Homogenization for Sea Ice
Sea ice is a critical component of Earth's climate system, and a leading indicator of climate change. The precipitous losses of summer Arctic sea ice observed in the past few decades have a significant impact on Earth's climate system, and have far outpaced the projections of most global climate models. One of the fundamental challenges of climate science is to develop more rigorous representations of sea ice in climate models, and incorporate important small scale processes and structures into these large scale models. The research funded by this grant will address this central issue. The investigators will use the mathematics of composite materials and statistical physics to develop methods of rigorously calculating the effective or homogenized properties of the sea ice pack which are necessary for improving projections of the fate of Earth's ice packs, and how polar ecosystems may respond. The effects of planetary warming are far reaching, and a better understanding of sea ice and its role in climate will improve our ability to predict changes in storm tracks, precipitation and temperature patterns, etc., affecting large populations. Moreover, this work will advance our understanding of the properties of composite materials and their use in industrial, engineering, and medical applications. The research topics in this grant encompass a range of key problems which will not only advance how sea ice can be represented in climate models, but will the push the boundaries of the mathematics of composite materials. The marginal ice zone (MIZ) is the outer region of the ice pack where dense pack ice transitions to open ocean, and its "width" is an important climatic length scale. Recent advances in objectively identifying MIZ width and geometry have led to the discovery of striking trends as the climate has warmed, which are based on an idealized concentration field satisfying Laplace's equation. Here we will generalize this analysis to include an inhomogeneous, effective diffusivity in the multiscale transport equation, which can, through inversion schemes, capture the actual satellite-derived concentration field. We will investigate how this effective coefficient is then related to smaller scale information about floe geometry and configurations. This approach will provide a basis for analytical investigation of MIZ dynamics including its susceptibility to deformation. In related work, we will explore representations for ice pack rheology similar to a recently obtained polydisc integral formula for the effective elasticity of two phase composites. Such representations involve spectral measures on the torus whose moments are related to microstructural statistics, and we will investigate the structure of the spectral measures and their dependence on composite microgeometry.