A comparison of vertical coordinate systems for numerical modeling of the general circulation of the atmosphere

Abstract

The Colorado State University general circulation model has been dramatically changed in the last few years. The horizontal grid has been changed from a latitude/longitude grid with an Arakawa C-grid staggering of mass, zonal and meridional wind to a geodesic grid in which mass, vorticity and divergence are predicted at cell centers. Throughout this change the vertical structure has remained unchanged. Now, we are poised to revamp the vertical structure of the model. We have studied several possible alternative vertical coordinate systems in order to pick the one best suited for long-term climate prediction. After a brief historical review of various vertical coordinates used in numerical modeling, we will focus on three models — one based on the co-called sigma-coordinate, on based on a pure isentropic coordinate and one based on a hybrid σ -θ vertical coordinate. We will show how the continuous equations are transformed to finite-difference analogs, and how the transformation preserves many of the conservation properties of the continuous equations. We will show how different vertical discretization of the prognostic variables — Lorenz or Chamey-Phillips vertical staggering — can influence the quality of the numerical simulation. Many fundamental questions about the isentropic- and hybrid-coordinate need to be answered. Since the isentropic-coordinate surfaces behave as Lagrangian surfaces, the ideas of grid resolution from the Eulerian framework are not applicable. Also, in the isentropic- and hybrid- coordinates, there is a much greater variation in layer thickness. Excessive vertical resolution in the extra-tropics where coordinate surfaces are close, may become inadequately coarse in the tropics as the coordinate surfaces spread apart. We will show how the quality of the Held and Suarez test case changes as a function of resolution. We have performed a simulation of stratospheric sudden warming with the isentropic-coordinate model. We will compare our results with observations. We have also performed a simulation of baroclinic instability with the hybrid-coordinate model.