A geodesic grid is a spatial grid based on a geodesic polyhedron or

Goldberg polyhedron In mathematics, and more specifically in polyhedral combinatorics, a Goldberg polyhedron is a convex polyhedron made from hexagons and pentagons. They were first described in 1937 by Michael Goldberg (1902–1990). They are defined by three p ...

Construction

Geodesic grid used in atmosphere simulation

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 symmetric ...

, 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 othe ...

of the geodesic polyhedron, which is the

. Goldberg polyhedra are made up of hexagons and (if based on the icosahedron) 12 pentagons. One implementation that uses an

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 the

weather 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 meteorologica ...

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

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 manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...

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. 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 to a spherical surface.

Pros and cons

Pros: *Largely isotropic. *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). *No single points of contact between neighboring grid cells. Square grids 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.

References

External links

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BUGS 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

Construction

Applications

Pros and cons

History

See also

References

External links