a sea ice model with rheology, and detailed flux parameterizations. The ocean itself was formulated with primitive equations in flux form. Due to the use of isopycnal as vertical coordinates it is natural to write equations as prognostic equations for layer thickness, the distance of two isopycnals. Thus, the prognostic variables are the integrals of mass flux, mass, heat, and salt over the column bounded by two interfaces. A realistic equation of state is used to relate density with temperature and salinity as well as potential temperature and potential density. The mixed layer model is based on the assumption that turbulent kinetic energy is dissipated within a length scale determined by the Ekman-layer thickness. A similar assumption holds for the buoyancy flux. Solar radiation is allowed to penetrate through the surface and is absorbed below the surface determined by given water properties. Further parameterizations for vertical mixing, convection, and the sea-ice mixed layer coupling are introduced. The sea ice model is written in flux form for the ice thickness, ice concentration, and ice flow as prognostic variables. Besides the thermodynamical forcing a viscous plastic reology as well as a lead parametrization are included.
The model is formulated on spherical coordinates. On the isopycnals, which run essentially in the horizontal, the discritization is based on a staggered grid while vertically the prognostically determined interface heights represent Lagrangian coordinates. The time stepping scheme is a combination of the semi-implicit technique and a predictor-corrector scheme. Besides the conservation of mass, heat, and salt that are ensured through the use of the flux form, a potential vorticity conserving scheme is included to formulate the momentum transport.
2.1. Interior isopycnal Layers
The primitive equations of motion are formulated in flux form as conservation equations for the vertical means of the mass flux, Ψk = (pvh)k, the mass contentΨk = (ph)k, the heat content Θk = (phθ)k, and the salt content II = (ph S)k, in the k-th layer,
