Data exchange

Atmospheric forcing

The atmospheric forcing is provided by a data set including wind stress forcing (λ- and φ- components and the mean scalar wind), air temperature and dew point temperature at two metres above sea level, precipitation and total cloud cover. Observations were assimilated into models to give consistent data on a uniform grid. On the one hand, the model results from the NCEP/NCAR reanalysis (KALNAY ET AL., 1996), covering the years 1948 - 1998, are used. The data are stored every six hours and are computed on a global grid with approximately 2°spatial resolution. For the present study, the data is interpolated onto the model grid, as daily mean values for wind stress and monthly mean data for the scalar fields. On the other hand, data of theECMWFreanalysis project from 1979 - 1993 (GIBSON ET AL.,1997) are applied. TheECMWFdata have been interpolated to the model grid in a similar way as the NCEP/NCAR data. A detailed description of which data set is actually chosen and how the data have been prepared, will be given in the chapter4.

The wind stress field is used in the model directly as a source of momentum acting on the surface. The other parameters are necessary to calculate the heat and freshwater fluxes for the sea ice and the ocean model. The heat flux from the atmosphere to the ice has been described briefly in the discussion of the energy balance of the ice model; it is determined similarly in the ocean model. The air temperature, dew point temperature and the cloud cover are used to derive the sensible and latent heat fluxes and the net short–wave and net long–wave radiation. The freshwater flux into the ocean is calculated from precipitation, evaporation and river runoff. Evaporation is a function of latent heat including the dew point temperature. Precipitation is prescribed.

The ocean model needs special treatment for the sea surface salinity. This is done using a weak linear restoring to a climatological field (see Table3.1). This treatment is necessary to parametrise the lateral freshwater input through the Bering Strait and the river run off into the Arctic ocean. The climatology used is obtained from the data ofLEVITUS ET AL. (1994) and the EWG-atlas (EWG - ENVIRONMENTAL W^ORKING G^ROUP, 1997) for the area north of 72°N.

Models communicate

The models are computed with the same time step (tracer time step) of 21600s. Upon completion, the ice model provides heat, freshwater and momentum fluxes for the ocean.

The ocean model, in turn, supplies current and heat exchange information for the ice model.

Data exchange

The sea ice and the ocean model calculate the atmospheric heat fluxes separately, be-cause they depend on the surface properties of the underlying medium (such as temper-ature and albedo). In addition, the ice model needs the ocean surface tempertemper-atureT_o to compute the heat fluxes at the bottom of the ice. The energy balance of the ice model has been discussed in detail in the thermodynamic part of section 3.2.1. For grid boxes which are partly covered by sea ice the fluxes into the ocean are weighted according to the percentage of ice coverage:

Q_ocean=₍₁−^Ai)·^Qopen water−^Ai·^Qo (3.38)

The open-water fraction is calculated by the ocean model, the ocean-ice part Q_o by the ice model (compare equation3.32).

Beside the heat flux, the freshwater flux is also altered by the ice due to snow and ice formation or melting. Net precipitation (precipitation minus evaporation) which falls over ice–covered regions will be snow when the air temperature is below the freezing point. It is also weighted with the snow covered area according to equation3.38. When the temperature is above the freezing point, the net precipitation of the grid box flows into the open water. The fraction belonging to the ice model is multiplied by the average salinity of sea water and transferred to the ocean as an additional term to the salinity restoring. This formulation is chosen because it conserves the salt budget. The fact that the sea ice retains a small amount of salt when ice forms and releases a brine while aging is neglected. The ice model also needs the geostrophic velocity to calculate the heat flux, Q_o, and the shear stress,τ_w.

The technique of coupling of the two models has been described by H^{IBLER AND} B^RYAN (1987). The numerical representation of the temporal dependencies of the mo-mentum exchange has been illustrated by simplified one-dimensional equations:

∂u_i

∂t =_F(ui)+∂p

∂x −^D(ui−^uw)+τ_a (3.39)

∂u_w

∂t = ∂p

∂x+_F(ui)+τ_a . (3.40)

The nonlinear ice interaction terms are embodied in F, and D denotes the drag term.

The most important feature of this approach is that the sea ice is handled as a part of the uppermost layer of the ocean. The wind stress transmitted into the ocean is equal to the wind stress plus the internal ice stress. Additionally, the convergence of ice must be considered in the Ekman convergence. When ice is present, the whole mixed layer is at the freezing temperature. The ocean transfers heat to the ice by warming up this layer.

This implicit procedure therefore forces the ice cover and the SST to stay in balance and at the same time ensures conservation of heat.

Chapter 3 Model description

The leapfrog scheme is used as the time-stepping discretisation:

u_iⁱ⁺¹−^uii−¹=_2∆t

F(u_iⁱ⁺¹)+∂pⁱ

∂x −^D(uii−¹−^uwi−¹)+τ_aⁱ

(3.41) u_wⁱ⁺¹−^uwi−¹=_2∆t

∂pⁱ⁺¹

∂x +_F(uwⁱ₎+τ_aⁱ

. (3.42)

The past is labelledi−1 and the future time stepsi+1. The exchange terms are centred differences wherever this is possible. A detailed discussion of the discretisation can be found in the publication ofH^{IBLER AND}B^RYAN(1987).

Starting point

The surface forcing fields consist of monthly mean data sets for the scalar properties such as air and dew point temperature, cloud cover and mean scalar wind. The wind stress data is given to the model as daily data.

Ice and ocean models start from a state of rest, but they need hydrographic starting val-ues. Thus, the ocean below the surface is assigned salinity and potential temperature data as initial conditions, which are spatially interpolated from the Levitus data set (LEVITUS ET AL.,1994). The continental run-off is not taken into account, and the lateral boundaries are closed except in the south, where the barotropic streamfunction of the FLAME 4/3°

Atlantic ocean model is prescribed as described in section3.1.2. The sea surface salinity (SSS) gets an initial climatological data field, which is also used for restoring. The data are based on the climatology ofLEVITUS ET AL.(1994) and the EWG-atlas (EWG - E^NVI

-RONMENTALW^ORKINGG^ROUP,1997) for the area north of 72°N, because of the regional unreliability of the Levitus data. The same procedure is adopted for the initialisation of the sea surface temperature (SST). However, there is no restoring of the sea surface temperature in the model calculation.

The initial sea ice concentration is a climatology calculated from the SSM/I data for the period 1986-1992. The initial sea ice thickness is a linearly interpolated field between 0m for ice free grid cells and a maximum of 4m thickness for completely ice covered areas.