Gaussian grid

A Gaussian grid is used in the earth sciences as a grid 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 latitude and longitude), such that they can be easily accessed in a fixed array.

The longitudes are equally spaced, while the latitudes are "not" equally spaced, and are defined by their Gaussian quadrature. There are no grid points at the poles, and the number of longitudes are usually double the number of latitudes.

A "reduced" Gaussian grid can also be used, in which the number of gridpoints in the rows decreases towards the poles, which keeps the grid-point separation approximately constant across the sphere.

Naming conventions

The names of Gaussian grids often have a T, R, or N, followed by a number (e.g., T62). This indicates the type of spectral truncation used and the wavenumber. The T indicates triangular truncation, the R indicates rhomboidal truncation, while the N indicates the largest associated Legendre polynomial for the wavenumber (which is also the number of grid points between the equator and pole). Grid names can also have an L followed again by a number, which indicates the number of vertical levels to the model grid (e.g., CGCM2 has a T32L10 atmospheric grid).

Examples of Gaussian grids

* NCEP/NCAR Reanalysis Project from historic weather observations [http://www.cdc.noaa.gov/cdc/reanalysis/reanalysis.shtml]
** T62 – 144×73
* CCCma global climate models of climate change
** [http://www.cccma.bc.ec.gc.ca/data/grids/geom_llg_97x48.shtml 97×48] - T32 resolution used for CGCM1 and CGCM2 (same as 96×48 grid below, except repeat 0 and 360 longitudes)
** [http://www.cccma.ec.gc.ca/data/grids/geom_llg_96x48.shtml 96×48] – T47 resolution used for CGCM3
** [http://www.cccma.ec.gc.ca/data/grids/geom_llg_128x64.shtml 128×64] – T63 resolution also used for CGCM3
* European Centre for Medium-Range Weather Forecasts [http://www.ecmwf.int/products/data/technical/gaussian/]
** [http://www.ecmwf.int/publications/manuals/libraries/interpolation/n48FIS.html N48] – 192×96
** [http://www.ecmwf.int/publications/manuals/libraries/interpolation/n80FIS.html N80] – 320×160
** [http://www.ecmwf.int/publications/manuals/libraries/interpolation/n128FIS.html N128] – 512×126
** [http://www.ecmwf.int/publications/manuals/libraries/interpolation/n160FIS.html N160] – 640×320
** [http://www.ecmwf.int/publications/manuals/libraries/interpolation/n200FIS.html N200] – 800×400
** [http://www.ecmwf.int/publications/manuals/libraries/interpolation/n256FIS.html N256] – 1024×512
** [http://www.ecmwf.int/publications/manuals/libraries/interpolation/n400FIS.html N400] – 1600×800
** [http://www.ecmwf.int/publications/manuals/libraries/interpolation/n512FIS.html N512] – 2048×1024

See also

*Global climate model
*Spectral method
*Spherical harmonics

References

* [http://www.ncl.ucar.edu/Document/Functions/sphpk_grids.shtml#GaussianGrids NCAR Command Language documentation]
*W.M. Washington and C.L. Parkinson, 2005. An Introduction to Three-Dimensional Climate Modeling. Sausalito, CA, University Science Books. 368 pp.