Space and Time Scaling Laws Induced by the Multiscale Fracturing of The Arctic Sea Ice Cover

  • Jérôme Weiss
  • David Marsan
  • Pierre Rampal
Part of the Iutam Bookseries book series (IUTAMBOOK, volume 10)


Recent analyses of in-situ and satellite observations of arctic sea ice stresses and strain-rates revealed a highly intermittent and heterogeneous dynamics characterized by temporal and spatial scaling laws, a vision at odds with the classical smooth, fluid-like modelling framework of the sea ice cover. We propose here a simple multiscale fracturing model that explains the observed scaling properties of the deformation fields from the fractal properties of fracturing.


Sea ice scaling laws dispersion deformation fracture 


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  1. 1.
    Heil, P. and W.D.I. Hibler, Modeling the high frequency component of arctic sea ice drift and deformation. J. Physical Oceanography, 2002. 32: pp. 3039–3057.CrossRefGoogle Scholar
  2. 2.
    Hibler, W.D.I., A dynamic thermodynamics sea ice model. J. Phys. Oceanogr., 1979. 9: pp. 815–846.CrossRefGoogle Scholar
  3. 3.
    Schulson, E.M., Compressive shear faults within the arctic sea ice: Fracture on scales large and small. J. Geophys. Res., 2004. 109: doi:10.1029/2003JC002108.Google Scholar
  4. 4.
    Weiss, J. and D. Marsan, Scale properties of sea ice deformation and fracturing. C.R. Physique, 2004. 5(7): pp. 683–685.CrossRefGoogle Scholar
  5. 5.
    Moritz, R.E. and H.L. Stern, Relationships between geostrophic winds, ice strain rates and the piecewise rigid motions of pack ice, in Scaling Laws in Ice Mechanics and Ice Dynamics, J.P. Dempsey and H.H. Shen, Editors. 2001, Kluwer Academic Publishers: Dordrecht. pp. 335–348.Google Scholar
  6. 6.
    Weiss, J., E.M. Schulson, and H.L. Stern, Sea ice rheology from in-situ, satellite and laboratory observations: Fracture and friction. Earth Planet. Sci. Lett., 2006. 255: pp. 1–8.CrossRefGoogle Scholar
  7. 7.
    Nye, J.F., Is there any physical basis for assuming linear viscous behavior for sea ice. AIDJEX Bulletin, 1973. 21: pp. 18–19.Google Scholar
  8. 8.
    Martin, S. and A.S. Thorndike, Dispersion of sea ice in the Bering Sea. J. Geophys. Res., 1985. 90(C4): pp. 7223–7226.Google Scholar
  9. 9.
    Rampal, P., et al., Scaling properties of sea ice deformation from buoy dispersion analyses. J. Geophys. Res., 2008. 113: p. C03002.CrossRefGoogle Scholar
  10. 10.
    Richardson, L.F., Atmospheric diffusion shown on a distance-neighbour graph. Proc. R. Soc. London A, 1926. 110: pp. 709–737.CrossRefGoogle Scholar
  11. 11.
    Marsan, D., et al., Scale dependence and localization of the deformation of arctic sea ice. Phys. Rev. Lett., 2004. 93(17): p. 178501.CrossRefGoogle Scholar
  12. 12.
    Thorndike, A.S., Diffusion of sea ice. J. Geophys. Res., 1986. 91(C6): pp. 7691–7696.CrossRefGoogle Scholar
  13. 13.
    Scholz, C.H. and P.A. Cowie, Determination of total strain from faulting using slip measurements. Nature, 1990. 346: pp. 837–839.CrossRefGoogle Scholar
  14. 14.
    Wells, D.L. and K.J. Coppersmith, New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull. Seism. Soc. Am., 1994. 84(4): pp. 974–1002.Google Scholar
  15. 15.
    Lindsay, R.W. and D.A. Rothrock, Arctic sea ice leads from advanced very high resolution radiometer images. J. Geophys. Res., 1995. 100(C3): pp. 4533–4544.CrossRefGoogle Scholar
  16. 16.
    Weiss, J., Scaling of fracture and faulting in ice on Earth. Surv. Geophy., 2003. 24: pp. 185–227.CrossRefGoogle Scholar
  17. 17.
    Dudko, Y.V., Analysis of seismo-acoustic emission from ice fracturing events during SIMI’94, in Oceanographic Engineering. 1999, Massachusetts Institute of Technology: Boston, MA.Google Scholar
  18. 18.
    Sornette, D., Critical phenomena in natural sciences. Springer Series in Synergetics. 2000, Berlin: Springer.zbMATHGoogle Scholar
  19. 19.
    Kwok, R. Deformation of the Arctic Ocean sea ice cover between November 1996 and April 1997: A survey. in IUTAM Scaling Laws in Ice Mechanics and Ice Dynamics. 2000. Fairbanks, Alaska: Kluwer Academic Publishers, Dordrecht.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Jérôme Weiss
    • 1
  • David Marsan
  • Pierre Rampal
  1. 1.LGGE, CNRS

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