Arakawa grids#Arakawa E-grid

{{Short description|Method of representing orthogonal quantities}}

The Arakawa grid system depicts different ways to represent and compute orthogonal physical quantities (especially velocity- and mass-related quantities) on rectangular grids used for Earth system models for meteorology and oceanography. 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.{{Cite journal | last = Arakawa | first = A. | last2 = Lamb | first2 = V.R. | title = Computational design of the basic dynamical processes of the UCLA general circulation model | journal = Methods in Computational Physics: Advances in Research and Applications | volume = 17 | pages = 173–265 | year = 1977 | doi = 10.1016/B978-0-12-460817-7.50009-4 | isbn = 9780124608177 }}

For an image of the five grids, see the following picture, or Fig. 1 in Purser and Leslie 1988.{{Cite journal | last = Purser | first = R. J. | first2 = L. M. | last2 = Leslie | title = A Semi-Implicit, Semi-Lagrangian Finite-Difference Scheme Using Hligh-Order Spatial Differencing on a Nonstaggered Grid | journal = Monthly Weather Review | volume = 116 | issue = 10 | pages = 2069–2080 | date = October 1988 | issn = 0027-0644 | doi = 10.1175/1520-0493(1988)116<2069:ASISLF>2.0.CO;2 | doi-access = free }}

File:Discretization for the different Arakawa grids correct.svg

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.