  Sea ice is not continuous and homogeneous on large scales. Its morphology is
inherently discrete and made of individual floes. In recent years, sea ice
models have incorporated this horizontal heterogeneity. The modelling framework
considers an evolution equation for the probability density function of the
floe size distribution (FSD) with forcing terms that represent the effects of
several physical processes. Despite the modelling effort, a key question
remains: what is the FSD emerging from the collection of all forcing processes?
Field observations have long suggested the FSD follows a power law, but this
result has not been reproduced by models or laboratory experiments. The
theoretical framework for FSD dynamics in response to physical forcings is
presented. Wave-induced breakup is further examined with an emphasis on how it
affects the FSD. Recent modelling results suggesting the consistent emergence
of 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 originally
analysed under the power law hypothesis. We then propose a simple stochastic
process of FSD dynamics, based on random fragmentation theory, that predicts
log-normality. We therefore conjecture that the emergent FSD follows a
lognormal distribution.
