Large Scale Sea Ice Modeling – Problems and Perspectives.

Abstract

AbstractThe visco‐plastic sea ice model based on [7] describes the movement of sea ice over large areas of several thousand square kilometers in time. This model has been considered in many publications and has been extended and adapted by numerically motivated and physically‐based approaches. The basic model for the simulation of sea ice circulation considers sea ice velocities and stresses coupled to the field quantities of sea ice thickness and concentration. Two transient advection equations describe the development of sea ice thickness and concentration coupled with sea ice velocity. Furthermore, the viscosity in the constitutive equation is dependent on the sea ice velocities in the sense of a non‐Newtonian fluid, which makes the constitutive relationship strongly nonlinear. An extension of the model is, for example, the elasto‐visco‐plastic constitutive law proposed by [10], which gives numerical stabilization. Recent research on the finite element implementation of the sea ice model is turned to formulations based on the (mixed) Galerkin variation approach, see for example [1] and [20]. Likewise, in [15], [16], and [18] solvers are proposed for the efficient solution of the problem.In this paper, we discuss the obstacles and possibilities of a sea ice model implementation, among others, within a least‐squares finite element method (LSFEM). The mixed LSFEM is well established in fluid mechanics, and a significant advantage of the method is its applicability to first‐order systems, see e.g. [12]. Thus, this method leads to stable and robust formulations for non‐self‐adjoint systems, as they are, for example, for the tracer equations. Based on the results of the Taylor least‐squares scheme and a first‐order Crank‐Nicolson time integrator scheme for the tracer equations, see [21], we discuss here possible steps towards an adequate solution strategy for the complete sea ice model.