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A geodesic grid is a spatial grid based on a
A geodesic grid is a global Earth reference that uses triangular tiles based on the subdivision of a polyhedron (usually the
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Discrete Global Grids
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the PYXIS innovation Digital Earth Reference Model
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Interpolation on spherical geodesic grids: A comparative study
Finite differences Geodesy Geometric data structures Numerical climate and weather models
geodesic polyhedron
A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices which have 5 triangles. They are the dual of corresponding Goldberg polyhed ...
or Goldberg polyhedron.
Construction
A geodesic grid is a global Earth reference that uses triangular tiles based on the subdivision of a polyhedron (usually the icosahedron
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
, and usually a Class I subdivision) to subdivide the surface of the Earth. Such a grid does not have a straightforward relationship to latitude and longitude, but conforms to many of the main criteria for a statistically valid discrete global grid. Primarily, the cells' area and shape are generally similar, especially near the poles where many other spatial grids have singularities or heavy distortion. The popular Quaternary Triangular Mesh (QTM) falls into this category.
Geodesic grids may use the dual polyhedron
In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other. ...
of the geodesic polyhedron, which is the Goldberg polyhedron. Goldberg polyhedra are made up of hexagons and (if based on the icosahedron) 12 pentagons. One implementation that uses an icosahedron
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...
as the base polyhedron, hexagonal cells, and the Snyder equal-area projection is known as the Icosahedron Snyder Equal Area (ISEA) grid.
Applications
In biodiversity science, geodesic grids are a global extension of local discrete grids that are staked out in field studies to ensure appropriate statistical sampling and larger multi-use grids deployed at regional and national levels to develop an aggregated understanding of biodiversity. These grids translate environmental and ecological monitoring data from multiple spatial and temporal scales into assessments of current ecological condition and forecasts of risks to our natural resources. A geodesic grid allows local to global assimilation of ecologically significant information at its own level of granularity. When modeling theweather
Weather is the state of the atmosphere, describing for example the degree to which it is hot or cold, wet or dry, calm or stormy, clear or cloudy. On Earth, most weather phenomena occur in the lowest layer of the planet's atmosphere, the ...
, ocean circulation, or the climate
Climate is the long-term weather pattern in an area, typically averaged over 30 years. More rigorously, it is the mean and variability of meteorological variables over a time spanning from months to millions of years. Some of the meteorologic ...
, partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function.
The function is often thought of as an "unknown" to be sol ...
s are used to describe the evolution of these systems over time. Because computer programs are used to build and work with these complex models, approximations need to be formulated into easily computable forms. Some of these numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...
techniques (such as finite differences) require the area of interest to be subdivided into a grid — in this case, over the shape of the Earth
Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A sphere is a well-known historical approxim ...
.
Geodesic grids can be used in video game development to model fictional worlds instead of the Earth. They are a natural analog of the hex map
A hex map, hex board, or hex grid is a game board design commonly used in wargames of all scales. The map is subdivided into a hexagonal tiling, small regular hexagons of identical size.
Advantages and disadvantages
The primary advantage of a he ...
to a spherical surface.
Pros and cons
Pros: *Largelyisotropic
Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
.
*Resolution can be easily increased by binary division.
*Does not suffer from over sampling near the poles like more traditional rectangular longitude–latitude square grids.
*Does not result in dense linear systems like spectral methods do (see also Gaussian grid
A Gaussian grid is used in the earth sciences as a gridded horizontal coordinate system for scientific modeling on a sphere (i.e., the approximate shape of the Earth). The grid is rectangular, with a set number of orthogonal coordinates (usually ...
).
*No single points of contact between neighboring grid cells. Square grid
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of meaning it has 4 squares around every vertex.
Conway called it a quadrille.
The internal angle of the s ...
s and isometric grids suffer from the ambiguous problem of how to handle neighbors that only touch at a single point.
*Cells can be both minimally distorted and near-equal-area. In contrast, square grids are not equal area, while equal-area rectangular grids vary in shape from equator to poles.
Cons:
*More complicated to implement than rectangular longitude–latitude grids in computers
History
The earliest use of the (icosahedral) geodesic grid in geophysical modeling dates back to 1968 and the work by Sadourny, Arakawa, and Mintz and Williamson. Later work expanded on this base.Randall ''et al.'', 2000; Randall ''et al.'', 2002.See also
* geodesics on an ellipsoid *geographic coordinate system
The geographic coordinate system (GCS) is a spherical or ellipsoidal coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various ...
* Grid reference
* Discrete Global Grid
* Spherical design A spherical design, part of combinatorial design theory in mathematics, is a finite set of ''N'' points on the ''d''-dimensional unit n-sphere, ''d''-sphere ''Sd'' such that the average value of any polynomial ''f'' of degree ''t'' or less on the se ...
, generalization to more than three dimensions
* The quadrilateralized spherical cube
In mapmaking, a quadrilateralized spherical cube, or quad sphere for short, is an equal-area polyhedral map projection and discrete global grid scheme for data collected on a spherical surface (either that of the Earth or the celestial sphere). It ...
, a grid over the earth based on the cube and made of quadrilaterals instead of triangles
* Polyhedral map projection
A polyhedral map projection is a map projection based on a spherical polyhedron. Typically, the polyhedron is overlaid on the globe, and each face of the polyhedron is transformed to a polygon or other shape in the plane. The best-known polyhedral ...
References
External links
{{sisterlinks, d=Q1898473, b=no, n=no, v=no, voy=no, s=no, m=no, mw=no, species=no, q=no, c=Geodesic diagrams, wikt=noBUGS climate model
page on geodesic grids
Discrete Global Grids
page at the Computer Science department at Southern Oregon University
the PYXIS innovation Digital Earth Reference Model
">Digital Earth Reference Model">the PYXIS innovation Digital Earth Reference Model
Interpolation on spherical geodesic grids: A comparative study
Finite differences Geodesy Geometric data structures Numerical climate and weather models