The development of sea-ice parameterizations for use in general circulation models (GCMs) has historically been characterized by a focus on increasing the complexity of the parameterization. Early one-dimensional thermodynamic models (e.g. Maykut and Untersteiner 1971) included heat flux influences, but ignored any dynamical impacts. Two-dimensional dynamic-thermodynamic models (e.g. Hibler 1979) include the effects of wind and ocean currents on ice movement, and account for internal motion using a variety of different rheologies. Currently, ice model development has involved adding previously unrepresented or under-represented physics, such as melt ponds, ice ridging, etc. (e.g. Arbetter et al. 1999, Holland and Curry 1999, Arbetter et al. 2000).
Increased physical complexity, however, is not the core issue in the GCM parameterization problem. As Arakawa (1993) points out in the case of parameterizing moist convection, parameterization is the link between that which provides a "control" upon the physical process being parameterized and the "feedback" the physical process provides. Another way of considering the issue is to ask in what way does the large-scale affect the physical process being parameterized, and how does the physical process in turn influence the large-scale? With sea-ice parameterizations, there does not currently appear to be an adequate understanding of how the large and small-scales interact. I am involved in developing theoretical archetypes relating sub-grid scale sea-ice and large-scale atmospheric dynamics, using principles taken from cumulus parameterization development as a starting point.