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The Arakawa grid system depicts different ways to represent and compute 
orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
physical quantities
A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...
(especially velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
- and mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
-related quantities) on rectangular grids used for Earth system models for meteorology
Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
and oceanography
Oceanography (), also known as oceanology and ocean science, is the scientific study of the oceans. It is an Earth science, which covers a wide range of topics, including ecosystem dynamics; ocean currents, waves, and geophysical fluid dynamic ...
. For example, the Weather Research and Forecasting Model uses the Arakawa Staggered C-Grid in its atmospheric calculations when using the ARW core. The five Arakawa grids (A-E) were first introduced in Arakawa and Lamb 1977.
For an image of the five grids, see the following picture, or Fig. 1 in Purser and Leslie 1988.
Arakawa A-grid
The "unstaggered" Arakawa A-grid evaluates all quantities at the same point on each grid cell, e.g., at the grid center or at the grid corners. The Arakawa A-grid is the only unstaggered grid type.Arakawa B-grid
The "staggered" Arakawa B-grid separates the evaluation of the two sets of quantities. e.g., one might evaluate velocities at the grid center and masses at grid corners.Arakawa C-grid
The "staggered" Arakawa C-grid further separates evaluation of vector quantities compared to the Arakawa B-grid. e.g., instead of evaluating both east-west (u) and north-south (v) velocity components at the grid center, one might evaluate the u components at the centers of the left and right grid faces, and the v components at the centers of the upper and lower grid faces.Arakawa D-grid
An Arakawa D-grid is a 90° rotation of an Arakawa C-grid. E.g., instead of evaluating the v velocity components at the centers of the upper/lower grid faces and the u velocity components at the centers of the right/left grid faces, one would evaluate the v velocity components at the centers of the right/left grid faces and the u velocity components at the centers of the upper/lower grid faces.Arakawa E-grid
The Arakawa E-grid is "staggered," but also rotated 45° relative to the other grid orientations. This allows all variables to be defined along a single face of the rectangular domain.References
Further reading
*Haltiner, G. J., and R. T. Williams, 1980. Numerical Prediction and Dynamic Meteorology. John Wiley and Sons, New York. {{DEFAULTSORT:Arakawa Grids Numerical climate and weather models