The effects of plastic waves on the numerical convergence of the viscous-plastic and elastic-viscous-plastic sea-ice models

The plastic wave speed is derived from the linearized 1-D version of the widely used viscousplastic (VP) and elasticviscousplastic (EVP) sea-ice models. CourantFriedrichsLewy (CFL) conditions are derived using the propagation speed of the wave. 1-D numerical experiments of the VP, EVP and EVP models successfully recreate a reference solution when the CFL conditions are satisfied, in agreement with the theory presented. The IMplicitEXplicit (IMEX) method is shown to effectively alleviate the plastic wave CFL constraint on the timestep in the implicitly solved VP model in both 1-D and 2-D. In 2-D, the EVP and EVP models show first order error in the simulated velocity field when the plastic wave is not resolved. EVP simulations are performed with various advective timestep, number of subcycles, and elastic-wave damping timescales. It is found that increasing the number of subcycles beyond that needed to resolve the elastic wave does not improve the quality of the solution. It is found that reducing the elastic wave damping timescale reduces the spatial extent of first order errors cause by the unresolved plastic wave. Reducing the advective timestep so that the plastic wave is resolved also reduces the velocity error in terms of magnitude and spatial extent. However, the parameter set required for convergence to within the error bars of satellite (RGPS) deformation fields is impractical for use in climate model simulations. The behavior of the EVP method is analogous to that of the EVP method except that it is not possible to reduce the damping timescale with =.

[1]  David Marsan,et al.  Scale dependence and localization of the deformation of Arctic sea ice. , 2004, Physical review letters.

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

[3]  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..

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

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

[6]  Hrvoje Jasak,et al.  A strength implicit correction scheme for the viscous-plastic sea ice model , 2004 .

[7]  Dana A. Knoll,et al.  A second-order accurate in time IMplicit-EXplicit (IMEX) integration scheme for sea ice dynamics , 2014, J. Comput. Phys..

[8]  Jack Oliver,et al.  Elastic waves in Arctic pack ice , 1954 .

[9]  K. Hunkins,et al.  Seismic studies of sea ice , 1960 .

[10]  Sergey Danilov,et al.  On the convergence of the modified elastic-viscous-plastic method for solving the sea ice momentum equation , 2015, J. Comput. Phys..

[11]  Ron Lindsay,et al.  Sea‐ice deformation rates from satellite measurements and in a model , 2003 .

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

[13]  Mark A. Hopkins,et al.  Four stages of pressure ridging , 1998 .

[14]  Sylvain Bouillon,et al.  The elastic–viscous–plastic method revisited , 2013 .

[15]  William H. Lipscomb,et al.  Ridging, strength, and stability in high-resolution sea ice models , 2007 .

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

[17]  Sergey Danilov,et al.  The adaptive EVP method for solving the sea ice momentum equation , 2016 .

[18]  R. Pritchard.  An Elastic-Plastic Constitutive Law for Sea Ice , 1975 .

[19]  J. Gray.  Loss of hyperbolicity and ill-posedness of the viscous-plastic sea ice rheology in uniaxial divergent flow , 1999 .

[20]  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..

[21]  M. Mcphee.  Sea Ice Drag Laws and Simple Boundary Layer Concepts, Including Application to Rapid Melting, , 1982 .

[22]  Stephen J. Thomas,et al.  Using the preconditioned Generalized Minimum RESidual (GMRES) method to solve the sea‐ice momentum equation , 2008 .

[23]  Harry L. Stern,et al.  The RADARSAT Geophysical Processor System: Quality of Sea Ice Trajectory and Deformation Estimates , 2003 .

[24]  Wilford F. Weeks,et al.  The mechanical properties of sea ice , 1967 .