6.7 Open-Water Growth and Ice Concentration Evolution

When coupled to a mixed layer ocean, the ice model must account for new ice growth over open water and other processes that alter the lateral sea ice coverage. New ice growth occurs whenever the surface layer in the ocean is at the freezing temperature and the fluxes would draw additional heat out of the ocean (see Eq. 5.1). In this case the additional heat comes from freezing sea water, as the ocean cannot supercool in this model. Hence

$$q_f {\partial h_{new} \over \partial t} = F_{frz} (1-A)$$ (6.48)

where $q_f$ is the energy of melting for new ice growth (assuming the salinity is 4psu and the new ice temperature is -1.8$^o$C), $h_{new}$ is the thickness of the new ice, and $F_{frz}$ is the additional heat lost by slab ocean once it reaching the freezing point (see section 5.1). When new ice grows over open water, it is recombined with the rest of the ice in the grid cell by first reshaping the new ice volume so its thickness is at least 15 cm - this recreates ice-free ocean if the thickness was below 15 cm. Then the new ice is added to the old ice in the grid cell and a new thickness and concentration are computed by conserving ice volume.

In motionless sea ice model, such as this one, open water is not created by deformation as in nature, and hence the ice concentration would tend to 0 or 100% unless open water production is parameterized somehow. A typical method is to assume the ice thickness on a subgrid-scale is linearly distributed between 0 and $2h$, so that when ice melts vertically, it also reduces the concentration:

$$\left(A-{\partial A \over \partial t}\right)^2 = {A^2 \over h_i} \left( h - {\partial h_i \over \partial t} \right)$$ (6.49)

The ice concentration is also reduced by a lateral heat flux from the ocean (see Eq. 6.36):

$${\partial A \over \partial t} = A {F_{SID} \over E_{TOT}}$$ (6.50)

although it is typically only a small contribution to the concentration tendency.

It is not possible to combine Eqs. 6.48-6.50 to make a single analytic expression for $\cal A$ in Eq. 6.6. Instead the model using time splitting to solve the three equations independently.