Smoluchowski Coagulation Models Of Sea Ice Thickness Distribution Dynamics

Sea ice thickness distributions display a ubiquitous exponential decrease with thickness. This tail characterises the range of ice thickness produced by mechanical redistribution of ice through the process of ridging, rafting, and shearing. It is possible to simulate thickness distribution dynamics by representing mechanical redistribution as a generalized stacking process. Stacking processes may be described by a class of models known as Smoluchowski Coagulation models, which originated in Statistical Mechanics and describe the dynamics of a population of fixed-mass "particles" which combine in pairs to form a "particle" with the combined mass of the constituent pair at a rate which depends on the mass of the interacting particles. We use SCMs to model sea ice, identifying mass-increasing particle combinations with thickness-increasing ice redistribution processes. Our model couples an SCM component with a thermodynamic component and generates qualitatively accurate thickness distributions. The model behaviour suggests that the exponential tail of the sea ice thickness distribution arises from the nature of the ridging process, rather than specific physical properties of sea ice or the spatial arrangement of floes, and that the relative strengths of the dynamic and thermodynamic processes are key in accurately simulating the rate at which the sea ice thickness tail drops off with thickness.