Smoluchowski coagulation models of sea ice thickness distribution dynamics

Abstract

[1] Sea ice thickness distributions display a ubiquitous exponential decrease with thickness. This tail characterizes the range of ice thickness produced by mechanical redistribution of ice through the process of ridging, rafting, and shearing. We investigate how well the thickness distribution can be simulated by representing mechanical redistribution as a generalized stacking process. Such processes are naturally described by a well-studied class of models known as Smoluchowski Coagulation Models (SCMs), which 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. Like observed sea ice thickness distributions, the mass distribution of the populations generated by SCMs has an exponential or quasi-exponential form. 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 with a variety of rate kernels. Our results suggest 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.