A geometrical view of the shallow-atmosphere approximation, with application to the semi-Lagrangian departure point calculation

Quarterly Journal of the Royal Meteorological Society

Volumn 139, Issue 670, 2013, Pages 261-268

  Thuburn, J ^a   White, A A ^b  

^a UNIVERSITY OF EXETER   (United Kingdom)

^b MET OFFICE   (United Kingdom)

Author keywords

Geodesic; Instability; Position vector; Riemannian geometry; Rotation matrix

Indexed keywords

CRANK-NICOLSON; DISCRETIZATIONS; DYNAMICAL CORE; EUCLIDEAN; EUCLIDEAN METRICS; GEODESIC; NON-EUCLIDEAN; NON-EUCLIDEAN GEOMETRY; POSITION VECTOR; RIEMANNIAN GEOMETRY; ROTATION MATRICES; SEMI-IMPLICIT; SEMI-LAGRANGIAN; VERTICAL COMPONENT;

GEOMETRY; MACHINERY; PLASMA STABILITY; VECTOR SPACES; VECTORS;

EARTH ATMOSPHERE;

ATMOSPHERE; EARTH ROTATION; GEODESY; GEOMETRY; LAGRANGIAN ANALYSIS; NUMERICAL MODEL; VECTOR;

EID: 84873313438     PISSN: 00359009     EISSN: 1477870X     Source Type: Journal    
DOI: 10.1002/qj.1962     Document Type: Article

References (17)

1. Bannon PR, Bishop CH, Kerr JB. 1997. Does the surface pressure equal the weight per unit area of a hydrostatic atmosphere? Bull. Amer. Meteorol. Soc. 78: 2637-2642.
2. Côté J. 1988. A Lagrange multiplier approach for the metric terms of semi-Lagrangian models on the sphere. Q. J. R. Meteorol. Soc. 114: 1347-1352.
3. Daley R. 1988. The normal modes of the spherical non-hydrostatic equations with applications to the filtering of acoustic modes. Tellus 40A: 96-106.
4. Melvin T, Dubal M, Wood N, Staniforth A, Zerroukat M. 2010. An inherently mass-conserving iterative semi-implicit semi-Lagrangian discretization of the non-hydrostatic vertical-slice equations. Q. J. R. Meteorol. Soc. 136: 799-814.
5. Müller R. 1989. A note on the relation between the 'traditional approximation' and the metric of the primitive equations. Tellus 41A: 175-178.
6. Phillips NA. 1966. The equations of motion for a shallow rotating atmosphere and the 'traditional approximation'. J. Atmos. Sci. 23: 626-628.
7. Salmon R. 1998. Lectures in Geophysical Fluid Dynamics. Oxford University Press: Oxford, UK.
8. Schutz B. 1980. Geometrical Methods in Mathematical Physics. Cambridge University Press: Cambridge, UK.
9. Staniforth A, White AA, Wood N. 2010. Treatment of vector equations in deep-atmosphere, semi-Lagrangian models. I: Momentum equation. Q. J. R. Meteorol. Soc. 136: 497-506.
10. Temperton C, Hortal M, Simmons A. 2001. A two-time-level semi-Lagrangian spectral model. Q. J. R. Meteorol. Soc. 127: 111-127.
11. Thuburn J, Wood N, Staniforth A. 2002. Normal modes of deep atmospheres. I: Spherical geometry. Q. J. R. Meteorol. Soc. 128: 1771-1792.
12. Thuburn J, Zerroukat M, Wood N, Staniforth A. 2010. Coupling a mass conserving semi-Lagrangian scheme (SLICE) to a semi-implicit discretization of the shallow-water equations: minimizing the dependence on a reference atmosphere. Q. J. R. Meteorol. Soc. 136: 146-154.
13. White AA. 2003. Dynamical equivalence and the departure-point equation in semi-Lagrangian numerical models. Q. J. R. Meteorol. Soc. 129: 1317-1324.
14. White AA, Hoskins BJ, Roulstone I, Staniforth A. 2005. Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic. Q. J. R. Meteorol. Soc. 131: 2081-2107.
15. Wood N, Staniforth A, White AA. 2009. Determining near-boundary departure points in semi-Lagrangian models. Q. J. R. Meteorol. Soc. 135: 1890-1896.
16. Wood N, White AA, Staniforth A. 2010. Treatment of vector equations in deep-atmosphere, semi-Lagrangian models. II: Kinematic equation. Q. J. R. Meteorol. Soc. 136: 507-516.
17. Zerroukat M, Wood N, Staniforth A, White AA, Thuburn J. 2009. An inherently mass-conserving semi-implicit semi-Lagrangian discretisation of the shallow-water equations on the sphere. Q. J. R. Meteorol. Soc. 135: 1104-1116.