Wave-triggered breakup in the marginal ice zone generates lognormal floe size distributions

Abstract

Abstract. Fragmentation of the sea ice cover by ocean waves is an important mechanism impacting ice evolution. Fractured ice is more sensitive to melt, leading to a local reduction in ice concentration, facilitating wave propagation. A positive feedback loop, accelerating sea ice retreat, is then introduced. Despite recent efforts to incorporate this process and the resulting floe size distribution (FSD) into the sea ice components of global climate models (GCM), the physics governing ice breakup under wave action remains poorly understood, and its parametrisation highly simplified. We propose a two-dimensional numerical model of wave-induced sea ice breakup to estimate the FSD resulting from repeated fracture events. This model, based on linear water wave theory and viscoelastic sea ice rheology, solves for the scattering of an incoming time-harmonic wave by the ice cover and derives the corresponding strain field. Fracture occurs when the strain exceeds an empirical threshold. The geometry is then updated for the next iteration of the breakup procedure. The resulting FSD is analysed for both monochromatic and polychromatic forcings. For the latter results, FSDs obtained for discrete frequencies are combined appropriately following a prescribed wave spectrum. We find that under realistic wave forcing, lognormal FSDs emerge consistently in a large variety of model configurations. Care is taken to evaluate the statistical significance of this finding. This result contrasts with the power-law FSD behaviour often assumed by modellers. We discuss the properties of these modelled distributions, with respect to the ice rheological properties and the forcing waves. The projected output will be used to improve empirical parametrisations used to couple sea ice and ocean waves GCM components.

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

“…In §5, we make the case that the FSD resulting from repeated, continuous fragmentation should be described by a log-normal distribution, instead of a power law. Our conjecture is supported by multiple lines of evidence including (i) numerical simulations of repeated wave-induced breakup in a fully coupled linear hydroelastic model [28], (ii) an analysis of floe size field data [6] showing the relative performance of several parametric distributions including the power law and the log-normal distribution, and (iii) the theoretical description of ice floe size dynamics as a stochastic exponential growth/decay process, which is exactly described by a log-normal distribution. Although we do not expect the log-normal FSD formalism to be universal and fit perfectly all observational datasets, we demonstrate that it should be considered as a potentially superior alternative to the power law.…”

“…Our goal was to show that the log-normal parametric formulation for the FSD should be recognized as a viable candidate. We demonstrated that the log-normal FSD naturally emerges from (i) direct wave-induced breakup simulations in a hydroelastic deterministic model [28], (ii) analysis of field data [6] and (iii) a simple stochastic dynamical system [58].…”

“…Current parametrizations of wave-induced fragmentation are particularly simplified in the FSD modelling framework, and so in §4, we present an overview of the theory governing the flexurally induced breakup of sea ice and review the literature that has attempted to describe the FSD resulting from this phenomenon. We show that apart from a handful of simulation-based studies [23,24,28], most descriptions of the FSD in the context of ocean waves/sea ice interactions assume the power law formalism.…”

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.…”