Coriolis parameter ($f$)

The Coriolis parameter is $f=2\Omega \sin \phi$ for planetary rotation rate $\Omega$ and latitude $\phi$. It controls the vertical component of the Coriolis acceleration acting on horizontal flow.

An f-plane approximates the Coriolis parameter by a constant $f_0$ over a limited horizontal region.

A beta plane retains the leading meridional variation $f=f_0+\beta y$ of the Coriolis parameter.