Abstract
Sea ice exists only in the polar regions, and yet affects the global climate by dominating heat, matter, and momentum exchanges between oceans and atmosphere. The consequences of its retreat, and eventual summer disappearance, are unfathomable and stretch across scales going from microscopic algae to the world ocean circulation. Fragmentation of the sea ice cover by ocean waves is an important mechanism impacting the evolution of this inhomogeneous, dynamical medium. With an increased surface area, fractured ice is more sensitive to melt, leading to a local reduction in ice concentration that facilitates further 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, 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 visco-elastic sea ice rheology, describes 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, and the geometry is then updated for the next iteration of the breakup procedure.
We analyse the resulting FSDs for both monochromatic and polychromatic forcings, by comparing two polychromatic parametrisations, combining FSDs obtained for discrete frequencies by following a prescribed wave spectrum. We find that under this realistic wave forcing, lognormal FSDs emerge consistently in a large variety of model configurations, independently of the shape of the spectrum. We discuss the properties of these modelled distributions with respect to the ice rheological properties and the forcing waves. The projected output can be used as a step to improve empirical parametrisations coupling global models of sea ice and ocean waves in climate studies.
This result contrasts with the power law FSD behaviour often assumed by modellers. We revisit remote-sensing studies of floe size distributions conducted in both polar oceans, and show the applicability of the lognormal model. Our assessment comes with limitations, as the processes having led to these observed distributions are unknown. Nonetheless, it indicates that the lognormal distribution is a valid alternative for the representation of the floe size distribution when analysing future measurements.
We then loop back to considering the attenuation undergone by waves propagating through an array of ice floes, by conducting further numerical experiments. Our results suggest that the shape of the FSD, and some of its statistics such as the minimum floe size, impact attenuation more than other measures such as the mean floe size. We reiterate the need for more measurements, particularly of concomitant floe size, wave field, and weather data; as well as the need for a better physical understanding of the physical processes leading to the emergence of a distribution of floe sizes.