Thickness distributions of sea ice (g(h)) display a ubiquitous exponential decay (’tail’) in ice above approximately 2 meters thick. This work uses idealised models to examine the root causes of the exponential tail of the sea ice thickness distribution. The ice of thickness greater than 2 meters is formed through the fracture and piling of ice caused by interactions between floes, driven by winds and currents. The material properties of sea ice are complex and mathematical descriptions of the relationship between force and deformation of a floe are still a topic of study. Smoluchowski Coagulation Models (SCMs) are used to develop an abstract representation of redistribution dynamics. SCMs describe populations whose members of fixed size combine at size-dependent rates. SCMs naturally produce exponential or quasi-exponential distributions. An SCM coupled with a thermodynamic component produces qualitatively realistic g(h) under a wide range of conditions. Using the abstract representation of redistribution dynamics from SCMs, a model developed from physical processes specific to sea ice is introduced. Redistribution events occur at rates dependent on the change in potential energy. This model is demonstrated to produce qualitatively realistic g(h). Sensitivity analysis shows that primary model sensitivities are to the relative strengths of the dynamic and thermodynamic components of the model; and to the relative occurrence of ice ridging, shearing and rafting. The exact relationship between the rate of redistribution events and the energy they consume is shown to be of lesser importance. We conclude that the exponential tail of g(h) is a mathematical consequence of the coagulative nature of the ice thickness redistribution process, rather than the material properties of sea ice. These model results suggest the strongest controls on the form of the tail are the relative strengths of thermodynamic and dynamic action, and the relative occurrence of ice ridging, shearing and rafting.
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