Sea-Ice Roughness, Morphogenesis and Kinematics --- Approaches to Learn from the Complexity of Sea Ice

Recent studies of the alarming retreat of the Arctic sea ice have been largely based on observations of sea-ice coverage. This is not sufficient to capture changes in the sea-ice's mass, hence there is an increasing interest in measuring the thickness of sea-ice. However, the complexity of sea ice renders the latter a difficult task: (1) at any time, the sea ice has a complex form and appearance in remote-sensing observations, (2) due to ridging and rubbling, the mass of sea ice is not directly related to its thickness, (3) sea ice forms in a series of morphogenetic processes, and (4) sea ice moves. Here we present mathematical approaches to analyze spatial roughness of the surface of sea ice and of its snow-layer thickness, morphogenetic processes and deformation characteristics as a means to quantify and characterize sea-ice properties, processes and provinces. Applications include analyses of passive microwave data, SAR data, laser and radar elevation data and multispectral image data, from satellite, unmanned aerial vehicle and aircraft platforms, and field data.