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Sea ice is not continuous and homogeneous on large scales. Its morphology isinherently discrete and made of individual floes. In recent years, sea icemodels have incorporated this horizontal heterogeneity. The modelling frameworkconsiders an evolution equation for the probability density function of thefloe size distribution (FSD) with forcing terms that represent the effects ofseveral physical processes. Despite the modelling effort, a key questionremains: what is the FSD emerging from the collection of all forcing processes?Field observations have long suggested the FSD follows a power law, but thisresult has not been reproduced by models or laboratory experiments. Thetheoretical framework for FSD dynamics in response to physical forcings ispresented. Wave-induced breakup is further examined with an emphasis on how itaffects the FSD. Recent modelling results suggesting the consistent emergenceof a lognormal distribution as a result of that process are further discussed.Log-normality is also found in a dataset of floe sizes, which was originallyanalysed under the power law hypothesis. We then propose a simple stochasticprocess of FSD dynamics, based on random fragmentation theory, that predictslog-normality. We therefore conjecture that the emergent FSD follows alognormal distribution.

Theoretical framework for the emergent floe size distribution: the case for log-normality