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models, the ice cover is characterised by just two scalar quantities, namely mean
thickness and compactness. The complete ice model consists of a dynamic part (drift)
and a thermodynamic part (growth and melting). The basic ice drift equations for a
continuum mechanics model were introduced by Campbell (1965). The constitutive law
describing the mechanical behaviour of sea ice is a slight modification of Hibler’s
rheology (1979), see Kleine and Sklyar (1995). The model of ice growth and melting
largely follows Parkinson and Washington (1979) but retains the heat storage term in
the thermal budget. Hibler’s equation (1979) is used for the thermodynamic evolution of
compactness.
In principle, atmospheric forcing is applied to whatever medium is at the surface: open
sea, ice floes, or leads (open water within a fragmented ice cover). The presence of sea
ice has a considerable impact on the transfer properties. It significantly modifies the
momentum fluxes (shear stress) and heat fluxes. Ice forming on the sea surface has the
shape of an ice sheet, which is driven by the wind. The motions of the ice sheet, in turn,
produce drag which forces the water column below. The momentum transferred to the
water column is expressed by a formula for shear stress at the interface between water
and ice. Likewise, the atmosphere-ocean heat flux is split into transfer at the upper and
lower surfaces of the ice. As regards the effect of air pressure as a boundary condition,
the presence of sea ice makes no difference compared to open-sea conditions because
it is assumed to be in isostatic equilibrium.
At the sea bottom, the model basin is isolated inasmuch as there is no mass flux.
However, in sufficiently shallow water, particularly the Wadden Sea tidal flats, the flux and
storage of heat within the sediment must be taken into account. Firstly, the shallower the
water column the more warming sunlight radiation passes through the water column,
heating up the sediment below it. Secondly, both heating and cooling at the sedimentwater
interface are damped by conduction. The geothermal heat flux from the earth’s
crust into the sediment layers below the sea floor is of minor importance and is set to
0.06 W/m 2 in the model.
In shallow areas, also the flooding and falling dry of tidal flats is simulated. As a result,
the lateral boundary is moving in time, especially in the Wadden Sea. There is no mass
flux across the coastline except in those areas where freshwater is discharged by the
major rivers.
The circulation model for the North Sea and Baltic Sea is embedded in a North East
Atlantic model allowing disturbances caused by meteorological forcing of the Northeast
Atlantic to be taken into account. Gravity waves should cross the open boundary of the
NE-Atlantic model without major reflections, which is achieved by imposing a radiation
condition (Heaps 1974). The purpose of NE-Atlantic model is to provide water level
variations at the outer boundary of the North Sea model which are due to external
surges. The NE-Atlantic model thus does not provide tides. The tides of the North Sea
are forced at its open boundary, where a total of 14 harmonic constituents are
superposed by the incoming surge. Before applying these data (of barotropic origin) as
boundary forcing to the baroclinic North Sea model, the water level is redistributed along
the open boundary in order to restore the vertically integrated acceleration term.
