  Climate change, amplified in the far north, has led to rapid sea ice decline
in recent years. In the summer, melt ponds form on the surface of Arctic sea
ice, significantly lowering the ice reflectivity (albedo) and thereby
accelerating ice melt. Pond geometry controls the details of this crucial
feedback; however, a reliable model of pond geometry does not currently exist.
Here we show that a simple model of voids surrounding randomly sized and placed
overlapping circles reproduces the essential features of pond patterns. The
only two model parameters, characteristic circle radius and coverage fraction,
are chosen by comparing, between the model and the aerial photographs of the
ponds, two correlation functions which determine the typical pond size and
their connectedness. Using these parameters, the void model robustly reproduces
the ponds' area-perimeter and area-abundance relationships over more than 6
orders of magnitude. By analyzing the correlation functions of ponds on several
dates, we also find that the pond scale and the connectedness are surprisingly
constant across different years and ice types. Moreover, we find that ponds
resemble percolation clusters near the percolation threshold. These results
demonstrate that the geometry and abundance of Arctic melt ponds can be simply
described, which can be exploited in future models of Arctic melt ponds that
would improve predictions of the response of sea ice to Arctic warming.
