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Geophysically Realistic, Ellipsoidal, Analytically Tractable (GREAT) coordinates for atmospheric and oceanic modelling
Author(s) -
Staniforth Andrew,
White Andy
Publication year - 2014
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.2467
Subject(s) - geopotential , geopotential height , coordinate system , ellipsoid , spherical coordinate system , gravitational field , hydrostatic equilibrium , geodesy , geology , geometry , physics , meteorology , classical mechanics , mathematics , precipitation , quantum mechanics
Suitable models of Earth's geopotential field provide foundations for developing geopotential coordinate systems for modelling Earth's atmosphere and oceans. Earth's geopotential surfaces are traditionally represented as spheres. However, the suitability of this spherical representation for state‐of‐the‐science models is debatable: the geopotentials are more accurately approximated by ellipsoids. A new, ellipsoidal, geopotential approximation is proposed. It is not based on confocal or similar ellipses (as used in previous studies) but is nevertheless relatively simple and analytically tractable. It properly represents the underlying physics, and gives geophysically realistic horizontal and vertical variation of apparent gravity. Exploiting this geopotential approximation, an orthogonal, ellipsoidal, geopotential coordinate system for atmospheric and oceanic modelling is developed analytically and in a self‐consistent manner. By construction, the horizontal coordinate surfaces coincide with geopotential surfaces. This ensures that there is no component of apparent gravity in any direction tangential to coordinate surfaces. Accurate representation of intrinsic horizontal and vertical force balances, such as geostrophic and hydrostatic balance, is thereby facilitated. The proposed coordinate system has the potential not only to improve the quality of terrestrial model forecasts in the future, but to be used to model the atmospheres and oceans of mildly oblate planetary bodies, and also for space weather simulation.