On the approximations involved in transforming the equations of motion from a spherical surface to the β-plane. II. Baroclinic systems
When the hydrodynamic equations of motion for large-scale geophysical flows are transformed from a spherical surface to the p-plane, the validity and usefulness of the resulting simplified system of equations are subject to certain restrictive conditions. These conditions are investigated and are found to be considerably weaker for baroclinic flows than for barotropic flows. In particular, if the locally horizontal component of the earth's rotation vector is to be neglected, it is necessary that the ratio of a characteristic vertical to a characteristic horizontal scale be much smaller than the tangent of the latitude....
Veronis, George. 1963. "On the approximations involved in transforming the equations of motion from a spherical surface to the β-plane. II. Baroclinic systems." Journal of Marine Research 21, (3). https://elischolar.library.yale.edu/journal_of_marine_research/1007