Submarine melting of the calving face of tidewater glaciers and the mechanical back force applied by the ice mélange layer are two mechanisms generally proposed to explain seasonal variations at the calving front of tidewater glaciers. However, the way these processes affect the calving rate and glacier dynamics remains uncertain. In this study, we used a finite element-based model that solves the full Stokes equations to simulate the impact of these forcings on two-dimensional theoretical flow line glacier configurations. The model, which includes calving processes, suggests that frontal melting affects the position of the terminus only slightly (less than a few hundred metres) and does not affect the multiannual glacier mass balance at all. However, the ice mélange has a greater impact on the advance and retreat cycles of the glacier front (more than several kilometres) and its consequences for the mass balance are not completely negligible, stressing the need for better characterization of forcing properties. We also show that ice mélange forcing against the calving face can mechanically prevent crevasse propagation at sea level and hence prevent calving. Results also reveal different behaviours in grounded and floating glaciers: in the case of a floating extension, the strongest forcings can disrupt the glacier equilibrium by modifying its buttressing and ice flux at the grounding line.
In the context of global warming, the cryosphere's contribution to sea level
rise is a major concern. Depending on the four RCP scenarios (representative
concentration pathways) considered in the IPCC fifth assessment
Increasing ice loss highlights the need for accurate estimations of the
future mass balance, but the large discrepancies in the behaviour of
Greenland's outlet glaciers make a simple mass balance extrapolation
unreliable unless we understand the processes that control their dynamics
Another quantity, that of ice mélange, a heterogeneous
mixture of sea ice, marine ice, blown snow, and fragments of icebergs, is
suspected to play an important role in the seasonal cycles of the glacier
front
Several attempts have been made to incorporate frontal melting and the ice
mélange back force in ice flow models. In particular, the relation between
calving and undercutting was investigated by
In this article we examine the consequence of submarine frontal melting and
the ice mélange on glacier dynamics and on the behaviour of the glacier
front using a full Stokes ice-flow finite element model combined with calving
parameterization based on damage and fracture mechanics. This enables a
complete representation of the stress field in the vicinity of the front and
provides a reliable tool to study front dynamics. To be sure our conclusions
are robust for a number of glacier geometries and flow specifications, we ran
more than 200 simulations combining a wide range of glacier sizes, flow and
damage parameters, and forcing constraints. We provide a brief description of
the model in Sect.
We considered an incompressible, isothermal, and gravity-driven ice flow. The
ice exhibits non-linear viscosity, and the flow is ruled by the Stokes
equations, which reads
The ice-flow model described above was coupled with a calving model based on damage and fracture mechanics. Damage mechanics were used to describe the slow degradation of the mechanical properties of ice under the stress field, averaged at a mesoscale. Linear elastic fracture mechanics (LEFM) were used to describe the brittle initiation and propagation of crevasses.
Our damage model is inspired from the work of
This damage model was coupled with an LEFM
model
Among the numerical parameters required to run the model, three have to be
calibrated, and are discussed below: the damage critical value
The model summarized here is described in detail in
Setup of the experiment.
We wanted to generalize our conclusions to a wide range of two-dimensional
synthetic flow line glacier geometries of time-varying length (
Boundary conditions are the same as those given in
At the bed, the glacier can be either grounded or floating. The grounding
line position is obtained through the resolution of a contact problem
As glacier thickness can vary with time, the total
depth-integrated flux through the inlet boundary is kept constant ( A lateral friction is prescribed to account for a
constant fjord width of 10 km. This parameterization follows
List of geometries and their associated
parameters used for the model experiments.
Complete list of the experiments performed for each
setup listed in Table
For the purpose of comparison, we chose to apply submarine melting and ice
mélange forcing on glaciers in a quasi-steady-state (QSS) mode,
i.e. their front has to stabilize within a given range
lower than the length of one calving event.
Among the 60 simulations generated by the LHS sampling, 20 had this
feature and are listed in Table
For the sake of clarity, out of the 20 representative
geometries, unless otherwise specified, in Sects.
The 20 setups summarized in Table
The perturbations described in Sect.
Glacier frontal melting usually results from warm saline ocean water entering
the fjord and mixing with fresh and cold subglacial
freshwater flow. The resulting current melts the ice it meets as it rises
along the calving face
Most parameterizations of frontal melt in ice flow models published so far
assume a linear variation of melt from 0 at sea level to a maximum value at
the lowest point of the front. Following these
parameterizations, the maximum value is used to characterize the intensity
of the melt and is referred to as maximal melt rate (MMR).
Following these studies and measurements, we tested different MMR summer
values ranging from 0.41 to 12 m day
In addition, some modelling work suggest that “the melting increases with
height above the freshwater subglacial discharge”, leading to an
Although ice mélange and its effect on glacier dynamics have been studied
for a few decades The question of the force transmitted up glacier by the ice mélange is
more complex: using a two-dimensional flow line model, the back force must be represented
as pressure applied over a thickness. Measurements of the back pressure
Considering that sea ice binds fragments of icebergs together, we can
reasonably assume its stiffness is the first-order control on mélange
strength.
Shape of perturbations over a period of 1 year.
Finally, the ice mélange was prescribed through a time-varying back-stress
assumed to be homogeneous over its thickness and resulting in a total
back force equal to the product
Glacier response in the
undercutting experiments (Geo 9, Table
Illustrative example of the glacier shape.
The simulation starts on 1 January (time
As soon as the forcing was removed, all the fronts reached their QSS position
within a few months, except in simulation U4 (whose specific behaviour is
discussed in Sect.
Considering the contribution of melting and calving to ice loss, the volume
of calved ice always appears to be larger than the melted volume. During
summer, melting accounted for up to
Mean daily winter and summer ice loss due to calving (blue) and melting (green) for five values of melt rate, over 5 years. Computed from the control run (CR) and Geo 9, perturbations U1 to U4.
To account for the different geometries, we summarized them as a function of
their QSS mean thickness and velocity at the terminus for a given realistic
forcing in melting (U2) (Fig.
Daily averaged ice loss over the winter and
summer seasons for the 5 years of the simulation for the setups listed in
Table
To measure the impact of ice mélange, we ran simulations S1 to S4
(Table
Glacier response in ice
mélange experiments (Geo 9, Table
Figure
Such rapid acceleration of the flow was observed during calving events at the
front of the Jakobshavn glacier in May 2007 by
Figure
Daily averaged ice loss over the winter and
summer seasons for the 5 years of the simulation for the setups listed in
Table
According to
Concerning perturbations caused by the ice mélange, our model suggests that
calving ceases as soon as the applied back force reaches a given value. We
investigated model sensitivity to the applied back force by evaluating the
value of this threshold. To this end, we isolated the pairs of parameters
(
Histogram of the back force from an
ice mélange required to prevent calving. The mean of the distribution is
1.1
Our coupled ice flow and calving model enabled us to distinguish between the
different processes that culminate in iceberg calving that could be affected
by the ice mélange. In the first stage, development of the crevasse field
is determined by the damage criterion
Following damage to the ice, three criteria have to be fulfilled to trigger
calving: the condition on damage contour
Regarding model sensitivity to the thickness of the ice mélange, we observed that a thinner layer associated with a stronger back force reduced the calving rate more than a thicker layer associated with a weaker back force, with the same total back force (data not shown). This is because the thinnest layer of ice mélange is concentrated at sea level, which significantly reduces the stress intensity factor at this depth, thereby preventing crevasse propagation.
These mechanisms could explain the behaviour observed in
Fig.
The results presented in this section are in direct contrast with those of
Figure
Concerning the behaviour of the grounded geometry of Helheim Glacier,
Sketch of the process suggested for glacier equilibrium destabilization.
In our simulations, another difference appeared between grounded and floating
glaciers. In Sect.
Concerning these processes, we propose an explanation for this phenomenon
(see Fig.
Ice mélange and melting of the glacier front have been reported by many authors to influence the behaviour of tidewater glaciers. In particular, they have been cited as a possible explanation for the seasonal advance and retreat cycles of glacier fronts, among other external forcings. However, although some correlations between these mechanisms and the advance/retreat of the front have been established on many outlet glaciers in Greenland, little is known about the exact role of these forcings.
In this study, we combined a full Stokes ice flow model with a calving framework using damage and fracture mechanics to investigate the impact of these forcings on glacier dynamics. This allowed us to represent the slow degradation of the mechanical properties of the ice and the initiation and propagation of pre-existing fractures, which are essential to describe the processes occurring at the front. We performed experiments on a large set of synthetic geometries using different values for melting and ice mélange back-stress and thickness, and the conclusions we have drawn are robust in all these experiments. However, it is important to note that the model used here considers surface crevasses only. A deeper analysis would require the modelling of the development and propagation of basal crevasses, and their feedback with the stress field and the glacier dynamics.
Our modelling showed that frontal melting has an impact on
the calving rate and on the position of the front (less than a few hundred
metres), but no effect on inter-/multiannual mass loss. On
the contrary, applying an ice mélange layer against the front affects its
position to a larger extent (up to several kilometres) compared to melting.
In addition, its consequences for the inter-/multiannual mass loss, when
slight, may not be completely negligible and thus support
Finally, our results also reveal a feature that is specific to glaciers with floating termini, i.e. that strong perturbations (either in melting or in ice mélange) may affect their multiannual behaviour. By affecting the buttressing effect of the tongue, the perturbation may modify the subsequent glacier equilibrium and lead to a new stable geometry for the same model parameters. This new stable position then depends on feedback between glacier flow and calving law parameters.
This study was funded by the Agence Nationale pour la Recherche (ANR) through
the SUMER, Blanc SIMI 6-2012. All the computations presented in this paper
were performed using the CIMENT infrastructure
(