Gridding the Earth for Climate Models

Weather prediction and climate modeling are computations whose
domain is a very large sphere, the Earth.  Before a scientist
can specify what equations are to be solved, the geometry of
the Earth's surface must be approximated by a grid of area patches.
Accurate calculations require small patches; if we want patches
that are about 10 miles across, we'll need 2,000,000 of them.

Designing a good grid for the Earth's surface is greatly complicated
by the curvature of the surface, the fact that there are land and 
sea surfaces, and that populated regions are much more important to
handle accurately than unoccupied wastelands.

In this talk, we will outline methods for producing grids in a
2d planar region, discuss the corresponding problem for the sphere,
and consider a new method for spherical grids that is highly efficient,
and can be carried out in parallel.