'Unified' Laguerre-Power Meshes for Coupled Earth System Modelling

The representation of physical processes in earth system models is often constrained and simplified by details of the underlying numerical model. Ocean, atmosphere, ice, land and river dynamics are typically discretised over incompatible computational grids, and are coupled together via ‘lossy’ interpolation schemes. In this work, we describe an alternative ‘unified’ approach, in which components are represented on a common multi-scale unstructured mesh, and employ compatible numerical formulations and ‘interpolation-free’ coupling across embedded boundaries. This unified strategy is built on an unstructured primal-dual meshing workflow, in which a global surface mesh conforming to various coastline, river network and land process boundaries is formed as a ‘restricted’ Laguerre-Power tessellation. This mesh layout enables coupled physics to be discretised over the set of staggered edge-, triangle- and cell-based control-volumes, leading to a conforming representation. Key to this process is the use of restricted triangulations to approximate complex boundaries and constraints in a multi-scale manner, enabling a transition from high-resolution regional representations to coarser global scales. Initial work on the ‘unified’ representation is reported here, focusing on development of the restricted triangulation kernels, and subsequent staggered Laguerre-Power mesh optimisation techniques.