Developing dynamical core of a GCM in Sigma-Pressure vertical coordinate

Developing atmospheric General Circulation Models (GCMs) and, in particular, their dynamical cores are important steps towards future model improvements. For this reason, most GCMs of the atmosphere are developed in various vertical coordinates and grids. The diabatic contour-advective semi-Lagrangian method (DCASL) is an algorithm based on the use of contour representation for a fundamental dynamic quantity such as a potential vorticity. Previously, DCASL algorithms have been constructed for the shallow-water and multilayer Boussinesq primitive equations and also multilayer non-Boussinesq equations on the sphere using a hybrid terrain-following–isentropic (Sigma-Theta) vertical coordinate on the Charney-Philips grid (CP-grid). In this research, the results of the dynamical core constructed based on the DCASL algorithm are presented for the hybrid terrain-following–pressure (Sigma-P) vertical coordinate and compared with the results in the previously constructed model in coordinate. Also in this study, the performance of the coordinate models constructed using the CP-grid and the Lorenz grid (L-grid) are compared. For assessment and comparison of the dynamical cores in representations of different fields, we have used the baroclinic instability test case introduced by Jablonowski and Williamson in 2006. Qualitative and quantitative comparisons have been made with the results of four dynamical cores of global reference models (three hydrostatic dynamical cores that are parts of NCAR’s Community Atmosphere Model version 3 (CAM3) and also the dynamical core of the operational weather forecast model GME at the German Weather Service (DWD)). The comparisons show that the initialization problem present in the Sigma-Theta vertical coordinate in this test case is removed by the use of the Sigma-P vertical coordinate and thus results become ever closer to the references solutions. Also results of the Sigma-P vertical coordinate in the Lorenz grid for this dynamical core have the least difference with the reference results in the first 15 days of the test case.