Carr, Daniel B., Ralph Kahn, Kevin Sahr, and Anthony R. Olsen. 1998. ISEA Discrete Global Grids Statistical Computing and Graphics Newsletter 8 (2/3):31-39
This article describes a recently proposed standard, ISEA discrete global grids, for gridding information on the surface of the earth. The acronym ISEA stands for icosahedral Snyder equal area. The impetus for the global grid system came from what many would call an unusual perspective - survey sampling. It is the basis for all surveys conducted as part of the Environmental Monitoring and Assessment Program (EMAP). ISEA grids are simple in concept. Begin with a Snyder Equal Area projection to a regular icosahedron inscribed in a sphere. In each of the 20 equilateral triangle faces of the icosahedron inscribe a hexagon by dividing each triangle edge into thirds. Then project the hexagon back onto the sphere using the Inverse Snyder Icosahedral equal area projection. This yields a coarse-resolution equal area grid called the resolution 1 grid. To form higher resolution grids, tessellate each equilateral triangle in the planar view with more hexagons and use the inverse projection back to the sphere. The advantages of the ISEA grids are (1) they have irregularities (12 pentagonal cells) that are minor nuisances rather than being pathological singularities, (2) they are suitable for modeling on all parts of the globe including the poles, (3) they preserve symmetry about the equator, (4) they provide an infinite nesting of equal-area sub-grids, and (5) they provide a basis for uniform global density of sampling for data at all spatial resolutions. The grid facilitates comparisons between high and low latitude data and high and low spatial-resolution data. The grid also improves the isotropy of finite-difference quantities compared to those calculated for rectangular grid schemes. For example, two-dimensional Navier-Stokes implementations are optimal with hexagons. Finally, no ambiguity exists about nearest neighbors as all nearest neighbor cells share an edge with a reference cell and their distances to the center of a reference cell are nearly equal.