DYNAMICALLY CONSISTENT, QUASI-HYDROSTATIC EQUATIONS FOR GLOBAL-MODELSWITH A COMPLETE REPRESENTATION OF THE CORIOLIS-FORCE

The spherical polar components of the Coriolis force consist of terms in sin phi and terms in cos phi, where phi is latitude (referred to th e frame-rotation vector as polar axis). The cos phi Coriolis terms are not retained in the usual hydrostatic primitive equations of numerica l weather prediction and climate simulation, their neglect bring consi stent with the shallow-atmosphere approximation and the simultaneous e xclusion of various small metric terms. Scale analysis for diabaticall y driven, synoptic-scale motion in the tropics, and for planetary-scal e motion, suggests that the cos phi Coriolis terms may attain magnitud es of order 10% of those of key terms in the hydrostatic primitive equ ations. It is argued that the cos phi Coriolis terms should be include d in global simulation models. A global, quasi-hydrostatic model havin g a complete representation of the Coriolis force is proposed. Conserv ation of axial angular momentum and potential vorticity, as well as en ergy, is achieved by a formulation in which all metric terms are retai ned and the shallow-atmosphere approximation is relaxed. Distance from the centre of the earth is replaced by a pseudo-radius which is a fun ction of pressure only. This model is put forward as a more accurate a lternative to the traditional hydrostatic primitive equations; it pres erves the desired conservation laws and may be integrated by broadly s imilar grid-point methods.