  This article establishes local strong well-posedness and global strong
well-posedness close to constant equilibria of a model coupling the primitive
equations of ocean and atmospheric dynamics with Hibler's viscous-plastic sea
ice model. In order to treat the coupling conditions, an approach involving the
hydrostatic Dirichlet and Dirichlet-to-Neumann operator is developed. Mapping
properties of the latter operators are investigated for the first time and are
of central importance for showing that the operator associated with the
linearized coupled system admits a bounded $\mathcal{H}^\infty$-calculus on
suitable $\mathrm{L}^q$-spaces. Quasilinear methods allow then to obtain the
strong well-posedeness results described above.
