Consistent approximate models of the global atmosphere in non‐spherical geopotential coordinates

Abstract

Abstract Taking the spherical geopotential approximation as a starting point, previous work has revealed a quartet of dynamically consistent models of the global atmosphere according to whether approximations of shallow and quasi‐hydrostatic type are or are not made. The generalization of this quartet of consistent models is sought within the framework of geopotential surfaces that are zonally symmetric but not assumed to be spherical. The distinction between approximations of shallow and quasi‐hydrostatic type is more subtle than in the spherical case: consistent quasi‐hydrostatic approximation requires the simultaneous omission of two metric terms that vanish identically in the spherical case (and indeed whenever the vertical metric factor is independent of the meridional coordinate). These two metric terms are not eliminated by the formal process of metric factor approximation by which consistent models of shallow type may be generated. Consistently approximated, hydrostatic, shallow forms are obtained by applying quasi‐hydrostatic and shallow approximations successively, and are comparable with the well‐known spherical geopotential forms as regards the number and nature of the terms present. The formulation of shallow‐water models in non‐spherical geopotential coordinates is considered in conclusion. Copyright © 2011 British Crown copyright, the Met Office. Published by John Wiley & Sons Ltd.