5 
2 
Model physics 
A numerical implementation of the common boundary layer equations of geophysical fluid 
dynamics constitutes the core of the circulation model. Sea ice has been included in the 
model as an extra feature. The hydrodynamical model is three-dimensional, except for the 
shallow water approximation (hydrostatics in the vertical). It consists of conservation 
equations for mass (continuity equation) and horizontal momentum on the rotating earth. 
The complete system also includes budget equations for heat and salt, along with an 
equation of state. The model thus is fully prognostic. Details are given in the appendix. 
The sub-scale closure formulation (viscous type) for horizontal flow of (horizontal) 
momentum is taken from Smagorinsky (1963). A novel model of the mixing-length type is 
used to simulate vertical exchange. 
Another sub-scale process that has to be taken into account because it affects large- 
scale circulation is surface wave action (both wind-sea and swell). Compared to wave- 
free circulation, waves give rise to an extra flux of mass (Stokes flow) and momentum 
(radiation stress). Physically and from a Lagrangian point of view, Stokes flow stems from 
the residual displacement of each particle during a wave cycle. On the other hand, from a 
Eulerian point of view, the locally averaged velocity of the (oscillatory) wave motion 
vanishes. However, if waves are present - which is virtually always the case - our model 
should return the effective velocity of mass displacement (total flow), Stokes flow 
included. To accommodate Stokes flow as part of the effective velocity, the pertinent 
forcing term has to be included in the momentum budget, which is then considered to 
apply to the total flow. The residual sub-scale effect is introduced to the momentum 
equations by what is known as radiation stress. A consistent evaluation based on a 
harmonic wave was carried out by Dolata and Rosenthal (1984). In our practical setup, 
the wave data are predicted by the operational WAM (WAMDIG, 1988, Komen et al., 
1994) at the DWD. 
Wind shear stress is prescribed as a dynamic surface boundary condition. Air pressure, 
as another surface boundary condition, is required for vertical integration of hydrostatics. At 
the surface, vertical heat flux (thermodynamic boundary condition) controls the heat 
budget. The total surface heat flux consists of four components: insolation, long wave 
heat radiation, sensible heat flux, and latent heat flux through evaporation (Müller- 
Navarra and Ladwig, 1997). It is parameterised in terms of bulk quantities of both 
atmosphere and sea or sea ice, respectively. The heat exchange between atmosphere 
and sea (or sea ice) depends on the properties of both air and sea. In the model, predicted 
meteorological parameters (wind, air pressure, air temperature, humidity, cloud cover) enter 
as boundary conditions into the bulk parameterisation of the vertical heat flux at the sea 
surface (one-way coupling). The evaporation flux is taken into account only in the heat 
budget. Changes of water volume due to evaporation, precipitation and ice formation are 
ignored. However, in the presence of ice, latent heat flux may well contribute to ablation 
through evaporation. 
Any ice forming on the sea surface is considered an integral part of the system, and 
the coupled ice-ocean model works in both directions. As in many other Hibler-type