Vulnerability of Antarctica’s ice shelves to meltwater-driven fracture

Abstract

Atmospheric warming threatens to accelerate the retreat of the Antarctic Ice Sheet by increasing surface melting and facilitating ‘hydrofracturing’1,2,3,4,5,6,7, where meltwater flows into and enlarges fractures, potentially triggering ice-shelf collapse3,4,5,8,9,10. The collapse of ice shelves that buttress11,12,13 the ice sheet accelerates ice flow and sea-level rise14,15,16. However, we do not know if and how much of the buttressing regions of Antarctica’s ice shelves are vulnerable to hydrofracture if inundated with water. Here we provide two lines of evidence suggesting that many buttressing regions are vulnerable. First, we trained a deep convolutional neural network (DCNN) to map the surface expressions of fractures in satellite imagery across all Antarctic ice shelves. Second, we developed a stability diagram of fractures based on linear elastic fracture mechanics to predict where basal and dry surface fractures form under current stress conditions. We find close agreement between the theoretical prediction and the DCNN-mapped fractures, despite limitations associated with detecting fractures in satellite imagery. Finally, we used linear elastic fracture mechanics theory to predict where surface fractures would become unstable if filled with water. Many regions regularly inundated with meltwater today are resilient to hydrofracture—stresses are low enough that all water-filled fractures are stable. Conversely, 60 ± 10 per cent of ice shelves (by area) both buttress upstream ice and are vulnerable to hydrofracture if inundated with water. The DCNN map confirms the presence of fractures in these buttressing regions. Increased surface melting17 could trigger hydrofracturing if it leads to water inundating the widespread vulnerable regions we identify. These regions are where atmospheric warming may have the largest impact on ice-sheet mass balance.

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Fig. 1: Conceptualizing the regions of Antarctic ice shelves that will control the ice sheet’s response to atmospheric warming.
Fig. 2: Continent-wide fracture map.
Fig. 3: Model–observation comparison of fracture locations.
Fig. 4: Map of ice-shelf vulnerability to hydrofracture.

Data availability

The training, validation, and testing datasets are available at https://github.com/chingyaolai/Antarctic-fracture-detection and https://doi.org/10.5281/zenodo.3949427. The neural-network mapped fracture locations on the MOA 2009 (125 m resolution) imagery (Fig. 2) and the data required to construct the vulnerability map (Fig. 4) are available at https://doi.org/10.15784/601335. MOA (2009) imagery (https://doi.org/10.7265/N5KP8037) is available at the National Snow and Ice Data Center (NSIDC). Strain-rate fields are calculated from the dataset SUMER Antarctic Ice-shelf Buttressing, Version 1 (https://doi.org/10.5067/FWHORAYVZCE7) available via the NSIDC. Ice-shelf thickness data are from Bedmap2 (https://www.bas.ac.uk/project/bedmap-2/). The surface temperature data from the RACMO2.3p2 regional climate model are available from J.M.v.W. (j.m.vanwessem@uu.nl).

Code availability

The code for our experiment is available at https://github.com/chingyaolai/Antarctic-fracture-detection (https://doi.org/10.5281/zenodo.3949427). The U-Net implementation65 is available at https://github.com/jakeret/tf_unet. The FPN implementation is available at https://github.com/qubvel/segmentation_models. The deep learning framework, TensorFlow, is available at https://www.tensorflow.org/. Scripts for calculating the fracture stability diagram (Fig. 3c) are available from the corresponding author upon request.

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Acknowledgements

We thank R. Bell, T. Scambos, R. Duddu, O. Sergienko and B. Minchew for discussions. We acknowledge the National Science Foundation for funding via grant no. OPP-1743310. C.-Y.L. thanks the Lamont-Doherty Earth Observatory for funding through the Lamont Postdoctoral Fellowship. J.M.v.W. acknowledges the Dutch Research Council (NWO) for funding through Veni grant no. VI.Veni.192.083. Disclaimer: For P.-H.C.C., the work was done in personal time. The views expressed in this article are those of the authors and do not necessarily reflect the official policy or position of Google LLC.

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Contributions

C.-Y.L. led the project and the preparation of the manuscript. C.-Y.L. and J.K. designed the research. M.G.W. helped with development of the research, contributed strain rate data and ideas related to buttressing. C.-Y.L. developed the fracture model and the stability diagram. P.-H.C.C. provided guidance regarding the selection and evaluation of machine learning models. C.-Y.L. conducted the machine learning experiments and P.-H.C.C., P.G. and H.L. assisted with the neural networks. J.J.S. prepared the Landsat images. J.M.v.W. provided RACMO2.3p2 climate model output. C.-Y.L. wrote the manuscript with help from J.K., M.G.W., and P.-H.C.C. and input from all authors. All authors contributed to discussions of the research.

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Correspondence to Ching-Yao Lai.

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P.-H.C.C. is an employee of Google and owns Alphabet stock. Other authors declare no competing interests.

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Peer review information Nature thanks Jeremy Bassis, Javier Plaza, Stephen Price, Xiaoxiang Zhu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Data preparation and the neural network architecture.

a, The training and validation data were taken from a 8,000 pixel × 8,000 pixel subset (covering the Larsen and George VI ice shelves) of the 125-m-resolution MODIS imagery, which produced 32 tiles of 1,000 pixel × 1,000 pixel images containing ice shelves. The tiles were randomly separated into training (26 tiles) and validation (6 tiles) sets. b, Example of a training tile. c, The corresponding labels with white pixels indicating fractures. d, The U-Net architecture. The contracting and expansive paths give the U-Net29 its U-shaped architecture. Arrows illustrate operations within the network and at each stage the data dimension is noted. The input image (left) is 1,000 pixels × 1,000 pixels with one channel and the output prediction (right) of the U-Net contains two classes (fracture and non-fracture).

Extended Data Fig. 2 Performance of the DCNN and fracture classification.

a, (i), Comparisons of AUC for the validation data over number of parameters (N) for an edge detector44, single-layer CNN with different filter sizes (1 × 1, 28 × 28, 56 × 56; denoted by k), U-Net with different depths of first-layer feature maps (1, 2, 4, 16, 32, 64; denoted by d) and FPN43 using a ResNet-18 backbone. (ii), The AUCs and N values of each model evaluated against the validation data are summarized in the table. b, The performance of the U-Net (with d = 32) evaluated against an unseen testing set is shown by the ROC curves. c, d, Examples of validation label images (c) and original MOA images (d). e, Output of the model, continuous values between 0 and 1. f, Binarized classification of fractures that used a threshold (0.2), maximizing the F1 score on the validation set. Fracture features with predictions exceeding the threshold are marked in white. g, The resolution of the fracture map was reduced to 1 km, the resolution of the strain rate data, before we incorporated the DCNN result with other data in Extended Data Fig. 6.

Extended Data Fig. 3 Stresses acting on a surface fracture and fracture stability.

a, b, The effects of tensile resistive stress, hydrostatic stress of water and overburden stress of ice on opening or closing of a surface fracture in dry (a) and water-filled fractures (b). c, The stress intensity factor (KI) as a function of surface fracture depth (ds) (Supplementary equation (5)) computed with Rxx = [0.5, 1] MPa, H = 300 m, surface firn density ρs = 400 kg m−3 and C = 0.02 m−1 (see Supplementary equation (6); ref. 2). (The solution derived in this work is shown with a solid curves and that of Van der Veen (ref. 2) by dashed curves.) d, e, The additional impacts of a firn layer are due to reduced density (d) and reduced viscosity (e). Reduced overburden stress due to lower density firn compared with ice acts to deepen surface fractures (black dot on green curve in c). In contrast, the reduced tensile resistive stress due to the reduced firn viscosity reduces surface fracture depth. The net effects of firn, shown by the red curve in c, are secondary compared with the effects from tensile resistive and overburden stresses of ice. We therefore did not include the effect of firn in the main analysis.

Extended Data Fig. 4 Physical regimes of surface and basal fractures.

a, b, The schematics of a surface (a) and basal crevasse (b) with depth varying resistive stress Rxx(z) due to the vertical temperature gradient (assumed to be linear). c, The fracture stability diagram for surface and basal crevasses with and without temperature effects (assuming the surface and the base of ice shelf are −30 and 0 °C, respectively). Dashed and solid lines represent the transition boundaries of stable-to-unstable and no fracture-to-stable fracture regions, respectively. Warmer ice at the base reduces the ice viscosity (and thus stress), which impacts the locations of the stability boundaries of basal crevasse. d, The five physical regimes (I–V) defined by the transition boundaries for surface crevasse (black curves in c) and basal crevasse with temperature effects (light blue curves in c). e–h, The locations corresponding to regimes I–V on ice shelves are determined by different estimates of stress. The percentage values denote the portion of ice-shelf area containing the physical condition in each regime. The green, pink, blue, red, yellow and white areas correspond to regimes I, II, III, IV, V and the U-Net-detected fracture locations, respectively. e, f, The stress field determined by the temperature dependent viscosity factor B(T) (equation (6) in ref. 57) combined with along-flow strain rates obtained by Fürst et al.13 (e) and Wearing61 (f). g, h, The stress fields in the along-flow (g) and 1st principal (h) stress directions calculated by ref. 13 include the effects of damage-induced ice softening through the data assimilation and model inversion process. The second row of e–h is the close-up view of the white box in the first row. Note that the spatial areas of regimes I—V were calculated solely on the basis of the dimensionless stress and toughness, and are independent of the U-Net result. The spatial resolution is 1 km, the same as the stress field resolution used in ref. 13.

Extended Data Fig. 5 Comparison between dry and water-filled fractures in LEFM.

a, The stress intensity factor (Supplementary equation (5)) as a function of surface fracture depth was calculated for hydrofractures (blue curves) and dry surface fractures (black curves) for H = 1,000 m. The number alongside each curve is the corresponding Rxx. Above the critical stress \({R}_{xx}^{* }\,\approx \,60\,{\rm{kPa}}\) (calculated using equation (2) and KIc ≈ 150 kPa m1/2) dry-surface-fracture depths are stable (black dot). Hydrofractures can become unstable when a pre-existing flaw filled with water reaches a depth denoted by the white dots. Water-filled initial flaws smaller than di will remain closed. When stress is sufficiently compressive, water-filled fractures will not grow (for example, the blue curve has negative slopes for any surface fracture depth below the red line). b, Comparison of ds with previous theories. Our numerical solution approaches Weertman’s solution at large ice thickness. c, d, The required di to destabilize a hydrofracture as a function of stress is shown by blue curves. The pre-existing flaw depths required to initialize stable dry surface fractures are plotted as a red curve in c, and reach a maximum of ~3.8 m at the critical stress \({R}_{xx}^{* }\) (dashed line). Note that at \({R}_{xx}^{* }\) the required initial flaw depth is the same as fracture depth, that is, \({d}_{{\rm{i}}}={d}_{{\rm{s}}}={d}_{s}^{* }\approx 3.8\,{\rm{m}}\) (half-white half-black dot in a).

Extended Data Fig. 6 Antarctic-wide data used to predict vulnerability to hydrofracture.

ad, The dimensionless toughness and dimensionless stress were evaluated using strain rates (a), ice-shelf thickness (b), surface temperature (c) and viscosity factor B (d, calculated from surface temperature) and plotted on the fracture stability diagram (Fig. 3c).

Extended Data Fig. 7 Surface fracture stability diagram.

The two parameters determining fracture stability, \({\tilde{K}}_{{\rm{Ic}}}\) and \({\tilde{R}}_{xx}\), were computed at every 1 km × 1 km location on all ice shelves marked as red (n = 1,258,908 points) and all fracture features detected by the DCNN marked as yellow dots (n = 31,962). The frequency distribution of the yellow points is shown in Fig. 3c.

Extended Data Fig. 8 Alternative stress computations.

Sensitivity of surface fracture stability diagram (top) and the vulnerability map (bottom) to choices of stress and strain rate data. ac, Results computed using strain rates calculated by ref. 61 (a) and ref. 13 along-flow stress (b) and first principal stress (c), which includes damage-induced ice softening. The colour scale for the bottom row is the same as Fig. 4. The percentage values in the bottom row denote the percentage of the total ice-shelf area that is in the red regime in the second row (that is, both buttressed and vulnerable to hydrofracture). Our main conclusions—that ice-shelf stresses closely agree with the fracture criteria, and that large buttressed areas are vulnerable to hydrofracture—are not affected by the use of these alternative stress fields.

Extended Data Fig. 9 Advection of fracture and stress history.

We tracked the resistive stress upstream along streamlines (assuming steady-state) and identified the maximum dimensionless stress \({\tilde{R}}_{xx{\rm{\max }}}\) each fracture feature had experienced in the past. a, The dimensionless parameters \({\tilde{R}}_{xx}\) and \({\tilde{K}}_{{\rm{Ic}}}\) evaluated directly at the locations of fracture features are shown (same as Fig. 3c) for comparison. b, For each location identified as a fracture by the DCNN, we evaluated \({\tilde{R}}_{xx{\rm{\max }}}\) and the corresponding \({\tilde{K}}_{{\rm{Ic}}}\) at the location where \({\tilde{R}}_{xx{\rm{\max }}}\) occurred. \({\tilde{R}}_{xx{\rm{\max }}}\) calculated for most fractures features exceeds the threshold for surface fracture formation (red line; equation (2)).

Extended Data Fig. 10 East Antarctic lake locations compared with vulnerability map.

Stokes et al.25 have mapped lakes across much of East Antarctica for one melt season (2017), enabling us to compare these locations with our vulnerability map (Fig. 4). ae, The lakes mapped by Stokes et al. are marked in light blue with expanded views shown in be. We find that only a tiny proportion of the ice-shelf area in East Antarctica accumulates meltwater, provides buttressing and is vulnerable to hydrofracture. An upper estimate of the overlap between lake-covered area (top circle of Fig. 1) and stress state-related vulnerable area (bottom left circle of Fig. 1) is only ~0.63% of the East Antarctic ice-shelf area.

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Supplementary Information

This file contains Supplementary Information on the theory of ice-shelf fractures 1–7.

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Lai, C., Kingslake, J., Wearing, M.G. et al. Vulnerability of Antarctica’s ice shelves to meltwater-driven fracture. Nature 584, 574–578 (2020). https://doi.org/10.1038/s41586-020-2627-8

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