Stress-flow angles on Larsen C ice shelf

Our first stage of argument considers that both the first and the second principal stresses have highest absolute magnitudes near Larsen C’s grounding line and decrease non-uniformly towards the calving front (Fig. 2). Stress-flow angles tend towards 90° near Larsen C’s grounding line (Fig. 2a) where feeding glaciers accelerate and spread out laterally as the ice begins to float and basal drag is removed. In the central portion of the ice shelf, the first principal stress aligns with ice-shelf flow (Fig. 2c), and the stress-flow angles thus approach zero (Fig. 2a). Downstream of the embayment, stress-flow angles once more tend towards 90° as the ice shelf spreads out laterally (Fig. 2a,b). Here the tensile first principal stress is oriented along the ice front and parallel to rift zones R1 to R3 (Figs 1 and 2a), favouring a stable ice shelf. Consistently, Larsen C’s calving style is presently dominated by infrequent detachment of large tabular icebergs, as demonstrated by the most recent large calving event in 2008 (Fig. 1). With the removal of the stabilizing frontal portion, the largest tensile stress would be oriented perpendicular to the calving front and to the surface and basal crevasses5,6,7 that are numerous in this area, thus destabilizing them. Larsen C’s frontal portion therefore provides essential restraint for the shelf’s central portion that may otherwise be unstable. The transition from compressive to tensile second principal stresses in Larsen C’s central to southern frontal portion defines a ‘compressive arch’8 (Fig. 2d), extending from the Kenyon Peninsula in the south towards the Bawden ice rise in the north (Figs 1 and 2a). It was proposed previously that ice-shelf retreat beyond a critical arch may result in rapid disintegration8. Because the transition from low to high stress-flow angles is located closer to the calving front than the compressive arch (Fig. 2a), a hypothetical retreating Larsen C ice shelf may become unstable well before the compressive arch is breached.

Stress-flow angles on Larsen B ice shelf

Our second stage of argument considers that the distribution of stress-flow angles on Larsen B ice shelf in 1986 before its collapse (1995–2002, Fig. 3) was similar to those of present-day Larsen C (Fig. 2a), and the stress field in Larsen B’s frontal portion was likewise marked by a compressive arch8. Larsen B’s evolution towards rapid disintegration in 2002 (ref. 1) may therefore offer insights into Larsen C’s future stability. Comparable patterns of first principal stresses perpendicular to the flow direction at the grounding line and calving margin, and parallel to flow in the centre, were present before 1995 (ref. 8), and Larsen B calved large tabular icebergs just as Larsen C currently does. In 1995, Larsen B’s entire frontal portion calved away (top inset in Fig. 3), resulting in near-zero stress-flow angles at the new calving front and fracture-orthogonal tensile stresses that then encouraged the propagation of existing rifts and crevasses. Larsen B’s load-bearing capacity subsequently decreased9, causing the shelf to crumble by frequent calving of small icebergs and its calving front to continue to retreat (Fig. 3), concluding in its eventual collapse in 2002 (refs 9, 10). Owing to the similarity of shelf-wide stress-angle distributions, Larsen C might similarly disintegrate if its frontal portion, and thus the restraint it provides for the shelf’s central portion, is lost. Ongoing preservation of Larsen C’s frontal portion is therefore necessary for its stability.

Figure 3: Stress-flow angles on Larsen B ice shelf calculated from modelled velocity data. The background is a Landsat image taken on 1 March 1986 ( http://nsidc.org/data/nsidc-0280.html). The red box outlined in the bottom inset shows the location of the Larsen B ice shelf in relation to the Larsen C ice shelf (grey box outlined) on the Antarctic Peninsula. The 1995 and 2002 calving fronts are shown in thick black lines, and the major calving event that removed Larsen B’s entire frontal portion in 1995 is shown in the European Remote Sensing Satellite (ERS) image in the top inset. Full size image

Sensitivity of model outputs to boundary conditions

Larsen C ice shelf has experienced recent mass and dynamic changes that are particularly pronounced in its northern part. These include ice-shelf acceleration11, surface lowering due to melt-driven firn compaction11,12,13,14 and thinning of feeding glaciers15. We have therefore conducted a series of perturbation experiments with our continuum-mechanical ice-flow model to ascertain the sensitivity of Larsen C’s velocity and stress fields to hypothetical changes in the ice-shelf’s calving front geometry, the inflow velocities of the feeding glaciers and the thickness of ice shelf (Supplementary Fig. 1). A comparison of the first and the second principal stress fields before and after a major calving event that occurred between 2002 and 2008 (see superimposed calving front in Fig. 1) demonstrates only weak sensitivity of Larsen C’s principal stress fields to simulated changes in the geometry of its calving front (Supplementary Fig. 1). A 20% acceleration of the feeding glaciers would increase the mean velocity of the ice shelf by 12% from 362 m a−1 to 403 m a−1. However, because the spatial velocity gradients across Larsen C ice shelf, and thus the strain rates, remain largely unaffected, the first and second principal stress fields have comparable magnitudes and directions with and without acceleration (Supplementary Fig. 1). If Larsen C experienced firn compaction or basal melting that spatially averaged 20 m, its mean velocity would decrease by~7% from 362 m a−1 to 338 m a−1. However, once again the first and second principal stress fields with and without thinning have comparable magnitudes (Supplementary Fig. 1).

Despite the recent mass and dynamic changes that Larsen C ice shelf has been experiencing11,12,13,14,15,16, our model sensitivity tests thus reveal that the integrity of Larsen C’s stabilizing frontal portion is unlikely to be compromised by mass and dynamic changes in the foreseeable future. Following a brief introduction to ice-shelf suture zones and their anomalous mechanical properties, our third stage of argument considers instead that marine ice-bearing suture zones2,3 preserve this portion because they prevent rifts from propagating laterally across and coalescing within it; and by implication therefore stabilize the whole of Larsen C ice shelf.

Marine ice in the Larsen C ice shelf

Larsen C, like most other Antarctic Peninsula ice shelves, is principally composed of flow-parallel units of meteoric ice that are sustained by feeding glaciers and snow accumulation1 (Fig. 1), and narrow interstitial suture zones. Suture zones are partially composed of marine ice and commonly appear as smooth flow-parallel bands in satellite imagery2 (Fig. 1). Prominent suture zones on Larsen C include those originating leeward of the Joerg Peninsula (‘J’ and red stripe in Fig. 1), Tonkin and Francis Islands (respectively ‘TO’ and ‘FI’ in Fig. 1) in the south, and Churchill Peninsula (‘C’ in Fig. 1) in the north. These zones serve to isolate the prominent areas of fracturing (‘R1’ to ‘R5’ in Fig. 1) in the ice-shelf’s frontal portion. The presence of marine ice within these suture zones was revealed by airborne radio-echo sounding, substantiated by mathematical modelling of sub-shelf freeze-on (ref. 2) and, within Joerg Peninsula suture zone, delineated at high spatial resolution by our ground-penetrating radar surveys (GPR) undertaken in the 2008/09 and 2009/10 austral summers (Fig. 4). Our GPR profiles delineate the base of the meteoric Trail-Inlet and Solberg-Inlet flow units, but cannot detect the suture zone’s base2 (Fig. 4a,b). We therefore used seismic reflection data acquired at P1 (ref. 4) (2008–09; Fig. 4a) and calculations of ice-shelf draft at P2 (refs 4, 12) (2009–10; Fig. 4b) to delineate the base of the marine ice within the Joerg Peninsula suture zone. Marine-ice bodies have a temperature similar to the sub-shelf ocean waters from which they are formed (−1.5 °C to −2 °C), and are therefore anomalously soft17. In contrast, meteoric ice-shelf units are much colder because they are derived from feeding glaciers and snow accumulation subject to annually averaged surface temperatures of −15 °C and below. Because the thermal diffusivity of ice is very small, the marked contrast in meteoric versus marine ice temperatures is expected to persist along the entire length of an ice shelf18. Warmer marine ice deforms more readily under the same long-term stress loading, imposed upon the ice shelf by gravity-driven flow, than colder meteoric ice12,19. A larger proportion of that long-term loading is therefore available to drive elastic fracture in meteoric than in marine ice, so that warmer marine ice-bearing suture zones are less prone to elastic fracture than surrounding, colder meteoric ice units20,21.

Figure 4: Ground-penetrating radar profiles crossing the Joerg Peninsula suture zone. (a) Downstream profile P1. (b) Upstream profile P2. The base of the meteoric ice is traced with a purple line, and marine-ice bodies are shown in green. The marine-ice bodies are dissected by meteoric ice derived from the Joerg Peninsula bound glacier (light purple stripe in the bottom inset in Fig. 1). Full size image

Stress-flow angles from observed data

Interferometric Synthetic Aperture Radar (InSAR)-derived flow velocities of Larsen C ice shelf22 allow, initially, calculation of the spatial distributions of ice-shelf strain rates. Subsequently, the principal stresses and stress-flow angles at the ice-shelf surface are calculated by assuming that the temperature of all shelf ice is equal to Larsen C’s annually averaged surface temperature of −15 °C (Supplementary Fig. 2). Stresses will be higher in colder meteoric ice than in warmer marine ice at a given strain rate, so that marine ice is less likely to fracture20,21,23. The assumption of a spatially invariant temperature of −15 °C is consequently violated in major rift zones filled with warmer ice mélange, where strain rates are therefore anomalously high and stress magnitudes overestimated by our calculations (Supplementary Fig. 2). The assumption is also violated in the suture zones containing warm bodies of marine ice, although here shear stress bridging between neighbouring meteoric flow units minimizes the build-up of anomalously high strain rates, so that stress magnitudes are not normally overestimated. Despite these potential limitations, a comparison of Fig. 2a and Supplementary Fig. 2 reveals good overall agreement between the spatial patterns of principal stresses and stress-flow angles reconstructed from modelled and observed data. However, the patterns inferred from observed data (Supplementary Fig. 2) are relatively noisy and lack prognostic capabilities4. We therefore prefer to adopt our previous approach4 that focuses on analyses of ice-shelf flow velocities modelled with a continuum-mechanical model constrained by spatially uniform ice properties (Fig. 2).