An unstructured C-grid type variational formulation for the sea ice dynamics

• Main Authors: Capodaglio, Giacomo, Petersen, Mark R., Turner, Adrian K., Roberts, Andrew F.
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: arXiv 2021
• Subjects: Computational Physics physics.comp-ph; FOS Physical sciences; Curl; Sea ice
• Online Access: https://dx.doi.org/10.48550/arxiv.2112.14993; https://arxiv.org/abs/2112.14993

Historically, B-grid formulations of sea ice dynamics have been dominant because they have matched the grid type used by ocean models. The reason for the grid match is simple - it facilitates penetration of the curl of ice-ocean stress into the deep ocean with minimal numerical diffusivity because sea ice and ocean velocity are co-located. In recent years, as ocean models have increasingly progressed to C-grids, sea ice models have followed suit on quadrilateral meshes, but few if any implementations of unstructured C-grid sea ice models have been developed. We present an unstructured C-grid formulation of the elastic-viscous-plastic rheology, where the velocity unknowns are located at the edges rather than at the vertices, as in the B-grid. The mesh cells in our analysis have $n$ sides, with $n$ greater than or equal to four. Numerical results are also included to investigate the features of the proposed method. Our framework of choice is the Model for Prediction Across Scales (MPAS) within E3SM, the climate model of the U.S. Department of Energy, although our approach is general and could be applied to other models as well. While MPAS-Seaice is currently defined on a B-grid, MPAS-Ocean runs on a C-grid, hence interpolation operators are heavily used when coupled simulations are performed. The discretization introduced here aims at transitioning the dynamics of MPAS-Seaice to a C-grid, in order to ultimately facilitate the coupling with MPAS-Ocean and reduce numerical errors associated with this communication.