ICON-O is the global ocean model within the ICON-ESM. ICON-O is based on the primitive equations that describe the ocean as an incompressible fluid on a rotating sphere with a free surface and subject to the hydrostatic and Boussinesq approximation. The equations are discretized on the ICON’s icosahedral grid with triangular grid cells and an Arakawa C-type staggering of variables. The vertical coordinate axis is a z-coordinate. The ocean primitive equations are discretized with a structure-preserving discretization that is described in (P. Korn,
J. Comp. Phys. 339, 2017). The oceanic parametrizations for ICON-O comprise a vertical mixing based on a modified PP-scheme and a new discretization for isoneutral diffusion and the eddy prametrization of Gent-McWilliams on unstructured grids. For velocity closure a number of options is available, that comprise harmonic and  harmonic diffusion with different parameter scalings as well as an adaptive Leith closure.    

ICON-O uses a dynamic/thermodynamic sea ice model with a viscous-plastic rheology following Hibler (1979). The discretization of the sea ice dynamics is based on the finite-element sea-ice model FESIM of the Alfred-Wegener Institute for Polar and Marine Research (Q. Wang et al., Geosci Model Dev. 7, 2017).
HAMOCC is a sub-model simulates biogeochemical tracers in the oceanic water column and in the sediment. HAMOCC has been transferred to ICON-O and the biogeochemical tracers use the advection and mixing algorithms of ICON-O.