Modeling the atmospheric general circulation using a spherical geodesic grid: A new class of dynamical cores

This paper documents the development and testing of a new type of atmospher ic dynamical core. The model solves the vorticity and divergence equations in place of the momentum equation. The model is discretized in the horizont al using a geodesic grid that is nearly uniform over the entire globe. The geodesic grid is formed by recursively bisecting the triangular faces of a regular icosahedron and projecting those new vertices onto the surface of t he sphere. All of the analytic horizontal operators are reduced to line int egrals, which are numerically evaluated with second-order accuracy. In the vertical direction the model can use a variety of coordinate systems, inclu ding a generalized sigma coordinate that is attached to the top of the boun dary layer. Terms related to gravity wave propagation are isolated and an e fficient semi-implicit time-stepping scheme is implemented. Since this mode l combines many of the positive attributes of both spectral models and conv entional finite-difference models into a single dynamical core, it represen ts a distinctively new approach to modeling the atmosphere's general circul ation. The model is tested using the idealized forcing proposed by Held and Suarez . Results are presented for simulations using 2562 polygons (approximately 4.5 degrees x 4.5 degrees) and using 10 242 polygons (approximately 2.25 de grees x 2.25 degrees). The results are compared to those obtained with spec tral model simulations truncated at T30 and T63. In terms of first and seco nd moments of stare variables such as the zonal wind, meridional wind, and temperature, the geodesic grid model results using 2562 polygons are compar able to those of a spectral model truncated at slightly less than T30, whil e a simulation with 10 242 polygons is comparable to a spectral model simul ation truncated at slightly less than T63. In order to further demonstrate the viability of this modeling approach, pr eliminary results obtained from a full-physics general circulation model th at uses this dynamical core are presented. The dominant features of the DJF climate are captured in the full-physics simulation. In terms of computational efficiency, the geodesic grid model is somewhat s lower than the spectral model used for comparison. Model timings completed on an SGI Origin 2000 indicate that the geodesic grid model with 10 242 pol ygons is 20% slower than the spectral model truncated at T63. The geodesic grid model is more competitive at higher resolution than at lower resolutio n, so further optimization and future trends toward higher resolution shoul d benefit the geodesic grid model.