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

TL;DR

This paper develops a theoretical framework for sea ice floe size distribution, proposing that a log-normal distribution naturally emerges from physical processes like wave-induced breakup, challenging the traditional power law assumption.

Contribution

It introduces a new stochastic model predicting log-normal FSD emergence, supported by theoretical analysis and empirical data, contrasting previous power law hypotheses.

Findings

Log-normal distribution emerges from wave-induced breakup processes.

Empirical data supports the log-normal FSD hypothesis.

Theoretical model aligns with observed floe size data.

Abstract

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.