As the melt season progresses, sea ice in the Arctic often becomes permeable enough to allow for nearly complete drainage of meltwater that has collected on the ice surface. Melt ponds that remain after drainage are hydraulically connected to the ocean and correspond to regions of sea ice whose surface is below sea level. We present a simple model for the evolution of melt pond coverage on such permeable sea ice floes in which we allow for spatially varying ice melt rates and assume the whole floe is in hydrostatic balance. The model is represented by two simple ordinary differential equations, where the rate of change of pond coverage depends on the pond coverage. All the physical parameters of the system are summarized by four strengths that control the relative importance of the terms in the equations. The model both fits observations and allows us to understand the behavior of melt ponds in a way that is often not possible with more complex models. Examples of insights we can gain from the model are: (1) the pond growth rate is more sensitive to changes in bare sea ice albedo than changes in pond albedo, (2) ponds grow slower on smoother ice, and (3) ponds respond strongest to freeboard sinking on first year ice and sidewall melting on multiyear ice. We also show that under a global warming scenario, pond coverage would increase, decreasing the overall ice albedo, and leading to ice thinning that is likely comparable to thinning due to direct forcing. Since melt pond coverage is one of the key parameters controlling the albedo of sea ice, understanding the mechanisms that control the distribution of pond coverage will help improve large-scale model parameterizations and sea ice forecasts in a warming climate.



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