The frontal flux balance of a medium-sized tidewater glacier in western
Greenland in the summer is assessed by quantifying the individual components
(ice flux, retreat, calving, and submarine melting) through a combination of
data and models. Ice flux and retreat are obtained from satellite data.
Submarine melting is derived using a high-resolution ocean model informed by
near-ice observations, and calving is estimated using a record of calving
events along the ice front. All terms exhibit large spatial variability along
the ∼5 km wide ice front. It is found that submarine melting accounts
for much of the frontal ablation in small regions where two subglacial
discharge plumes emerge at the ice front. Away from the subglacial plumes,
the estimated melting accounts for a small fraction of frontal ablation.
Glacier-wide, these estimates suggest that mass loss is largely controlled by
calving. This result, however, is at odds with the limited presence of
icebergs at this calving front – suggesting that melt rates in regions
outside of the subglacial plumes may be underestimated. Finally, we argue
that localized melt incisions into the glacier front can be significant
drivers of calving. Our results suggest a complex interplay of melting and
calving marked by high spatial variability along the glacier front.
Introduction
The retreat of Greenland's tidewater glaciers may be among the
most noticeable manifestations of a changing global climate
. Tidewater glaciers act as thermodynamic
buffers as well as mechanical buttresses between the ocean and the main
Greenland ice sheet . The
speedup of the Greenland ice sheet observed since the early 2000s
has likely been caused (at least to some
degree) by the thinning of the glaciers' termini and, in
some cases, the disappearance of their floating tongues
. The processes that
determine the flux balance at the glacier front therefore impact the ice
sheet as a whole, yet a comprehensive understanding of these processes
remains elusive. Increased ocean and air temperatures are expected to further
increase the rates of glacier retreat in the coming decades
, lending additional weight and urgency to
the study of calving front dynamics.
For a retreating glacier, the delivery of upstream ice to the terminus is
outweighed by the loss of ice due to frontal ablation. At tidewater glaciers
this frontal ablation occurs predominantly through two distinct processes:
submarine melting and calving, both of which remain very difficult to
constrain observationally.
Recent studies have reported ways to measure submarine melting either
directly from repeat multibeam sonar surveys;, or
indirectly by considering the ocean heat transport toward the
glacier;. In most cases, however, melt is estimated using
parameterizations that require local ocean temperatures and water
velocities . Constraining melt rates at glacier fronts
then relies on accurate observations of the ocean properties at these
hard-to-reach ice–ocean interfaces and on finding appropriate
parameterizations that translate these observations to melt rates. The
continued scarcity of near-terminus data results in large uncertainties in
current melt parameterizations .
While melting is a continuous process, calving is discontinuous, highly
complex, and influenced by a multitude of environmental factors, as well as
the condition of the ice itself . In recent years, much
effort has been dedicated to studying the calving of tidewater
glaciers (see the review by ), yet a
comprehensive understanding of what processes and variables determine the
frequency and magnitude of calving events is still lacking.
Oftentimes calving and melt fluxes are not considered separately but rather
as a single ablation term, in particular when derived from satellite imagery
. In situ ablation data remain scarce, and previous
studies of explicit calving activities of Greenland's tidewater glaciers have
typically been limited to visible daylight hours see, for example, the
calving event catalogue of or somewhat indirect detection
methods such as teleseismicity and measuring
calving-generated surface gravity waves .
Finally, the calving and melt fluxes of glaciers are oftentimes described by
single (horizontally and vertically averaged) mean values
. However, both melting and calving can vary
substantially along the front of a glacier, with largely unknown implications
for the overall stability of a glacier front. For example, submarine melt is
enhanced in the vicinity of subglacial discharge plumes, leading to
pronounced undercutting and incisions into the ice front
. Spatially resolving these differences is challenging,
and in particular spatial calving distributions are difficult to obtain.
Here we use a multifaceted dataset for a first attempt at quantifying the
relative contribution of calving and melting and their spatial variability
along a glacier front. The dataset consists of both in situ and
remotely sensed observations of the front of Saqqarliup Sermia, a midsized
Greenland tidewater glacier. The dataset is unique in its detail, in its close
proximity to the glacier front, and in that it contains observations of all
of the main physical quantities of interest. The dataset consists of
(i) detailed bathymetry at the glacier front, (ii) high-resolution
ice-surface elevations, (iii) InSAR-derived ice velocities at and upstream
from the glacier front, (iv) a continuous 3-week calving event catalogue,
(v) local hydrographic measurements that allow for estimates of melt rates,
and (vi) multibeam sonar imagery of the underwater shape of the glacier
front. The spatial and temporal concurrence of these observations allows us
to compare and contrast the individual components that make up the frontal
mass budget of the glacier.
Specifically, we first derive ice flux and retreat using satellite data
collected over the observational period. We then compute submarine melting
using a numerical model that is constrained (and validated) by near-ice
hydrographic observations. Next, we estimate calving as a residual of the
other terms in the frontal mass budget and compare this estimate with the
observed calving frequencies. Finally, we bring our findings together to
assess the overall mass budget and discuss how calving may be enhanced by
highly focused melt “hot spots”.
(a) Landsat 8 image of the lower part of Saqqarliup Sermia
and Sarqardleq Fjord. The inset of Greenland shows the location of the
glacier. (b) Gridded bathymetry from in situ observations (readings
indicated by gray dots). Also shown is the surface height from ArcticDEM
(digital elevation map created by the Polar Geospatial Center from
DigitalGlobe, Inc. imagery). The red line shows the front position on 9 July
2013. (c) Surface height (blue) and bathymetry (black) along the glacier
front (following the red line in b). Also shown is the isostatic
bottom of the ice (blue dashed). Locations of the two main plumes are highlighted
in (b, c) by
and
▿; two additional surface dips are indicated by
▴ and •. The green horizontal line above
panel (c) and the letters A–D indicate the locations of the front
profiles shown in Fig. .
Field campaigns and physical setting
Saqqarliup Glacier and the adjacent Sarqardleq Fjord were visited during two
field seasons in the summers of 2012 and 2013. This site was chosen because
ocean properties and bathymetry could be measured within 100 m of the ice
front. Such observations are exceedingly difficult to obtain at larger
glaciers that often have an ice mélange that obstructs access and where
calving poses a major threat to equipment and personnel. The fjord is a
tributary of the Ilulissat Icefjord, with the northwest-facing front of the
glacier (Fig. ) located 30 km southeast of Ilulissat
Icefjord. At the glacier front, the fjord is about 5 km wide and the
terminus is mostly, if not completely, grounded.
Since 2004, the main northeastern part of the terminus has been retreating
more rapidly than the southwestern section, which now juts out by almost
1 km from the rest of the glacier front (Fig. S2 in the Supplement). This
part of the glacier, which we refer to as the “promontory”
(Fig. ), is grounded in shallow bathymetry and features
tall ice cliffs (40–50 m above mean sea level; see Sect. ).
Overall, the glacier advanced slightly between 1975 and the early 1990s, but
experienced an accelerating retreat from the mid-1990s until 2016
Fig. S2; . The front position has been relatively
stable from 2016 to 2018.
The 2012 survey, described by , revealed the presence
of two main subglacial discharge plumes along the glacier front, which, in
turn, drained the two dominant catchment basins. The plume entering the fjord
at the eastern edge of the promontory (Fig. ) has drainage an order
of magnitude greater and can result in an outcropping surface pool
. We refer to this as the “main plume”. While this
plume appears to be an annually recurring feature, its discharge is likely
amplified episodically by the cyclical drainage of the ice-dammed Lake
Tininnilik located to the southwest of the promontory
. We note that the dramatic retreat of the glacier
front in 2015 coincided with a major drainage event of Lake Tininnilik
. The second recurring plume, which we will refer to
as the “secondary plume”, is located closer to the northeastern margin of
the glacier (Fig. ).
In what follows, we use bathymetry data from both years, while the other in
situ observations were mostly collected during the 2013
season (see , for further details on the field
campaigns).
Bathymetry
The bathymetry of Sarqardleq Fjord was first mapped in detail during the 2012
and 2013 field seasons and the immediate bay in front of the terminus was
found to feature depths of up to 150 m . These initial
results were limited to data from a Remote Environmental Monitoring UnitS
(REMUS) acoustic Doppler current profiler (ADCP) and a shipboard ADCP, which
did not get closer than ∼200 m to the glacier front. Here, we
supplement these data with several additional near-terminus datasets from the
2013 field campaign (Fig. S1), which allows for a detailed bathymetry map
along the grounding line. The new data consist of circa 39 000 depth
readings taken with Jetyak-mounted and ship-mounted
ADCPs. In addition, there are approximately 6000 readings from a ship-mounted
National Marine Electronics Association (NMEA) bottom-range profiler and six
readings from expendable CTD sensors (XCTDs) deployed in the otherwise
undersampled region of the main plume. Most of these readings are within
10–100 m of the glacier front.
Figure c shows the new bathymetry at the glacier front as a
function of x, the distance along the glacier front. The bathymetry can be
split into two main regimes: for x<1800 m (the promontory) the glacier
is grounded in shallow waters and its surface heights are elevated
substantially above flotation. From here on, we refer to the eastern part of
the glacier (x>1800 m) as the “main” glacier. In 2013, the front of
the promontory was grounded on a sill that runs parallel to the glacier
front. This sill coincides approximately with the furthest advance of the
glacier in 1992 . By 2013 the main glacier had
retreated ∼500 m from the sill, but the promontory was still perched
on it in a bathymetry of 60 m in depth or less (Fig. c). Since
2013, this part of the glacier front has also retreated by several hundred
meters (Fig. S2). In 2013, the main part of the glacier front was in waters
of a depth of up to 150 m. A pronounced dip in bathymetry – suggestive of a
subglacial channel – is found near the location of the main plume (x= 2000–2400 m). A number of smaller dips are observed between x= 3400 and 4700 m. Beyond 4700 m the water depth decreases rapidly as one
approaches the northeastern shoreline.
Glacier surface topography
We obtained a digital elevation map (DEM) from an ArcticDEM overflight on
22 March 2013, which covers the full span of the Saqqarliup glacier front and
some of the upstream region (Fig. ). The DEM has a
horizontal resolution of 2 m and is capable of resolving individual
crevasses on the glacier surface.
The DEM shows that the front of the glacier is heavily crevassed and has
several pronounced dips in the surface elevation at the terminus. The ice
cliff is highest (up to 50 m) and most uniform in the region of the
promontory, while the main glacier is much more variable with
four distinct depressions that reach below 10 m in surface elevation (indicated
by symbols in Fig. ).
The coincident high-resolution surface elevation and bathymetry data near the
terminus enable us to compute the total ice thickness along the glacier
front,
which allows for an estimation of the total ice flux (discussed in
Sect. ).
Components of the frontal mass balance
In order for the mass budget along the glacier front to be balanced, the sum
of advective ice flux and frontal retreat must be balanced by total ablation
(i.e., by the sum of melting and calving fluxes). Here we consider a steady-state, vertically averaged balance. At a given point x along the glacier
front this can be written as
HR+vi=DM‾+C.
The left-hand side represents retreat and advection, where H is the ice
thickness (in meters), R is the retreat rate, and vi is the ice
velocity at the terminus (both in meters per year). The first term on the right
represents the ice loss due to submarine melting, where D is the draft of
the glacier (in meters) and M‾ is the depth-averaged melt rate (in
meters per year). The final term, C, is the ice loss due to calving (in
square meters per year). In this section we discuss the data used and assumptions
made to estimate each term in detail.
Ice velocity and advective ice flux
Several dozen ice velocity reconstructions of the lower part of the glacier
are available for the years 2009–2015 from InSAR data
. The mean ice velocity at the glacier front
(space- and time-averaged over all available fields) is ∼350 m yr-1 with minima
at the edges of the glacier. There is a notable peak in time-mean ice velocity (up to
750 m yr-1) near the location of the main plume (Fig. ).
A second region of elevated velocities is found near x=4500 m and is
more pronounced further upstream from the glacier front. The drainage
location of this second ice stream coincides with that of the secondary
plume. It is worth noting that the spatial distribution of velocities was
remarkably consistent during summer months (June–September) from 2012 to 2014
(Fig. b), followed by a substantial overall slowdown in 2015.
This slowdown is not included here as it has been linked to a major drainage
event of Lake Tininnilik and therefore is subject to
altogether different environmental forcing. In what follows, we will consider
the 2012–2014 mean July velocity profile along the glacier front. Using the
mean summer (June–September) velocities instead does not change the results
appreciably.
(a) InSAR ice velocity data near the glacier front. Shown
are mean summer (June–September) values averaged over 28 velocity fields,
collected during 2012–2014. Note that there is a consistent data gap near
the promontory. The shading represents the horizontal velocity magnitude.
(b) Velocity profiles along the glacier front. Here, as in all
figures, the orientation is looking down-glacier. The faint gray lines show
the 28 individual velocity fields. Also indicated are the approximate
locations of the two plumes
(,
▿).
The magnitude of the summer ice velocity along the glacier front,
vi(x), shown in Fig. b, together with the ice
thickness profile H(x), allows for an estimate of total advective ice flux
(Fig. ). This assumes plug flow, i.e., that the ice velocity is
approximately constant from the surface to the ice–bedrock interface. Note
that for a glacier with no sliding and uniform temperature, the
depth-averaged velocity is 80 % of the surface velocity. For fast-flowing
tidewater glaciers with concentrated deformation at depth, such as
Saqqarliup, plug flow is therefore considered a good approximation
.
(a) Mean July ice velocity along the glacier front in blue
(right vertical axis). Here we used cubic interpolation to fill the data gap
shown in Fig. b. In red (left vertical axis) is shown the
estimated ice thickness along the glacier front, obtained by computing the
difference of the surface and bathymetry profiles of
Fig. c. The red dotted line shows the ice thickness at the
glacier front assuming the ice is locally in isostatic equilibrium
everywhere. (b) Ice flux per unit width along the glacier front (in
black), computed from the product of velocity and thickness (shown in
a). The shaded gray areas under the curve show the ice-flux range
due to potential flotation. This is a result of the thickness ranges
indicated as red shaded areas in (a). Uncertainties for thickness,
velocity, and ice flux are shown by the red, blue, and black standard error
bars, respectively. Also indicated are the approximate locations of the two
known plumes
(,
▿), which coincide with two areas of possible
flotation.
We note that the thickness data suggest that the terminus might be floating
at several locations: the four highlighted surface depressions at the glacier
front are all low enough to raise the isostatic bottom of the ice above the
local sea floor. The locally isostatic bottom of the ice is indicated in
Fig. c (blue dashed line). Here we assume an average ice
density of 883 kg m-3, obtained as a mean of low and high values
commonly used for glacier and ice shelf front densities, namely
850 kg m-3 and 917 kg m-3 (pure ice). The
surrounding ice and the associated stiffness of the glacier will likely
prevent the ice from assuming local isostasy along the glacier front.
However, the isostatic bottom can be used to compute a lower bound on the ice
thickness in regions where the ice may be floating. It may be speculated that
the ice appears to be floating in these regions due to undercutting by
submarine melt (which in turn is associated with rising discharge plumes, as
discussed in Sect. ). The ice would be grounded everywhere else.
In particular, the ice surface is elevated substantially beyond its isostatic
height in the region of the promontory. The uncertainty in ice thickness
associated with the glacier potentially floating at several points is
illustrated by the shaded areas in Fig. . In the figure, the
upper bound of the ice thickness assumes a fully grounded glacier front,
while the lower (dashed) bound assumes local isostasy everywhere. The ice
flux is highest when assuming a fully grounded glacier, while a partially
floating glacier front would have a correspondingly reduced flux.
Changes in glacier front position
Superimposed on the aforementioned long-term retreat of the glacier front
over the past decades (Fig. S2) we observe a seasonal advance–retreat cycle
during 2012 and 2013 (Fig. ). A total of 27 front positions
between January and October 2012 and between January and October 2013 were digitized from
TerraSAR-X satellite images. The 15 profiles from 2013 are shown in
Fig. a. Both years exhibit a clear, albeit modest, seasonal
cycle in terminus position, with a mean advance for the entire front of
roughly 30 m from January through April/May, followed by a more rapid retreat
from June to September of ca. 80 m (Fig. b). However, there
is substantial variability along the glacier front in this cycle. Near the
edges of the glacier, and in particular at the promontory, the glacier
exhibits a much reduced advance–retreat cycle, and more variable regions are
found in the main dynamic section of the glacier.
Seasonal advance and
retreat of glacier front. (a) The total 15 front profiles acquired
from February to September 2013; the legend lists every second profile. The
thick red and blue profiles represent the May–June and September averages,
respectively. Also indicated are the locations of the two plumes
(,
▿). (b) Mean front position, shown as an anomaly from
the yearly mean position. The 2012 values are shown in gray and 2013 in
black. The 2013 spring profiles used
in (a) are highlighted in red, fall profiles in blue, and July
profiles in green. The vertical dotted lines demarcate the period from 12 to
31 July during which calving was observed. (c) Retreat rates,
R(x), along the glacier front. Positive R represents glacier retreat and
negative R glacier advance. The dashed line represents the spring–fall
2013 mean retreat rates; the solid line shows the retreat rates between 9
and 31 July, computed from the
profiles marked green in (b).
R(x) is computed as the rate of retreat perpendicular to the initial
glacier front. The most rapid retreat in 2013 was observed at the time of the
July study period. Figure b shows the spatial-mean seasonal
retreat anomalies for 2012 and 2013, with profiles from 9 and 31 July 2013
highlighted in green. Such rapid retreat is spatially highly variable
(Fig. c) and strongly impacted by sporadic large
individual calving events. Longer-term mean retreat rates, computed from
average spring and fall glacier front positions (highlighted in
Fig. in red and blue, respectively) may therefore be more
representative on longer timescales.
Submarine melting
Submarine melt rates at Saqqarliup Sermia during summer 2013 have been
estimated by . Here we provide only a brief overview
of the approach and build on the results of to
investigate the glacier's flux balance. Melt rates within the two plumes were
estimated using standard buoyant plume theory
.
Melt rates outside of the plumes were estimated using a high-resolution
numerical model of the fjord in the Massachusetts Institute of Technology
general circulation model (MITgcm), which has become the leading model for
simulating the circulation and water properties of glacial fjords and for
estimating the resulting submarine melt rates
e.g.,.
Both buoyant plume theory and MITgcm were forced with runoff from the
regional climate model RACMO and initialized with hydrographic profiles from
the fjord. also presented observationally inferred
melt rates using water property and velocity measurements collected within
100 m of the calving front. In each approach, then
used the standard three-equation melt rate parameterization of
to convert the modeled or observed water properties
and velocities to an estimated submarine melt rate. There is good agreement
between the melt rates estimated with MITgcm and with
observations (, their Fig. 3). Here,
we only consider the modeled melt rates (Fig. ), which have
the advantage of covering the whole extent of the glacier front (unlike rates
inferred from observations, which have data gaps in and around the plumes).
(a) Time-mean melt rates along the glacier front as
estimated from MITgcm, adapted from , their Fig. 3f.
The bathymetry in the model (white) is based on that of
. (b) Melt rates averaged inside the main
discharge plume (blue) and outside of both plumes (red).
There is large spatial variability in submarine melt rates along the glacier
front (Fig. ). Submarine melt rates are highest (in both a
depth-averaged and maximum sense) within the two plumes in which the
discharge of buoyant surface meltwater from beneath the glacier gives high
water velocities. Outside of the two plumes melt rates are much smaller in a
depth-averaged sense; however the lateral circulation excited by the plumes
combines with warm surface waters to give high melt rates near the surface
outside of the plumes (Fig. b; see also
).
While these melt rate estimates represent the state of the art in terms of
melt rate modeling, we stress that they are based on a melt rate
parameterization that has not been confirmed by observations, especially for
the case of a mostly vertical front of a tidewater glacier. The uncertainty
associated with these melt rate estimates is further discussed in
Sect. .
Calving frequency and distribution
Calving events were detected over a 19-day period from 12 July to 31 July
2013, using two pressure sensor moorings located on the western and eastern
banks of the fjord, each at a distance roughly 2 km from the nearest point
along the glacier front (Fig. a). The dispersion of waves
that are created by individual calving events can be inverted to estimate the
distance between the mooring and the origin of the wave. Wave packets that
are detected by both moorings can be used to triangulate the time and
position of the corresponding calving event . For the
present dataset, this method has been validated against a photography-derived
calving record and good correspondence was observed (not shown). The study by
provides a detailed description of the method.
(a) Spatial calving distribution as estimated from pressure
sensor data; the shaded rectangle indicates the promontory. The inset shows a
close-up of the glacier front and adjacent fjord, with the red rectangle
outlining the region of interest and red stars indicating the location of the
wave moorings. (b) Calving count along the glacier front, obtained
as the total number of calving events detected within a 300 m running window
along the glacier front (red bars, left axis). Also shown is an estimate for
the relative calving volume, computed from the product of the frequency of
calving events and the corresponding magnitudes of the detected waves (black
line, right axes). Plume and surface dip locations are indicated as in
previous figures.
In total, 336 calving events were identified using this method over the
period that both sensors were recording. Figure a shows the
location and wave amplitude of the individual events. The calving frequency
distribution along the glacier front is illustrated in
Fig. b.
A pronounced peak in frequency is found at the promontory, where shallow
bathymetry causes the glacier to be elevated substantially beyond its
isostatic height of flotation. With its high ice cliffs the promontory can be
regarded as a region that is subject to a rather different calving regime
than the rest of the glacier.
For the main glacier,
we observe a peak in calving activity at a distance x≈2400 m along
the glacier front, near the concave bend in the glacier front. A second peak
in calving activity is found around x≈4300 m. Both peaks appear
slightly offset from the location of the two plumes. The calving activity is
lowest at the northeastern edge of the terminus.
Even though this dataset presents a rather accurate record of calving
frequencies, it remains challenging to infer a total volume of calved ice
. This is due to the different modes of calving (e.g.,
ice-cliff calving versus submarine calving), as well as the different shapes
of calved ice blocks and the differing heights from which they fall (or
depths from which they rise). Distinguishing between these events from the
pressure sensor data is a difficult task and beyond the scope of this study.
The pressure sensors do record an amplitude of the incoming wave packet
associated with a given calving event. Crudely approximating that this
amplitude is proportional to the size of the calved ice, we can estimate a
relative calving volume (black curve in Fig. b). However,
since, for example, a small cone-shaped ice block
can act as a more efficient wave generator than a large flat piece of ice
(Nicholas Pizzo, personal communication, 2018; ), it
is difficult to ascertain a direct relation between wave amplitudes and
calving volume. In what follows we therefore only consider the calving
frequency record and will scale this record such that the resulting calving
flux approximately closes the mass budget at the glacier front (see
Sect. ). Given the limitations of the data, we take such a
scaling to be the most justifiable first-order approximation, supported by
the rather uniform distribution of estimated calving event sizes along the
glacier front. The scaling factor is chosen such that the mean calving volume
is equal to the mean of the residual, i.e., 〈C〉=〈H(R+vi)-DM‾〉, where 〈〉
denotes the spatial mean along the glacier front.
Overall flux balance and spatial variability
In what follows we consider the volume flux across the glacier front during
the summer of 2013. We make the assumption that this flux was steady during
the study period and ignore time dependencies of the individual terms in
Eq. ().
To compare the different terms in the mass budget, we consider the retreat
rate as computed from the two fronts measured on 9 and 31 July 2013 since
this is almost the exact time window of the calving observations
(12–31 July). For the advection term we use the July average over the years
2012–2014 since the July 2013 ice velocity fields have substantial data
gaps at the glacier front. However, as discussed above, there is little
interannual variability in vi over these years, so the 3-year
mean likely gives a close approximation to the July 2013 velocity field.
Front retreat and advective flux along the glacier front (i.e., the left-hand
side of Eq. ) are shown in Fig. a. The sum of
ice advection and retreat is compared to the estimated melt fluxes in
Fig. b. Figure c shows the calving flux
as estimated from the observations (Sect. 3.4), compared to the residual C
of the other three terms in Eq. (), such that C=H(R+vi)-DM‾.
Flux balance along the glacier front. Dashed lines indicate
uncertainties as discussed in the text. (a) The green line
represents the July 2013 retreat rate and the blue line the advective ice
flux. (b) Sum of retreat and advection (gray) and melt flux
(orange). (c) Approximate closure of the volume flux budget along
the glacier front. The black line shows the residual of advection plus
retreat minus melting, while the red line shows the observational calving
estimate as in (b). Note that the calving flux has been scaled to
approximately close the budget for the main part of the
glacier.
High spatial variability along the glacier front
A striking feature of almost all components of this multipartite dataset is
their high spatial variability along the glacier front.
Away from the margins, the ice thickness at the front ranges from thin
(<40 m) sections near the northeast edge to ∼100 m along the
promontory and up to 192 m near the main plume, with substantial variations
throughout. Overall, we observe a mean thickness of 128 m with a variability
of ±38 m (1 standard deviation).
We find that the advective flux is the most uniform component; still it is
notably suppressed at the promontory and highest near the outflow location of
the main plume (Figs. , a).
The retreat rates are of comparable magnitude to the advective flux overall.
However, the retreat rates are spatially extremely variable, in particular
the observed July 2013 rates, which exhibit three regions of enhanced
retreat, two of which are close to the two discharge plumes, with peaks at x=2400 and 4400 m (Figs. c, a). Averaged
over longer time periods, the retreat rates become more uniform. Over shorter
time periods retreat rates are more strongly influenced by individual calving
events.
The melting estimates feature two pronounced maxima at the plumes and are
small everywhere else (Fig. b). The maximum melt flux value
at the main plume (1.5×105 m2 yr-1) is slightly higher
than the mean retreat and advective flux values (1.0×105 and
0.8×105 m2 yr-1, respectively). Outside the two plumes the
mean melting flux (0.04×105 m2 yr-1) is an order of
magnitude lower than inside the plume and than the other budget terms.
Dividing these depth-integrated flux values by the average thickness
(128 m), we obtain depth-averaged velocities for each term. These are ice
advection of 780 m yr-1, retreat of 620 m yr-1, maximum melt rate
at the main plume of 1200 m yr-1, and mean melt rate outside the plumes of
30 m yr-1.
Calving frequencies are strongly enhanced at the promontory, which – given
the reduced advection and retreat in this area – implies that calved pieces
are in general smaller here. Since we are unable to adequately distinguish
between the different calving sizes, the heightened calving activity at the
promontory results in a large discrepancy between the computed residual C
and the observationally estimated calving flux in that region
(Fig. c). We may also be underestimating the advective flux
at the promontory slightly since we only consider horizontal velocities, and
the ice flow may have a non-negligible vertical component as the glacier
rides onto the local sill. Even though calving frequencies are overall lower
for the main part of the glacier, we observe two slight local maxima, slightly offset from the plumes
(Fig. b). The lowest calving frequencies are found between
the two plumes in the region farthest from both plumes. The two peaks in
depth-averaged melt flux (Fig. b), co-located with the two
discharge plumes, are just offset from the two maxima in frontal retreat and calving.
Spatially integrated mass budget
Integrated along the main part of the glacier front we estimate an ice
advection rate of 0.2±0.05 Gt yr-1 and a retreat rate of 0.3±0.03 Gt yr-1. This gives ∼0.5 Gt yr-1 as a best estimate for the total rate of ice
loss. The uncertainty in ice advection corresponds
to 1 standard deviation in the spread of mean July ice velocities. The
uncertainty in the retreat rate is largely due to the somewhat arbitrary
selection of “before” and “after” dates, and the resultant
disproportionate impact of individual calving events. The error reported here
is 1 standard deviation in the difference in retreat when choosing the
frontal profiles of 28 June (instead of 9 July) as the before date or
22 August (instead of 31 July) as the after date.
Integrating the estimated melt over the main glacier front gives a total
melting flux of 0.03 Gt yr-1. This would suggest that ∼0.47 Gt yr-1 (or 94 %) of ablation occurs in the form of calving,
thus implying that the glacier balances the ice flux almost exclusively
through calving (except in the narrow regions at the discharge plumes). The
lack of an ice mélange in the fjord and the anecdotal observation of
limited calving are, however, at odds with this finding. This raises the
question of whether the melt term – estimated using state-of-the-art
parameterizations informed by observations very close to the ice front – is
incorrect? This is discussed further in Sect. .
While we have no direct measurement of calving volume, we can close the
integrated mass budget by scaling the observed relative calving frequencies
to give the required total calving flux of 0.47 Gt yr-1
(Fig. c). This corresponds to a mean calving flux of
1.7×105 m2 yr-1 along the glacier front (compared to a
mean melting flux of 0.1×105 m2 yr-1). Again dividing by
the average thickness, we estimate 1300 m yr-1 of ice loss due to calving, compared
80 m yr-1 of melting.
Variations in the vertical glacier front profile
A final piece of observational evidence that may help in the interpretation
of the results above is provided by point cloud images of the glacier front
profile. These were collected during the 2013 field season using an
autonomous surface vehicle, the Woods Hole Oceanographic Institution
“Jetyak” . Among other instruments,
the Jetyak carried a multibeam sonar that was mounted sideways facing the
glacier, which collected three-dimensional maps of the underwater portion of
the glacier front. Further details of the Jetyak's operation and data can be
found in . Here, we highlight several characteristic
frontal profiles. Figure shows a point-cloud transect of the
northeastern flank of the glacier, as well as four vertical line profiles at
different locations along the transect.
Multibeam sonar data of glacier front from 26 July 2013.
(a) Map illustrating the location of the multibeam cross sections
A–D and the two plumes
(,
▿). (b) The 3-D point-cloud transect showing a part of the
eastern side of the glacier (distance along glacier front,
∼ 4000–4800 m). Data are color-coded by depth below sea level.
Indicated are the locations of the four cross sections A–D shown
in (c, d). (c) Cross sections A and B near subglacial
plume, exhibiting characteristic undercutting. (d) Cross sections C
and D away from plume, showing submarine protrusions without
undercutting.
The first two profiles (A and B) are placed near the secondary plume. Both
profiles are marked by two features: (i) a sloped upper 20–25 m, which
results in the above-water cliff of the glacier being set back by 10–20 m,
relative to the most ocean-ward point of the glacier face, and (ii) up to 10 m of undercutting below 40 m
in depth, such that the protrusion beyond
the above-water cliff is most pronounced at depths of 20–40 m, and the ice is
substantially eroded at greater depths. This is likely caused by the rising
subglacial plume, which leads to preferential melt of the deeper parts of the
glacier front . Note that the high
turbidity of water within the main plume prevented the Jetyak from surveying
the shape of the glacier front occupied by that plume.
Profiles C and D, which are located far from the plume, also feature said
underwater ice protrusion; however, they show no signs of undercutting. The
presence of such net-buoyant underwater protrusions and their potential
impact on calving has been studied previously
and will be discussed
further in the next section.
We note that the bathymetry reaches depths of around 130 m for this part of
the glacier and the bottom ∼50 m is unfortunately not captured by the
multibeam sonar. However, the profiles located near the melt (A and B) can be
expected to be further undercut below the observed range
, while profiles C and D likely do not feature such
undercutting.
The role of melting in the frontal mass budgetUncertainty in melt rate estimates
The finding that calving appears to make up almost the entire loss of ice is
somewhat unexpected, in particular since during the study period the
glacier's calving activity was limited to relatively small events, and the
fjord was by-and-large devoid of icebergs. Furthermore, the melt rates used
here are roughly double that of what previous estimates would have been since
we account for additional melt that arises from the recirculation of warm
ambient surface waters . However, melting supposedly only
makes up ∼6 % of the total ablation.
Given the lack of observational verification of the current melt rate
parameterization, it is worth considering end-member melt rate scenarios. A
key parameter in the melt rate parameterization is the thermal Stanton
number, which directly controls the rate of transfer of heat from the ocean
to the ice. Its canonical value is based largely on field observations at a
cold Antarctic ice shelf and there are as yet no strong observational
constraints from tidewater glaciers. Furthermore,
have recently argued for a larger Stanton number based on
numerical simulations. We
thus consider lower and upper bounds for melt rates in which the thermal
Stanton number is respectively reduced and increased by 50 %
(Fig. b, c).
To obtain the upper-bound melt rate scenario, we also increase the
outside-of-plume water velocity that enters the melt rate parameterization.
While vertical velocities inside of plumes might be considered reliable based
on well-validated plume theory , one could argue that
the mean modeled outside-of-plume velocities may be too small for a number of
reasons, including coarse model resolution and the lack of tides, surface
waves, and calving events that may excite water motion. These factors might
crudely be taken into account by placing an additional velocity in the melt
rate parameterization. Such an approach has some precedent with the inclusion
of tides beneath ice shelves . In the upper-bound melt
rate scenario, we thus add 0.2 m s-1 to the outside-of-plume water
velocity entering the melt rate parameterization.
In the lower-bound melt rate scenario, melting accounts for an even smaller
fraction of mass loss than in our best estimate but is still significant
inside the plumes. In the upper-bound melt rate estimate, melting accounts
for a significant proportion of mass loss both inside and outside of the
plumes (Fig. b). Clearly this is an observationally
under-constrained discussion, and we emphasize that these upper and lower
bounds are very rough error estimates as the state of understanding of
submarine melting does not yet permit rigorous quantitative assessment of
uncertainties. However these bounds do show that through reasonable modification
of the melt rate parameterization, melting can account for a larger fraction
of the ice loss than reported in our best estimate. Even by introducing these
uncertainties, however, the analysis presented still indicates that calving
is the dominant mode of mass loss for most of the glacier front (except at
the localized melt plumes).
Impact of melting on calving
In addition to balancing the frontal ice flux, the data allow us to examine
how melting and calving may be interlinked. Specifically, one consequence of
melting being focused on narrow regions is that it can lead to sharp
incisions in the glacier front, which in turn may enhance calving.
found that fjord-scale circulations driven by plumes
can result in enhanced submarine melting near the fjord surface in regions
distant from the plume Fig. b). This near-surface melting
has in turn been suggested as a potential driver for large calving events at
glacier fronts that are floating or close to floating :
preferential near-surface melting at the glacier front leads to a horizontal
melt incision near the water surface, which in turn causes erosion of the
above-water ice cliff. As a result, the front of the glacier is left with an
underwater protrusion (or “ice foot”) as in profiles C and D of
Fig. . This frontal profile is statically unstable since the
ice foot is net buoyant and exerts bending stresses on the glacier
. Calving events occur when
such stresses surpass the yield strength of the terminus. It is likely that
profiles C and D represent sizable ice feet that exert bending stresses that
enhance the calving flux in this region.
Furthermore, it is possible that the regions adjacent to the meltwater plumes
are more prone to calving since the high melt rates at the plumes cause
vertical incisions in the glacier front . These in turn
would reduce the transverse (i.e., along-front) stability of the terminus
and trigger further calving. A surface expression of such a vertical incision
in the glacier front can be found near the main plume in the profile of
August 2012 (Fig. S2). Considering the particular geometry of Saqqarliup, as
the two main plumes drive rapid melt near the two edges of the main part of
the glacier, this may cause the entire front between the plumes to be more
prone to calving, in particular since we have found this region to be close
to (or at) flotation.
In summary, from the observations presented in the previous sections, we
propose that there are two distinct regimes driving ablation at Saqqarliup:
(a) melting-dominated ablation in spatially confined regions near the
discharge plumes, and (b) calving-dominated ablation in the regions away from
the plumes (which may be enhanced by near-surface horizontal melt incisions).
This is further supported by the local minima in calving activity at the
location of the two discharge plumes (Fig. b). The two
ablation regimes are summarized in the schematic of Fig. .
Schematic of two distinct ablation regimes.
(a) Melt-dominated regime: the vertical structure of melting due to
a rising subglacial discharge plume that entrains warm ambient water results
in substantial undercutting of the glacier front (as in profiles A and B in
Fig. ). These front profiles likely do not cause large
calving events, with calving mostly confined to the smaller above-water cliff.
Profiles are drawn for an earlier time t1 and a later time t2 by which
the glacier has retreated mostly due to melting.
(b) Calving–dominated regime: here the growth of sizable and
buoyant underwater feet (as in profiles C and D in Fig. ) can
accelerate calving, with the melt contribution confined to a small region
near the water surface. Again, profiles are shown at t1 and t2 (pre- and
post-calving), as part of the “footloose” calving cycle
.
Conclusions
We have presented a multifaceted dataset of a Greenland
tidewater glacier and its surroundings. The unique dataset enables us to
investigate the individual terms that determine the flux balance along the
glacier front.
We find that the individual terms that comprise the glacier's frontal mass
budget are marked by high spatial variability. Ice velocities feature maxima
that coincide with troughs in the bathymetry and locations of subglacial
discharge plumes. The retreat rates are spatially particularly variable when
calculated over shorter periods of time (days to weeks) and are likely
dominated by somewhat stochastic calving events over such short timescales.
Estimated submarine melt rates from numerical modeling of fjord circulation
show rapid melting within the two discharge plumes and more widely at the
fjord surface but limited melting elsewhere. If we use the inferred melt
rate to scale the calving flux we find that 94 % of the mass balance of
this glacier must be balanced by calving. This finding appears to be at odds
with the observation of limited calving and the lack of icebergs in the
fjord. We suggest that the numerical model – even though constrained by
direct measurements and using the standard melt parameterization – may
underestimate melting outside of the plumes, indicating that current melt
models for tidewater glacier fronts may need to be reviewed and should be
treated with caution.
The spatial variability of the observed processes suggests the presence of
two distinct ablation regimes: a melting-dominated regime near the discharge
plumes and a calving-dominated regime away from the plumes. We discuss that
melting, through its horizontal and vertical variability, may play an
important role in driving calving, thus having a dynamic effect out of
proportion to the fraction of mass lost by melting. If calving is indeed
dependent on the localized melt rates, this may have far-reaching
implications for the overall stability of the glacier. Understanding the
impact of these spatially highly variable processes on ice sheet dynamics
should thus be a priority in the study of ice–ocean interactions.
Data availability
Temperature and salinity profiles collected near the glacier
front are available at 10.18739/A2B853H78. Water pressure data used to
detect calving events are available at 10.18739/A24Q7QP6V. ADCP-derived
water velocities near the terminus are available at
https://data.nodc.noaa.gov/cgi-bin/iso?id=gov.noaa.nodc:0177127. InSAR-derived surface ice velocities
are available at https://nsidc.org/data/nsidc-0478/versions/1.
The supplement related to this article is available online at: https://doi.org/10.5194/tc-13-911-2019-supplement.
Author contributions
TW led the analysis and integrated the data. FS, SD, and CR
planned and supervised the project. FS, SD, CR, LS, and HS carried out the
field work. DS developed the melt model and performed the melt simulations.
TW, DS, and FS drafted the paper. All authors discussed the results and
commented on the paper.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
We acknowledge support from the Woods Hole Oceanographic Institution Ocean
and Climate Change Institute Arctic Research Initiative, and NSF OPP-1418256
and OPP-1743693, to Fiamma Straneo and Sarah B. Das. Till J. W. Wagner was
further supported by NSF OPP award 1744835. Geospatial support for this work
was
provided by the Polar Geospatial Center under NSF OPP awards 1043681 and
1559691. DEMs provided by the Polar Geospatial Center under NSF OPP awards
1043681, 1559691, and 1542736. Donald A. Slater acknowledges the support of
Scottish Alliance for Geoscience, Environment and Society early-career
research exchange funding.
Edited by: Benjamin Smith
Reviewed by: two anonymous referees
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