Discrete Global Grid

A Discrete Global Grid (DGG) consists of a set of regions that form a partition of the Earth’s surface, where each region has associated with it a single point contained in that region. A Discrete Global Grid System (DGGS) is a series of discrete global grids, usually consisting of increasingly finer resolution grids.[1] [2]

Discrete Global Grids are used as the geometric basis for the creation of geospatial data structures. Each region/point combination in the grid is a called a "cell," and depending on the application, data objects or values may be associated with the cells themselves, or with either the cell regions or cell points. DGGs have been proposed for use in a wide range of geospatial applications, including vector and raster location representation, data fusion, and spatial databases.[2]

Examples

Grids based on Latitude/Longitude

The most common class of Discrete Global Grids are those that place cell center points on longitude/latitude meridians and parallels, or which use the longitude/latitude meridians and parallels to form the boundaries of rectangular cells. Examples of such grids include:

Arakawa grids

Arakawa grids are used for Earth system models for meteorology and oceanography. For example, the Global Environmental Multiscale Model (GEM) uses Arakawa grids for global climate modeling.[3]

Digital Elevation Models

Many Digital Elevation Models are created on a grid of points placed at a regular angular increments of latitude and longitude. Examples include the Global 30 Arc-Second Elevation Dataset (GTOPO30).[4] and the Global Multi-resolution Terrain Elevation Data 2010 (GMTED2010) [5]

Geodesic Discrete Global Grid Systems

A Geodesic Discrete Global Grid System (sometimes called simply a geodesic grid) is formed by recursively sub-dividing a planar or spherical polyhedra.[2] Examples of such grids include:

ISEA DGGs

ISEA Discrete Global Grids are a class of grids proposed by researchers at Oregon State University.[2] The grid cells are created as regular polygons on the surface of an icosahedron, and then inversely projected using the Icosahedral Snyder Equal Area (ISEA) map projection[6] to form equal area cells on the sphere. Cells may be hexagons, triangles, or quadrilaterals. Multiple resolutions are indicated by choosing an aperture, or ratio between cell areas at consecutive resolutions. Some applications of ISEA DGGs include data products generated by the European Space Agency's Soil Moisture and Ocean Salinity (SMOS) satellite, which uses an ISEA4H9 (aperture 4 Hexagonal DGGS resolution 9),[7] and the commercial software WordView,[8] which uses an ISEA3H (aperture 3 Hexagonal DGGS).

HEALPix

The Hierarchical Equal Area isoLatitude Pixelization (HEALPix) has equal area quadrilateral-shaped cells and was originally developed for use with full-sky astrophysical data sets.[9]

Quaternary Triangular Mesh (QTM)

QTM has triangular-shaped cells created by the 4-fold recursive subdivision of a spherical octahedron.[10]

History

Discrete Global Grids with cell regions defined by parallels and meridians of latitude/longitude have been used since the earliest days of global geospatial computing. The first published references to Geodesic DGGS systems are to systems developed for atmospheric modeling and published in 1968. These systems have hexagonal cell regions created on the surface of a spherical icosahedron. [11] [12]

While specific instances of these grids have been in use for decades, the terms Discrete Global Grids and Discrete Global Grid Systems were coined by researchers at Oregon State University in 1997[1] to describe the class of all such entities.

Evaluation

The evaluation Discrete Global Grid consists of many aspects, including area, shape, compactness, etc. Evaluation methods for map projection, such as Tissot's indicatrix, are also suitable for evaluating map projecion based Discrete Global Grid.

In addition, Averaged ratio between complementary profiles (AveRaComp) [13] gives a good evaluation of shape distortions for quadrilateral-shaped Discrete Global Grid.

References

  1. 1 2 Sahr, Kevin; White, Denis; Kimerling, A.J. (18 March 1997), "A Proposed Criteria for Evaluating Discrete Global Grids", Draft Technical Report, Corvallis, Oregon: Oregon State University
  2. 1 2 3 4 Sahr, Kevin; White, Denis; Kimerling, A.J. (2003). "Geodesic discrete global grid systems" (PDF). Cartography and Geographic Information Science. 30 (2): 121–134. doi:10.1559/152304003100011090.
  3. ↑ Arakawa, A.; Lamb, V.R. (1977). "Computational design of the basic dynamical processes of the UCLA general circulation model". Methods of Computational Physics. 17. New York: Academic Press. pp. 173–265.
  4. ↑ "Global 30 Arc-Second Elevation (GTOPO30)". USGS. Retrieved October 8, 2015.
  5. ↑ "Global Multi-resolution Terrain Elevation Data 2010 (GMTED2010)". USGS. Retrieved October 8, 2015.
  6. ↑ Snyder, J.P. (1992). "An equal-area map projection for polyhedral globes". Cartographica. 29 (1): 10–21. doi:10.3138/27h7-8k88-4882-1752.
  7. ↑ Suess, M.; Matos, P.; Gutierrez, A.; Zundo, M.; Martin-Neira, M. (2004). "Processing of SMOS level 1c data onto a discrete global grid". Proceedings of the IEEE International Geoscience and Remote Sensing Symposium: 1914–1917.
  8. ↑ "WorldView Studio". Pyxis Innovation. Retrieved October 8, 2015.
  9. ↑ "HEALPix Background Purpose". NASA Jet Propulsion Laboratory. Retrieved October 8, 2015.
  10. ↑ Dutton, G. (1999). A hierarchical coordinate system for geoprocessing and cartography. Springer-Verlag.
  11. ↑ Sadourny, R.; Arakawa, A.; Mintz, Y. (1968). "Integration of the nondivergent barotropic vorticity equation with an icosahedral-hexagonal grid for the sphere". Monthly Weather Review. 96 (6): 351–356. doi:10.1175/1520-0493(1968)096<0351:iotnbv>2.0.co;2.
  12. ↑ Williamson, D.L. (1968). "Integration of the barotropic vorticity equation on a spherical geodesic grid.". Tellus. 20 (4): 642–653. doi:10.1111/j.2153-3490.1968.tb00406.x.
  13. ↑ Yan, Jin; Song, Xiao; Gong, Guanghong (2016). "Averaged ratio between complementary profiles for evaluating shape distortions of map projections and spherical hierarchical tessellations". Computers & Geosciences. 87: 41–55. doi:10.1016/j.cageo.2015.11.009. Retrieved 2015-11-27.

External links

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