## Abstract

This paper documents the development and testing of a new type of atmospheric dynamical core. The model solves the vorticity and divergence equations in place of the momentum equation. The model is discretized in the horizontal 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 the sphere. All of the analytic horizontal operators are reduced to line integrals, which are numerically evaluated with second-order accuracy. In the vertical direction the model can use a variety of coordinate systems, including a generalized sigma coordinate that is attached to the top of the boundary layer. Terms related to gravity wave propagation are isolated and an efficient semi-implicit time-stepping scheme is implemented. Since this model combines many of the positive attributes of both spectral models and conventional finite-difference models into a single dynamical core, it represents a distinctively new approach to modeling the atmosphere’s general circulation.

The model is tested using the idealized forcing proposed by Held and Suarez. Results are presented for simulations using 2562 polygons (approximately 4.5° × 4.5°) and using 10 242 polygons (approximately 2.25° × 2.25°). The results are compared to those obtained with spectral model simulations truncated at T30 and T63. In terms of first and second moments of state variables such as the zonal wind, meridional wind, and temperature, the geodesic grid model results using 2562 polygons are comparable to those of a spectral model truncated at slightly less than T30, while a simulation with 10 242 polygons is comparable to a spectral model simulation truncated at slightly less than T63.

In order to further demonstrate the viability of this modeling approach, preliminary results obtained from a full-physics general circulation model that 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 slower than the spectral model used for comparison. Model timings completed on an SGI Origin 2000 indicate that the geodesic grid model with 10 242 polygons is 20% slower than the spectral model truncated at T63. The geodesic grid model is more competitive at higher resolution than at lower resolution, so further optimization and future trends toward higher resolution should benefit the geodesic grid model.

*Corresponding author address:* Dr. Todd D. Ringler, Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523-1371.