A spatial melt pond model for ice with surface and bottom height variations

A spatial model of melt ponds is described for sea ice with thickness variations. The model is based on a pond heat budget that accounts for surface fluxes, solar radiation, and side and bottom melting. Pond depth is determined by assuming that the ice is saturated with fresh water and that the pond level is equal to the local sea level. Pond bottom and sidewall melting rates are determined as part of the pond heat budget with pond water assumed to have a uniform thermal structure. Ponds grow by both melting through the ice and by filling low lying areas that fall below sea level as the ice sheet melts. Results from the model are shown using assumed initial ice thicknesses based on estimates from field data. Pond statistics, such as depth and pond coverage are presented demonstrating the validity of the modeling approach.