Wave–ice interactions in the marginal ice zone. Part 1: Theoretical foundations

A wave-ice interaction model for the marginal ice zone (MIZ) is reported that calculates the attenuation of ocean surface waves by sea ice and the concomitant breaking of the ice into smaller floes by the waves. Physical issues are highlighted that must be considered when ice breakage and wave attenuation are embedded in a numerical wave model or an ice/ocean model. eoretical foundations of the model are introduced in this paper, forming the first of a two-part series. The wave spectrum is transported through the ice-covered ocean according to the wave energy balance equation, which includes a term to parameterize the wave dissipation that arises from the presence of the ice cover. The rate of attenuation is calculated using a thin-elastic-plate scattering model and a probabilistic approach is used to derive a breaking criterion in terms of the significant strain. This determines if the local wave field is sufficient to break the ice cover. An estimate of the maximum allowable floe size when ice breakage occurs is used as a parameter in a floe size distribution model, and the MIZ is defined in the model as the area of broken ice cover. Key uncertainties in the model are discussed.