Observations over the past 2 decades show substantial ice loss associated with the speed-up of marine-terminating glaciers in Greenland. Here we use a regional three-dimensional outlet glacier model to simulate the behaviour of Jakobshavn Isbræ (JI) located in western Greenland. Our approach is to model and understand the recent behaviour of JI with a physical process-based model. Using atmospheric forcing and an ocean parametrization we tune our model to reproduce observed frontal changes of JI during 1990–2014. In our simulations, most of the JI retreat during 1990–2014 is driven by the ocean parametrization used and the glacier's subsequent response, which is largely governed by bed geometry. In general, the study shows significant progress in modelling the temporal variability of the flow at JI. Our results suggest that the overall variability in modelled horizontal velocities is a response to variations in terminus position. The model simulates two major accelerations that are consistent with observations of changes in glacier terminus. The first event occurred in 1998 and was triggered by a retreat of the front and moderate thinning of JI prior to 1998. The second event, which started in 2003 and peaked in the summer 2004, was triggered by the final break-up of the floating tongue. This break-up reduced the buttressing at the JI terminus that resulted in further thinning. As the terminus retreated over a reverse bed slope into deeper water, sustained high velocities over the last decade have been observed at JI. Our model provides evidence that the 1998 and 2003 flow accelerations are most likely initiated by the ocean parametrization used but JI's subsequent dynamic response was governed by its own bed geometry. We are unable to reproduce the observed 2010–2012 terminus retreat in our simulations. We attribute this limitation to either inaccuracies in basal topography or to misrepresentations of the climatic forcings that were applied. Nevertheless, the model is able to simulate the previously observed increase in mass loss through 2014.
The rate of net ice mass loss from Greenland's marine-terminating glaciers
has more than doubled over the past 2 decades (Rignot et al., 2008; Moon et
al., 2012; Shepherd et al., 2012; Enderlin et al., 2014). Jakobshavn
Isbræ, located mid-way up the western side of Greenland, is one of the
largest outlet glaciers in terms of drainage area as it drains
Over the past decade, we have seen significant improvements in the numerical modelling of glaciers and ice sheets (e.g. Price et al., 2011; Vieli and Nick, 2011; Winkelmann et al., 2011; Larour et al., 2012; Pattyn et al., 2012; Seroussi et al., 2012; Aschwanden et al., 2013, 2016; Nick et al., 2013; Mengel and Levermann, 2014) and several processes have been identified as controlling the observed speed-up of JI (Nick et al., 2009; Van der Veen et al., 2011; Joughin et al., 2012). One process is a reduction in resistance (buttressing) at the marine front through thinning and/or retreat of the glacier termini. However, the details of the processes triggering and controlling thinning and retreat remain elusive. Accurately modelling complex interactions between thinning, retreat, and acceleration of flow speed as observed at JI is challenging. Our knowledge of the mechanisms triggering these events is usually constrained to the period covered by observations. The initial speed-up of JI occurred at a time when the satellite and airborne observations were infrequent and therefore insufficient to monitor the annual to seasonal evolution of glacier geometry and speed.
Here, we use a high-resolution, three-dimensional, time-dependent regional outlet glacier model that has been developed as part of the Parallel Ice Sheet Model (PISM; see Sect. 2.1) (Khroulev and the PISM Authors, 2014) to investigate the dynamic evolution of JI between 1990 and 2014. While previous three-dimensional modelling studies have mostly concentrated on modelling individual processes using stress perturbations (e.g. Van der Veen et al., 2011; Joughin et al., 2012), the present study aims to model the recent behaviour of JI with a process-based model. Our modelling approach is based on a regional equilibrium simulation and a time integration over the period 1990 to 2014, in which the grounding lines and the calving fronts are free to evolve under the applied ocean parametrization and monthly atmospheric forcing.
The ice sheet model used in this study is the PISM (stable version 0.6). PISM
is an open-source, parallel, three-dimensional, thermodynamically coupled,
and time-dependent ice sheet model (Bueler and Brown, 2009; Khroulev and the PISM Authors,
2014). The model uses the superposition of the non-sliding shallow ice
approximation (SIA; Hutter, 1983) for simulating slowly moving grounded ice
in the interior part of the ice sheet and the shallow shelf approximation
(SSA; Weis et al., 1999) for simulating fast-flowing outlet glaciers and ice
shelf systems. We solve the SIA with a non-sliding base and use the SSA as a
basal sliding velocity for the ice grounded regions (Winkelmann et al.,
2011). This superposition of SIA and SSA (the “SIA
In PISM, the basal shear stress is related to the sliding velocity through a nearly plastic power law (Schoof and Hindmarsh, 2010). The Mohr–Coulomb criterion (Cuffey and Paterson, 2010) is used to connect a saturated and pressurized subglacial till with a modelled distribution of yield stress. The yield stress depends on the effective pressure and on a spatially varying till friction angle derived heuristically as a piecewise-linear function of the bed elevation (Martin et al., 2011; Winkelmann et al., 2011; Aschwanden et al., 2013). The effective pressure on the till is determined by the ice overburden pressure and the effective thickness of water in the till (Tulaczyk et al., 2000a, b). In this subglacial hydrology model the water is not conserved and it is only stored locally in the till up to a maximum thickness of 2 m. The ice flow therefore develops in PISM as a consequence of plastic till failure, i.e. where the basal shear stress exceeds the yield stress, and is influenced by the thermal regime and the volume of water at the ice sheet bed.
The underlying equations are further illustrated in the Supplement.
We use the bed topography from Bamber et al. (2013). This 1 km bed elevation
data set for all of Greenland was derived from a combination of multiple
airborne ice thickness surveys and satellite-derived elevations during
1970–2012. The data set has an increased resolution along the ice sheet
margin. In the region close to the outlet of JI, data from an 125 m CReSIS
digital elevation model (that includes all the data collected in the region by CReSIS between
1997 and 2007) have been used to improve the accuracy of the data set. Errors
in bed elevation range from 10 to 300 m, depending on the distance from an
observation and the variability of the local topography (Bamber et al.,
2013). The terminus position and surface elevation in the Jakobshavn region
are based on 1985 aerial photographs (Csatho et al., 2008). Ice thickness in
the JI basin is computed as the difference between surface and bedrock
elevation. The model of the geothermal flux is adopted from Shapiro and
Ritzwoller (2004). We use monthly input fields of near-surface air
temperature and surface mass balance (SMB) from the regional climate model
RACMO2.3 (Noël et al., 2015; Figs. S2 and S3 in the Supplement), which
here represent the only seasonal input used in the model. The version used in
this study is produced at a spatial resolution of
In our model, the three-dimensional ice enthalpy field, basal melt for
grounded ice, modelled amount of till-pore water, and lithospheric
temperature are obtained from an ice-sheet-wide palaeoclimatic spin-up. The
palaeoclimatic spin-up follows the initialization procedure described by
Bindschadler et al. (2013) and Aschwanden et al. (2013). We start the spin-up
on a 10 km grid, and then we further refine it to 5 km at
In the regional outlet glacier model of PISM, the boundary conditions are
handled in a 10 km strip positioned outside of the JI's drainage basin and
around the edge of the computational domain (Fig. 1b). In this strip, the
input values of the basal melt, the amount of till-pore water, ice enthalpy,
and lithospheric temperature (Aschwanden et al., 2013) are held fixed and
applied as Dirichlet boundary conditions in the conservation of energy model
(Khroulev and the PISM Authors, 2014). The boundary conditions for the enthalpy at the
ice–bedrock interface follow Aschwanden et al. (2012). We start our regional
JI runs with an equilibrium simulation on a horizontal grid with 5 km
spacing. The enthalpy formulation models the mass and energy balance for the
three-dimensional ice fluid field based on 200 regularly spaced ice layers
within a domain extending 4000 m above the bed elevation. The temperature of
the bedrock thermal layer is computed up to a depth of 1000 m with 50
regularly spaced layers. The first step is to obtain a 5 km regional
equilibrium model for JI using constant mean climate (i.e. repeating the
1960–1990 mean air temperature and SMB; see Sect. 2.1.1). We consider that
equilibrium has been established when the ice volume in the regional domain
changes by less than 1 % in the final 100 model years. Grid refinements
are made from 5 km (125
In our regional model, all boundaries (calving fronts, grounding lines,
upper, and lower surfaces) are free to evolve in time both during the
regional equilibrium and the forward simulations. Along the ice shelf
calving front, we superimpose a physically based calving (eigen-calving)
parametrization (Winkelmann et al., 2011; Levermann et al., 2012) and a
basic calving mechanism (Albrecht et al., 2011) that removes any floating
ice at the calving front thinner than a given threshold at a maximum rate of
one grid cell per time step. The average calving rate (
A partially filled grid cell formulation (Albrecht et al., 2011), which allows for sub-grid-scale retreat and advance of the ice shelf front, is used to connect the calving rate computed by the calving parametrizations with the mass transport scheme at the ice shelf terminus. This sub-grid-scale retreat and advance of the shelf allows for realistic spreading rates that are important for the eigen-calving parametrization. The sub-grid interpolation is performed only when a floating terminus exists. In both situations (i.e. floating ice or grounded terminus), the stress boundary conditions are applied at the calving front and in the discretization of the SSA equations (Winkelmann et al., 2011). The retreat and advance of the front through calving is restricted to at most one grid cell length per adaptive time step.
The parametrization of the grounding line position is based on a linear
interpolation scheme (the “LI” parametrization; Gladstone et al., 2010)
extended to two horizontal dimensions (
We use a simple parametrization for ice shelf melting where the melting effect of the ocean is based on both sub-shelf ocean temperature and salinity (Martin et al., 2011). To accommodate this parametrization, several changes have been made to PISM at the sub-shelf boundary (Winkelmann et al., 2011). First, the ice temperature at the base of the shelf (the pressure-melting temperature) necessary for the enthalpy solver (Aschwanden et al., 2012) is calculated from the Clausius–Clapeyron gradient and the elevation at the base of the shelf. The ice temperature is then applied as a Dirichlet boundary condition in the conservation of energy equation.
Secondly, basal melting and refreezing is incorporated through a sub-shelf mass flux used as a sink/source term in the mass-continuity equation. This mass flux from shelf to ocean (Beckmann and Goosse, 2003) is computed as a heat flux between the ocean and ice and represents the melting effect of the ocean due to both temperature and salinity (Martin et al., 2011).
In our simulations we use a constant ocean water temperature (
Following for this melting parametrization, the highest melt rates are
modelled in the proximity of the glacier grounding lines and decrease with
elevation such that the lowest melt rates are closer to the central to
frontal area of the modelled ice shelf. At the grounding line, PISM computes
an extra flotation mask that accounts for the fraction of the cell that is
grounded by assigning 0 to cells with fully grounded ice, 1 to cells with
ice-free or fully floating ice, and values between 0 and 1 to partially
grounded grid cells. The basal melt rate in the cells containing the
grounding line is then adjusted based on this flotation mask as follows
(Khroulev and the PISM Authors, 2014):
This section is organized in two main subsections. Section 3.1 introduces the results obtained relative to observations, and Sect. 3.2 focuses mainly on the limitations of the model that need to be considered before a final conclusion can be drawn. A short introduction to the different simulations and preparatory experiments performed is given below.
A total number of 50 simulations with different sets of parameters (excluding preparatory and additional experiments on the 1 km grid) are performed on a 2 km grid. We alter six parameters that control the ice dynamics (e.g. the flow enhancement factor, the exponent of the pseudo-plastic basal resistance model, the till effective fraction overburden), the ice shelf melt, the ocean temperature, and the calving (i.e. the ice thickness threshold in the basic calving mechanism). These parameters are modified only during the regional JI runs such that the model reproduces the frontal positions and the ice mass change observations at JI during the period 1990–2014 (Fig. 2) and 1997–2014 (Figs. 3 and 4) respectively. From these results, we present the parametrization that best captures (i.e. we estimate the residual between modelled and observed ice mass change and select the smallest residual signal) the full observed evolution of JI during the period 1990–2014 (Figs. 2, 3, 4, and 5). The values of the ice sheet model parameters used and the ice sheet model sensitivity to parameters controlling ice dynamics, basal processes, ice shelf melt, and ocean temperature are further illustrated in the Supplement.
Modelled velocities at Jakobshavn Isbræ for December are shown for 8 different years. The black line represents the modelled front positions, the black dotted line denotes the observed front position, and the thick black dashed line represents the modelled grounding line position. The velocities are superimposed over a Landsat 8 image acquired in August 2014.
We investigate the processes driving the dynamic evolution of JI and its variation in velocity between 1990 and 2014 with a focus on the initial speed-up of JI (1990) and the 2003 break-up of the ice tongue. The overall results from our simulations suggest a gradual increase in velocities that agree well with observations (Joughin et al., 2014) (Fig. 3). Three distinct stages of acceleration are identified in Fig. 3 (see also Movie 1 in the Supplement) and discussed in detail below.
Modelled and observed cumulative mass change for Jakobshavn
Isbræ. The blue curve represents the mass change due to SMB (Noël et
al., 2015) after the 1960–1990 baseline is removed. The green curve
represents the modelled ice dynamics mass change (i.e. modelled mass change
minus SMB change). The red curve represents the total modelled mass change
including both SMB and ice dynamic changes. The black curve with grey error
limits represents the total observed mass change including both SMB and ice
dynamic changes. The modelled mass change for the period 1997–2014 is
The first speed-up produced by the simulation is caused by a retreat of the front position by approximately 2 to 4 km between 1990 and 1991. There is no observational evidence to confirm that this retreat actually occurred. The simulated retreat is probably a modelling artefact as the geometry obtained during the regional equilibrium simulation is forced with monthly atmospheric forcing and new oceanic conditions. This simulated acceleration (Fig. 3) is caused in our model by a reduction in buttressing due to a reduction in lateral resistance (Van der Veen et al., 2011), which is generated by the gradual retreat of the front and triggers a dynamic response in the upstream region of JI.
Starting in 1992, the modelled and observed terminus positions agree (not shown in Fig. 2). Apart from the acceleration in 1991–1992, no significant seasonal fluctuations in flow rate are found in our simulations for this period, a result that is consistent with observations (Echelmeyer et al., 1994). From 1993 a stronger sub-annual velocity signal begins to emerge in our simulation that continues and intensifies in magnitude during 1994 and 1995. Modelled mean-annual velocities for 1992 and 1995 are consistent with observed velocities for the same period (Joughin et al., 2008; Vieli and Nick, 2011). In 1996 and 1997, the frontal extent and the grounding line position remain relatively stable (Figs. 2, 6, and 7), and no significant seasonal fluctuation in ice flow rate is observed in the simulation. These model results agree well with observations, which indicate that the glacier speed was relatively constant during this period (Luckman and Murray, 2005).
According to observations (Joughin et al., 2004; Luckman and Murray, 2005;
Motyka et al., 2011; Bevan et al., 2012), the initial acceleration of JI
occurred in May–August 1998, which coincides with our modelled results. In
our simulation, the 1998 acceleration is generated by a retreat of the ice
tongue's terminus in 1997–1998, which may be responsible for reducing
buttressing (Fig. 7 and Movie 1 in the Supplement). Thinning, both near the
terminus and inland (up to 10 km away from the 1990 front position), starts
in our model in the summer of 1995 and continues to accelerate after 1998
(Figs. 3, 6, and 7). The modelled behaviour agrees well with the observed
behaviour (Krabill et al., 2004). Although thinning appears to have increased
in our model during 3 continuous years, it produced only minor additional
speed-up during the period prior to 1998 (Figs. 2, 6, and 7). In our
simulation, JI's speed increased in the summer of 1998 by
Observed versus modelled uplift in millimetres for the stations
KAGA
In the late summer of 2003, the simulated flow velocity increases (Fig. 3).
This acceleration of JI is driven in our simulations by the final break-up of
the ice tongue (see Figs. 2 and 6). The period 2002–2003 is characterized in
our model by substantial retreat of the front (
In agreement with previous studies (e.g. Joughin et al., 2012), our results suggest that the overall variability in the modelled horizontal velocities is a response to variations in terminus position (Fig. 7). In our simulation, the retreat of the front reduced the buttressing at the terminus and generated a dynamic response in the upstream region of JI which finally led to flow acceleration. In contrast, when the front advanced the modelled flow slowed as the resistive stresses at the terminus were reinforced. This buttressing effect tends to govern JI's behaviour in our model. Regarding the overall terminus retreat, our simulations suggest that it is mostly driven by the sub-shelf melting parametrization applied (Figs. S5 and S14). Although the heat flux supplied to the shelf evolves in time based on the modelled terminus geometry, the input ocean temperature is kept constant throughout the simulations. This constant ocean forcing at the terminus leads, in our simulation, to gradual thinning of JI and favours its retreat without any shift (e.g. increase) in ocean temperature. In terms of seasonality, the only seasonal input into the model is introduced by the monthly atmospheric forcing that is applied (Sect. 2.1.1). In our model, the atmospheric forcing that is applied (Figs. S2 and S3) can influence JI's dynamics through changes in SMB (i.e. accumulation and ablation), which affects both the SIA and the SSA (Sect. 2.1). However, the modelled sub-annual variability in terms of terminus retreat and velocities does not always follow the seasonal signal (Fig. 3). We investigate this higher than seasonal variability in Sect. 3.2.
Figure 4 shows observed and modelled mass change for the period 1997 to 2014.
We estimate the observed rate of ice volume changes from airborne and
satellite altimetry over the same period and convert these to rates of mass
change (Supplement, Sect. 2). Overall we find good agreement between modelled
and observed mass change (Fig. 4), and our results are in agreement with
other similar studies (Howat et al., 2011; Nick et al., 2013). Dynamically
driven discharge is known to control Jakobshavn's mass loss between 2000 and
2010 (Nick et al., 2013). The modelled cumulative mass loss is 269 Gt, of
which 93 % (
Modelled evolution of surface elevation (floating ice tongues thinner than 50 m are not shown) and horizontal velocities of Jakobshavn Isbræ for December along the flow line shown in Fig. 1c. Note the acceleration in speed between 1994 and 1998 and between June 2003 and September 2003 corresponding to the final break-up of the floating tongue. The red star denotes the observed 2012 terminus position.
Although the terminus has ceased to retreat in our simulations after 2009 (Figs. 6 and 7), the modelled mass loss, and more importantly the dynamic mass loss, continues to accelerate (Fig. 4). Our results show (Fig. 7) that during this period the mass change is mostly driven by the sub-annual terminus retreat and advance, which continues to generate dynamic changes at JI through seasonal (sub-annual scale) reductions in resistive stresses.
Representing the processes that act at the marine boundary (i.e. calving and
ocean melt) is important for understanding and modelling the retreat/advance
of marine-terminating glaciers like JI. Determining terminus positions by
using the superposition of a physically based calving (eigen-calving)
parametrization (Winkelmann et al., 2011; Levermann et al., 2012) and a basic
calving mechanism (Albrecht et al., 2011) is motivated by the model's ability
to maintain realistic calving front positions (Levermann et al., 2012). The
eigen-calving parametrization cannot resolve individual calving events, and,
thus, the introduction of the basic calving mechanism was necessary in order
to accurately match observed front positions. Preparatory experiments have
shown that calving is mostly driven in our model by the basic calving
mechanism used (
As introduced in Sect. 2, our approach here is to adjust the terminus in the
JI region to simulate the 1990s observed front position and surface elevation
based on 1985 aerial photographs (Csatho et al., 2008). The glacier terminus
in 1990s was floating (Csatho et al., 2008; Motyka et al., 2011). Motyka et
al. (2011) calculated the 1985 hydrostatic equilibrium thickness of the south
branch floating tongue from smoothed surface digital elevation models and
obtained a height of 600 m near the calving front and 940 m near the
grounding zone. In this paper, however, we compute the thickness as the
difference between the surface elevation and the bed topography and allow the
glacier to evolve its own terminus geometry during the equilibrium
simulation. Preparatory experiments have shown that in our model
(disregarding its initial geometry floating/grounded terminus) JI attains
equilibrium with a grounding line position that stabilizes close to the 1990s
observed terminus position. According to observations, JI is characterized in
1990 by a large floating tongue (
The geometry of the terminus plays an important role in parametrizing ice
shelf melting, and therefore our pre-1999 geometry will influence the
magnitude of the basal melt rates (Sect. 2.1.3). The difference in geometry
results in modelled mean basal melt rates that are larger for the period
1999–2003 (Table S3), when JI begins to develop a large floating tongue and
when the calving front was already largely floating. The modelled mean melt
rates for the period 1999–2003 are large and likely overestimated. Relative
to other studies, e.g. Motyka et al. (2011), our yearly mean melt rate for
1998 is
Starting in 2010, the retreat of the terminus modelled in our simulations did not correlate well with observations (Fig. 2). The observed terminus and the grounding line retreats do not cease after 2010. Further, observed front positions (Joughin et al., 2014) suggest that by the summer 2010 JI was already retreating over the sill and on the over deepening indicated by the red star in Fig. 6. The observed retreat is not reproduced in our simulations suggesting that additional feedbacks and/or forcings most likely affect the glacier. Alternatively, the mismatch between observations and simulation results may represent an incomplete modelling of the physics, inaccuracies in atmospheric/oceanic conditions, or other various limitations (e.g. bed topography model constraints and grid resolution constraints). The particular influence of these potential limitations on our model is detailed below.
The basal topography of JI's channels represents a large source of uncertainty. JI is a marine-terminating glacier whose bedrock topography is characterized by a long and narrow channel with deep troughs that contribute to its retreat and acceleration; e.g. once the grounding line starts to retreat on a down-sloping bed the flow increases, leading to further retreat and acceleration (Vieli et al., 2011). The timing and the magnitude of these retreats depend on bed topography and the glacier width changes (Jamieson et al., 2012; Enderlin et al., 2013). Accurate modelling of the grounding line behaviour is, therefore, crucial for JI's dynamics as its retreat removes areas of flow resistance at the base and may trigger unstable retreat if the glacier is retreating into deeper waters. In our simulation, the grounding line position stabilizes downstream of the sill after 2005 (Figs. 2 and 6), which is in accordance with previous modelling studies (Vieli et al., 2001; Vieli and Nick, 2011). Vieli and Nick (2011) found that, by artificially lowering the same bed sill by 100 m, the grounding line eventually retreats and triggers a catastrophic retreat of 80 km in just over 20 years. In an equivalent experiment with Vieli and Nick (2011) but performed with our model, lowering the bed sill by 100 m did not result in a retreat of the grounding line over the sill. Regarding the grid resolution, simulations performed on a 1 km grid did not improve our simulations of ice thickness (Fig. S10) or surface speed (i.e. trend, overall magnitude, and shape of the flow; Fig. S11).
From a climatic perspective, the summer of 2012 was characterized by exceptional surface melt covering 98 % of the entire ice sheet surface and including the high-elevation summit region (Nghiem et al., 2012; Hanna et al., 2014). Overall, the 2012 melt season was 2 months longer than the 1979–2011 mean and the longest recorded in the satellite era (Tedesco et al., 2013). Furthermore, the summer of 2012 was preceded by a series of warm summers (2007, 2008, 2010, and 2011) (Hanna et al., 2014). Surface melt above average was already recorded in May–June 2012 (see Fig. 3 from NSIDC, 2015) when most of the 2011–2012 winter accumulation melted and over 30 % of the ice sheet surface experienced surface melt. An intense and long melt year leads to extensive thinning of the ice and has the potential to enhance hydrofracturing of the calving front due to melt water draining into surface crevasses (MacAyeal et al., 2003; Joughin et al., 2013; Pollard et al., 2015), resulting in greater and/or faster seasonal retreat and an increase in submarine melt at the terminus and the sub-shelf cavity (Schoof, 2007; Stanley et al., 2011; Kimura et al., 2014; Slater et al., 2015).
The seasonal retreat of JI's terminus started relatively early in 2012, with a large calving event having already occurred in June. While it seems difficult to attribute this particular calving event solely to processes related to the 2012 melt season, it does seem probable that the series of warm summers (2007–2011) together with the 2012 exceptional melt season could have enhanced hydrofracturing of the calving front. In turn, this could have induced a retreat of the terminus that cannot be captured by our model (i.e. in its present configuration the model cannot account directly for the influence of meltwater runoff and its role in the subglacial system during surface melt events). However, changes in ice thickness affect both the SIA and the SSA (Sect. 2.1). While the effect on the SIA is very weak as the driving stresses are not affected by a few metres of difference in thickness induced by SMB variability, in the SSA, the coupling is achieved via the effective pressure term in the definition of the yield stress (see Supplement, Sect. 1.2, for detailed equations). The effective pressure is determined by the ice overburden pressure (i.e. ice thickness) and the effective thickness of water in the till, where the latter is computed by time integrating the basal melt rate. Compared with SIA, this effect is stronger and may explain why in our model some seasonal velocity peaks could potentially be influenced by the atmospheric forcing applied (Figs. S9 and S14).
We study the sensitivity of the model to atmospheric forcing by performing a simulation where we keep the atmospheric forcing constant (mean 1960–1990 temperature and SMB). By comparing this simulation with a simulation that includes full atmospheric variability (monthly temperature and SMB) we find that to only a relatively small degree some of the variability appears to be influenced by the atmospheric forcing applied (Figs. S2 and S14), which also represents the only seasonal input into the model. Some of the greater than seasonal frequency could be an issue with resolution in the model. We examined this sensitivity by performing additional runs at a higher spatial resolution. Simulations on a 1 km grid did show some improvement with respect to surface speed sub-annual variability (Fig. S12), suggesting that in our model the stress redistribution might be sensitive to the resolution of the calving event. However, given the short period spanned by the simulations, the stress redistribution does not change the overall modelled results, as seen in Figs. S10 and S11. Although we acknowledge that some of the variability is due to the grid resolution, part of it may also be related to unmodeled physical processes acting at the terminus. We suggest that additional contributions to the seasonality, e.g. from ice mélange or seasonal ocean temperature variability, which are not included in our model, could potentially influence the advance and retreat of the front at seasonal scales (Fig. S14). For example, the ice mélange can prevent the ice at the calving front from breaking off and could therefore reduce the calving rates. Consequently, the introduction of an ice mélange parametrization will probably help to minimize some of the sub-annual signal modelled in our simulations. Similarly, seasonal ocean temperature variability can influence ice mélange formation and/or clearance and the melt rates at the glacier front and can accentuate seasonal glacier terminus and grounding line retreat and/or advance. However, at this point we find it difficult to determine the relative importance of each process.
Finally, regarding the ocean conditions, warm water temperatures in the fjord
were recorded in 2012. Besides a cold anomaly in 2010, which was sustained
until early 2011, the period 2008–2013 is characterized by high fjord water
temperatures – equal to or warmer than those recorded in 1998–1999 (Gladish
et al., 2015a, b). In our model, the ice melt
rates are determined from the given conditions in temperature
(
In this study, a three-dimensional, time-dependent regional outlet glacier model is used to investigate the processes driving the dynamic evolution of JI and its seasonal variation in ice velocity between 1990 and 2014. Here, we attempted to simulate the recent behaviour of JI with a process-based model. The model parameters were calibrated such that the model reproduced observed front positions (Fig. 2) and ice mass change observations (Fig. 4) at JI over the periods 1990–2014 and 1997–2014 respectively. We obtain a good agreement of our model output with time series of measured horizontal velocities, observed thickness changes, and GPS-derived elastic uplift of the crust (Figs. 3 and 5). Overall, the study shows progress in modelling the temporal variability of the flow at JI.
Our results suggest that most of the JI retreat during 1990–2014 is driven by the ocean parametrization and the glacier's subsequent response, which is largely governed by its own bed geometry (Figs. 6, 7, and S5). In agreement with previous studies (e.g. Joughin et al., 2012), our simulations suggest that the overall variability in the modelled horizontal velocities is a response to variations in terminus position (Fig. 7). In our model, the seasonal variability is likely driven by processes related to the atmospheric forcing applied (e.g. temperature and SMB variability), which in fact represents the only seasonal input used in the model. The greater-than-seasonal frequency seen in our simulations is attributed to grid resolution and missing seasonal-scale processes (e.g. ice mélange variability or seasonal ocean temperature variability) in the model. Sensitivity experiments performed on a 1 km grid did not show significant improvement with respect to ice thickness (Fig. S10) or surface speed (i.e. shape of the flow and overall magnitude; Fig. S11).
In 1990, JI had a large floating tongue (
Our model reproduces two distinct flow accelerations in 1998 and 2003 that
are consistent with observations. The first was generated by a retreat of the
terminus and moderate thinning prior to 1998; the latter was triggered by the
final break-up of the floating tongue. During this period, JI attained unprecedented velocities as high as 20 km a
In accordance with previous studies (Thomas, 2004; Joughin et al., 2012), our findings suggest that the speeds observed today at JI are a result of thinning-induced changes due to reduction in resistive stress (buttressing) near the terminus correlated with inland steepening slopes (Figs. 6 and 7). Both model and observations suggest that JI has been losing mass at an accelerating rate and that the glacier has continued to accelerate through 2014 (Fig. 4).
Ioana S. Muresan was responsible for the numerical modelling part. Jonathan Bamber provided the bed model. Michiel R. van den Broeke and Peter Kuipers Munneke provided climate data. Shfaqat A. Khan and Bert Wouters provided observational data. Ioana S. Muresan and Shfaqat A. Khan created the figures and wrote the manuscript with contributions from Andy Aschwanden, Jonathan Bamber, Tonie Van Dam, Michiel R. van den Broeke, Bert Wouters, Peter Kuipers Munneke, Kurt H. Kjær, and Constantine Khroulev.
Ioana S. Muresan is funded by the Forskningsraadet for Natur og Univers (grant no. 12-155118). Shfaqat A. Khan is supported by Carlsbergfondet (grant no. CF14-0145). Jonathan Bamber was part funded by UK NERC grant NE/M000869/1. Bert Wouters is funded by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme (FP7-PEOPLE-2011-IOF-301260). The development of PISM is supported by NASA grants NNX13AM16G and NNX13AK27G. We thank the editor, five anonymous reviewers for their valuable comments and suggestions to improve and clarify the manuscript, and Veit Helm for providing cryosat-2 data.Edited by: O. Gagliardini