Derivation of a numerical solution of the 3D coupled velocity field for an ice sheet – ice shelf system, incorporating both full and approximate stress solutions

Abstract

Abstract. To overcome the mechanical coupling of an ice sheet with an ice shelf, one single set of velocity equations is presented covering both the sheet and the shelf. This set is obtained by applying shared sheet-shelf approximations. The hydrostatic approximation and a constant density are the only approximations that are applied to the full-Stokes momentum equations. The remaining stress terms from the momentum equations and the stress terms from the usual ice-flow law are multiplied by coefficients which can be put to zero or one, facilitating several stress approximations per domain within one model. In addition we derived a matrix format for the discretized set of the fully coupled velocity equations on a three-dimensional vertically scaled grid, in which all linear derivative terms are treated implicitly. The compact vector format of this sparse matrix equation is developed, including the boundary conditions.

Mapping technique of climate fields between GCM's and ice models

“…Contrary, the ice dynamical equations are favorably solved on a grid with rectangular coordinates because the transformation of the ice dynamical equations to geographical coordinates introduces many extra complicating terms, in particular given the tendency of including more and more stress terms (see e.g. Pattyn, 2003;Reerink et al, 2009). Moreover calculations with a GCM are very time consuming and therefore only limited runs can be performed with a relatively coarse resolution.…”