A toy model of sea ice growth

My purpose here is to present a simplified treatment of the growth of sea ice. By ignoring many details, it is possible to obtain several results that help to clarify the ways in which the sea ice cover will respond to climate change. Three models are discussed. The first deals with the growth of sea ice during the cold season. The second describes the cycle of growth and melting for perennial ice. The third model extends the second to account for the possibility that the ice melts away entirely in the summer. In each case, the objective is to understand what physical processes are most important, what ice properties determine the ice behavior, and to which climate variables the system is most sensitive.