Melt Ponds: Fractals, Metastability and Ising Model

Viewed from high above, the sea ice surface can be thought of as a two-phase composite of ice and melt water (so-called melt ponds). The boundaries between the two phases evolve with increasing complexity and a rapid onset of large scale connectivity, or percolation of the melt phase. The fractal dimension of melt ponds transitions from about 1 to 2 around a critical length scale of 100 m2 in area . We have developed a new two dimensional Ising model for melt ponds on Arctic sea ice to explain the fractal dimension transition in their evolution, and to provide a statistical physics approach to sea ice modeling. The key assumption of our model is that the melt pond system tends to minimize an Ising Hamiltonian with a random "magnetic field" representing the initial ice topography, and the interaction term representing horizontal heat transfer. 

Also, we arise a question about the stability of the climate system and its energy balance when the complex melt ponds cover the surface of the Arctic Ocean. The goal is to understand if the summer Arctic sea pack has passed through a critical threshold on its way to a state of ice-free summers. First of all, we study the complex changing of melt pond geometry, namely a critical characteristic size (so-called radius) and an area of melt ponds. After that, we incorporate the complex melt pond geometry into a conceptual climate model with ice-albedo feedback. We can then investigate the stable/metastable/unstable states of the climate system during melt pond evolution.

More information:

• I. Sudakov, S.A. Vakulenko, and K.M. Golden, Arctic melt ponds and bifurcations in the climate system. Communications in Nonlinear Science and Numerical Simulation, V. 22, Iss. 1–3, 2015, Pages 70-81.