# Beta plane

From AMS Glossary

## beta plane

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 cosφ

_{0})/*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*=*f*_{0}, when it appears in undifferentiated form. Although it applies precisely to no physical situation, this model has gained wide acceptance in dynamic meteorology.