On a new numerical scheme for ice dynamics models

Recent anisotropic ice dynamics models have emphasized that velocity can be discontinuous across active leads, rafts, or ridges and have described these discontinuities explicitly. Here the authors use the fact that velocity discontinuities must be aligned with characteristic directions (slip lines) in these models. The analysis is limited to quasi-steady behavior, where time is a parameter in the mechanical behavior (no time derivatives in the momentum balance or constitutive law). The quasi-steady model must neglect tidal oscillations as well as inertia in the momentum equations for ice and upper ocean and resolve time steps to at least a day. The spatial derivatives are written in characteristic coordinates, a nontrivial transformation to non-orthogonal, curvilinear coordinates. The authors assume that each nodal point can be split into four or two nodes if the solution is hyperbolic or parabolic there. The authors have not yet determined which basic variables must appear in the equations, but expect that velocity and traction will appear. Since the characteristic directions must be determined as part of the solution, and the logical connectivity of nodes in characteristic coordinates is very difficult, it is not desirable to introduce a grid to describe the solution field. Therefore, meshless solutions methods will be investigated. The authors expect the characteristic solution method will provide a better description of small-scale ice behavior to better support offshore operations and shipping because of the explicit description of leads, rafts, and ridges. This new numerical approach will also allow comparison with other recent model developments.