# Colorado State University
General Circulation Model

### Ross Heikes* and David A. Randall*

#### Monthly Weather Review Vol. 123, 1862-1880.

Monthly Weather Review Vol. 123, 1881-1887.

Department of Atmospheric Science, Colorado State University, Fort Collins,
Colorado 80521, USA

Spherical geodesic grids offer an attractive solution to many of the problems
associated with fluid-flow simulations in a spherical geometry. Williamson
(1968) and Sadourny et al. (1968) simultaneously introduced this approach to
isotropically and homogeneously discretize the sphere. Their new grids were
inspired by Buckminster Fuller's geodesic dome, and tile the sphere with
spherical triangles that are nearly equal in area and nearly equilateral. These
grids offer several advantages over the more common latitude/longitude grids
which tend to unnecessarily concentrate grid points in the zonal direction near
the poles.

Heikes, R. and Randall, D.A. 1995a. Numerical integration of the shallow-water equations of a twisted icosahedral grid. Part I: basic design and results of tests. *Mon. Wea. Rev*. **123**, 1862-1880.
Heikes, R. and Randall, D.A. 1995b. Numerical integration of the shallow-water equations of a twisted icosahedral grid. Part II: a detailed description of the grid and an analysis of numerical accuracy. *Mon. Wea. Rev*. **123**, 1881-1887.

Sadourny, R., A. Arakawa, and Y. Mintz, 1968: Integration of the non-divergent barotropic vorticity equation with an icosahedral-hexagonal grid for the sphere. *Mon. Wea. Rev*., **96**, 351-356.

Williamson, D. L., 1968: Integration of the barotropic vorticity equation on a spherical geodesic grid. *Tellus*, **20**, 642-653.
-----, J. B. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, 1992: A standard test set for numerical approximations to the shallow-water equations in spherical geometry. *J. Comput. Phy.*, **102**, 221-224.

Ross Heikes

Dept of Atmospheric Science

Colorado State University

(970)491-8432

ross.heikes@atmos.colostate.edu