Theoretical framework for the emergent floe size distribution in the marginal ice zone: the case for log-normality

Abstract

Sea ice is not horizontally 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 that 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 log-normal 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. A simple stochastic process of FSD dynamics, based on random fragmentation theory, is further shown to predict log-normality. We therefore conjecture that, in some situations, the emergent FSD follows a log-normal distribution. This article is part of the theme issue ‘Theory, modelling and observations of marginal ice zone dynamics: multidisciplinary perspectives and outlooks’.

Floes, the marginal ice zone and coupled wave-sea-ice feedbacks

“…It is clear that the FSD in the MIZ does not always have a power law tail, influenced as it is by small-spatial-scale processes that do not permit large floes-often the MIZ is comprised of a single peak floe size, or floes all near the same scale. Modelling and observational work aimed at reconstructing the FSD under the influence of waves has pointed to a lognormal or Gaussian distribution for the FSD in these regions [52][53][54][55].…”

“…The viscous layer models are most appropriate when sea ice floe sizes are either much smaller than typical wavelengths, or much larger. However, an increasing number of theoretical, numerical, and observational studies evince that the impact of both wind-wave and swell energetics are to fracture sea ice floes into a lognormal distribution of floe sizes with modal peaks near the peak wavelength of the wave spectrum [52][53][54][55][56]73]. Thus waves may by their presence alter their own attenuation by changing the sea ice from an apparent viscous medium to an apparent scattering medium and back.…”

A prognosticative synopsis of contemporary marginal ice zone research

“…FSD is recognized as a determinative ingredient of coupled ocean-wave–sea-ice models of the MIZ, so it is important that an accurate distribution of floe sizes is used and that the physics describing how FSD mutates due to wave-induced flexural and collisional break-up and melting, for example, is accurate. The present volume has three relevant papers: [18] is concerned with modelling, [19] discusses a broken power-law distribution in the context of the physics that creates it, and [20] argues for a lognormal FSD instead of a power law. The informative mini-review by Horvat [21], who re-examines the history and current state of FSD observations and modelling, argues that further high-temporal-resolution investigations of the FSD are needed, e.g.…”

Granular effects in sea ice rheology in the marginal ice zone

“…they are well described by a tapered power law [ 1 ]. The relationship between floe size and dynamic/thermodynamic processes in the MIZ is very complex and mutual: the response of the ice to oceanic and atmospheric forcing is FSD dependent [ 2 , 3 ]. Granular effects in sea ice dynamics have received much attention of researchers in recent years, with several studies exploring the influence of FSDs on selected processes (e.g.…”