A discrete global grid (DGG) is a mosaic that covers the entire Earth's surface. Mathematically it is a space partitioning: it consists of a set of non-empty regions that form a partition of the Earth's surface. In a usual grid-modeling strategy, to simplify position calculations, each region is represented by a point, abstracting the grid as a set of region-points. Each region or region-point in the grid is called a cell.
When each cell of a grid is subject to a recursive partition, resulting in a "series of discrete global grids with progressively finer resolution", forming a hierarchical grid, it is called a hierarchical DGG (sometimes "global hierarchical tessellation" or "DGG system").
Discrete global grids are used as the geometric basis for the building of geospatial data structures. Each cell is related with data objects or values, or (in the hierarchical case) may be associated with other cells. DGGs have been proposed for use in a wide range of geospatial applications, including vector and raster location representation, data fusion, and spatial databases.
The most usual grids are for horizontal position representation, using a standard datum, like WGS84. In this context, it is common also to use a specific DGG as foundation for geocoding standardization.
In the context of a spatial index, a DGG can assign unique identifiers to each grid cell, using it for spatial indexing purposes, in geodatabases or for geocoding.
Reference model of the globe
The "globe", in the DGG concept, has no strict semantics, but in geodesy a so-called "grid reference system" is a grid that divides space with precise positions relative to a datum, that is an approximated a "standard model of the Geoid". So, in the role of Geoid, the "globe" covered by a DGG can be any of the following objects:
The topographical surface of the Earth, when each cell of the grid has its surface-position coordinates and the elevation in relation to the standard Geoid. Example: grid with coordinates (φ,λ,z) where z is the elevation. A standard Geoid surface. The z coordinate is zero for all grid, thus can be omitted, (φ,λ). Ancient standards, before 1687 (the Newton's Principia publication), used a "reference sphere"; in nowadays the Geoid is mathematically abstracted as reference ellipsoid. A simplified Geoid: sometimes an old geodesic standard (e.g. SAD69) or a non-geodesic surface (e. g. perfectly spherical surface) must be adopted, and will be covered by the grid. In this case, cells must be labeled with non-ambiguous way, (φ',λ'), and the transformation (φ,λ) ⟾ (,) must be known. A projection surface. Typically the geographic coordinates (φ,λ) are projected (with some distortion) onto the 2D mapping plane with 2D Cartesian coordinates (x, y).
As a global modeling process, modern DGGs, when including projection process, tend to avoid surfaces like cylinder or a conic solids that result in discontinuities and indexing problems. Regular polyhedra and other topological equivalents of sphere led to the most promising known options to be covered by DGGs, because "spherical projections preserve the correct topology of the Earth – there are no singularities or discontinuities to deal with".
When working with a DGG it is important to specify which of these options was adopted. So, the characterization of the reference model of the globe of a DGG can be summarized by:
The recovered object: the object type in the role of globe. If there is no projection, the object covered by the grid is the Geoid, the Earth or a sphere; else is the geometry class of the projection surface (e.g. a cylinder, a cube or a cone). Projection type: absent (no projection) or present. When present, its characterization can be summarized by the projection's goal property (e.g. equal-area, conformal, etc.) and the class of the corrective function (e.g. trigonometric, linear, quadratic, etc.).
NOTE: when the DGG is covering a projection surface, in a context of data provenance, the metadata about reference-Geoid is also important — typically informing its ISO 19111's CRS value, with no confusion with the projection surface.
Types
The main distinguishing feature to classify or compare DGGs is the use or not of hierarchical grid structures:
In hierarchical reference systems each cell is a "box reference" to a subset of cells, and cell identifiers can express this hierarchy in its numbering logic or structure. In non-hierarchical reference systems each cell have a distinct identifier and represents a fixed-scale region of the space. The discretization of the Latitude/Longitude system is the most popular, and the standard reference for conversions.