From AMS Glossary
The derivative of the Coriolis parameter with respect to latitude.
The beta-plane approximation, useful for the study of equatorial and midlatitude flow, assumes that the Coriolis parameter varies linearly with latitude. Explicitly, the Coriolis parameter is given approximately by
in which y is the meridional distance from some fixed latitude where the Coriolis parameter is f0 and β (from which the beta plane gets its name) is the meridional gradient of f at that fixed latitude.