The earliest use of the (icosahedral) geodesic grid in geophysical modeling dates back to 1968 and the work by Sadourny, Arakawa, and Mintz[1] and Williamson.[2][3] Later work expanded on this base.[4][5][6][7][8]
A geodesic grid is a global Earth spatial reference that uses polygon tiles based on the subdivision of a polyhedron (usually theicosahedron, 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.[9] 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.[10]
Geodesic grids may use thedual polyhedron of the geodesic polyhedron, which is theGoldberg polyhedron. Goldberg polyhedra are made up of hexagons and (if based on the icosahedron) 12 pentagons. One implementation that uses anicosahedron as the base polyhedron, hexagonal cells, and theSnyder equal-area projection is known as the Icosahedron Snyder Equal Area (ISEA) grid.[11]
An icosahedron.
A highly divided geodesic polyhedron based on the icosahedron.
A highly divided Goldberg polyhedron; the dual of the previous image.
A variation of geodesic grid withadaptive mesh refinement which devotes higher resolution mesh at regions of interests increasing the simulation precision while keeping the memory footage at manageable size.[12]
Inbiodiversity 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.[13]
When modeling theweather, ocean circulation, or theclimate,partial differential equations 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 thesenumerical analysis techniques (such asfinite differences) require the area of interest to be subdivided into a grid — in this case, over theshape of the Earth.
Geodesic grids can be used invideo game development to model fictional worlds instead of the Earth. They are a natural analog of thehex map to a spherical surface.[14]
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.
Volume rendering of Geodesic grid[15] applied in atmosphere simulation using Global Cloud Resolving Model (GCRM).[16] The combination of grid illustration and volume rendering of vorticity (yellow tubes).[a]
High quality volume rendering[15] of atmosphere simulation at global scale based on Geodesic grid. The colored strips indicate the simulated atmosphere vorticity strength based on GCRM model.[16]
High quality volume rendering[12] of ocean simulation at global scale based on Geodesic grid. The colored strip indicate the simulated ocean vorticity strength based on MPAS model.[17]
^Cullen, M. J. P. (1974). "Integrations of the primitive equations on a sphere using the finite-element method".Quarterly Journal of the Royal Meteorological Society.100 (426):555–562.Bibcode:1974QJRMS.100..555C.doi:10.1002/qj.49710042605.
^Masuda, Y. Girard1 (1987). "An integration scheme of the primitive equation model with an icosahedral-hexagonal grid system and its application to the shallow-water equations".Short- and Medium-Range Numerical Weather Prediction. Japan Meteorological Society. pp. 317–326.{{cite conference}}: CS1 maint: numeric names: authors list (link)
^abXie, J.; Yu, H.; Maz, K. L. (November 2014).Visualizing large 3D geodesic grid data with massively distributed GPUs. 2014 IEEE 4th Symposium on Large Data Analysis and Visualization (LDAV). pp. 3–10.doi:10.1109/ldav.2014.7013198.ISBN978-1-4799-5215-1.S2CID306780.
^White, D; Kimerling AJ; Overton WS (1992). "Cartographic and geometric components of a global sampling design for environmental monitoring".Cartography and Geographic Information Systems.19 (1):5–22.Bibcode:1992CGISy..19....5W.doi:10.1559/152304092783786636.
^Ringler, Todd; Petersen, Mark; Higdon, Robert L.; Jacobsen, Doug; Jones, Philip W.; Maltrud, Mathew (2013). "A multi-resolution approach to global ocean modeling".Ocean Modelling.69:211–232.Bibcode:2013OcMod..69..211R.doi:10.1016/j.ocemod.2013.04.010.
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