We present a mathematical model describing the summer melting of sea ice. We simulate the evolution of melt ponds and determine area coverage and total surface ablation. The model predictions are tested for sensitivity to the melt rate of unponded ice, enhanced melt rate beneath the melt ponds, vertical seepage, and horizontal permeability. The model is initialized with surface topographies derived from laser altimetry corresponding to first-year sea ice and multiyear sea ice. We predict that there are large differences in the depth of melt ponds and the area of coverage between the two types of ice. We also find that the vertical seepage rate and the melt rate of unponded ice are important in determining the total surface ablation and area covered by melt ponds.