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...