This memo is a specific application of "Continuity equation for non-spherical geometries..." for the case of a spherical planet with meridionally varying gravity but shallow-atmosphere approximation.

This specific case may be implemented with very minimal changes to the existing code, while allowing to assess the magnitude of gravity errors of the spherical approximation.

This memo describes an application of the parent memorandum "Continuity equation for non-spherical geometries...", for the special case of a spherical planet with meridionally varying gravity but shallow-atmosphere approximation.

This specific case may be implemented with very minimal changes to the existing ARPEGE code, while allowing to assess the magnitude of "gravity errors" of the spherical approximation. This case does not allow to assess the "geometric errors" of the scpherical approximation. See details in BÃ©nard 2014a, 2014b in Q. J. R. Meteor. Soc.