A hybrid ice-mélange model based on particle and continuum methods

Ice mélange, a composite of sea ice and icebergs, can have a major influence on sea-ice-ocean interactions. However, ice mélange could so far not be represented in climate models because numerically efficient realizations did not exist. This motivates the development of a prototype dynamic hybrid ice-mélange model that we present in this paper. In our approach, icebergs are included as particles while sea ice is treated as a continuum. To derive a joint continuum for the ice mélange, we integrate particle properties into the sea-ice continuum. Thus, icebergs are viewed as thick, compact pieces of sea ice. The ice-mélange formulation is derived based on the viscous-plastic sea-ice rheology, which is currently the most widely used material law for sea ice in climate models. Starting from the continuum mechanical formulation, we modify the rheology such that icebergs are held together by a modified tensile strength in the material law. Due to the particle approach, we do not need high resolved spatial meshes to represent the typical size of icebergs in ice mélange (< 300 m). Instead, icebergs can be tracked on a subgrid level while the typical resolution of the sea-ice model can be maintained (≥10 km). This is an appealing property in respect to computational efficiency. Applying idealized test cases, we demonstrate that the proposed changes in the material law allow for a realistic representation of icebergs within the viscous-plastic sea-ice rheology. Furthermore, we show that subgrid dynamics, such as polynya formation due to grounded icebergs, can be modelled with the hybrid approach. Overall, this suggested extension of the viscous-plastic sea-ice model is a promising path towards the integration of ice mélange into climate models.