| Abstract: |
| Polar sea ice is a critical component of Earth`s climate system. As a material it exhibits composite structure on length scales ranging over 10 orders of magnitude. Tiny brine inclusions inside sea ice, large melt ponds on its surface, and even the ice pack itself are all fractals. Here we discuss how the fractal dimension of these structures depends on the parameters that characterize their evolution. For example, we find that box-counting computations of the fractal dimension of liquid brine in sea ice as a function of its porosity agree almost perfectly with the corresponding exact formula for the famous Sierpinski triangle. We also examine the fractal dimension of melt pond boundaries, which transitions from 1 to about 2 as the ponds grow and coalesce, and explore the role of saddle points of the sea ice surface in driving the fractal transition. Such questions lead us into Morse theory, and then into topological data analysis, where we will discuss persistent homology and the Euler characteristic curve for sea ice topography as a function of the water level. |
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