Solving the primitive equations on a spherical geodesic grid: a technical report to a new class of dynamical cores

Abstract

This report documents the development and testing of a new type of dynamical core. Toe· model uses the invariant form of the primitive equations, solving the vorticity and divergence equations in place of the momentum equation. In the horizontal directions the model is discretized on a geodesic grid which is nearly uniform over the entire globe. In the vertical direction the model can use a variety of coordinate systems, including the generalized sigma coordinate of Suarez et al. (1983) and the Phillips (1957) sigma coordinate. By integrating the vorticity and divergence equations, terms related to gravity wave propagation are isolated and an efficient semi-implicit time stepping scheme is implemented. The model is tested using the idealized forcing proposed by Held and Suarez (1994). Results are presented for a variety of vertical coordinate systems with horizontal resolutions using 2562 polygons (approximately 4.5° x 4.5°) and using 10242 polygons (approximately 2.25° x 2.25° ). The results are compared to standard spectral model simulations truncated at T30 and T63. In terms of averages and variances of state variables, e geodesic grid model results using 2562 polygons are comparable to those of a spectral model truncated at slightly less than TIO, while a simulation with 10242 polygons is comparable to a spectral model simulation truncated at slightly less than T63. In terms of computational efficiency, further development of this geodesic grid model is required. Model timings completed on an SGI Origin 2000 indicate that the geodesic grid model with 10242 polygons is 2.7 times slower than the spectral model truncated at T63. At these resolutions, the MFlop rate of the geodesic grid model is 15% faster than the spectral model, so the differences in model speed are due to differences in the number of floating point operations required per day of simulation. 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.