Modeling the geometry of melt ponds on Arctic sea ice

In late spring small pools of melt water on the surface of Arctic sea ice begin to grow and coalesce to form large connected labyrinthine ponds. The fractal geometry of these iconic blue patterns is both beautiful to the eye and important to the evolution of sea ice albedo and its role in the climate system. Here we report on recent results in modeling the geometry of Arctic melt ponds. We consider two models, first where pond boundaries are the level curves of random surfaces representing snow topography, and then an Ising model, originally developed a century ago to understand ferromagnetic materials, adapted to describe melt ponds. Our melt pond Ising model requires only one measured input - a length scale from snow topography data. Then energy minimization produces realistic ponds whose sizes and transition in fractal dimension with increasing area agree closely with observations. Finally we examine how the random snow topography influences the evolution of pond fractal geometry and find that the saddle points of the surface play the critical role in transitional behavior.