In order to track temporal changes to the length of Chasm 1, the distance between the crack tip and a fixed reference point on the ice shelf has been calculated. The reference point is indicated by A in Fig. a and corresponds to a persistent surface feature that gets advected with the flow, known as a deflation hollow . It is visible in all the satellite images used. The propagation of Chasm 1 is approximated by the straight-line distance between A and the tip of the rift as estimated from the outlines in Fig. a. Results for this analysis are shown in Fig. c and point towards a near-linear growth between late 2012 and early 2017, with two episodes of significant slowdown in 2012 and 2016.

The accuracy of these results is limited by our inability to detect potential sub-surface propagation of the rifts, the variability in image contrast due to solar azimuth and zenith angles and the resolution of the panchromatic images (15 m), which prevents the reliable detection of fine surface cracks less than a pixel wide. It is also impossible to track progress during the austral winter months (April–September) when visible images are unavailable. In order to address these issues and improve the accuracy of the location of the rift tip, ground penetrating radar (GPR) measurements were acquired once every month from January 2016 to February 2017. Surveys were carried out using a radar unit with 400 MHz antenna from Geophysical Survey Systems, Inc., set to operate at a depth range of 30 m and tied to a dual-frequency GPS to guarantee accurate geolocation of the radar traces. During each survey, a series of parallel lines was acquired to cover the area around the rift tip, with a spatial separation of 100 m and directed approximately perpendicular to the propagation direction of the rift. An example of such a set of survey lines for 24 February 2017 is shown by the white lines in Fig. b.

The GPR data were detrended and a divergence compensation scheme was applied to enhance the intensity of the deeper layers, using the post-processing software package ReflexW from Sandmeier Geophysical Research. The processed data were used to detect narrow cracks less than 1 m wide, both at the surface and at depth, allowing to determine the exact extent of Chasm 1 much more precisely and at regular time intervals both in summer and throughout the winter. The black dots in Fig. b represent all locations where cracks were detected within the vertical range of the GPR, for a total of 15 monthly acquisitions between 1 January 2016 and 24 February 2017.

In general, the tip of Chasm 1 is not uniquely defined but consists of a number of parallel branches at a spacing of several hundred metres, approximately aligned with the overall propagation direction. This non-simple structure of the rift tip is particularly evident between 1 January 2016 and 1 January 2017 during a phase of reduced rift tip propagation and is illustrated in Fig.  using data from a GPR survey carried out on 4 May 2016. Figure a shows the GPR track in white, overlying a Landsat 8 image that predates the survey by about 2 months. Two radar profiles along sections A and B in Fig. a are shown in Fig. b and c, allowing the identification of two fractures along section A and three fractures along section B, marked by vertical black stripes. A detailed view of these fractures is shown in Fig. d and e. All branches of the rift follow the edge of a large structure within the ice, marked by “meteoric”. The full spatial extent of this feature is shown in Fig. a and has been identified as a block of meteoric ice that originated at the grounding line and got embedded within the firn pack. This is not a unique feature and similar structures of variable size and orientation have been observed from GPR surveys all across the ice shelf . It is very likely that such large-scale and wide-spread irregularities in ice properties are responsible for a significant dispersion of the crack tip growth. As the tip of Chasm 1 continued to propagate, some branches eventually became inactive, whereas others continued to grow. From January 2017 onwards, only one branch was apparent near the tip.

For each monthly GPR survey, the tip of the most advanced branch of Chasm 1 is highlighted in magenta in Fig. b, and the corresponding extent of the rift is represented by magenta markers in Fig. c. A comparison between the GPR data and Landsat-derived results in Fig. c shows that the latter systematically underestimate the extent of Chasm 1 by up to a kilometre. Not only are satellite data resolution limited, but GPR data also show that the tip of the rift tends to be further advanced at depth, and only becomes detectable at the surface at a later stage. In agreement with the satellite data, GPR measurements show a deceleration in the propagation between January 2016 and early 2017. However, a subsequent surge of the crack tip in January and February 2017 was only captured by the GPR data, and satellite data alone would have led to the erroneous conclusion that Chasm 1 has stagnated until propagation once again became apparent.

The gradual lengthening of Chasm 1 in the horizontal plane is caused by tensile stresses normal to the fracture plane. After fracture initialization, such stresses tend to widen the rift at a rate which a priori depends on the far-field stresses and on material properties local to the fracture tip. The precise nature of this relationship cannot be determined due to a lack of observational data. However, for Chasm 1 a network of snow stakes and permanent GPS stations was installed to monitor rift widening rates at regular intervals. The network is shown in Fig. b and consists of six stakes (yellow markers) at 1 km separation on each side of Chasm 1, named A100–A600 on the west and B100–B600 on the east side. The relative location of all stakes was measured once a month between December 2015 and February 2017, using a GPS base station at A600 and roving stations at all other stakes. Two stakes, O0 and N0, were occupied permanently and have provided a daily measurement of their location since January 2016. A further pair of permanent GPS stations, named M1 and B2 in Fig. a, was installed in May 2015 and has provided additional baseline measurements across Chasm 1 further to the south and away from the tip. By combining these data, the widening of Chasm 1 has been measured along seven different baselines, some across the historical extent of the crack (M1–B2), others across the recently formed branch (A100–B100, A200–B200, O0–N0, A400–B400), and some ahead of the current crack tip (A500–B500, A600–B600).

All data were post-processed using the advanced baseline analysis tool within the Infinity software package from Leica Geosystems, and a summary of the results from 1 December 2016 until 27 February 2017 is shown in Fig. d. All baselines get longer over time, ranging from less than 2 cmday-1 ahead of the rift tip to 2.4 cmday-1 between A400 and B400 and 14.2 cmday-1 between M1 and B2. Part of the lengthening can be attributed to the background spreading of the ice shelf, as is apparent along A500–B500 and A600–B600 where the crack has not yet propagated, whereas the remainder of the extension is due to widening of the rift.

Further details about the propagation behaviour of Chasm 1 can be obtained from a full strain rate analysis of the stake network. Strain rosettes in Fig. b show the principal strain rate directions and magnitudes, as computed for five different squares within the network. Note that towards the south of the A500–B500 line, these results also incorporate widening (Mode I) and shear (Mode II) of the rift, and they are therefore not material strain rates in the strictest sense. The first principal components are extensive, confirming earlier results from the baseline analysis. They are oriented perpendicular to the rift trajectory, indicating minimal shear along the rift and hence a negligible Mode II component. The second principal components are also extensive, but about 2 orders of magnitude smaller.

The strain rates show an increasing trend away from the rift tip, and have a non-negligible second-order component in time, which indicates that Chasm 1 is widening at an accelerating rate. Unlike the spatial propagation of the tip location, the widening of Chasm 1 happens evenly and without significant deviations from the trend line. For example, the transition from a period of slow crack propagation to a rapid change in the location of the crack tip in early 2017 (Fig. c) is not obviously reflected in the widening rates (Fig. d). This suggests that the widening is dominated by the slowly varying far-field stresses, and is uncorrelated to the rift tip propagation, which is sensitive to spatially variable properties of the ice shelf local to the tip, such as the ice viscosity and ice thickness. Similar observations have previously been made by for two rifts that led to the calving of tabular icebergs from the Ross Ice Shelf, Antarctica, and we will come back to this result in Sect. .

The HC originated about 15 km east of the MIR, and its tip propagated rapidly in opposite directions. From November 2016 onwards, growth stagnated in the west as the rift approached the MIR but continued at an unabated rate towards the east. When plotted as a function of time (see blue dots in Fig. a), the total length of the HC increased by 34.2 km over 158 days, or an average of 216 mday-1, subject to observational errors related to our inability to detect subsurface or narrow surface cracks using visible satellite images, as discussed in Sect. . Discarding such uncertainties, it is clear that the propagation rate has been highly variable in time, with very little, if any, propagation in early November 2016 and periods during January, February and March 2017 yet more than 600 mday-1 during intervening periods.

This variability has also been observed for Chasm 1 and is at least partly related to the heterogeneous structure of the ice shelf. As the tip of the rift propagates, it encounters areas with higher (lower) fracture toughness, which requires a higher (lower) energy to break through, and leads to a slowdown (speedup) of the propagation. In the case of the HC, a period of slow propagation from mid-October to mid-November 2016 occurred when the rift tip encountered successive bands of thicker meteoric ice, apparent in the surface topography in Fig.  and outlined by the black box. These blocks of ice are of the same origin as the meteoric ice structure near the tip of Chasm 1, as discussed in Fig. . The blocks originate at the grounding line, where the grounded ice calved at regular intervals leaving spaces between icebergs that were gradually filled by sea ice, marine ice and surface accumulation . As the heterogeneities and the direction of rift propagation were misaligned by about 70∘, the HC changed direction as it followed a staircase-like trajectory with successive phases of propagation along and perpendicular to the icebergs. This caused temporary changes in its alignment with respect to the large-scale stress field, which might explain part of the slowdown. Other studies have suggested that the presence of marine ice can suppress the speed at which rifts propagate, and several ice shelves such as Larsen C and Filchner-Ronne ice shelves contain rifts that terminate in marine ice-rich suture zones . However, very few studies have investigated the relationship between rift tip propagation and fracture toughness of ice directly (see for example ) and the dynamics of rift tip propagation remains subject to large uncertainties.

The sudden fracture of the ice shelf and the abrupt formation of the HC suggests a period of critical crack growth, which typically occurs in materials that are subjected to high tensile stresses or stresses that are applied for long enough such that initial fractures grow to a critical length, after which catastrophic failure happens . Satellite images from 2014 and 2015 show early indications of small segmented fractures at the surface in the area where the HC subsequently originated, and it is feasible that in October 2016 these segments reached a critical length, which led to the rapid formation of the HC. During this short phase of critical growth, the rift propagation might have reached a considerable fraction of the speed of sound, and continued until changes in the remote stress field stabilized the crack and a quasi-static regime with slower growth rates was reestablished.

Once failure occurred, the ice adjacent to the free surfaces of the rift became fully unloaded, and the strain was entirely converted into opening of the rift. The transition from a loaded to an unloaded state of the ice shelf was measured using a network of four permanent GPS stations positioned on both sides of the HC trajectory. As shown in Fig. , stations K0 and L2 were located south of the HC, and stations I0 and H0 were positioned towards the north, forming two independent baselines across the rift: K0–I0 and L2–H0.

Daily values for the length of each baseline were obtained using the baseline processing toolbox in Leica Infinity, and results are presented in Fig. b (L2–H0) and Fig. c (K0–I0). Phase-fixed solutions with a precision of about 1 mm were obtained for 45 % of the measurements despite the length of the baselines (16 and 22 km) and are highlighted in blue and red in Fig. b and c. The remaining float solutions have a precision on the order of 5 cm and are coloured in grey. Although all stations were installed prior to 2013, only data after 1 January 2016 were used in this study, providing 10 months of coverage leading up to the formation of the HC in early October 2016. Note that a failure at I0 caused a gap in the K0–I0 baseline between August and November 2016, and the L2–H0 time series ended in February 2017, when station L2 was removed.

Both baselines show a qualitatively similar behaviour over the measurement period, with a close-to-linear extension rate (dashed blue line in Fig. b and c) followed by a rapid deviation from the historical trend line and a significant acceleration. For the L2–H0 baseline, the transition happened abruptly on 3 October 2016, as indicated by the kink in the deviation from the historical trend, which is plotted on the right axis in Fig. b (black line). On that date, spreading rates along L2–H0 increased near-instantaneously from 22.2 to 34.7 cmday-1 with an acceleration of 0.142 cmday-2.

For the K0–I0 baseline, a gap in the data prevents precise dating of the transition, but extrapolation of the trend lines indicates early October as the most likely time of change. Although the stations are positioned on opposite sides of the MIR, an area of naturally diverging flow, it is unlikely that the large change in separation between K0 and I0 can be attributed to background flow dynamics during the 3-month period of missing data. From the 2015 flow lines in Fig.  (prior to the formation of the HC) it is clear that the divergence of flow is localized around the MIR, and all GPS stations are located on continuously diverging paths without abrupt changes to their direction and speed that could explain the sudden acceleration in baseline distance.

Based on these observations we conclude that the sharp increase in extension rate between L2 and H0 on 3 October 2016 can be fully attributed to the formation, opening and shear displacement of the HC. Equally, the increased divergence between K0 and I0 in early October 2016 is attributed to the formation of the HC and indicates an increased separation between the north and south sides of the MIR. A full strain rate analysis of the differential movement between stations L2, K0 and H0 between 3 October 2017 and 1 February 2017 shows that the principle strain rate directions are both extensive and oriented perpendicular and parallel to the HC. The corresponding strain rosette is shown in Fig.  and provides evidence for a pure Mode I loading of the rift.

In order to pinpoint the exact source for the increase in baseline extension after the formation of the HC, absolute locations of the GPS stations were obtained from a precise point positioning analysis using the Bernese GNSS software. Results indicate that the signal is caused by an acceleration of the surface velocities at I0 and H0 to the north of the HC, following the physical separation of the northern and southern parts of the ice shelf. This signal has subsequently been confirmed by satellite-derived surface velocities, which show a clear discontinuity in surface velocities across the rift with higher velocities towards the north across its entire length, including the area downstream of the MIR. An example of such a velocity field for May 2017 is shown in Fig. a.

Due to the fast propagation of the HC and the complexity of the terrain, it is unfeasible to carry out ground-based radar measurements to accurately track the location of the crack tip. In addition, satellite coverage of the ice shelf in the visible spectrum is lost during the austral winter months, so alternative methods need to be developed to provide year-round coverage of the propagation. Data from the Sentinel-1A/B satellites provide a viable alternative, as they carry an active C-band SAR instrument that is not affected by cloud cover or the absence of visible light.

A well-known method to study fracture propagation using SAR data exploits the phase difference between two images taken several days apart and is known as interferometric SAR or InSAR. This method is routinely used in earth surface deformation monitoring (see e.g. , for a review), ice flow monitoring (see e.g. , for one of the earliest examples) and grounding line tracking. Its application to ice shelf rift deformation has been limited (see e.g. ) although there has been a renewed interest in the method due to the improved spatial and temporal coverage of SAR data for Antarctica's ice shelves.

Discontinuities in the differential phase (or interferogram) typically correspond to areas of anomalously high surface deformation, which can be traced manually and associated with active fracture zones. The technique is demonstrated in Fig. , which shows three interferograms for the area around HC separated by about 2 months. In each image a discontinuity in the interferometric fringes marks the trajectory of the rift as it propagates from the MIR towards the east. Black diamond markers in Fig. a specify the length of each outline, and a good agreement is found between SAR-derived estimates of the rift length and earlier results obtained from visible satellite images.

Despite the success of this technique, interferograms are often difficult to interpret, especially in places with a complex surface topography such as the BIS, and phase discontinuities caused by artefacts in the data are easily mistaken for physical signals. The method is also less appropriate for slowly propagating rifts with surface deformations that are too small to detect over the 6-day repeat cycle, such as Chasm 1. To avoid these issues, a more quantitative and robust approach to monitor fracture deformation is explored, based on SAR-derived velocity fields and the corresponding horizontal strain rates. As the dual satellite configuration of Sentinel-1A/B provides complete coverage of the BIS every 6 days, it is ideally suited for the frequent recovery of surface velocities using an iterative offset tracking method developed by . As an example, Fig. a shows the horizontal velocity field derived from two Sentinel-1 SAR images taken on 14 and 20 May 2017. The horizontal strain rate components ϵ˙xx, ϵ˙xy and ϵ˙yy were calculated using a local quadratic regression of the velocity field over a 2km×2km square and used to obtain the effective strain rate ϵ˙e=(ϵ˙xx2+2ϵ˙xy2+ϵ˙yy2)/2 shown in Fig. b. Again it should be noted that these values also incorporate widening (Mode I) and shearing (Mode II) of the rifts, and they are therefore not material strain rates in the strictest sense. Average values across the ice shelf are less than 0.01 yr-1, whereas higher-than-average strain rates up to 0.1 yr-1 are found in the vicinity of the MIR and along the HC and Chasm 1. Other areas with high strain rate are the grounding line and a shear margin, which extends from the grounding line at around x=-645 km towards the northeast.

In order to define an objective measure for the extent of the HC based on strain rates, the ϵ˙e=0.025 yr-1 contour is used as an approximate outline of the rift, and the easternmost extent of the contour is used as a proxy for the location of the crack tip. From this location, indicated by the white star in Fig. b, the length of the HC can be calculated. This process removes biases related to the manual interpretation of images and has been applied to 22 velocity maps and corresponding effective strain rates, acquired by Sentinel-1A/B between November 2016 and July 2017. For each acquisition, the ϵ˙e=0.025 yr-1 contour was identified and used to track the extent of the HC. The results are shown by the magenta lines in Fig. a, where the horizontal limits of each line indicate the acquisition dates of the SAR image pair used to derive the velocity field.

The precision of our method to estimate the length of the rifts can be determined by comparing results for overlapping periods and shows a spread of around 2 km. A comparison to manual tracking from visible images (Landsat 8, Sentinel-2) shows that the two independent measurements are generally in good agreement, although there is a bias towards smaller values for the SAR-derived values. This is in part due to a systematic underestimation of the strain rates at the rift tip due to smoothing by the quadratic regression method, and in part because the ϵ˙e=0.025 yr-1 contour fails to capture the lower strain rates near the very tip of the rift. However, the record is internally consistent and, importantly, presents a reliable extension beyond previous summer measurements. It shows a sustained reduction in lengthening rate of the HC since February 2017, as the tip covered about 5 km or 32 mday-1 between early February 2017 and mid-July 2017, compared to 366 mday-1 during the first 4 months of propagation.

In order to predict the propagation direction of existing fractures in the BIS based on the calculated stresses, surface velocities from Sentinel-1 and ice thickness data were assimilated in the SSA (shallow shelf approximation) flow model Úa . The boundaries of the model domain were chosen to coincide with the grounding line and ice front of the BIS and extended a further 150 km towards the east to include the neighbouring Stancomb-Wills Glacier Tongue, in order to fully capture the spatial variability in strain rates and to allow a sufficiently large domain to propagate the existing rifts. A triangular mesh with linear elements was used, with the distance between nodes varying from 250 m for the BIS to 1 km elsewhere. The flow at the grounding line was prescribed by a Dirichlet condition, and Chasm 1 was represented as an ice-free area, i.e. a gap in the model domain.

Ice thickness values for the BIS were derived from a high-resolution (3 m) WorldView surface digital elevation model acquired between 2012 and 2014, and values were binned onto a coarser 1km×1km grid. Elevations above the ellipsoid were translated into elevations above sea level using a tidal correction and a EIGEN-6C geoid correction and converted into ice thickness values assuming floatation and a two-layer density model with a constant 30 m firn column (750 kgm-1) overlaying pure ice (920 kgm-3). For the Stancomb-Wills Glacier Tongue a subset of the Antarctica-wide ice shelf thickness dataset by was used.

The mismatch between observed and modelled surface velocities was minimized through an iterative optimization (or inversion) of the rate factor in Glen's flow law with exponent n=3. A Tikhonov regularization was used and the regularization multiplier, λAGlen=103, was determined through a L-curve approach to optimize the misfit and avoid overfitting. In areas away from the grounding line and the immediate vicinity of the MIR, the solution converged towards observed values of the surface velocities within 100 iterations, and the inversion was ended after 200 iterations. The resulting stress field was used to calculate the fracture trajectories as follows.

Each rift was seeded at a predefined location in the model, informed by the observed location of an initial fracture or the tip of an existing rift in the ice shelf. Subsequently, the local direction of maximum tensile stress was identified from a linear interpolation of the modelled stresses, and the crack was propagated perpendicular to this direction along a line segment with fixed length. The end point of this segment was marked as the new location of the rift tip, and the process was repeated for updated values of the local stress tensor. Through this algorithm, a fracture trajectory was constructed consisting of line segments with fixed length, and each segment was oriented perpendicular to the local direction of maximum tensile stress. The length of the segments was chosen to be on the order of the minimum mesh resolution, i.e. 250 m, although the algorithm could easily be adapted to allow for a variable step size, based on the local gradients in the stress field or other suitable criteria. It was shown that a step size of 250 m was sufficiently small for the results to be independent of its exact value. The automated process was iterated for a fixed number of steps or until a certain rift length was reached. It should be noted that the algorithm is diagnostic and does not contain a time component, nor does it include any dynamic feedback between the formation of the rift and the background stress field.

Two separate inversions were performed with Úa, one for surface velocities in late June 2015, prior to the formation of the HC, and a second inversion for mid-March 2017, after the formation of the HC. The first inversion was used to hindcast the propagation trajectory of the HC as a way to validate the model and methods, while the second inversion was used to predict the future direction of propagation for Chasm 1 and the HC using a more recent stress field. Results are discussed in Sects.  and , respectively.

For validation purposes, the first experiment was designed to hindcast the observed trajectory of the HC based on the state of stress in the ice shelf shortly before fracture formation in October 2016. For this purpose, a surface velocity field obtained from a Sentinel-1 image pair on 18 and 30 June 2015 was assimilated in Úa. The corresponding tensile stress orientations were used to propagate a crack in opposite directions from the location indicated by the magenta circle in Fig. a, which corresponds to the location where the HC was first observed. The resulting trajectory is shown by the magenta line in Fig. a and follows the observed extent of the HC (in black) to within 1 km along its entire length. This excellent agreement between model results and observations underlines the validity of the simple fracture propagation algorithm and provides confidence in the predictive skills of the method. Localized deviations from the observed rift trajectory are likely caused by the interaction of the rift with spatial variations in ice properties, such as fracture toughness, that cannot be captured by a propagation algorithm based on stress directions alone.

The principal stress rosettes in Fig. a (red arrows are compressive, blue arrows are extensive) display a radially symmetric pattern around the MIR, with compressive stresses at oblique angles to the flow in the upstream direction, and compensating tensile stresses perpendicular to the flow. This pattern is generated by the point-interaction between the ice shelf and the bedrock at the MIR and has resulted in the radially outward growth of the HC, perpendicular to the tensile stresses.

The success of the algorithm relies on an accurate representation of the stresses in the ice shelf, which largely depends on the accuracy of the inversion procedure in Úa. The mean residual and standard deviation between observed and modelled surface speeds for the BIS was found to be 1.4(16.6) myr-1 or 0.2(4)%, which is a significant improvement over and due to recent improvements in the inversion procedure in Úa and over , who found a best match for the BIS of around 10 %. A priori, the calculated fracture trajectories depend on the amount of regularization (λAGlen) and the model resolution. Sensitivity tests were carried out for both variables and the final trajectories of the HC were found to be independent of the exact value of λAGlen and mesh resolution. A further reduction of the regularization and additional mesh refinement did not significantly change the results, and only for a much coarser mesh (2 km nodal separation) or a much larger amount of regularization (λAGlen>105) did the modelled trajectories start to deviate from the observed trajectory. It should be noted that this result is case specific, and robustness of the fracture trajectories should be considered on a case-by-case basis, in particular for applications with a more complex stress distribution.

The second experiment was designed to propagate Chasm 1 and the HC beyond their present-day extent, based on the stress distribution in the ice shelf after the formation of the HC. The model domain was adjusted for a minor advance of the ice front between 2015 and 2017, and updated outlines of Chasm 1 and the HC for 15 March 2017 were introduced as gaps in the mesh. Surface velocities in Úa were optimized to match observed velocities based on a pair of Sentinel-1 images acquired on 9 and 15 March 2017, with a final residual between observed and modelled surface speeds of -2.4±13.5 myr-1 or -0.2±2.6%.

The model domain was seeded with initial fractures at the tips of the HC and Chasm 1, indicated by the magenta circles in Fig. b. The rifts were propagated perpendicular to the direction of maximum tensile stress, up to the edge of the model domain for Chasm 1 and for a total length of 50 km for the HC, as shown by the magenta lines in Fig. b. According to these trajectories, the HC is expected to continue along its current west–east trajectory towards the Stancomb-Wills Glacier Tongue, cutting across a region with uniform tensile stresses that are aligned north–south perpendicular to the grounding line and second principal stresses that are compressive throughout. The estimated trajectory therefore cuts deep into an area of buttressed ice, which could have important implications for the structural integrity of the ice shelf . Note that the estimated trajectory was ended after 50 km because of possible interactions with the active Brunt–Stancomb-Wills Chasm (see Fig. b and ), which could affect the growth of the HC in uncertain ways.

Furthermore, based on the current stress configuration, the model predicts a continued propagation of Chasm 1 towards the MIR, as shown in Fig. b. The path passes through a region with extensive stresses in both principal directions before cutting into the compressive stress region south of the MIR, which could give rise to a possible further reduction in buttressed ice.