From AMS Glossary
The model, introduced by C. G. Rossby, of the spherical earth as a plane with a rate of rotation f (corresponding to the Coriolis parameter) that varies linearly with the north–south direction y:
The constant β (the Rossby parameter) is given its value at a central latitude on the spherical earth, (2Ω cosφ0)/a, where Ω is the angular speed of the earth and a its mean radius. Used chiefly in association with the vorticity equation, this model is usually accompanied by the assumption that the Coriolis parameter is constant, f = f0, when it appears in undifferentiated form. Although it applies precisely to no physical situation, this model has gained wide acceptance in dynamic meteorology.