Dynamically consistent, quasi‐hydrostatic equations for global models with a complete representation of the Coriolis force

Abstract

The spherical polar components of the Coriolis force consist of terms in sin ϕ and terms in cos ϕ, where ϕ is latitude (referred to the frame‐rotation vector as polar axis). The cos ϕ Coriolis terms are not retained in the usual hydrostatic primitive equations of numerical weather prediction and climate simulation, their neglect being consistent with the shallow‐atmosphere approximation and the simultaneous exclusion of various small metric terms. Scale analysis for diabatically driven, synoptic‐scale motion in the tropics, and for planetary‐scale motion, suggests that the cos ϕ Coriolis terms may attain magnitudes of order 10% of those of key terms in the hydrostatic primitive equations. It is argued that the cos ϕ Coriolis terms should be included in global simulation models. A global, quasi‐hydrostatic model having a complete representation of the Coriolis force is proposed. Conservation of axial angular momentum and potential vorticity, as well as energy, is achieved by a formulation in which all metric terms are retained and the shallow‐atmosphere approximation is relaxed. Distance from the centre of the earth is replaced by a pseudo‐radius which is a function of pressure only. This model is put forward as a more accurate alternative to the traditional hydrostatic primitive equations; it preserves the desired conservation laws and may be integrated by broadly similar grid‐point methods. Copyright © 1995 Royal Meteorological Society