The elastic–viscous–plastic method revisited

In this paper, we show that one of the most widely used methods to solve the non-linear viscous–plastic (VP) sea ice rheology, the elastic–viscous–plastic (EVP) method, generates artificial linear bands of high deformation that may be confounded with real linear kinematic features observed in the Arctic ice pack. These numerical artefacts are easily filtered out by using a slightly different regularization of the internal stress. In addition, the EVP method is reinterpreted as an iterative solver and a clear distinction appears between the numerical and physical parameters. Two numerical parameters determine the stability and accuracy of the method and are adjusted to avoid the noisy ice deformation fields frequently observed with the EVP method in nearly rigid ice areas. This study also confirms the unsatisfactory numerical convergence of the EVP method and investigates the effects of the numerical parameters on sea ice deformation, internal stress and velocity fields obtained with unconverged solutions.

[1]  D. Menemenlis,et al.  On the formulation of sea-ice models. Part 1: Effects of different solver implementations and parameterizations , 2010 .

[2]  W. Hibler A Dynamic Thermodynamic Sea Ice Model , 1979 .

[3]  Eric P. Chassignet,et al.  Ocean modeling and parameterization , 1998 .

[4]  Randy Showstack,et al.  World Ocean Database , 2009 .

[5]  Keguang Wang,et al.  Modeling linear kinematic features in pack ice , 2009 .

[6]  John K. Dukowicz,et al.  The Elastic Viscous Plastic Sea Ice Dynamics Model in General Orthogonal Curvilinear Coordinates on a Sphere—Incorporation of Metric Terms , 2002 .

[7]  M. Maqueda,et al.  An elastic-viscous-plastic sea ice model formulated on Arakawa B and C grids , 2009 .

[8]  David M. Holland,et al.  A comparison of the Jacobian-free Newton-Krylov method and the EVP model for solving the sea ice momentum equation with a viscous-plastic formulation: A serial algorithm study , 2012, J. Comput. Phys..

[9]  Timothy P. Boyer,et al.  World ocean database 2009 , 2006 .

[10]  Ron Kwok,et al.  Elastic‐decohesive constitutive model for sea ice , 2006 .

[11]  G. Madec NEMO ocean engine , 2008 .

[12]  Hugues Goosse,et al.  On the large-scale modeling of sea ice-ocean interactions , 1998 .

[13]  D. Feltham,et al.  A continuum anisotropic model of sea-ice dynamics , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  Thierry Penduff,et al.  An ERA40-based atmospheric forcing for global ocean circulation models , 2010 .

[15]  D. Sulsky,et al.  Arctic Ice Dynamics Joint Experiment (AIDJEX) assumptions revisited and found inadequate , 2007 .

[16]  On the Consistent Scaling of Terms in the Sea-Ice Dynamics Equation , 2004 .

[17]  D. Rothrock,et al.  Modeling Arctic sea ice with an efficient plastic solution , 2000 .

[18]  Elizabeth C. Hunke,et al.  Viscous–Plastic Sea Ice Dynamics with the EVP Model: Linearization Issues , 2001 .

[19]  D. Rothrock,et al.  Effect of sea ice rheology in numerical investigations of climate , 2005 .

[20]  William H. Lipscomb,et al.  High resolution simulations of Arctic sea ice, 1979–1993 , 2003 .

[21]  William D. Hibler,et al.  On an efficient numerical method for modeling sea ice dynamics , 1997 .

[22]  Paul F. Tupper,et al.  Improving the numerical convergence of viscous-plastic sea ice models with the Jacobian-free Newton-Krylov method , 2010, J. Comput. Phys..

[23]  E. Schulson,et al.  On modeling the anisotropic failure and flow of flawed sea ice , 2000 .

[24]  M. Maqueda,et al.  Sensitivity of a global sea ice model to the treatment of ice thermodynamics and dynamics , 1997 .

[25]  Ron Kwok,et al.  Contrasts in sea ice deformation and production in the Arctic seasonal and perennial ice zones , 2006 .

[26]  Stephen G. Yeager,et al.  Diurnal to decadal global forcing for ocean and sea-ice models: The data sets and flux climatologies , 2004 .

[27]  E. Hunke,et al.  A Comparison of Sea Ice Dynamics Models at High Resolution , 1999 .

[28]  E. Hunke,et al.  An Elastic–Viscous–Plastic Model for Sea Ice Dynamics , 1996 .

[29]  Jean-Marc Molines,et al.  Evaluation of high-resolution sea ice models on the basis of statistical and scaling properties of Arctic sea ice drift and deformation , 2009 .

[30]  R. Gerdes,et al.  Sea ice drift variability in Arctic Ocean Model Intercomparison Project models and observations , 2007 .

[31]  P. Delecluse,et al.  OPA 8.1 Ocean General Circulation Model reference manual , 1998 .

[32]  Jean-François Lemieux,et al.  Numerical convergence of viscous‐plastic sea ice models , 2009 .

[33]  Ron Kwok,et al.  Variability of sea ice simulations assessed with RGPS kinematics , 2008 .

[34]  M. Losch,et al.  Solving the Momentum Equations of Dynamic Sea Ice Models with Implicit Solvers and the Elastic-Viscous-Plastic Technique , 2009 .

[35]  Sylvain Bouillon,et al.  A new modeling framework for sea-ice mechanics based on elasto-brittle rheology , 2011, Annals of Glaciology.