i. Abstract

This document specifies the core Abstract Specification and extension mechanisms for Discrete Global Grid Systems (DGGS). A DGGS is a spatial reference system that uses a hierarchical tessellation of cells to partition and address the globe. DGGS are characterized by the properties of their cell structure, geo-encoding, quantization strategy and associated mathematical functions.The OGC DGGS Abstract Specification supports the specification of standardized DGGS infrastructures that enable the integrated analysis of very large, multi-source, multi-resolution, multi-dimensional, distributed geospatial data. Interoperability between OGC DGGS implementations is anticipated through implementation standards, and extension interface encodings of OGC Web Services.

ii.    Keywords

The following are keywords to be used by search engines and document catalogues.

ogcdoc, OGC document, Discrete Global Grid System, DGGS, Digital Earth, DGGS-core, Spatial Reference System, Global Data Structure, Geographic Information Systems, DE-9IM, standard, specification

iii.  Preface

This document specifies the core of an OGC Discrete Global Grid System Abstract Specification.

The intention of this Abstract Specification is to provide the geomatics and decision-making community with a formal document with which DGGS can be recognized, designed, built and used. This Abstract Specification defines the framework components that make up a compliant DGGS and the variability within those components.  The value of a DGGS as a spatial reference system is also discussed, as is the opportunity to interoperate between other DGGS and to utilize other OGC/ISO standards within the implementation of DGGS. As with any spatial reference, and especially an approach that is early in adoption, intellectual property rights pertaining to various methods of creating and using DGGS should be expected. For example, there exist multiple patents for indexing DGGS, and the implementers of this Abstract Specification should make themselves aware of these patents.

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. The Open Geospatial Consortium shall not be held responsible for identifying any or all such patent rights.

Recipients of this document are requested to submit, with their comments, notification of any relevant patent claims or other intellectual property rights of which they may be aware that might be infringed by any implementation of the Abstract Specification set forth in this document, and to provide supporting documentation.

iv. Submitting organizations

The following organizations submitted this Document to the Open Geospatial Consortium (OGC):

Geoscience Australia

Landcare Research New Zealand

University of Calgary

PYXIS

SpaceCurve

Zhengzhou Institute of Surveying & Mapping

ESRI

v. Submitters

All questions regarding this submission should be directed to the editor or the submitters:

Roger Lott’s significant contribution is acknowledged for his eleventh-hour assistance in working through the relationship between DGGS concepts and ISO concepts and for ensuring the document structure complies with both OGC and ISO requirements.

vi.   Introduction

A Discrete Global Grid System (DGGS) is designed as a framework for information as distinct from conventional coordinate reference systems originally designed for navigation. For a grid based global spatial information framework to operate effectively as an analytical system it should be constructed using cells that represent the surface of the Earth uniformly. This ensures that, at multiple resolutions, each cell has an equal probability of contributing to an analysis. A DGGS is a spatial reference system that uses a hierarchy of equal area tessellations to partition the surface of the Earth into grid cells or their analogous lattice points. In this way information recorded about phenomena at a location can be easily referenced to the explicit area of the associated cell, integrated with other cell values, and provides statistically valid summaries based on any chosen selection of cells. With equal area partitioning, spatial analysis can be replicated consistently anywhere on the Earth independent of resolution or scale.

OGC DGGS reference systems are polyhedral reference systems on the surface of a base unit polyhedron’s circumscribed ellipsoid. The base unit polyhedron’s location and orientation is defined in Earth Centered (EC) coordinates. The initial equal area tessellation of the chosen ellipsoidal Earth model is achieved by scaling a unit polyhedron of defined orientation until its vertices all touch the ellipsoid and connecting adjoining vertices with arcs selected from the set of permitted arcs, the simplest of which are geodesic, small circle or small ellipse arcs. Appropriate differential scaling is applied to the unit polyhedron to ensure an equal area initial tessellation. For the simple case of regular polyhedra and geodesic (i.e. great circle) arcs on its circumscribed spheroid the scaling is uniform. Figure 1 illustrates their simplest form using a regular spherical polyhedron with a spheroidal circumscribing ellipsoid and geodesic arcs. Small circle arcs are typically used to construct arcs along lines of latitude for both ellipsoids and spheroids. Both small circle and small ellipse arcs are formed from the intersection of a defined plane with the ellipsoid, and in that sense they can be considered equivalent to the ‘straight’ lines of 2D cell boundaries. More complex forms of straight line, such as arcs that project to a straight line in an equal area projection are also allowed.

There is a gap between conventional coordinate reference systems and the reference system needed to define DGGS. This OGC Abstract Specification fills the gap in existing OGC and ISO standard reference systems and establishes requirements for globally interoperable equal-area cell- or lattice-based information frameworks.

Existing spatial reference systems (e.g. ECEF [Earth Centered Earth Fixed], WGS 84 or Web Mercator) build grids from projected Cartesian or ellipsoidal coordinate axes. Rectangular planar grids are typically formed by establishing a set of regular ticks on a pair of linear axes with grids cells being formed by the intersection of straight lines drawn normal to the ticks on each axis. Analogous construction techniques can be used to create triangular or hexagonal grids. The properties of grids built this way arise from the premise of planar geometry and not the curved geometry of the surface of a sphere or ellipsoid. While these properties hold true at local scales, in curved geometries they increasingly fail at progressively larger regions of interest (see Figure 2). Take for example the assumption that a grid cell’s geometric properties are independent of its size or resolution – which is implicit in constructing sets of planar aligned (or ‘nested’) 10m, 30m and 90m grids. As shown in Figure 3, a 90m square cell formed from nine 30m square child cells has the following properties:

1. It is also square;
2. Its edges are three times the edge length of its 30m child cells, which in turn all are three times the edge length of their 10m child cells;
3. Its interior angles are all right angles and identical to the interior angles of all of the child cells;
4. Its edges follow the shortest linear path between neighboring cell vertices; and,
5. The angles or bearings from centroid to centroid between cells are preserved irrespective of the direction of travel.