Abstract
Perhaps the most iconic feature of melting Arctic sea ice is the distinctive ponds that form on its surface. The geometrical patterns describing how melt water is distributed over the surface largely determine the solar reflectance and transmittance of the sea ice cover, which are key parameters in climate modeling and upper ocean ecology. In order to help develop a predictive theoretical approach to studying melting sea ice, and the resulting patterns of light and dark regions on its surface in particular, we look to the statistical mechanics of phase transitions and introduce a two-dimensional random field Ising model which accounts for only the most basic physics in the system. The ponds are identified as metastable states in the model, where the binary spin variable corresponds to the presence of melt water or ice on the sea ice surface. With the lattice spacing determined by snow topography data as the only measured parameter input into the model, energy minimization drives the system toward realistic pond configurations from an initially random state. The model captures the essential mechanism of pattern formation of Arctic melt ponds, with predictions that agree very closely with observed scaling of pond sizes and transition in pond fractal dimension.
Highlights
While snow and ice reflect most of the sunlight incident on Arctic sea ice, melt ponds absorb most of it
The impact of melt pond evolution extends into the biosphere as well [2, 19, 11], where the ponds act as windows for light to shine into the upper ocean, affecting Arctic marine ecology
Our melt pond Ising model – with only one measured input parameter – produces ponds that are quite realistic in appearance, but with geometrical characteristics that quantitatively match very closely the observations on pond sizes and fractal dimension. This one parameter sets the length of a side of a square pixel in the lattice, and represents the scale above which the variations in snow topography are significant
Summary
While snow and ice reflect most of the sunlight incident on Arctic sea ice, melt ponds absorb most of it. The geometry of melt ponds and their spatial patterns impacts various sea ice and upper ocean processes such as albedo evolution, the break-up of floes, the evolution of the floe size distribution, and the patterns of light in and under the ice, which can affect photosynthetic activity and the ecology of microbial communities. We address the challenge of developing a predictive theoretical model of melt ponds which accounts for the most basic physics of the system, and which yields realistic pond configurations obtained through minimization of the energy of the model. We envision a square lattice of surface patches or pixels of melt water or ice, corresponding to the classical spin up or spin down states, respectively They are collectively influenced by an external forcing field, and interact only with their nearest neighbors. Illustrating the potentially broad applicability of this approach, an Ising model for tropical convection was developed [13] to represent atmospheric processes unresolved by coarse scale climate models
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