An accurate estimate of the fraction of the Arctic upper sea-ice surface covered in melt ponds during the summer melt season is essential for a realistic estimate of the albedo for global climate models. Presented here is a melt-pond-sea-ice model that simulates the evolution of melt ponds across an Arctic sea-ice surface. Thermodynamic processes are modelled using the mushy-layer equations in sea ice, heat diffusion equations in snow and using assumptions of turbulent heat flux in melt ponds, along with a three-layer two-stream radiation model. There is a realistic hydraulic balance and drainage rates of melt water through the ice are calculated using Darcy''s Law. The model is initialised with ice and snow topographies that represent conditions on first-year and multi-year ice. Simulations confirmed observed differences in individual pond size and depth between first-year and multi-year ice. Sensitivity studies showed that pond fraction is most sensitive to mean initial snow depth on first-year ice and reduction in ice permeability in all cases.