Smoluchowski Coagulation Models Of Sea Ice Thickness 1 Distribution Dynamics

Sea ice thickness distributions display a ubiquitous exponential de-3 crease with thickness. This tail characterises the range of ice thickness produced 4 by mechanical redistribution of ice through the process of ridging, rafting, and 5 shearing. We investigate how well the thickness distribution can be simulated 6 by representing mechanical redistribution as a generalized stacking process. Such 7 processes are naturally described by a well-studied class of models known as 8 Smoluchowski Coagulation models, which describe the dynamics of a popula-9 tion of fixed-mass " particles " which combine in pairs to form a " particle " with 10 the combined mass of the constituent pair at a rate which depends on the mass 11 of the interacting particles. Like observed sea ice thickness distributions, the mass 12 distribution of the populations generated by SCMs has an exponential or quasi-13 exponential form. We use SCMs to model sea ice, identifying mass-increasing 14 particle combinations with thickness-increasing ice redistribution processes. Our 15 model couples an SCM component with a thermodynamic component and gen-16 erates qualitatively accurate thickness distributions with a variety of rate ker-17 nels. Our results suggest that the exponential tail of the sea ice thickness dis-18 tribution arises from the nature of the ridging process, rather than specific phys-19 ical properties of sea ice or the spatial arrangement of floes, and that the rel-20 ative strengths of the dynamic and thermodynamic processes are key in accu-21 rately simulating the rate at which the sea ice thickness tail drops off with thick-22 ness.