Notes. Φ and G are the geopotential and gravitational constant respectively. M_p and M_atm are the total masses of the planet below the inner boundary, and of the atmosphere, respectively. z is the vertical height from the inner boundary. H and L are the vertical and horizontal sizes of the atmospheric domain. Finally, N is the buoyancy (or Brunt-Väisälä) frequency, . SI units are used unless otherwise stated.

Reference. (1) For a full discussion on the impact of the spherical geopotentials approximation see White et al. (2008). (2) This condition neglects tidal deformation, essentially assuming the planetary gravitational field is well isolated (see discussion in text). (3) Condition from Phillips (1968), but may not be sufficient (see discussion in White & Bromley 1995).