Numerical Instability in a Viscous Plastic Sea-Ice Model Arising from Unresolved Plastic Deformation

The plastic deformation wave in a viscous plastic sea-ice model travels at speeds greater than 25 m/s, as shown by Gray. It is this wave which dictates, in a CFL sense, the maximum allowable time step for a given model grid spacing. We find that typical configurations of high resolution (dx=5km) sea-ice models require a time step of less than ~100 second to resolve the plastic deformation wave. The constraint on the timestep will become more strict as models continue towards higher spatial resolution. We show that failure to correctly resolve this wave introduces first order noise into the model deformation fields and that the resulting error is exacerbated by use of the elastic-viscous-plastic integration technique. It is important that the model deformation fields be correctly resolved as they are increasingly being analyzed as a means to validate and compare different sea-ice rheologies. The underlying issue is the splitting in time of the sea-ice momentum and continuity equations, resulting in a discrepancy between the sea-ice mass and momentum at a given model time step. We propose the IMplicit-EXplicit (IMEX) method for coupling the momentum and continuity equations as a way of correctly resolving the propagation of the plastic wave while maintaining a longer time step.