Calving-front dynamics is an important
control on Greenland's ice mass balance. Ice front retreat of
marine-terminating glaciers may, for example, lead to a loss in resistive
stress, which ultimately results in glacier acceleration and thinning. Over
the past decade, it has been suggested that such retreats may be triggered by
warm and salty Atlantic Water, which is typically found at a depth below
200–300 m. An increase in subglacial water discharge at glacier ice fronts
due to enhanced surface runoff may also be responsible for an intensification
of undercutting and calving. An increase in ocean thermal forcing or
subglacial discharge therefore has the potential to destabilize
marine-terminating glaciers along the coast of Greenland. It remains unclear
which glaciers are currently stable but may retreat in the future and how far
inland and how fast they will retreat. Here, we quantify the sensitivity and
vulnerability of marine-terminating glaciers along the northwest coast of
Greenland (from 72.5 to 76∘ N) to ocean forcing and subglacial
discharge using the Ice Sheet System Model (ISSM). We rely on a
parameterization of undercutting based on ocean thermal forcing and
subglacial discharge and use ocean temperature and salinity from
high-resolution ECCO2 (Estimating the Circulation and Climate of the Ocean,
Phase II) simulations at the fjord mouth to constrain the ocean thermal
forcing. The ice flow model includes a calving law based on a tensile von
Mises criterion. We find that some glaciers, such as Dietrichson Gletscher or
Alison Glacier, are sensitive to small increases in ocean thermal forcing,
while others, such as Illullip Sermia or Cornell
Gletscher, are remarkably stable,
even in a +3∘C ocean warming scenario. Under the most intense
experiment, we find that Hayes Gletscher retreats by more than 50 km inland by 2100 into a deep trough,
and its velocity increases by a factor of 3 over only 23 years. The model
confirms that ice–ocean interactions can trigger extensive and rapid glacier
retreat, but the bed controls the rate and magnitude of the retreat. Under
current oceanic and atmospheric conditions, we find that this sector of the
Greenland ice sheet alone will contribute more than 1 cm to sea level rise
and up to 3 cm by 2100 under the most extreme scenario.
Introduction
Over the past 2 decades, many glaciers along the northwest
coast of Greenland have been retreating and accelerating, sometimes
dramatically e.g.,. It has been suggested that
the retreat of these glaciers is initiated by the presence of warm and salty
subsurface Atlantic Water (AW) in the fjords
e.g.,. This water
is typically found 200 to 300 m below the surface
e.g.,. Surface runoff has also been
increasing over the past decades
, which enhances subglacial
water discharge at the base of calving fronts. This freshwater flux enhances
the circulation of the ocean in the fjord , which in turn
further increases the melting rate and therefore the rate of undercutting at
the calving face of marine-terminating glaciers. While we expect both surface
runoff and ocean heat content to continue to increase over the next
century, it remains unclear how they are going to affect ice dynamics and
ice discharge into the ocean.
While geographically close, individual outlet glaciers along the coast
respond differently to frontal forcing. It has been proposed
e.g., that this heterogeneity in glacier
behavior may be due to differences in bed topography and fjord bathymetry,
which may prevent AW
from interacting with calving fronts
due to the presence of sills in the fjord. It has also been suggested that
many glaciers are currently resting on pronounced ridges, or in regions of
lateral constrictions, which stabilizes the glaciers' calving fronts and
prevents warm water from dislodging them from their current position
. The idea that ice front dynamics is, to a large extent,
controlled by subglacial topography was first investigated in Alaska
and was more recently extended to Greenland
e.g.,. It is not certain
to which degree the glaciers of the northwest coast remain sensitive to
enhanced thermal forcing from the ocean: some glaciers are on the verge of a
fast and extensive retreat, others may continue retreating at the same rate,
and some may remain stable. Numerical modeling can help us assess the
sensitivity of these individual glaciers to ocean temperature along the coast
and their potential for fast retreat and mass loss, which affects sea level
rise.
While many model-based studies have focused on the response of the Greenland
ice sheet to climate change, they either (i) did not include moving calving
fronts e.g., or (ii) were
based on flow-line models e.g., that do not capture
changes in lateral drag well (since lateral drag is parameterized) or the
complex three-dimensional shape of the bed that affects the retreat rate
, and (iii) did not consider undercutting. Here,
we want to overcome these limitations by using a plan-view model with a
moving calving front. The calving-front position is allowed to move and is a
function of ice velocity, calving rate, and rate of undercutting. While much
progress has been made in terms of capturing ice flow through improved
datasets and through the development of new stress
balance solvers not based on the Shallow Ice Approximation, calving and
undercutting remain areas of active research. We use two existing
parameterizations of ocean undercutting and calving
. While these parameterizations are approximations and
do not include all the physics involved in ice–ocean interactions, they have
been tested with reasonable success on several glaciers of Greenland
e.g.,. The objective
of this study is not to make projections, as we are not forcing the model
with given representative concentration pathway (RCP) scenarios, but to
assess the sensitivity of northwestern Greenland using existing
parameterizations for iceberg calving and undercutting.
We focus here on the northwest coast of Greenland between 72.5 and
76∘ N: from Upernavik Isstrøm to Sverdrup
Gletscher (Fig. ). This is one of the regions of Greenland where
the bed is remarkably well constrained by ice thickness measurements from
NASA's Operation IceBridge mission and where NASA's
Oceans Melting Greenland mission has been collecting multibeam bathymetry
data in most fjords.
We first describe the numerical model and then run the model to 2100 under
different scenarios of increase in ocean thermal forcing and subglacial
discharge. We then discuss the implications of these experiments and the model
limitations, as well as make recommendations for future model studies.
Ocean bathymetry (m, blue color scale) and ice velocity
m a-1, of northwestern Greenland. The white line
shows the 2007 ice sheet extent and white crosses indicate the locations of
CTD data from NASA's Oceans Melting Greenland campaign that are used to
calibrate the thermal forcing.
Method and dataIce flow model setup
We use the Ice Sheet System Model ISSM, and initialize
the model with conditions similar to 2007, which is the nominal year of the
surface digital elevation map used here Greenland Ice Mapping Project Digital Elevation
Model,. The ice surface elevation and bed topography are from
BedMachine v3 , and we use satellite-derived surface
velocities from to invert for basal friction, following
. We use the shelfy-stream approximation
SSA, for the ice stress balance. While not accurate
in slow moving regions, this model is an excellent approximation for the fast
outlet glaciers (i.e., >200 m yr-1) that we are focusing on here,
where sliding velocities are significantly larger than deformational
velocities e.g.,. We assume a depth-averaged viscosity
equivalent to a temperature of -8∘C, which is consistent with
, and we use a linear viscous basal friction law
following :
τb=-C2Nvb,
where τb is the basal friction, vb is
the ice basal velocity, C is a friction coefficient that is inverted for
using surface velocities, and N is the effective pressure. For simplicity,
we assume that N is equal to the ice pressure above hydrostatic
equilibrium, as if the subglacial hydrological system was forming a sheet
connected to the ocean. The model mesh is comprised of 380 000 elements, and
its resolution varies between 100 m near the coast and 1 km inland. The
model time step is 1 week.
In order to capture the dynamic motion of the calving front, we rely on the
level-set method , where the velocity at which
the calving front moves is defined as follows:
vfront=v-c+M˙n,
where v is the ice horizontal velocity vector, c is the calving
rate, M˙ is the rate of undercutting at the calving face, and
n is a unit normal vector that points outward from the ice domain.
Much research is currently being dedicated to derive parameterizations for
c and M˙; here we chose to use two recent parameterizations, which
are described below.
Undercutting parameterization
We rely on the undercutting parameterization from , where
the rate of undercutting (in m day-1) at the calving face is assumed to
follow
M˙=Ahqsgα+BT̃β,
where h is the water depth at the calving front (in m), A=3×10-4 m-α dayα-1∘C-β, α=0.39, B=0.15 m day-1∘C-β, and β=1.18.
T̃ is the ocean thermal forcing (in ∘C), defined as the
difference in temperature between the potential temperature of the ocean and
the depth-dependent freezing point of sea water:
T̃=T-TF,
where T is the ocean temperature at a given depth, and TF is
the temperature of the local freezing point, which is assumed to be a linear
function of salinity and pressure, following Eq. (1) of .
qsg is the subglacial discharge at the glacier terminus
(in m day-1). Both T̃ and qsg
are monthly averaged. The coefficients α and β are close to the
ones expected from the plume theory but were
determined from a high-resolution ocean modeling study. The introduction of
B is necessary to account for the presence of melt in the case where there
is no subglacial discharge. The dependence on h was determined from model
experiments with different depths and seems to reflect an acceleration of the
melt plume when it rises from greater depths .
To estimate the subglacial discharge of melt water, qsg, we use
the results from the downscaled 1 km regional atmospheric climate model (RACMO) runoff field
with the subglacial melt rates from and
assume for simplicity that the discharge is uniformly distributed across the
calving face. showed that the assumption of uniformly
distributed melt only generates a 15 % difference in melt compared to a
distributed source of qsg.
The ocean thermal forcing, T̃, is derived from the Estimating the
Circulation and Climate of the Ocean, Phase II (ECCO2, 2007–2011) and
Phase IV (2007–2015), following the procedure described in .
To account for the presence of sills in the fjord, T̃ is depth
averaged between sea level and the deepest point for which there is a direct
horizontal connection to the fjord mouth. The calculated effective depth
assumes a perfectly stratified ocean and decreases as we get closer to the
calving front where ocean currents are potentially blocked by the bathymetry.
Figure illustrates the effective depth for the case of
Sverdrup Gletscher. Note that we
define the effective depth over the entire model domain, even under currently
ice-covered regions. If the modeled ice front retreats past a high bump, it
will be accounted for in the calculation of the thermal forcing and the rate
of undercutting will be reduced (see Fig. b and c). This
undercutting parameterization facilitates the definition of the rate of
undercutting everywhere in the model domain, and its magnitude depends on the
ice front location. The ice sheet model is forced by the surface mass balance
of RACMO 2.3 averaged between 1961 and 1990: the increase in runoff (due to
the anomaly applied) is assumed to not affect the surface mass balance but
only the rate of undercutting through the parameterization provided by
Eq. ().
(a) Effective depth (m) of the fjord of Sverdrup
Gletscher. The effective depth
decreases as we go from the fjord mouth (x=80 km) to the glacier
terminus (x=0 km). (b) Thermal forcing at the fjord's mouth
(∘C) for Sverdrup Gletscher from ECCO2.
(a) Bed topography (m), (b) effective depth (m),
(c) calculated mean rate of undercutting from 2007 to 2017
(m day-1), and (d) calibrated σmax
(kPa).
Calving parameterization
We assume that the calving rate follows the parameterization proposed by
, for which the calving rate is proportional to the
tensile von Mises stress:
c=‖v‖σ̃σmax,
where σ̃ is the tensile von Mises stress, as defined in
, and σmax is a threshold that needs to be
calibrated for each basin. This calving law is obviously a simplification
that may not capture all modes of calving as it only relies on tensile
stresses. It is also assumed here that c and M˙ are independent,
which is a simplification but has shown some promising results in real-world
applications e.g.,.
To calibrate the calving threshold, we run the model for 10 years (from 2007
to 2017), using the thermal forcing from ECCO2, and adjust σmax in
order to match the extent of Landsat-derived ice front retreat: we try to
match the observed retreat rather than the retreat rate from 2007 to 2017
along a central flow line for each glacier. This calving threshold is uniform
by basin and held constant through time in all simulations. Another possible
approach would be to calibrate σmax during a period of ice front
stability. One of the problems with this alternative approach is that stable
glaciers generally have their termini on distinct basal features, such as
ridges or ledges. The numerical model is also stable for a wide range of
σmax under these conditions, as shown in and
. The threshold σmax is easier to calibrate for
retreating glaciers, as it directly constrains the rate of retreat.
Experiments
After this calibration phase, we run the model forward, from 2017 to 2100,
under different scenarios of ocean forcings and different scenarios of
increase in subglacial discharge. analyzed the results of 19
climate models to quantify ocean warming around the coast of Greenland over
the coming centuries. They found that western Greenland's subsurface ocean
temperature reaches between 0.5 and 4 ∘C, with a mean of
1.5 ∘C by 2100. Coupled Model Intercomparison Project Phase 5
(CMIP5) results suggest similar rates of warming by the end of the century
under RCP8.5 (Donald Slater, personal communication, 2018). A 2 ∘C
increase is also in line with the global atmospheric temperature rise target
of the Paris Agreement. Even though there will be a lag in the response of
the ocean to atmospheric warming, we do expect that polar amplification could
increase ocean temperature further at high latitudes. We therefore consider
here a range in T̃ increase from 0 to +3∘C.
In terms of subglacial discharge, observations over the past decade have
shown that surface melting has increased over the entire Greenland ice sheet
. showed
that meltwater runoff could be multiplied by a factor of 10 by the end of the
century. We therefore multiply the subglacial discharge by a factor of up to
10, starting in 2017.
Overall, we perform 40 experiments here: we increase the ocean thermal
forcing, T̃, instantly by increments of 1 up to 3 ∘C and
multiply the ocean subglacial discharge by up to a factor of 10. We then run
the model forward from 2017 to 2100. The rate of undercutting
(Eq. ) is therefore modified as follows:
M˙=Ahqsg×qaα+BT̃+T̃aβ,
where the subglacial discharge anomaly factor qa varies from 1 to
10, and the thermal forcing anomaly, T̃a, varies from 0 to
3 ∘C. From 2007 to 2016, we rely on the thermal forcing
(T̃) and subglacial discharge (qsg) from ECCO2 and
RACMO. For 2017 to 2100, as we do not run a coupled model, we repeat the
thermal forcing and subglacial discharge of the year 2016 until the end of
the century, with the anomalies described above. While a gradual increase in
ocean thermal forcing and subglacial discharge would be more realistic, we
want to perform a sensitivity analysis in order to determine the glaciers
that are more at risk.
Additionally, we perform a control experiment where the ice front is
kept fixed. This control experiment is designed to quantify the impact of
including moving boundaries in future simulations.
Results
Figure d shows the chosen value of the stress threshold
over the model domain. For the southern half, we find a stress threshold
within 20 % of 1 MPa, which is consistent with what was found in other
studies . Over the northern side of the
domain, however, the stress threshold has to be decreased to ∼650 kPa
in order to match the pattern of retreat. This would suggest that the ice is
less resistant to tensile stress, but this is more likely an artifact that is
due to our underestimation of the rate of undercutting in this region.
noted that the north–south temperature gradient in the
ocean model was poorly represented in this region and that the resulting
thermal forcing was too cold. The model therefore requires a decrease in the
stress threshold, thereby increasing the calving rate, c, in order to
capture the correct amount of ice retreat over the past 10 years. We could
have kept σmax constant, equal to 1 MPa, and
optimized the ocean thermal
forcing instead, but the spatial and temporal variability in T̃
makes its calibration difficult. Optimizing a single scalar parameter per
glacier is more practical.
Figure shows ice front positions that were
manually digitized from Level 1 Landsat imagery, together with modeled ice
front positions between 2007 and 2017 for four glaciers along the coast. The
first two columns of Table list the observed and modeled
retreat for the same time period along a central flow line for the chosen
value of the stress threshold. By manually tuning the stress threshold
(σmax) for each basin, we are able to match the retreat of the
past 10 years for all 17 glaciers for which a change has been documented,
except for Ussing Bræer N (Table ), for which we model
a retreat of almost 3 km instead of an advance of 300 m. This inconsistency
may be due to errors in the bed topography near the front. We note, however,
that under all scenarios this glacier remains remarkably stable at its 3 km
retreated position, which coincides with a large bump in the bed topography.
Overall, we find that with a unique scalar parameter constant in time for
each glacier, the modeled ice front retreat is in very good agreement with
observations, which is consistent with . The retreat rate of
Dietrichson Gletscher is well captured (Fig. a
vs. b). While the model overestimates the retreat on the southern side of the
fjord, there is nonetheless an overall good agreement between the modeled and
observed retreat between 2007 and 2017. The front of Illullip Sermia is
remarkably stable in both observations and the
model (Fig. c and d), as it is currently located
on a pronounced sill in the bed topography. The modeled ice front of
Upernavik Isstrøm retreats more in the southern half of the fjord than the
northern half compared to the observations, but the increase in ice retreat
over the past 2 years is captured (Fig. e and f).
The complex pattern of ice front retreat of Kakivfaat Sermiat is also
reproduced with a slight difference in timing
(Fig. g and h). The 2017 modeled front position is
also more retreated than what has been observed, but we find the same strong
control of the bed topography in the pattern of retreat.
Observed and modeled ice front retreat (in km along a centerline)
between 2007 and 2017 under current forcing (first two columns) and modeled
retreat between 2007 and 2030 and between 2007 and 2100, under different
scenarios of ocean forcing with today's qsg for individual
glaciers along the northwest coast. A more complete table is provided in the
Supplement.
2017 retreat (km) 2030 modeled retreat (km) 2100 modeled retreat (km) Glacier nameObservedModeled+0∘C+1∘C+2∘C+3∘C+0∘C+1∘C+2∘C+3∘CSverdrup Gletscher2.892.898.012.913.314.81313.923.423.4Dietrichson Gletscher3.563.744.97.08.113.46.254.754.754.7Steenstrup Gletscher1.791.681.529.533.436.74.237.437.437.4Kjer Gletscher6.086.0328.93234.536.338.738.739.440.5Hayes Gletscher N-0.266-0.53327.530.430.737.953.954.354.377.1Hayes Gletscher0.4750.10412.925.43030.130.131.241.953.3Unnamed south Hayes N0.060.060.63.34.425.245.345.345.446.8Unnamed south Hayes M-0.280.130.22.112.112.139.940.34263.6Unnamed south Hayes SS1.121.123.14.05.37.33.56.51465.4Alison Gletscher2.362.649.59.810.510.610.510.514.518.3Illullip Sermia0.120.1200.94.69.501.417.116.9Cornell Gletscher0.8071.432.32.32.52.62.32.42.86.5Ussing Bræer N-0.2822.912.93.13.43.43.33.43.43.5Ussing Bræer0000.12.34.5402.28.415.1Qeqertarsuup Sermia0.1620.1620.20.31.12.20.20.94.19.6Kakivfaat Sermiat4.84.2712.819.119.319.519.419.419.519.5Upernavik Isstrøm N0.8130.6034.54.55.610.44.34.55.011.2Upernavik Isstrøm C2.932.934.56.38.48.46.37.78.815.1Upernavik Isstrøm S0.1050.1050.15.010.113.80.117.627.229.1
Observed (a, c, e, g) and modeled (b, d, f, h) ice
front position for Dietrichson Gletscher (a, b), Illulip
Sermia (c, d), Upernavik Isstrøm C (e, f), and Kakivfaat
Sermiat (g, h) under current conditions (T̃+0∘C, qsg×1). Yellow to red lines are annual ice front
position from 2007 to 2017, and light blue to pink are the model projections
for 2017 to 2100.
If we now look at projections, Tables and S1 in the
Supplement list the modeled retreated distance compared to the 2007 position
for all 40 experiments along a central flow line, and
Fig. shows velocity profiles for the
different experiments in 2030. Under today's oceanic conditions (T̃+0∘C and qsg×1), Sverdrup
Gletscher is predicted to continue to
retreat for another 5 km (i.e., 8 km upstream of its 2007 position) by 2030
and yet another 5 km by 2100. Under the strongest scenario (i.e., T̃+3∘C and qsg×10), Sverdrup
Gletscher retreats by 23 km compared
to 2007 by 2030 and remains there until the end of the century. We find that
Sverdrup Gletscher has three distinct
stable positions: ∼8, 13, and 23 km upstream of the 2007 terminus are
the ice front positions that we find for a majority of simulations, and they
coincide with clear features in the bed topography. Further south,
Dietrichson Gletscher will retreat another 1–3 km under the current thermal
forcing and may retreat by up to 55 km by 2100 compared to 2007 if
T̃ increases by 1 ∘C or more, or if the subglacial
discharge increases by a factor of 8 or more. Again, we find clear common
retreated positions, 5, 8, 30, 38, and 55 km upstream of the 2007 position,
which coincide with topographic features in the bed. Steenstrup
Gletscher remains somewhat stable
without further ocean warming but retreats by more than 30 km upstream,
where the bed rises above sea level if the ocean temperature warms by
1 ∘C or more, or if the subglacial discharge is doubled. Kjer
Gletscher exhibits almost the same
behavior for all scenarios: it will continue to retreat another ∼40 km
upstream over the coming 2 decades in a region of prograde bed slope and
remain stable there. Hayes Gletscher
N slightly readvanced over the past 10 years but the model suggests that it
will retreat by up to 70 km upstream to where the bed is higher than sea
level. Hayes Gletscher would retreat
13 km by 2030, in a marked overdeepening of the bed, and continues to
retreat another 17 km to reach a position 30 km upstream of its 2007
position by the end of the simulation. If the thermal forcing increases by 2
or 3 ∘C, the glacier retreats 20 km further inland. The different
branches of the unnamed glacier south of Hayes Gletscher also retreat; the northern
branch retreats 45 km by 2100 in all scenarios to reach a position where the
bed rises above sea level. The middle branch (M) retreats by about 40 km by
the end of the century in all cases except if the thermal forcing increases
by +3∘C, in which case its ice front retreats by 64 km by 2100.
The southern branch shows a more binary behavior: it retreats another
3–7 km, depending on the warming scenario but for enhanced thermal forcing
simulations it may retreat 43 km upstream or even 65 km upstream in the
case of a +3∘C warming in T̃. Alison
Gletscher has been retreating by
2.5 km over the past 10 years, and the model projects that by 2030, in all
cases, it will retreat another 7–8 km upstream due to the lack of features
in the bed topography that may stop the retreat. By 2100, the glacier may
retreat another 5 km if the thermal forcing increases by +2∘C or
more.
Modeled ice velocities (solid lines) and ice front positions (dashed
vertical lines) in 2030 for all 40 scenarios. The black dashed line is the
current ice velocity (m) and the x axis shows the distance to the current
calving-front position.
Illullip Sermia also has a binary behavior. For the strongest forcing, it
retreats by 17–18 km, but in the more conservative scenarios it stays at
its current position that coincides with a large bump in the bed topography.
Cornell Gletscher is one of the most
stable glaciers of the model: under all scenarios, it retreats another
kilometer upstream of its 2017 position and remains stable there, except in
the case of +3∘C increase in T̃, for which it could
retreat by another ∼10 km.
Ussing Bræer N is the glacier for which we do not capture the advance,
but under all scenarios the model projects that it will remain stable 3 km
upstream of its current position, where the bed is very shallow. Ussing
Bræer has been stable over the past 10 years, and the model suggests that
it may retreat by 9 to 15 km if the ocean thermal forcing increases by 2 to
3 ∘C, but the glacier does not retreat even when the subglacial
discharge is multiplied by 10 in the case of no additional increase in
T̃. Qeqertarsuup Sermia is also one of the stable glaciers of this
region: the model marginally retreats and under the strongest forcing
(+3∘C) retreats by about 10 km. Kakivfaat Sermiat, on the other
hand, has retreated more than 4 km since 2007. The model suggests that, in
all cases, it will retreat another 15 km, where a pronounced feature in the
bed topography keeps the ice front stable
(Fig. ). Our simulations suggest that the
glacier may reach this position by 2030 and remain stable there. Upernavik
Isstrøm N retreats by 4 or 11 km depending on the forcing, by 2100.
Upernavik Isstrøm C continues to retreat about 3–6 km upstream of its
2007 position, except in the case of a +3∘C ocean warming under
which it would retreat by 23 km. Finally, Upernavik Isstrøm S would
remain stable if the current conditions of qsg and T̃
are maintained but may retreat between 17 and 29 km if the subglacial
discharge is multiplied by a factor of 6 or if the thermal forcing increases.
Figure shows the contribution to sea level rise
of the entire domain for the 40 different scenarios. In all cases, even under
current conditions, our simulations suggest that this region will continue to
lose mass. The mass loss is significantly higher than in the control
experiment, in which we kept the ice front fixed. We also notice that the
spread in mass loss due to temperature change (with a fixed qsg)
is significantly larger than the spread in mass loss due to an increase in
subglacial discharge (with fixed T̃). Note that we rely here on a
1960–1991 average surface mass balance, and the projections of ice loss do
not account for the increase in surface melt. Our simulations are therefore
conservative and should not be used as actual projections.
Contribution to sea level rise (mm) for all 40 scenarios. The black
dashed line is the modeled contribution to sea level with a fixed calving
front. All simulations rely on a constant surface mass
balance.
Discussion
Our simulations suggest that all glaciers of the northwest coast, except for
four (Illullip Sermia, Ussing Bræer, Qeqertarsuup Sermia and Upernavik
Isstrøm S), will continue to retreat several kilometers inland under
today's thermal forcing and subglacial discharge. Under these conditions, we
do not find any glacier which advances.
In all scenarios, we find that the rate and extent of ice front retreat is
strongly dependent on the bed topography: ice fronts are stable on
topographic bumps and prograde bed slopes and unstable on retrograde bed
slope, which is consistent with previous studies
e.g.,. This
is, for example, illustrated in Fig. h, where the ice
front jumps from basal bump to basal bump and retreats rapidly in
overdeepenings. We find this behavior common to all glaciers in the model
domain. There is, however, no “intuitive” way to predict where the glaciers
will stabilize without running a model. In most cases, the fjords are not
symmetrical or ridges do not go all the way across the fjord walls, which
makes it difficult to determine whether the ice front will stabilize or not.
We find that some glaciers, such as Alison Gletscher or Upernavik Isstrøm S, are more sensitive to small
increases in ocean thermal forcing, while others, such as Cornell
Gletscher or Qeqertarsuup Sermia, are
very difficult to destabilize, even under a +3∘C increase in
ocean thermal forcing. On the other hand, we find that Hayes
Gletscher retreats more than 30 km
inland into a deep trough once it goes past a ridge, and its velocity
increases by a factor of 3 over only 23 years, before restabilizing, under
all warming scenarios.
We show here that calving dynamics is an important control on the ice sheet
mass balance that should not be ignored. It has been driving the recent
dynamic thinning of several Greenland outlet glaciers
e.g.,, and our
model study shows that it may continue to control the mass balance of
Greenland. Figure shows, for example, that in
all cases the system loses a significant amount of mass, and this mass loss
is not captured by the model that keeps a fixed calving front. Models that
keep the ice boundary fixed
e.g., will
consistently underestimate ice sheet mass loss as they do not capture the
effect of ocean warming. These conservative projections should therefore be
treated with caution and efforts should be made to include moving boundaries
in continental-scale simulations of the Greenland ice sheet in order to
account for ice–ocean interactions, despite the complexity and high
grid resolution needed to
resolve moving boundaries (∼1 km, ) of such
simulations. It is also important to note that the future evolution of
Greenland is strongly influenced by the ocean (through the ocean thermal
forcing). It is important not only to force predictive ice sheet models with
projections of surface mass balance but also to include projections of ocean
thermal forcing at the fjord mouth. There may also be some positive or
negative feedbacks between changes in surface mass balance and calving. More
surface melt, for example, could enhance calving through hydrofracture, while
at the same time reducing the ice thickness at the calving front, hence
reducing the stress. Ideally, the community should move towards
ice–ocean–climate coupled models to fully understand the processes that
control the stability of the ice sheet .
Another interesting aspect of this analysis is that glaciers are more
sensitive to an increase of 1–2 ∘C in ocean thermal forcing than
in a 5- to 10-fold increase in subglacial discharge. This is actually a result
of the parameterization of undercutting used here
(Eq. ), which is itself more sensitive to T̃
than qsg: the parameterization is sublinearly dependent on
qsg and above linear in T̃. The effect of surface runoff
is also limited to summer months, while the ocean thermal forcing affects the
glacier year-round. That being said, we do not account for other effects that
surface runoff may have on ice dynamics, such as enhanced damage due to
hydrofracture, which may lead to a decrease in the stress threshold
σmax. Glaciers might therefore be more prone to retreat as
qsg increases than what is captured by the current model.
Among other limitations in this study, no numerical ocean model is included:
the thermal forcing is prescribed and dictates the rate of undercutting.
Similarly, the calving law does not capture all the modes of calving and
requires more validation. This study indeed relies on two
parameterizations that drive the response of the model to ocean forcings. It
is therefore critical to further validate these parameterizations or develop
new ones that include more physics and better capture the transfer of heat
from the fjord mouth to the calving face as well as iceberg calving. We also
assumed that the subglacial discharge was distributed uniformly across the
calving front, but observations show that the majority of discharge is routed
to one or more large channel outlets e.g.,. Frontal
undercutting is therefore not distributed uniformly either, even though
numerical experiments suggest that the uncertainty in melt is on the order of
15 % . We have also shown how our results were strongly
influenced by the bed topography. While the bed is pretty well constrained in
this region , it is not free of error, and we have shown
again here how important features in the bed topography are for calving front
stability.
More importantly, this study paves the way for a Greenland-wide projection
that includes realistic parameterizations of moving boundaries, which will
provide more reliable estimates than current models that do not include
calving. This work also suggests that development of more accurate
parameterization of undercutting and calving should be developed as they
control the response of the model and its stability in future scenarios.
While this work is a first step in this direction, more validation should be
performed on these parameterizations, and future parameterizations of
undercutting and calving will make models more reliable.
Conclusions
In this study, we modeled the response of the northwest coast of
Greenland to enhanced oceanic forcing and subglacial discharge and found that
this sector will continue to lose mass over the coming decades, regardless of
the scenario adopted. The model confirms that ice–ocean interactions have
the potential to trigger extensive glacier retreat over a short amount of
time (i.e., decades), but the bed topography controls the magnitude and rate
of retreat. Overall, the model showed greater sensitivity to enhanced thermal
forcing compared to subglacial discharge but did not account for other
effects that runoff may have on ice flow. While more work on validating this
parameterization of undercutting and the calving law employed here is needed,
we showed that accounting for ice front dynamics can lead to significantly
more ice loss than with a fixed calving front. Under the current oceanic and
atmospheric conditions, this sector alone will contribute more than 1 cm to
sea level rise by the end of this century and up to 3 cm in the worst-case
scenario.
Code and data availability
The data used in this study are freely available from
the National Snow and Ice Data Center or upon request to the authors. ISSM is
open source and freely available at https://issm.jpl.nasa.gov/ (last
access: 15 November 2018, ).
The supplement related to this article is available online at: https://doi.org/10.5194/tc-13-723-2019-supplement.
Author contributions
MM set up the model, designed the experiments, ran the
simulations, and wrote the manuscript. MW provided the data required to compute the rate
of undercutting; HS and YC assisted in conducting the numerical experiments.
All authors participated in the writing of the manuscript.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
This work was performed at the University of California Irvine under a
contract with the National Aeronautics and Space Administration, Cryospheric
Sciences Program (no. NNX15AD55G), and the National Science Foundation's ARCSS
program (no. 1504230). Resources supporting this work were provided by the NASA
High-End Computing (HEC) program through the NASA Advanced Supercomputing
(NAS) Division at Ames Research Center. This work would not have been
possible without data from the NASA Ocean Melting Greenland EVS-3 mission, and
NASA Operation IceBridge. We thank Andy Aschwanden, an anonymous reviewer, and
the editor, Andreas Vieli, for their helpful and insightful
comments.
Edited by: Andreas Vieli
Reviewed by: Andy Aschwanden and one anonymous referee
ReferencesAschwanden, A., Fahnestock, M. A., and Truffer, M.: Complex Greenland outlet
glacier flow captured, Nat. Commun., 7, 1–8, 10.1038/ncomms10524,
2016.Bassis, J. N.: Diverse calving patterns linked to glacier geometry, Nat.
Geosci., 6, 833–836, 10.1038/ngeo1887, 2013.Bindschadler, R. A., Nowicki, S., Abe-Ouchi, A., Aschwanden, A., Choi, H.,
Fastook, J., Granzow, G., Greve, R., Gutowski, G., Herzfeld, U., Jackson, C.,
Johnson, J., Khroulev, C., Levermann, A., Lipscomb, W. H., Martin, M. A.,
Morlighem, M., Parizek, B. R., Pollard, D., Price, S. F., Ren, D., Saito,
F.and Sato, T., Seddik, H., Seroussi, H., Takahashi, K., Walker, R., and
Wang, W. L.: Ice-Sheet Model Sensitivities to Environmental Forcing and
Their Use in Projecting Future Sea-Level (The SeaRISE Project), J. Glaciol.,
59, 195–224, 10.3189/2013JoG12J125, 2013.Bondzio, J., Morlighem, M., Seroussi, H., Kleiner, T., Ruckamp, M., Mouginot,
J., Moon, T., Larour, E., and Humbert, A.: The mechanisms behind Jakobshavn
Isbræ's acceleration and mass loss: A 3-D thermomechanical model study,
Geophys. Res. Lett., 44, 6252–6260, 10.1002/2017GL073309, 2017.Bondzio, J. H., Seroussi, H., Morlighem, M., Kleiner, T., Rückamp, M.,
Humbert, A., and Larour, E. Y.: Modelling calving front dynamics using a
level-set method: application to Jakobshavn Isbræ, West Greenland, The
Cryosphere, 10, 497–510, 10.5194/tc-10-497-2016, 2016.Bondzio, J. H., Morlighem, M., Seroussi, H., Wood, M., and Mouginot, J.:
Control of ocean temperature on Jakobshavn Isbræ's present and future
mass loss, Geophys. Res. Lett., 45, 12912–12921, 10.1029/2018GL079827,
2018.
Budd, W. F., Keage, P. L., and Blundy, N. A.: Empirical studies of ice
sliding, J. Glaciol., 23, 157–170, 1979.Carr, J. R., Vieli, A., Stokes, C. R., Jamieson, S. S. R., Palmer, S. J.,
Christoffersen, P., Dowdeswell, J. A., Nick, F. M., Blankenship, D. D., and
Young, D. A.: Basal topographic controls on rapid retreat of Humboldt
Glacier, Northern Greenland, J. Glaciol., 61, 137–150,
10.3189/2015JoG14J128, 2015.Catania, G. A., Stearns, L. A., Sutherland, D. A., Fried, M. J.,
Bartholomaus, T. C., Morlighem, M., Shroyer, E., and Nash, J.: Geometric
Controls on Tidewater Glacier Retreat in Central Western Greenland,
J. Geophys. Res.-Earth, 123, 2024–2038, 10.1029/2017JF004499, 2018.Choi, Y., Morlighem, M., Rignot, E., Mouginot, J., and Wood, M.: Modeling the
response of Nioghalvfjerdsfjorden and Zachariae Isstrøm glaciers,
Greenland, to ocean forcing over the next century, Geophys. Res. Lett., 44,
11071–11079, 10.1002/2017GL075174,2017.Choi, Y., Morlighem, M., Wood, M., and Bondzio, J. H.: Comparison of four
calving laws to model Greenland outlet glaciers, The Cryosphere, 12,
3735–3746, 10.5194/tc-12-3735-2018, 2018.Felikson, D., Bartholomaus, T. C., Catania, G. A., Korsgaard, N. J., Kjaer,
K. H., Morlighem, M., Noel, B., van den Broeke, M., Stearns, L. A., Shroyer,
E. L., Sutherland, D. A., and Nash, J. D.: Inland thinning on the Greenland
Ice Sheet controlled by outlet glacier geometry, Nat. Geosci., 10,
366–371, 10.1038/ngeo2934, 2017.Fettweis, X., Franco, B., Tedesco, M., van Angelen, J. H., Lenaerts, J. T.
M., van den Broeke, M. R., and Gallée, H.: Estimating the Greenland ice
sheet surface mass balance contribution to future sea level rise using the
regional atmospheric climate model MAR, The Cryosphere, 7, 469–489,
10.5194/tc-7-469-2013, 2013a.Fettweis, X., Hanna, E., Lang, C., Belleflamme, A., Erpicum, M., and
Gallée, H.: Brief communication “Important role of the
mid-tropospheric atmospheric circulation in the recent surface melt increase
over the Greenland ice sheet”, The Cryosphere, 7, 241–248,
10.5194/tc-7-241-2013, 2013b.Fried, M. J., Catania, G. A., Bartholomaus, T. C., Duncan, D., Davis, M.,
Stearns, L. A., Nash, J., Shroyer, E., and Sutherland, D.: Distributed
subglacial discharge drives significant submarine melt at a Greenland
tidewater glacier, Geophys. Res. Lett., 42, 9328–9336,
10.1002/2015GL065806, 2015.Gillet-Chaulet, F., Gagliardini, O., Seddik, H., Nodet, M., Durand, G., Ritz,
C., Zwinger, T., Greve, R., and Vaughan, D. G.: Greenland ice sheet
contribution to sea-level rise from a new-generation ice-sheet model, The
Cryosphere, 6, 1561–1576, 10.5194/tc-6-1561-2012, 2012.Holland, D. M., Thomas, R. H., De Young, B., Ribergaard, M. H., and Lyberth,
B.: Acceleration of Jakobshavn Isbrae triggered by warm subsurface ocean
waters, Nat. Geosci., 1, 659–664, 10.1038/ngeo316, 2008.Howat, I. M., Negrete, A., and Smith, B. E.: The Greenland Ice Mapping
Project (GIMP) land classification and surface elevation data sets, The
Cryosphere, 8, 1509–1518, 10.5194/tc-8-1509-2014, 2014.Jenkins, A.: Convection-Driven Melting near the Grounding Lines of Ice
Shelves and Tidewater Glaciers, J. Phys. Oceanogr., 41, 2279–2294,
10.1175/JPO-D-11-03.1, 2011.
Jenkins, A., Dutrieux, P., Jacobs, S., McPhail, S., Perrett, J., Webb, A.,
and White, D.: Observations beneath Pine Island Glacier in West Antarctica
and implications for its retreat, Nat. Geosci., 3, 468–472, 2010.
Joughin, I., Smith, B. E., Howat, I. M., Scambos, T., and Moon, T.: Greenland
flow variability from ice-sheet-wide velocity mapping, J. Glaciol., 56,
416–430, 2010.Khan, S. A., Kjaer, K. H., Bevis, M., Bamber, J. L., Wahr, J., Kjeldsen,
K. K., Bjork, A. A., Korsgaard, N. J., Stearns, L. A., van den Broeke, M. R.,
Liu, L., Larsen, N. K., and Muresan, I. S.: Sustained mass loss of the
northeast Greenland ice sheet triggered by regional warming, Nat. Clim.
Change, 4, 292–299, 10.1038/NCLIMATE2161, 2014.Larour, E., Seroussi, H., Morlighem, M., and Rignot, E.: Continental scale,
high order, high spatial resolution, ice sheet modeling using the Ice Sheet
System Model (ISSM), J. Geophys. Res., 117, 1–20,
10.1029/2011JF002140, 2012.Lüthi, M. P., Vieli, A., Moreau, L., Joughin, I. R., Reisser, M., Small,
D., and Stober, M.: A century of geometry and velocity evolution at Eqip
Sermia, West Greenland, J. Glaciol., 62, 640–654,
10.1017/jog.2016.38, 2016.
MacAyeal, D. R.: Large-scale ice flow over a viscous basal sediment: Theory
and application to Ice Stream B, Antarctica, J. Geophys. Res., 94,
4071–4087, 1989.
Meier, M. F. and Post, A.: Fast tidewater glaciers, J. Geophys. Res., 92,
9051–9058, 1987.
Mercer, J. H.: The response of fjord glaciers to changes in the firn limit,
J. Glaciol., 3, 850–858, 1961.Moon, T., Joughin, I., Smith, B., and Howat, I.: 21st-Century Evolution of
Greenland Outlet Glacier Velocities, Science, 336, 576–578,
10.1126/science.1219985, 2012.Morlighem, M., Rignot, E., Seroussi, H., Larour, E., Ben Dhia, H., and Aubry,
D.: Spatial patterns of basal drag inferred using control methods from a
full-Stokes and simpler models for Pine Island Glacier, West
Antarctica, Geophys. Res. Lett., 37, 1–6, 10.1029/2010GL043853,
2010.Morlighem, M., Bondzio, J., Seroussi, H., Rignot, E., Larour, E., Humbert,
A., and Rebuffi, S.-A.: Modeling of Store Gletscher's calving dynamics,
West Greenland, in response to ocean thermal forcing, Geophys. Res.
Lett., 43, 2659–2666, 10.1002/2016GL067695, 2016.Morlighem, M., Williams, C. N., Rignot, E., An, L., Arndt, J. E., Bamber,
J. L., Catania, G., Chauché, N., Dowdeswell, J. A., Dorschel, B., Fenty,
I., Hogan, K., Howat, I., Hubbard, A., Jakobsson, M., Jordan, T. M.,
Kjeldsen, K. K., Millan, R., Mayer, L., Mouginot, J., Noël, B. P. Y.,
O'Cofaigh, C., Palmer, S., Rysgaard, S., Seroussi, H., Siegert, M. J.,
Slabon, P., Straneo, F., van den Broeke, M. R., Weinrebe, W., Wood, M., and
Zinglersen, K. B.: BedMachine v3: Complete bed topography and ocean
bathymetry mapping of Greenland from multi-beam echo sounding combined with
mass conservation, Geophys. Res. Lett., 44, 11051–11061,
10.1002/2017GL074954, 2017.Nick, F. M., Vieli, A., Howat, I. M., and Joughin, I.: Large-scale changes in
Greenland outlet glacier dynamics triggered at the terminus, Nat. Geosci.,
2, 110–114, 10.1038/NGEO394, 2009.Nick, F. M., Vieli, A., Andersen, M. L., Joughin, I., Payne, A., Edwards,
T. L., Pattyn, F., and van de Wal, R. S. W.: Future sea-level rise from
Greenland's main outlet glaciers in a warming climate, Nature, 497,
235–238, 10.1038/nature12068, 2013.Noël, B., van de Berg, W. J., Machguth, H., Lhermitte, S., Howat, I.,
Fettweis, X., and van den Broeke, M. R.: A daily, 1 km resolution data set
of downscaled Greenland ice sheet surface mass balance (1958–2015), The
Cryosphere, 10, 2361–2377, 10.5194/tc-10-2361-2016, 2016.Nowicki, S. and Seroussi, H.: Projections of future sea level contributions
from the Greenland and Antarctic Ice Sheets: Challenges beyond dynamical ice
sheet modeling, Oceanography, 31, 107–117, 10.5670/oceanog.2018.216,
2018.
Osher, S. and Sethian, J. A.: Fronts Propagating with
Curvature-Dependent Speed – Algorithms Based on
Hamilton-Jacobi Formulations, J. Comput. Phys., 79, 12–49, 1988.Petrovic, J. J.: Review Mechanical properties of ice and snow, J. Mater.
Sci., 38, 1–6, 10.1023/A:1021134128038, 2003.Rignot, E. and Mouginot, J.: Ice flow in Greenland for the International
Polar Year 2008-2009, Geophys. Res. Lett., 39, L11501,
10.1029/2012GL051634, 2012.Rignot, E., Fenty, I., Menemenlis, D., and Xu, Y.: Spreading of warm ocean
waters around Greenland as a possible cause for glacier acceleration, Ann.
Glaciol., 53, 257–266, 10.3189/2012AoG60A136, 2012.
Rignot, E., Fenty, I., Xu, Y., Cai, C., Velicogna, I., Ó Cofaigh, C.,
Dowdeswell, J. A., Weinrebe, W., Catania, G., and Duncan, D.: Bathymetry
data reveal glaciers vulnerable to ice-ocean interaction in Uummannaq and
Vaigat glacial fjords, west Greenland, Geophys. Res. Lett., 43,
2667–2674, 2016a.Rignot, E., Xu, Y., Menemenlis, D., Mouginot, J., Scheuchl, B., Li, X.,
Morlighem, M., Seroussi, H., den Broeke, M. v., Fenty, I., Cai, C., An, L.,
and de Fleurian, B.: Modeling of ocean-induced ice melt rates of five West
Greenland glaciers over the past two decades, Geophys. Res. Lett., 43,
6374–6382, 10.1002/2016GL068784, 2016b.Seroussi, H., Morlighem, M., Rignot, E., Khazendar, A., Larour, E., and
Mouginot, J.: Dependence of century-scale projections of the Greenland ice
sheet on its thermal regime, J. Glaciol., 59, 1024–1034,
10.3189/2013JoG13J054, 2013.Straneo, F. and Heimbach, P.: North Atlantic warming and the retreat of
Greenland's outlet glaciers, Nature, 504, 36–43, 10.1038/nature12854,
2013.Straneo, F., Hamilton, G. S., Sutherland, D. A., Stearns, L. A., Davidson, F.,
Hammill, M. O., Stenson, G. B., and Rosing-Asvid, A.: Rapid circulation of
warm subtropical waters in a major glacial fjord in East Greenland, Nat.
Geosci., 3, 182–186, 10.1038/NGEO764, 2010.Tedesco, M., Fettweis, X., Mote, T., Wahr, J., Alexander, P., Box, J. E., and
Wouters, B.: Evidence and analysis of 2012 Greenland records from spaceborne
observations, a regional climate model and reanalysis data, The Cryosphere,
7, 615–630, 10.5194/tc-7-615-2013, 2013.van den Broeke, M., Bamber, J., Ettema, J., Rignot, E., Schrama, E., van de
Berg, W. J., van Meijgaard, E., Velicogna, I., and Wouters, B.:
Partitioning Recent Greenland Mass Loss, Science, 326, 984–986,
10.1126/science.1178176, 2009.Warren, C. R.: Terminal environment, topographic control and fluctuations of
West Greenland glaciers, Boreas, 20, 1–15,
10.1111/j.1502-3885.1991.tb00453.x, 1991.Warren, C. R. and Glasser, N. F.: Contrasting response of south Greenland
glaciers to recent climatic change, Arctic Alpine Res., 24, 124–132, 1992.
Wood, M., Rignot, E., Fenty, I., Menemenlis, D., Millan, R., Morlighem, M.,
Mouginot, J., and Seroussi, H.: Ocean-induced melt triggers glacier retreat
in Northwest Greenland, Geophys. Res. Lett., 45, 8334–8342,
10.1029/2018GL078024, 2018.Xu, Y., Rignot, E., Menemenlis, D., and Koppes, M.: Numerical experiments on
subaqueous melting of Greenland tidewater glaciers in response to ocean
warming and enhanced subglacial discharge, Ann. Glaciol., 53, 229–234,
10.3189/2012AoG60A139, 2012.Xu, Y., Rignot, E., Fenty, I., Menemenlis, D., and Flexas, M. M.: Subaqueous
melting of Store Glacier, west Greenland from three-dimensional,
high-resolution numerical modeling and ocean observations, Geophys. Res.
Lett., 40, 4648–4653, 10.1002/grl.50825, 2013.Yin, J., Overpeck, J. T., Griffies, S. M., Hu, A., Russell, J. L., and
Stouffer, R. J.: Different magnitudes of projected subsurface ocean warming
around Greenland and Antarctica, Nat. Geosci., 4, 524–528,
10.1038/NGEO1189, 2011.