Modelling ice mélange based on the viscous-plastic sea-ice rheology

Ice mélange (mixture of sea ice, bergy bits and icebergs) can have a strong influence on the sea ice-ocean interaction. So far, ice mélange is not represented in climate models as numerically efficient realisations are missing. This motivates the development of  an ice mélange model based on the viscous-plastic sea-ice rheology which is currently the most used material law for sea ice in climate models. Starting from the continuum mechanical formulation, we modify the rheology so that icebergs are represented by  thick, highly compact pieces of sea ice. These compact pieces of sea ice are held together by a modified tensile strength in the material law. In this framework the ice mélange is considered as one single fluid, where the icebergs are tracked by a volume in fluid method. Using idealised test cases, we demonstrate that the proposed changes in the material law are crucial to represent icebergs with the viscous-plastic rheology. The ice mélange model is like the viscous-plastic sea-ice model highly nonlinear. Solving the model at the resolution needed to represent the typical size of icebergs in ice mélange (< 300m) is challenging. We show that the ice mélange formulation can be approximated efficiently with a modified Newton method. Overall, the simple extension of the viscous-plastic sea-ice model is a promising path towards the integration of ice mélange in climate models.