A Hexagonal C-Grid Formulation for Multiscale Atmospheric Simulation on the Sphere

William C. Skamarock NCAR/MMM

Abstract

In global atmospheric solvers using icosahedral grids based on hexagons, C-grid staggering of the horizontal velocities has been avoided because of spuriously non-stationary geostrophic modes present in solutions using the most obvious discretization. The C grid is, however, the preferred grid in mesoscale and cloud-scale models because of its very accurate representation of horizontally divergent motions. We have developed a formulation for arbitrarily structured C grids that, analysis reveals, recovers the stationary geostrophic mode on hexagonal grids and also allows for exact conservation of potential vorticity and conservation of energy to the time integration truncation error for the shallow water equations. We will present results from shallow water model tests demonstrating these properties.

Based on the new formulation, we have constructed and are testing a 3D hydrostatic variable-resolution solver for the sphere, and we have also constructed a 3D nonhydrostatic solver for a hexagonal cartesian grid in preparation for constructing a global nonhydrostatic solver. We will present results from these prototypes demonstrating the robustness of the solvers and their variable-resolution capabilities. Given the performance of these prototypes, we believe that a C-grid hexagonal global atmospheric solver is a viable candidate for future global weather, climate and regional climate applications requiring accuracy from cloud to global scales and scalability on existing and future MPP computers.