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Termini of calving glaciers as self-organized critical systems

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Over the next century, one of the largest contributions to sea level rise will come from ice sheets and glaciers calving ice into the ocean1. Factors controlling the rapid and nonlinear variations in calving fluxes are poorly understood, and therefore difficult to include in prognostic climate-forced land-ice models. Here we analyse globally distributed calving data sets from Svalbard, Alaska (USA), Greenland and Antarctica in combination with simulations from a first-principles, particle-based numerical calving model to investigate the size and inter-event time of calving events. We find that calving events triggered by the brittle fracture of glacier ice are governed by the same power-law distributions as avalanches in the canonical Abelian sandpile model2. This similarity suggests that calving termini behave as self-organized critical systems that readily flip between states of sub-critical advance and super-critical retreat in response to changes in climate and geometric conditions. Observations of sudden ice-shelf collapse and tidewater glacier retreat in response to gradual warming of their environment3 are consistent with a system fluctuating around its critical point in response to changing external forcing. We propose that self-organized criticality provides a yet unexplored framework for investigations into calving and projections of sea level rise.

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Figure 1: Numerical model and FSD.
Figure 2: Event sizes and waiting times.
Figure 3: Sensitivity of calving to external forcing.
Figure 4: Real geometry of Kronebreen, Svalbard, implemented in the particle model with a 4 m particle diameter.

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Change history

  • 18 November 2014

    In the version of this Letter originally published online, the following sentence should have appeared in the Acknowledgements section: "The simulated graphics have been rendered by J. Hokkanen (CSC-IT Centre for Science)". This error has been corrected in all versions of the Letter.


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We thank J. A. Jania, D. Ignatiuk, M. Laska, B. Luks, M. Ciepły, J. Halat, A. Piechota, M. Sund and crews from the Polish Polar Station in Hornsund (Institute of Geophysics, Polish Academy of Sciences) for their help collecting data at Paierlbreen; A. Hodson and D. Benn for their help at Tunabreen; and G. Hamilton for suggesting the Greenland data. Kronebreen geometry was provided by the Norwegian Polar Institute. The European Space Agency provided ENVISAT ASAR imagery for the Antarctic ice shelves. Support provided by: SvalGlac (Paierlbreen); SVALI (Tunabreen); US Geological Survey Climate and Land Use Change, Department of Interior Climate Science Center, and Prince William Sound Regional Citizens’ Advisory Council (Columbia Glacier); NSF-EAR-0810313 (Yahtse Glacier); National Basic Research Program of China (2012CB957704 and 2015CB953600) and Fundamental Research Funds for the Central Universities of China (2013NT5) (Antarctic ice shelves). This publication is contribution number 33 of the Nordic Centre of Excellence SVALI, ‘Stability and Variations of Arctic Land Ice’, funded by the Nordic Top-level Research Initiative (TRI). The simulated graphics have been rendered by J. Hokkanen (CSC–IT Centre for Science).

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Authors and Affiliations



J.A.Å. and T.I.R. constructed the calving model. J.A.Å. assembled and interpreted the calving observations. Co-authors collected, processed or interpreted the calving observations, as follows: Columbia (E.Z.W. and S.O’.N.), Yahtse (T.C.B. and S.O’.N.), Tunabreen (D.V.), Paierlbreen (M.S. and E.Z.W.), Helheim and Kangerdlugssuaq (M.S.), and Antarctic ice shelves (Y.L. and J.C.M.). T.Z. performed the ice-flow model simulations. E.Z.W. compiled the Calving Event Catalogue. All authors have contributed to, seen and approved the manuscript.

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Correspondence to D. Vallot.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (Methods 1, Methods 2 and Discussion) (PDF 12013 kb)

Supplementary Movie 1

2D Glacier in Deep Water (MOV 5049 kb)

Supplementary Movie 2

2D Glacier in Shallow Water (MOV 1971 kb)

Supplementary Movie 3

3D Glacier in Critical State (MOV 21643 kb)

Supplementary Movie 4

3D Glacier in Super-critical State (MOV 26149 kb)

Supplementary Information

Calving Event Catalogue (PDF 555 kb)

Supplementary Information

Supplementary Data (described in the Calving Event Catalogue) (ZIP 2364 kb)

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Åström, J., Vallot, D., Schäfer, M. et al. Termini of calving glaciers as self-organized critical systems. Nature Geosci 7, 874–878 (2014).

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