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Termini of calving glaciers as self-organized critical systems

Nature Geoscience volume 7, pages 874–878 (2014)Cite this article

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Abstract

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.

References

  1. Moore, J. C., Grinsted, A., Zwinger, T. & Jevrejeva, S. Semi-empirical and process-based global sea level projections. Rev. Geophys. 51, 484–522 (2013).

    Article  Google Scholar 

  2. Bak, P., Tang, C. & Wiesenfeld, K. Self-organized criticality: An explanation of the 1/f noise. Phys. Rev. Lett. 59, 381–384 (1987).

    Article  Google Scholar 

  3. Luckman, A., Murray, T., de Lange, R. & Hanna, E. Rapid and synchronous ice-dynamic changes in East Greenland. Geophys. Res. Lett. 33, L03503 (2006).

    Article  Google Scholar 

  4. Anthoff, D., Nicholls, R. J., Tol, R. S. J. & Vafeidis, A. T. Global and Regional Exposure to Large Rises in Sea-Level: A Sensitivity Analysis (Tyndall Centre for Climate Change Research, 2006).

    Google Scholar 

  5. Rignot, E., Velicogna, I., van den Broeke, M. R., Monaghan, A. & Lenaerts, J. Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise. Geophys. Res. Lett. 38, 1–5 (2011).

    Article  Google Scholar 

  6. Rignot, E., Jacobs, S., Mouginot, J. & Scheuchl, B. Ice-shelf melting around Antarctica. Science 341, 266–270 (2013).

    Article  Google Scholar 

  7. Bindschadler, R. A. et al. Ice-sheet model sensitivities to environmental forcing and their use in projecting future sea level (the SeaRISE project). J. Glaciol. 59, 195–224 (2013).

    Article  Google Scholar 

  8. Main, I. Is the reliable prediction of individual earthquakes a realistic scientific goal? Nature Debateshttp://www.nature.com/nature/debates/earthquake (1999).

  9. Fineberg, J. & Marder, M. Instability in dynamic fracture. Phys. Rep. 313, 2–108 (1999).

    Article  Google Scholar 

  10. Åström, J. A. Statistical models of brittle fragmentation. Adv. Phys. 55, 247–278 (2006).

    Article  Google Scholar 

  11. Kekäläinen, P., Åström, J. A. & Timonen, J. Solution for the fragment-size distribution in a crack-branching model of fragmentation. Phys. Rev. E 76, 026112 (2007).

    Article  Google Scholar 

  12. Bak, P. How Nature Works: The Science of Self-Organized Criticality (Springer, 1996).

    Book  Google Scholar 

  13. Jensen, H. J. Self-Organized Criticality (Cambridge Univ. Press, 1998).

    Book  Google Scholar 

  14. Dhar, D. The Abelian sandpile and related models. Physica A 263, 4–25 (1999).

    Article  Google Scholar 

  15. Dhar, D. Theoretical studies of self-organized criticality. Physica A 369, 29–70 (2006).

    Article  Google Scholar 

  16. Paczuski, M., Boettcher, S. & Baiesi, M. Interoccurrence times in the Bak–Tang–Wiesenfeld sandpile model: A comparison with the observed statistics of solar flares. Phys. Rev. Lett. 95, 181102–181105 (2005).

    Article  Google Scholar 

  17. Åström, J. A. et al. A particle based simulation model for glacier dynamics. Cryosphere 7, 1591–1602 (2013).

    Article  Google Scholar 

  18. Crocker, G. B. Size distributions of bergy bits and growlers calved from deteriorating icebergs. Cold Reg. Sci. Technol. 22, 113–119 (1993).

    Article  Google Scholar 

  19. Savage, S. B., Crocker, G. B., Sayed, M. & Carriers, T. Size distribution of small ice pieces calved from icebergs. Cold Reg. Sci. Technol. 31, 163–172 (2000).

    Article  Google Scholar 

  20. Scambos, T. A., Hulbe, C. L. & Fahnestock, M. A. Climate-induced ice shelf disintegration in the Antarctic Peninsula. Antarct. Res. Ser. 79, 79–92 (2003).

    Google Scholar 

  21. Bassis, J. N. & Jacobs, S. Diverse calving patterns linked to glacier geometry. Nature Geosci. 6, 833–836 (2013).

    Article  Google Scholar 

  22. Amundson, J. A. & Truffer, M. A unifying framework for iceberg-calving models. J. Glaciol. 56, 822–830 (2010).

    Article  Google Scholar 

  23. Bassis, J. N. The statistical physics of iceberg calving and the emergence of universal calving laws. J. Glaciol. 57, 3–16 (2011).

    Article  Google Scholar 

  24. Gagliardini, O. et al. Capabilities and performance of Elmer/Ice, a new-generation ice sheet model. Geosci. Model Dev. 6, 1299–1318 (2013).

    Article  Google Scholar 

  25. Chapuis, A. & Tetzlaff, T. The variability of tidewater-glacier calving: Origin of event-size and interval distributions. J. Glaciol. 60, 622–634 (2014).

    Article  Google Scholar 

  26. Padman, L. & Erofeeva, S. A. Barotropic inverse tidal model for the Arctic Ocean. Geophys. Res. Lett. 31, L02303 (2004).

    Article  Google Scholar 

Download references

Acknowledgements

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

  1. CSC–IT Centre for Science, PO Box 405, 02101 Espoo, Finland

    J. A. Åström & T. Zwinger

  2. Department of Earth Science, Uppsala University, Villavägen 16, 75236 Uppsala, Sweden

    D. Vallot & J. C. Moore

  3. Arctic Centre, University of Lapland, PL122, 96100 Rovaniemi, Finland

    M. Schäfer & J. C. Moore

  4. Finnish Meteorological Institute, PO Box 503, 00101 Helsinki, Finland

    M. Schäfer

  5. Institute of Arctic and Alpine Research, University of Colorado, Campus Box 450, Boulder, Colorado 80309, USA

    E. Z. Welty & S. O’Neel

  6. Alaska Science Center, US Geological Survey, 4210 University Drive Anchorage, Alaska 99508, USA,

    S. O’Neel

  7. University of Texas Institute for Geophysics, 10100 Burnet Road (R2200) Austin, Texas 78758, USA,

    T. C. Bartholomaus

  8. State Key Laboratory of Earth Surface Processes and Resource Ecology, College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China

    Yan Liu & J. C. Moore

  9. Department of Physics and Nanoscience Center, University of Jyväskylä, PO Box 35, 40014 Jyväskylä, Finland

    T. I. Riikilä & J. Timonen

  10. ITMO University, Kronverkskii ave. 49 197101, Saint Petersburg, Russia,

    J. Timonen

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  1. J. A. Åström
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Contributions

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.

Corresponding author

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). https://doi.org/10.1038/ngeo2290

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