Comparing Geometrical Properties of Global Grids

Abstract

Transforming raw observations into geometrically regular global grids is a fundamental data processing and storage problem underlying much of our global data analysis. The basic geometry of traditionally employed quadrilateral-based point or area grids, while well suited to array storage and matrix manipulation, may inherently hinder numerical and geostatistical modeling efforts. Several scientists have noted the superior performance of triangular point grids and associated triangular cells that can be aggregated into hexagonal surface tessellations, yet, no thorough evaluation of discrete global grid alternatives has been conducted. We present results from a global grid comparison study that focused on recursive tiling of polyhedral faces projected onto the globe. A set of evaluation criteria for global partitioning methods were developed. Of these, metrics for spheroidal surface area, compactness, and centerpoint spacing were found to be of particular importance. We present examples of these metrics applied to compare different recursive map projection-based and quadrilateral spherical partitionings. One map projection approach, the Icosahedral Snyder Equal Area (ISEA), shows particular promise due to its production of equal area triangular and hexagonal cells on the spheroid at all levels of recursive partitioning.