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In geophysical fluid dynamics, an approximation whereby the Coriolis parameter, f, is set to vary linearly in space is called a beta plane approximation.
On a rotating sphere such as the Earth, f varies with the sine of latitude; in the so-called f-plane approximation, this variation is ignored, and a value of f appropriate for a particular latitude is used throughout the domain. This approximation can be visualized as a tangent plane touching the surface of the sphere at this latitude.
A more accurate model is a linear Taylor series approximation to this variability about a given latitude ϕ 0 {\displaystyle \phi _{0}} :
f = f 0 + β y {\displaystyle f=f_{0}+\beta y} , where f 0 {\displaystyle f_{0}} is the Coriolis parameter at ϕ 0 {\displaystyle \phi _{0}} , β = | ϕ 0 = 2 Ω cos / a {\displaystyle \beta =|_{\phi _{0}}=2\Omega \cos/a} is the Rossby parameter, y {\displaystyle y} is the meridional distance from ϕ 0 {\displaystyle \phi _{0}} , Ω {\displaystyle \Omega } is the angular rotation rate of the Earth, and a {\displaystyle a} is the Earth's radius.