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
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 , so that when ice melts vertically, it also reduces the concentration:
The ice concentration is also reduced by a lateral heat flux from the ocean (see Eq. 6.36):
It is not possible to combine Eqs. 6.48-6.50 to make a single analytic expression for in Eq. 6.6. Instead the model using time splitting to solve the three equations independently.