for the ice across the
channel is not fully hydrostatic but includes some bridging
stresses, similar to an ice-shelf grounding zone (Fricker and
Ice thickness change with time
Repeat-track analyses for ICESat Track 220 (Figures 4 and
5), assuming general hydrostatic balance, suggest that the ice
shelf is thinning at that location by 3.1±2.4 m a−1. If this
thinning applied to the entire ice shelf, then it would account
for 4.8 Gt a−1or about 40% of the total loss of mass from
the 12 Gt a−1crossing the grounding line.
The repeated ﬂight lines in 2002, 2007, and 2010 allow us
to determine the spatial extent of the ICESat-detected thin-
ning. The repeats were always within 300 m of each other,
with a root-mean-square deviation of 63 m and 73 m for the
track over the central channel and the ambient ice shelf, re-
spectively (not shown). From the transects of MODIS surface
reﬂectance gradients (Figure 6), there was negligible lateral
migration of the central channel during this period. The ISR-
derived ice draft data show dramatic changes in the central
channel within ∼10 km of the grounding line between 2002
and 2010 (Figure 8b); draft changed from 400 m in 2002 and
2007 to ∼100-150 m in 2010. There was no discernible change
on the ambient ice shelf apart from the downstream migration
of O(100) m high perturbations in the ice base (Figure 8a).
We use the ISR ice thickness and corresponding ATM eleva-
tion data to quantify ice thickness change along these ﬂight
lines. Using only surface elevation data from the ATM, we
deﬁne an average ice thickness in hydrostatic equilibrium b
as the integral from near the grounding line at y1= 2 km to
some distance y2> y1km along the ice shelf with L=y2−y1,
H(x, t) = 1/LZy2
H(x, y, t)dy (2)
This reduces the noise of point-by-point elevation compar-
isons of a moving ice shelf with rough surface topography
such as PG; see, for other examples, Thomas et al. (2009)
and Schenk and Csatho (2012).
Figures 9a and b show H(y) and b
H, respectively, for the
central channel and the ambient ice shelf for 2007 and 2010.
M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012 5
Taking the 2012 terminus location as the limit, i.e., y2= 48
km, we ﬁnd that the value of b
Hdecreased from 216 m in 2007
to 203 m in 2010 over the central channel, and from 352 m to
339 m on the ambient ice shelf for the same period (Figure 9b;
Table 4). We estimate that the ﬂoating ice shelf thinned by
an average of 13 m along ice ﬂowlines between 2007 and 2010.
Note that the 2007 observations were taken in the summer
after some seasonal surface melting had taken place, while
the 2010 observations were taken in the spring when there
was no surface melting. The actual time separation of the
two proﬁles is 2.53 years.
Based on this comparison, the annual rate of hydrostatic
thinning from 2007 to 2010 is 5.0 m a−1for both the ambi-
ent ice shelf and the central channel. This corresponds to a
surface lowering of about 0.53 m a−1and is consistent with
both the linear trend of ICESat across-shelf averaged eleva-
tion data of -0.33 ±0.26 m a−1for track 220 (Figure 5, Table
4) and the regional value of -0.25±0.06 m a−1estimated by
Gardner et al. (2013) for all of North Central Greenland.
The vertically averaged conservation of mass gives:
∂H/∂t +∇(~uH ) = ˙a−˙m(3)
where His the ice thickness, ~u = (u, v) is the vertically
averaged velocity vector with across- and along-stream com-
ponents uand v, ˙ais the diﬀerence between surface abla-
tion and accumulation ( ˙a > 0 implies net accumulation), and
˙mis the basal melt. The term ∇(~uH) can be rewritten as
We ﬁrst considered the steady-state mass balance, i.e., ∂H/∂t =
0. Since the nonlinear dynamic thinning H∇~u is small (Hig-
gins, 1991) and the across-stream ﬂow is negligible, equation
(3) simpliﬁes to
v0∂H/∂y = ˙a−˙m(4)
Using this result, we estimate a net value of ˙a−˙mfrom
thickness variations Halong the ice shelf and a constant
along-shelf velocity that we take as 1.25 km a−1, based on
feature tracking along repeat ﬂight lines from 2010 to 2011
(Figure 3). To calculate spatial gradients, we re-sampled the
irregularly spaced ice thickness proﬁle into a constant along-
glacier grid with δy = 50 m spacing. This minimizes numer-
ical artifacts when estimating the gradient ∂H/∂y and net
melt-rate from Equation (4).
The estimated net steady-state melt rate v0∂H/∂y varies
from about 18 m a−1near the grounding line to the surface
ablation rate ˙a≃-1.2 m a−1at the terminus (Figure 9c).
Averaging these values along each track for y∈[2,75] km
in each year, we ﬁnd almost identical net melt rates in 2007
and 2010, ∼4.9 m a−1for the central channel and ∼8.0 m
a−1for the ambient ice shelf (Table 4). Across the 16 km
wide ice shelf the central channel accounts for about 2 km;
hence we partition the ice shelf into 1/8 central channel and
7/8 ambient shelf. Applying these weights to the melt rates,
we attribute 6.3 Gt a−1of ice loss to the steady-state term
represented by divergence of the ice volume ﬂux. This is only
about half of the 12 Gt a−1ice ﬂux into the fjord at the
grounding line Rignot and Steﬀen (2008); the remainder is
provided by calving and non-steady thinning.
Between September 2007 and May 2010, the glacier thinned
at a rate ∂b
H/∂t of 5.0 m a−1(Figure 9b and Table 4). These
values are of the same order of magnitude as the melt rates
from the steady divergence (Equation 4 and Figure 9c). We
thus conclude that PG’s ice shelf was not in steady state prior
to its extreme 2010 and 2012 calving events. The net melt rate
is the sum of the non-steady and steady thinning, e.g.,
H/∂ t +v0
∂H (yk)/∂y = ˙a−˙m(5)
where ∂H (yk)/∂y describes the thinning due to the ice
divergence estimated along ﬂow lines from 2007 and 2010 data
(Figure 9c). The net melt rate thus becomes 9.9 m a−1for the
central channel and 13.0 m a−1for the ambient ﬂoating ice
shelf. These numbers agree with those of Rignot and Steﬀen
(2008) and Rignot et al. (2001); however, we have shown that
a signiﬁcant fraction of this melting is from the non-steady
The melt rate maxima near the grounding line reach about
20 m a−1in our calculations. These are about 20% smaller
than those observed in 2002/2003 by Rignot and Steﬀen (2008),
who used the full velocity divergence ∇(~uH) and the ice
thickness ﬁeld was measured by the ice proﬁling ISR along 10
along-glacier ﬂight lines. In contrast, we here used hydrostatic
ice thickness derived from surface elevation ATM data along
just two repeat lines. We hypothesize that the discrepancy
arises because the ice shelf is not always in steady state at
interannual time scales and not all regions of the ice shelf are
in hydrostatic equilibrium, so that errors arise through inter-
preting surface elevation changes as hydrostatically-compensated
We noted above that some sections of the along-ﬂowline
transects of ice draft show large basal crevasses (Figures 3
and 10). These crevasses are likely to be suﬃciently small
that they are not hydrostatically balanced. A section along
the western wall of Petermann Gletscher surveyed in 2011
revealed a sequence of 8-10 subsurface crevasses: ice thick-
ness changes from 400 m to 150 m within less than 500 m in
the along-ﬂow direction (Figure 10). These undulations occur
near the grounding line and do not have surface expressions.
They appear similar in form to basal crevasses observed re-
cently at Pine Island Glacier, Antarctica (Bindschadler et al.,
2011; Vaughan et al., 2012), but have not previously been ob-
served in North Greenland. Following Vaughan et al. (2012),
we hypothesize that stresses across these crevasses may con-
tribute to structural weakening of the ice shelf. They may also
impact basal melting; however, we do not know whether the
net eﬀect will be to increase or decrease mass loss by basal
We have examined temporal variations of the Petermann Glacier
(PG) ice shelf in three dimensions for the decade leading up to
major calving events in 2010 and 2012, using available repeat-
track airborne and ICESat laser altimeter data for the 2002-
2011 period and MODIS imagery for 2000 to 2012. Following
6M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012
the 2012 calving event, PG ice shelf was shorter than in any
previous measurements since the ﬁrst records from 1876. We
ﬁnd spatially averaged melt rates of 10-13 m a−1, consistent
with those reported by Rignot and Steﬀen (2008) and mod-
eled by Gladish et al. (2012). This rate exceeds the value re-
quired for steady-state mass balance (∼7-8 m a−1), resulting
in net thinning of 3-5 m a−1during the 2003-2010 period. The
larger rates of 5 m a−1are based on evolution of ice thickness
2007 to 2010, while the lower estimate is based on 2003-2009
trends in elevation estimated by ICESat Track 220, about 15
km north of the grounding line. Trends derived from ICESat
tracks closer to the terminus are not signiﬁcantly diﬀerent
from zero (not shown); however, the interannual variability
on these estimates is larger and the sampling size is smaller,
hence we cannot rule out linear trend values similar to those
for ICESat Track 220.
The role of ice-shelf basal channels and crevasses in net
basal melting and ice-shelf structural integrity requires fur-
ther exploration and modeling (Sergienko, 2013). Our anal-
yses suggest similar rates of thinning in the central channel
and the ambient ice shelf. This observation implies a greater
fractional reduction rate in channels, where the ice is thin-
ner, and raises the possibility that the weakening of ice in
the channels reduces the ability of the fjord’s side-walls to
constrain development of rifts that might be precursors to
further large iceberg calving events. We did not ﬁnd any evi-
dence of cross-fjord migration of channels in MODIS imagery
for the period 2002-2012 (Figure 6), suggesting that basal
melting within the channel does not occur preferentially to
one side of the channel. Further interpretation is hampered
by uncertainty in ice thickness measurements from airborne
radio-echo sounding across such narrow features, implying the
need for repeated surface ISR measurements and/or subma-
rine proﬁling of ice-shelf basal topography (Vaughan et al.,
2012; Stanton et al., 2013).
While the ice shelf of PG was not in steady state during
the decade leading up to the large calving events in 2010
and 2012, we lack suﬃcient information to attribute its mass
loss in this period to speciﬁc environmental changes. Ris-
ing subsurface ocean temperatures in adjacent Nares Strait
(M¨unchow et al., 2011) may lead to warmer water entering
the ocean cavity under the ice shelf of PG to increase basal
melting. However, we cannot discount the potential role of
atmospherically-driven increases in summer surface meltwa-
ter runoﬀ, either directly from the ice-shelf surface or as a
basal freshwater ﬂux across the grounding line from surface
and basal melting further upstream. Large-scale ice-shelf re-
treat through calving also modiﬁes the geometry of the fjord
and, therefore, the thermohaline and atmospherically-driven
circulation of incoming warm water and outﬂowing upper-
ocean cold, fresh water. Additional measurements and mod-
eling are required to understand how projected changes in
large-scale environmental conditions might impact the ocean/ice
exchange processes within the fjord.
We acknowledge ﬁnancial support from National Science Foun-
dation grant 1022843 (AM) and NASA grant NNX10AG19G
(LP and HAF). We thank NASAs ICESat Science Project
and the US National Snow and Ice Data Center for distribu-
tion of the ICESat data (see http://icesat.gsfc.nasa.gov and
http://nsidc.org/data/icesat). The data and/or data prod-
ucts from CReSIS were generated with support from NSF
grant ANT-0424589 and NASA grant NNX10AT68G. Hum-
frey Melling kindly provided data used in Figure 2. This is
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60 70 80 90
2003 July 25
60 70 80 90
2010 Aug. 13
60 70 80 90
2012 July 30
Fig. 1. MODIS images acquired over Petermann Gletscher on 25
July 2003 (left), 13 August 2010 (center), and 30 July 2012 (right).
White lines on the left image are ICESat tracks, labeled by track
number. Blue and red lines on the left panel are survey lines ﬂown
by NASA in 2002, 2003, and 2007. Blue lines in the center panel
show the 2011 ﬂightlines. Red indicates ﬂightlines along the cen-
tral channel while blue marks ﬂightlines along the ambient ice
shelf. The thick black line across the glacier near y= 0 km is
the grounding line location from Rignot and Steﬀen (2008). The
horizontal black line near y= 15 km in the middle panel shows the
location of MODIS surface reﬂectance proﬁles presented in Figure
6. The black rectangle shows an area of large and non-hydrostatic
crevasses shown in Figure 10. Dark areas within 2 km oﬀ the west-
ern wall (x∼70 km) are shadows cast by high terrain, not ice-free
10 M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012
Fig. 2. Time series of the length of the ice shelf from 1876 to
2012. Selected shape of terminus are shown as inserts (from Falkner
et al. (2011)). Co-ordinates (x,y) for insets are same as Figure 1.
Symbols indicate observations; dashed and solid time series show
two alternate and hypothetical evolutions with the slope indicating
a 1 km a−1advance of the terminus. Red line connects modern
satellite data showing large calvings in 1991, 2001, 2010, and 2012.
M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012 11
Fig. 3. Surface and basal elevation proﬁles along Petermann
Gletscher from the Airborne Topographic Mapper (ATM) and Ice
Sounding Radar (ISR) for May 7, 2011 and March 24, 2010 (top).
The ice surface elevation relative to EGM2008 geoid (middle) and
ice thickness (bottom) reveal strong spatial correlation between
years for a uniform 1.26 km a−1advance of the glacier: the asso-
ciated advection distance of ∼1.4 km a−1has been applied to the
2010 data. The glacier is grounded near y=1 km. The 2010 and
2012 break-up locations at y=56 km and y=44.5 km are indicated
by vertical lines.
12 M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012
Fig. 4. ICESat-derived surface elevation proﬁles from selected re-
peat ICESat tracks across Petermann Gletscher from north (Track-
1336, top) to south (Track-339, bottom); see Figure 1 for track lo-
cations. Black, blue, and red colors indicate 2003, 2005, and 2007
(2008 for Track-101) as the year of observation. Across-fjord dis-
tance is shifted for each track (but not year) so that x′=0 indicates
the time-averaged location of the central channel. Vertical lines
indicate cross-over location with airborne ATM track along the
ambient ice shelf. Large grey boxed regions for Track-220 indicates
data used to generate Figure 5.
M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012 13
Fig. 5. ICESat-derived elevations for a segment of Track-220
across Petermann Gletscher as the mean elevation along 9 km of
track (top panel) and minimum elevation (bottom panel) over the
central section of the glacier (see Figure 4 for the segment of Track-
220 used for these averages) as a function of time. Dashed lines
indicate the linear trend that is signiﬁcantly diﬀerent from zero at
95% conﬁdence for the averaged elevation -0.33±0.26 m a−1(top)
but not the minimal elevation -0.20±1.5 m a−1(bottom).
14 M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012
Fig. 6. Spatial gradients of surface reﬂectance derived from
MODIS imagery across Petermann Gletscher at y=15 km (see Fig-
ure 1 for location). (a) Average proﬁle for 2000 through 2012. (b)
Reﬂectance proﬁle by year. Vertical lines indicates the location of
the central channel near x=78 km with 250 pixel size in (a) which
also indicates a large secondary channel near x=82.75 km.
M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012 15
Fig. 7. Ice shelf proﬁles of Petermann Gletscher from Ice Sound-
ing Radar (ISR) and Airborne Topographic Mapper for May-22,
2002: (a) Surface elevation from ATM, (b) ambient ice shelf, and
(c) central channel. Vertical reference is EGM2008 geoid. Colored
ATM bottom traces are surface elevations scaled for hydrostatically
16 M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012
Fig. 8. ISR-derived ice draft and elevation along ﬂowlines for (a)
ambient ice shelf and (b) central melt-channel for 2002, 2007, and
2010. Notice the retreat and steepening of the central melt-channel
from 2002 to 2010 towards the grounding line.
M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012 17
Fig. 9. ATM-derived ice shelf proﬁles from Petermann Gletscher
for the central channel and ambient ice shelf surveyed in 2007 and
2010: (a) ice thickness, (b) cumulative average ice thickness, and
(c) ice ﬂux divergence that in steady state corresponds to a melt
rate. See Equations 2 and 4 for details. The legend for each panel
is provided in panel (b).
18 M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012
Fig. 10. Surface and basal elevation proﬁles along Petermann
Gletscher derived from Airborne Topographic Mapper (ATM) sur-
face elevation in blue and Ice Sounding Radar (ISR) in black for
May-7, 2011. The ATM-derived ice draft is based on ATM elevation
assuming a hydrostatically ﬂoating ice shelf. The inset shows basal
crevasses of ∼150 m vertical excursion embedded in 400 m thick
ﬂoating ice near the grounding line. Figure 1 shows the location of
M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012 19
Table 1. Petermann Gletscher ISR data: Date, across-channel lo-
cation (xi), and regression parameters of ISR ice thickness and ISR
surface elevations (off setiand ratioi) along the central channel
(i=1) and along the ambient ice shelf (i=2) for proﬁling ISR and
ATM sections. Listed parameters are determined from data along
a common 30 km long segment of ﬂoating ice shelf y∈[21,51]
km; see Figure 1 for locations. Tidal elevation estimates are from
Padman and Erofeeva (2004) for 81.25 N and 62 W.
Date x1(km)of f set1(m)ratio1x2(km)offset2(m)ratio2T ide(m)
2011, May-7 77.47 -7.5 0.1065 0.08
2010, Mar.-24 76.02 2.9 0.1658 77.51 6.9 0.1325 0.15
2007, Sep.-13 76.08 532.4 0.1300 77.46 591.5 0.1154 0.15
2003, May-14 76.06 587.3 0.0800 77.48 574.8 0.0738 0.30
2002, May-28 76.06 -29.7 0.1159 77.47 -28.9 0.1007 0.13
Table 2. Petermann Gletscher ISR and ATM data: Date and
regression parameters of ISR ice thickness and ATM elevations
(offsetiand ratioi) along the central channel (i=1) and along the
ambient ice shelf (i=2). Listed parameters are determined from
data along a common 30 km long segment of ﬂoating ice shelf
y∈[21,51] km; see Figure 1 and Table 1 for locations.
Date off set1(m)ratio1of f set2(m)ratio2
2010, Mar.-24 -4.0 0.131 +0.5 0.103
2007, Sep.-13 -0.9 0.123 -0.0 0.115
2003, May-14 -1.1 0.127 +1.2 0.106
Table 3. Mean and standard deviation of ice thickness to the east
and west of central channel for ICESat sections. See Figure 1 for
locations and Figure 4 for selected across-glacier thickness proﬁles.
Track Years Thickness East (m) Thickness West (m)
1336 6 16.5±5.0 12.7±4.6
101 7 23.0±5.5 17.5±6.2
220 10 33.4±6.0 30.9±11.7
339 9 87.2±10.7 71.8±11.7
20 M¨unchow and others: Interannual Changes of the Floating Ice Shelf of Petermann Gletscher, North Greenland from 2000 to 2012
Table 4. ATM-derived mass-balance estimates of net melt-rates
(m a−1) averaged along two repeat ﬂow lines near the central chan-
nel and the ambient shelf from Eq.-5 for the ice shelf to the 2012
terminus, e.g., y∈[2,48] km. The ﬂux-gate estimates are from
Rignot et al. (2001) using radar interferometry and ATM data.
Y ear v0Pk∂Hk/∂y ∂ b
H/∂ t T otal T hickness
(m a−1) (m a−1) (m a−1) (m)
Centr al C hannel 2007 4.9 217
2010 4.8 203
2007 −2010 4.9 5.0 9.9
Ambient Shelf 2007 8.0 352
2010 7.9 339
2007 −2010 8.0 5.0 13.0
IC ESat −220 2003 −2009 3.1±2.4 330
F lux Gates 1999 8.4 0.8 9.2