An efficient multi-resolution grid for global models and coupled systems

Abstract

The latitude-longitude (lat-lon) grid is the most widely used global coordinate system for various purposes but its singularity at the Pole and the vector polar problems associated with its converging meridians hinder its applications. Well from the very start of numerical modelling history, quite a few grids have been attempted to tackle these problems and reduced grid is the simplest one among other grids. However, the reduced grid is almost abandoned by modern numerical modellers due to its unsatisfactory results for dynamical models in the polar region. Spherical multiple-cell (SMC) grid is similar to the reduced grid apparently but uses the unstructured technique for efficiency. It merges longitudinal cells at high latitudes like the reduced grid to overcome the CFL restriction and introduces a polar cell to remove the polar singularity. It also supports quad-tree-like mesh refinement to form a multi-resolution grid. To tackle the vector polar problem associated with the increased curvature at high latitudes, the SMC grid uses a new fixed reference direction to define vector components near the poles for improved polar performance. Global transportation is quite efficient on the SMC grid with optional second or third order transportation scheme. Present applications of the SMC grid, particularly in ocean surface wave models, are presented and possible future usage in global models and coupled systems are proposed.