Abstract

Sea ice exhibits composite structure on length scales ranging over many orders of magnitude. A principal challenge in modelling sea ice and its role in climate is how to use information on smaller scale structure to find the effective or homogenized behaviour on larger scales relevant to climate and ecosystem models. We’ll tour recent results on modelling macroscopic behaviour in the sea ice system, with a focus on novel mathematical approaches. Percolation theory for fluid flow, fractal geometry of the brine microstructure, and Stieltjes integral representations for homogenized parameters of two phase and polycrystalline composites will be considered. Spectral analysis of these representations leads to a random matrix theory picture of connectedness processes in sea ice, with parallels to Anderson localization and semiconductor physics. Melt pond connectedness and complexification is also viewed through the lens of Morse theory and persistent homology in topological data analysis, and the Euler characteristic in particular. Finally, related heterogeneity in the parameters of nonlinear algal bloom models is addressed through polynomial chaos methods in uncertainty quantification, to analyse effective bloom dynamics when the local parameters are random variables.