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The Arakawa grid system depicts different ways to represent and compute 
orthogonal
In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geometric notion of ''perpendicularity''. Although many authors use the two terms ''perpendicular'' and ''orthogonal'' interchangeably, the term ''perpendic ...
physical quantities
A physical quantity (or simply quantity) is a 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 '' ...
(especially velocity
Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical q ...
- and mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
-related quantities) on rectangular grids used for Earth system models for meteorology
Meteorology is the scientific study of the Earth's atmosphere and short-term atmospheric phenomena (i.e. weather), with a focus on weather forecasting. It has applications in the military, aviation, energy production, transport, agricultur ...
and oceanography
Oceanography (), also known as oceanology, sea science, ocean science, and marine science, is the scientific study of the ocean, including its physics, chemistry, biology, and geology.
It is an Earth science, which covers a wide range of to ...
. 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. (Note that the picture is incorrect; Arakawa C staggering has the velocities perpendicular to the cell 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. (Note that the picture is incorrect; the velocities are tangential to the cell 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