Coupling an XFEM code for linear elastic fracture propagation to a viscous flow model. GeoComputation 2019

Ice flow models used to project the mass balance of ice sheets in Greenland and Antarctica usually rely on the Shallow Ice Approximation (SIA) and the Shallow‐Shelf Approximation (SSA), sometimes combined into so‐called “hybrid” models. Such models, while computationally efficient, are based on a simplified set of physical assumptions about the mechanical regime of the ice flow, which does not uniformly apply everywhere on the ice sheet/ice shelf system, especially near grounding lines, where rapid changes are taking place at present. Here, we present a new thermomechanical finite element model of ice flow named ISSM (Ice Sheet System Model) that includes higher‐order stresses, high spatial resolution capability and data assimilation techniques to better capture ice dynamics and produce realistic simulations of ice sheet flow at the continental scale. ISSM includes several approximations of the momentum balance equations, ranging from the two‐dimensional SSA to the three‐dimensional full‐Stokes formulation. It also relies on a massively parallelized architecture and state‐of‐the‐art scalable tools. ISSM employs data assimilation techniques, at all levels of approximation of the momentum balance equations, to infer basal drag at the ice‐bed interface from satellite radar interferometry‐derived observations of ice motion. Following a validation of ISSM with standard benchmarks, we present a demonstration of its capability in the case of the Greenland Ice Sheet. We show ISSM is able to simulate the ice flow of an entire ice sheet realistically at a high spatial resolution, with higher‐order physics, thereby providing a pathway for improving projections of ice sheet evolution in a warming climate.

Detailed measurements of surface topography, ice motion, snow accumulation, and ice thickness were made in January 1974 and again in December 1984, along an 8 km stake network extending from the ice sheet, across the grounding line, and on to floating ice shelf in the mouth of slow-moving Ice Stream C, which flows into the eastern side of Ross Ice Shelf, Antarctica. During the 11 years between surveys, the grounding line retreated by approximately 300 m. This was caused by net thinning of the ice shelf, which we believe to be a response to the comparatively recent, major decrease in ice discharge from Ice Stream C. Farther inland, snow accumulation is not balanced by ice discharge, and the ice stream is growing progressively thicker.There is evidence that the adjacent Ice Stream B has slowed significantly over the last decade, and this may be an early indication that this fast-moving ice stream is about to enter a period of stagnation similar to that of Ice Stream C. Indeed, these large ice streams flowing from West Antarctica into Ross Ice Shelf may oscillate between periods of relative stagnation and major activity. During active periods, large areas of ice shelf thicken and run aground on seabed to form extensive “ice plains” in the mouth of the ice stream. Ultimately, these become too large to be pushed seaward by the ice stream, which then slows down and enters a period of stagnation. During this period, the grounding line of the ice plain retreats, as we observe today in the mouth of Ice Stream C, because nearby ice shelf, no longer compressed by ice-stream motion, progressively thins. At the same time, water within the deformable till beneath the ice starts to freeze on to the base of the ice stream, and snow accumulation progressively increases the ice thickness. A new phase of activity would be initiated when the increasing gravity potential of the ice stream exceeds the total resistance of the shrinking ice plain and the thinning layer of deformable till at the bed. This could occur rapidly if the effects of the shrinking ice plain outweigh those of the thinning (and therefore stiffening) till. Otherwise, the till layer would finally become completely frozen, and the ice stream would have to thicken sufficiently to initiate significant heating by internal deformation, followed by basal melting and finally saturation of an adequate thickness of till; this could take some thousands of years.

Marine ice sheets rest on land that, for the most part, is below sea-level. Ice that flows across the grounding line, where the ice sheet becomes afloat, either calves into icebergs or forms a floating ice shelf joined to the ice sheet. At the grounding line there is a transition from ice-sheet dynamics to ice-shelf dynamics, and the creep-thinning rate in this region is very sensitive to sea depth; rising sea-level causes increased thinning-rates and grounding-line retreat, falling sea-level has the reverse effect. If the bedrock slopes down towards the centre of the ice sheet there may be only two stable modes: a freely-floating ice shelf or a marine ice sheet that extends to the edge of the continental shelf. Once started, collapse of such an ice sheet to form an ice shelf may take place extremely rapidly. Ice shelves which form in embayments of a marine ice sheet, or which are partially grounded, have a stabilizing influence since ice flowing across the grounding line has to push the ice shelf past its sides. Retreat of the grounding line tends to enlarge the ice shelf, which ultimately may become large enough to prevent excessive outflow from the ice sheet so that a new equilibrium grounding line is established; removal of the ice shelf would allow retreat to continue. During the late-Wisconsin glacial maximum there may have been marine ice sheets in the northern hemisphere but the only current example is the West Antarctic ice sheet. This is buttressed by the Ross and Ronne Ice Shelves, and if climatic warming were to prohibit the existence of these ice shelves then the ice sheet would collapse. Field observations suggest that, at present, the ice sheet may be advancing into parts of the Ross Ice Shelf. Such advance, however, would not ensure the security of the ice sheet since ice streams that drain to the north appear to flow directly into the sea with little or no ice shelf to buttress them. If these ice streams do not flow over a sufficiently high bedrock sill then they provide the most likely avenues for ice-sheet retreat.

New data on the thermal regime of George VI Ice Shelf have been obtained by thermistor chains installed through the use of a hot-water drill. Twenty thermistors are used at each site, spaced close together at sea-level and at the base of the ice shelf, and farther apart elsewhere in the ice shelf and in the sea beneath. Based on earlier observations (Bishop and Walton 1981, fig. 7) that the 10 m temperature warms from around −10°C in the central melt-lake area of the ice shelf (from 70°45′ to 71°45′S) to around −2°C near the northern ice front (70°00′S), the thermistor chains were deployed at three sites (70°00′, 70°15′ and 70°30′S) along a presumed flow line. The observations show that as ice flows towards the northern ice front of George VI Ice Shelf, it becomes more temperate in character. Heat from the sea and from the percolation of melt water at the upper surface progressively warms the ice shelf. At mid-depth (the coldest level in the ice shelf) the recorded temperatures were −6°C off Moore Point (70°30′S), −4°C off Carse Point (70°15′S) and, near the northern ice front (70°00′S), between −1.6° and −1.8°C depending on the time of year. The ice-shelf temperatures near the ice front, warmer in mid-summer than the freezing point of fully saline sea-water, are most unusual. The only explanation of the high, fluctuating temperatures found 1 year after drilling is that the hole through the ice shelf was open, allowing unimpeded water movement. This implies that the ice shelf is also warmed by the percolation of sea-water, whose presence was confirmed by ice-core drilling to below sea-level. Confirmation of the presence of brine below sea-level in the ice shelf comes from geo-electrical investigations. A Schlumberger georesistivity array modelled the ice shelf as a simple two-layer structure, with ordinary glacier overlying highly conductive ice. This is consistent with the fact that no radio echoes have been received from the bottom of George VI Ice Shelf to the north of 70°09′S. A detailed analysis of the ice-shelf / ocean-temperature profiles was undertaken. This included an analysis of the fluctuation observed in mid-summer at the warmest site and the subsequent transition to a stable isothermal profile through the submerged part of the ice shelf.

Abstract. An extensive network of GPS sites on the Filchner–Ronne Ice Shelf and adjoining ice streams shows strong tidal modulation of horizontal ice flow at a range of frequencies. A particularly strong (horizontal) response is found at the fortnightly (Msf) frequency. Since this tidal constituent is absent in the (vertical) tidal forcing, this observation implies the action of some non-linear mechanism. Another striking aspect is the strong amplitude of the flow perturbation, causing a periodic reversal in the direction of ice shelf flow in some areas and a 10 %–20 % change in speed at grounding lines. No model has yet been able to reproduce the quantitative aspects of the observed tidal modulation across the entire Filchner–Ronne Ice Shelf. The cause of the tidal ice flow response has, therefore, remained an enigma, indicating a serious limitation in our current understanding of the mechanics of large-scale ice flow. A further limitation of previous studies is that they have all focused on isolated regions and interactions between different areas have, therefore, not been fully accounted for. Here, we conduct the first large-scale ice flow modelling study to explore these processes using a viscoelastic rheology and realistic geometry of the entire Filchner–Ronne Ice Shelf, where the best observations of tidal response are available. We evaluate all relevant mechanisms that have hitherto been put forward to explain how tides might affect ice shelf flow and compare our results with observational data. We conclude that, while some are able to generate the correct general qualitative aspects of the tidally induced perturbations in ice flow, most of these mechanisms must be ruled out as being the primary cause of the observed long-period response. We find that only tidally induced lateral migration of grounding lines can generate a sufficiently strong long-period Msf response on the ice shelf to match observations. Furthermore, we show that the observed horizontal short-period semidiurnal tidal motion, causing twice-daily flow reversals at the ice front, can be generated through a purely elastic response to basin-wide tidal perturbations in the ice shelf slope. This model also allows us to quantify the effect of tides on mean ice flow and we find that the Filchner–Ronne Ice Shelf flows, on average, ∼ 21 % faster than it would in the absence of large ocean tides.

Abstract. Ice-shelf thickness and velocity anomalies resulting from ice-stream discharge fluctuations are calculated for an ideal ice shelf fed by a single ice stream and confined within a rectangular coastal geometry. Ice-shelf response to periodic forcing is found to be linear (thickness and velocity anomalies oscillate at the forcing frequency, and response scales with the forcing). Thickness anomalies are trapped near the ice-stream outlet and propagate down-stream at a slow, advective time-scale. Velocity anomalies tend to be widespread and propagate instantaneously throughout the ice-shelf environment. Ice-shelf response is sensitive to ice-stream fluctuation time-scale in the manner of a low-pass filter; longer forcing time-scales produce more widespread ice-shelf response. If ice-stream velocity and thickness fluctuations are in phase, thickness-anomaly maxima typically occur down-stream of the ice-stream outlet. This effect may determine where ice rumples and rises are likely to form in response to stochastic ice-stream variability.

Estimation of leak area-pressure relationship for cracks on water pipes using models based on linear-elastic fracture mechanics

<strong class="journal-contentHeaderColor">Abstract.</strong> Basal ice-shelf melting is the key driver of Antarctica's increasing sea-level contribution. In diminishing the buttressing force of the ice shelves that fringe the ice sheet, the melting increases the ice discharge into the ocean. Here we contrast the influence of basal melting in two different ice-shelf regions on the time-dependent response of an isothermal, inherently buttressed ice-sheet-shelf system. In the idealized numerical simulations, the basal-melt perturbations are applied close to the grounding line in the ice-shelf's (1)Â ice-stream region, where the ice shelf is fed by the fastest ice masses that stream through the upstream bed trough and (2)Â shear margins, where the ice flow is slower. The results show that melting below one or both of the shear margins can cause a decadal to centennial increase in ice discharge that is more than twice as large compared to a similar perturbation in the ice-stream region. We attribute this to the fact that melt-induced ice-shelf thinning in the central grounding-line region is attenuated very effectively by the fast flow of the central ice stream. In contrast, the much slower ice dynamics in the lateral shear margins of the ice shelf facilitate sustained ice-shelf thinning and thereby foster buttressing reduction. Regardless of the melt location, a higher melt concentration toward the grounding line generally goes along with a stronger response. Our results highlight the vulnerability of outlet glaciers to basal melting in stagnant, buttressing-relevant ice-shelf regions, a mechanism that may gain importance under future global warming.

We modelled the flow of the Larsen C and northernmost Larsen D ice shelves, Antarctic Peninsula, using a model of continuum mechanics of ice flow, and applied a fracture criterion to the simulated velocities to investigate the ice shelf’s present-day stability. Constraints come from satellite data and geophysical measurements from the 2008/09 austral summer. Ice-shelf thickness was derived from BEDMAP and ICESat data, and the density–depth relationship was inferred from our in situ seismic reflection data. We obtained excellent agreements between modelled and measured ice-flow velocities, and inferred and observed distributions of rifts and crevasses. Residual discrepancies between regions of predicted fracture and observed crevasses are concentrated in zones where we assume a significant amount of marine ice and therefore altered mechanical properties in the ice column. This emphasizes the importance of these zones and shows that more data are needed to understand their influence on ice-shelf stability. Modelled flow velocities and the corresponding stress distribution indicate that the Larsen C ice shelf is stable at the moment. However, weakening of the elongated marine ice zones could lead to acceleration of the ice shelf due to decoupling from the slower parts in the northern inlets and south of Kenyon Peninsula, leading to a velocity distribution similar to that in the Larsen B ice shelf prior to its disintegration.

Abrupt climatic change related to unstable ice-sheet dynamics: toward a new paradigm

Core 2011804‐0010 from easternmost Lancaster Sound provides important insights into deglacial timing and style at the marine margin of theNELaurentide Ice Sheet (LIS). Spanning 13.2–11.0 cal. kaBPand investigated for ice‐rafted debris (IRD), foraminifera, biogenic silica and total organic carbon, the stratigraphy comprises a lithofacies progression from proximal grounding line and sub‐ice shelf environments to open glaciomarine deposition; a sequence similar to deposits from Antarctic ice shelves. These results are the first marine evidence of a former ice shelf in the eastern Northwest Passage and are consistent with a preceding phase of ice streaming in eastern Lancaster Sound. Initial glacial float‐off and retreat occurred &gt;13.2 cal. kaBP, followed by formation of an extensive deglacial ice shelf during the Younger Dryas, which acted to stabilize the retreating margin of theNE LISuntil 12.5 cal. kaBP.IRDanalyses of sub‐ice shelf facies indicate initial high input from source areas on northern Baffin Island delivered to Lancaster Sound by a tributary ice stream in Admiralty Inlet. After ice shelf break‐up, Bylot Island became the dominant source area. Foraminifera are dominated by characteristic ice‐proximal glaciomarine benthics (Cassidulina reniforme,Elphidium excavatumf.clavata), complemented by advected Atlantic water (Cassidulina neoteretis,Neogloboquadrina pachyderma) and enhanced current indicators (Lobatula lobatula). The biostratigraphy further supports the ice shelf model, with advection of sparse faunas beneath the ice shelf, followed by increased productivity under open water glaciomarine conditions. The absence of Holocene sediments in the core suggests that the uppermost deposits were removed, most likely due to mass transport resulting from the site's proximity to modern tidewater glacier margins. Collectively, this study presents important new constraints on the deglacial behaviour of theNELaurentide Ice Sheet, with implications for past ice sheet stability, ice‐rafted sediment delivery, and ice−ocean interactions in this complex archipelago setting.

ABSTRACTWe investigate the appropriateness of calving or crevasse models from the literature using linear elastic fracture mechanics (LEFM). To this end, we compare LEFM model-predicted stress intensity factors (SIFs) against numerically computed SIFs using the displacement correlation method in conjunction with the finite element method. We present several benchmark simulations wherein we calculate the SIF at the tips of water-filled surface and basal crevasses penetrating through rectangular ice slabs under different boundary conditions, including grounded and floating conditions. Our simulation results indicate that the basal boundary condition significantly influences the SIF at the crevasse tips. We find that the existing calving models using LEFM are not generally accurate for evaluating SIFs in grounded glaciers or floating ice shelves. We also illustrate that using the ‘single edge crack’ weight function in the LEFM formulations may be appropriate for predicting calving from floating ice shelves, owing to the low fracture toughness of ice; whereas, using the ‘double edge crack’ or ‘central through crack’ weight functions is more appropriate for predicting calving from grounded glaciers. To conclude, we recommend using the displacement correlation method for SIF evaluation in real glaciers and ice shelves with complex geometries and boundary conditions.

Antarctica's ice shelves are thinning at an increasing rate, affecting their buttressing ability. Channels in the ice shelf base unevenly distribute melting, and their evolution provides insight into changing subglacial and oceanic conditions. Here we used phase‐sensitive radar measurements to estimate basal melt rates in a channel beneath the currently stable Ross Ice Shelf. Melt rates of 22.2 ± 0.2 m a−1 (&gt;2500% the overall background rate) were observed 1.7 km seaward of Mercer/Whillans Ice Stream grounding line, close to where subglacial water discharge is expected. Laser altimetry shows a corresponding, steadily deepening surface channel. Two relict channels to the north suggest recent subglacial drainage reorganization beneath Whillans Ice Stream approximately coincident with the shutdown of Kamb Ice Stream. This rapid channel formation implies that shifts in subglacial hydrology may impact ice shelf stability.

Ice shelves are floating ice sheets attached either to land or to a grounded ice sheet. They represent seaward extensions of terrestrial glaciers in the majority of cases. A substantial part of the Antarctic coast line is fringed by ice shelves, while they are also present on a reduced scale in the Northern Hemisphere, for example the Ward Hunt Ice Shelf along the northern coast of Ellesmere Island in Arctic Canada. Ice shelves are nourished by snow accumulation on their upper surface, by flow of ice from adjoining ice masses and also by bottom freezing at the interface with sea water. Wastage is caused by ablation at the surface, which is in most cases not very significant, by bottom melting at the lower interface in contact with sea water and by calving at the frontal zone which produces icebergs. Where an ice shelf grounds locally it slows down and tends to thicken, resulting in an ice rise with its own flow pattern determined by grounded-ice dynamics.

Abstract. Calving is a major mechanism of ice discharge of the Antarctic and Greenland ice sheets, and a change in calving front position affects the entire stress regime of marine terminating glaciers. The representation of calving front dynamics in a 2-D or 3-D ice sheet model remains non-trivial. Here, we present the theoretical and technical framework for a level-set method, an implicit boundary tracking scheme, which we implement into the Ice Sheet System Model (ISSM). This scheme allows us to study the dynamic response of a drainage basin to user-defined calving rates. We apply the method to Jakobshavn Isbræ, a major marine terminating outlet glacier of the West Greenland Ice Sheet. The model robustly reproduces the high sensitivity of the glacier to calving, and we find that enhanced calving triggers significant acceleration of the ice stream. Upstream acceleration is sustained through a combination of mechanisms. However, both lateral stress and ice influx stabilize the ice stream. This study provides new insights into the ongoing changes occurring at Jakobshavn Isbræ and emphasizes that the incorporation of moving boundaries and dynamic lateral effects, not captured in flow-line models, is key for realistic model projections of sea level rise on centennial timescales.