Limitations in traditional approaches to the representation of geo-referenced data sets has led to the development of a number of data structures based on regular, multi-resolution partitions of spherical polyhedra. These constitute a new class of geospatial data structures that we call Discrete Global Grid Systems (DGGSs). After defining an abstract data type for structured geospatial data structures that encompasses DGGSs we survey the proposed DGGS approaches. We show that the primary DGGS alternatives can be constructed by specifying five substantially independent design choices: a base regular polyhedron, a fixed orientation of the base regular polyhedron relative to the Earth, a hierarchical spatial partitioning method defined symmetrically on a set of faces of the base regular polyhedron, a method for transforming that planar partition to the corresponding spherical/ellipsoidal surface, and a method for assigning point representations to grid cells. An examination of the design choice options leads us to the construction of the Icosahedral Snyder Equal Area aperture 3 Hexagon (ISEA3H) DGGS.

We next develop a topology-independent implementation of DGGSs based on our abstract data type that will enable us to perform empirical comparisons between the primary DGGS topologies of hexagons, triangles, and diamonds. Since a major advan­tage of DGGSs is that they can function as topologies for dynamic simulation and analysis, for our initial comparison we implement a simple dynamic simulation by extending the definition of a planar cellular automata to be spherical, multi-scale, and topology-independent. We then report the first results for a study of such simulations.

Finally, we note that the practical use of icosahedral aperture 3 DGGSs, such as the ISEA3H, has been hindered by a lack of efficient hierarchical location coding schemes. We introduce two path-based hierarchical location coding systems: the Icosahedral Modified Generalized Balanced Ternary approach for indexing point data, and the Icosahedral Aperture 3 Hexagon Tree for indexing raster data and for use in bucket-based spatial databases. Algorithms for conversion from geographic coordinates to these sys­tems are given.

This dissertation includes both my previously published and my co-authored materials.