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Kronebreen, Svalbard – Effects of Undercutting and Sliding on Calving: a
Global Approach
In this paper Vallot et al.
present the results of their study of the effects of basal friction,
subaqueous undercutting and glacier geometry on the process of calving
by combining 6 different models in an offline-coupled workflow:
1)
A continuum-mechanical ice flow model (Elmer/Ice),
2)
A climate mass balance model,
3)
a simple subglacial hydrology model,
4)
A plume model,
5)
an undercutting model, and
6)
a discrete particle model,
to investigate fracture dynamics (Helsinki Discrete Element Model,
HiDEM). They demonstrated the feasibility of reproducing the calving
that had been observed at the front of Kronebreen¸ a tidewater glacier
in Svalbard, during a melt season by using the output from the first 5
models as input to the HiDEM. The use of Elmer/Ice addressed the basal
sliding and glacier motion, while HiDEM modelled calving. A hydrology
model calculated subglacial drainage paths and it indicated 2 main
outlets with different discharges. Depending on the discharge, the
frontal melts rates, which are interatively projected to the actual
front of the glacier at locations of subglacial discharge. Undercutting
at different sizes is produced by this, as melt is concentrated close to
the surface for high discharge and for low discharge is more diffuse.
Vallot et al. have shown by
testing different configurations that a key role is played by
undercutting in the retreat of glaciers in the vicinity of the discharge
locations during the melting season. Basal friction often influenced
calving rates, by its effects on strain-rates and ice velocity near the
terminus.
A major contributor to the rising sea level is the accelerated rate of
discharge of ice into the oceans from the land, and it constitutes the
largest source of uncertainty in predictions of sea level rise for the
21st century and beyond (Church et
al., 2013). This uncertainty
reflects, to a large degree, the limited understanding of processes that
impact calving from tidewater glaciers and ice shelves, as well as
associated feedbacks with glacier dynamics. Calving occurs, in
particular, by the propagation of fractures, which are not represented
explicitly in the continuum models that are used to simulate the flow of
ice and the evolution of glaciers.
It has been suggested recently that the warming ocean could play an
important part in determining the calving rate and acceleration of a
glacier by impacting the rates of submarine melting (Holland et
al., 2008; Luckman et
al., 2015). There are 2
mechanisms that have been proposed to be responsible for the increase in
submarine melt rates at the ice-ocean interface in Greenland: A warmer,
thicker layer of Atlantic water in the fjords and subglacial discharge
has increased mainly during summer and autumn. Warm ocean water is
entrained by buoyant plumes of meltwater (Jenkins, 2011) and is believed
to enhance melt undercutting (Slater et
al., 2015) as the ice cliff
which triggers the collapse of iced above. Controls on seasonal
variations in calving rates were investigated (Luckman et
al., 2015) which showed that
calving variations at Kronebreen, the glacier this study was focused on,
correlated strongly with changes in temperature of the subsurface ocean
linked to melt undercutting of the calving front. Direct measurements of
oceanic properties, ice dynamics, frontal geometries and mean volumetric
frontal rates of ablation, however, are still too scarce to quantify the
relationship between ocean processes, subglacial discharge and ice
dynamics and modelling must be relied on. According to Vallot et
al. complex coupled process
models can help in leading to a better understanding of the physics that
are taking place at tidewater glacier fronts.
The dynamics of ice masses have been simulated in previous modelling
work, the dynamics of ice masses (Van der Veen, 2002; Benn et
al., 2007; Amundsen &
Truffer, 2010; Nick et al.,
2010; Cook et al., 2012; Krug
et al., 2014, 2015) by the
use of continuum models, in which the continuum space is discretised and
include mass and energy balance processes. According to Vallot et
al. continuum models cannot
model explicitly fracture but must use simple parametrisations such as
variables of damage or the criteria of phenomenological calving.
Discrete particle models, which represent ice as assemblages of
particles that are linked by breakable elastic bonds, can be used to
circumvent these problems. Each particle obeys Newton’s equations of
motion as ice is considered to be a granular material. The bond is
broken above a certain stress threshold, which allows the ice to
fracture. It has been shown, (Åström et
al., 2013,2014) that complex
crevasse patterns and processes of calving that are observed in nature
can be modelled using a particle model, the Helsinki Discrete Element
Model (HiDEM).
A compromise should be found by the coupling of a continuum model, such
as Elmer/Ice, to a discrete model, such as HiDEM, to successfully
describe the ice as a fluid and as a brittle solid. The discrete
particle model uses sliding velocities and ice geometry that are
calculated with a dynamic model to compute a new position for the
calving front. The effect of mixing subglacial drainage with the ocean
during the melt season is taken into account by the use of a plume model
that estimates melt rates at the ice front according to pro-glacial
ocean temperatures that are observed, subglacial discharge that is
derived from surface runoff and the height of the ice front, taking into
account.
In this paper Vallot et al.
use the capabilities of the continuum model Elmer/Ice and the discrete
element model HiDEM. They used the ability of HiDEM to model fracture
and calving events, while retaining the long-term ice flow solutions of
a continuum approach. The aim was to investigate the influence the
velocity of basal sliding, geometry, and undercutting at the calving
front has on the calving rate and location. The undercutting was
determined with a high-resolution plume model that calculated melt rates
from the rates of subglacial discharge. The simple hydrological model
that calculates subglacial discharge is based on surface runoff that is
assumed to be transferred directly to the bed and routed along the
surface of hydrological potential. Vallot et
al. illustrate the approach
by using data from Kronebreen, which is a fast-flowing glacier in
western Spitsbergen, Svalbard (topography, meteorological and
oceanographic data, as well as horizontal surface velocity and front
positions from 2013) to assess the feasibility of modelling retreat of
the calving front (rate and position).
Conclusions
In this study the abilities of different models were used which
represent different processes in glaciers at Kronebreen, Svalbard, with
the focus on calving during the melt season of 2013. Data were provided
for inputs to the models and validation, which included surface
velocity, position of the front, topography, bathymetry and ocean
properties.
The continuum ice flow model Elmer/Ice, which computes basal velocities
by inverting surface velocities that are observed and evolves the
geometry, which includes the position of the front, is the best model
for representing the long-term fluid-like behaviour of ice. A subglacial
hydrology system is formed during the melt season which allows the water
to be evacuated at the front of the glacier.
Vallot et
al. used a simple hydrology
model that was based on surface runoff to transmit directly to the bed
and routed the basal water along the deepest gradient of the hydraulic
potential. There are 2 subglacial discharge locations that have been
identified by this approach:
·
the northern one evacuates water of high rate (⁓10-100 m3/sec)
and
·
a southern one that has a low rate of ⁓1-3 m3/sec.
Subsequently this fresh water is mixed with ocean water. Warm fjord
water is entrained by rising plumes of meltwater [fresh water is
lighter, less dense, than sea water, so rises to the surface of the
ocean] which melts the subaqueous ice that forms undercuttings at the
location of the glacial discharge. The plume was modelled with a
simplified 2-D geometry by the use of a high-resolution plume model that
was based on the fluid dynamics code Fluidity adapted to the height of
the front and the ocean properties of Kronebreen. Melt rates are
dependent on the rates of discharge and the shape of the plume greatly
differs with its magnitude. There is a tendency for the plume to rise to
the surface close to where the melt rates are at their highest, while
low discharges concentrate the melt at lower elevations. While taking
into account the shape of the subaqueous ice front of the former time
step the melt rates are then projected to the actual frontal geometry.
According to Vallot et al. it
is interesting to note that the undercutting that is modelled for high
subglacial discharges are spatially close to the calving front that is
observed, whereas such a correspondence is not evident for small
discharges. A discrete particle model, HiDEM, was used to model the
elastic-brittle behaviour of the ice, such as the formation of crevasses
and calving processes. In this study 2 factors were investigated which
impact the calving of glaciers using the HiDEM model:
i)
melt undercutting that is associated with buoyant plumes, and
ii)
basal friction, which influences strain rates and velocity near the
terminus.
The performance of the calving model was quantitatively evaluated by
comparison of modelled mean volumetric and observed calving rate and
quantitatively by comparing calved regions. It was shown by results that
during the melt season in the absence of melt calving, modelled calving
rates are lower than observed values, and that there is a closer match
with observations if undercutting is included. Also there is good
agreement before (t0) and after (t11) the melt
season between modelled and observed calving, when there is no
undercutting. After the melt season the modelled and observed calving
rates are much greater than before, which Vallot et
al. attribute to lower basal
friction and higher strain rates in the region near the terminus at
t11. Model
experiments that transposed early- and late-season values of friction,
had a large effect on modelled calving, corroborating the influence of
basal friction on calving rates. These results are consistent with the
conclusions reached by Luckman et
al (2015), that the primary control on calving at Kronebreen at the
seasonal scale, is melt undercutting, whereas at times of higher
velocity (i.e. low basal friction) dynamic factors are important.
According to Vallot et al.,
they have shown in this paper that offline coupling the ice-flow,
surface melt, basal drainage, plume-melting, and ice-fracture models can
provide a good match to observations and yield improved understanding of
the controls on calving processes. Full model coupling, which includes
forward modelling of ice flow by the use of physical sliding law, would
allow a further extension of this work to include prediction of the
response of glaciers to atmospheric forcing and ocean forcing.
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Author: M.H.Monroe Email: admin@austhrutime.com Sources & Further reading |