Nonlocal ice strength regularization of the Viscous-Plastic sea ice rheology: resolving ill-posedness and resolution-dependent fracture patterns

Abstract. We implement a nonlocal ice strength regularization in the standard Viscous-Plastic (VP) and Elastic-Viscous-Plastic (EVP) models. To this end, we introduce an inhomogeneous Helmholtz equation for the ice strength that provides a physically based regularization of the ill-posed VP and EVP formulations while preserving the rate-independence of the plastic regime and the material instabilities that give rise to narrow deformation bands. A linear stability analysis of the new system of equations shows that the nonlocal regularization imposes an upper bound on the growth rates of perturbations, a necessary condition for well-posed problems. Those results are confirmed in idealized divergent numerical experiments: the standard (E)VP models yield resolution-dependent solutions with an increasing number of fractures as the spatial resolution is increased, whereas the nonlocal models produce a resolution-independent solution with a single fracture at the center of the ice plate. Numerical experiments demonstrating the ill-posedness of the hyperbolic tangent viscosity regularization previously identified through a linear stability analysis are also presented. With the advent of kilometer-scale sea ice simulations (Δx ≤ 2–3 km), a well-posed rheology is essential to ensure that fracture statistics reflect physical deformation processes rather than numerical instabilities.