Consistent approximate models of the global atmosphere: Shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic

Quarterly Journal of the Royal Meteorological Society

Volumn 131, Issue 609, 2005, Pages 2081-2107

  White, Andy A ^a   Hoskins, B J ^b   Roulstone, I ^a,c   Staniforth, A ^a  

^a MET OFFICE   (United Kingdom)

^b UNIVERSITY OF READING   (United Kingdom)

^c UNIVERSITY OF SURREY   (United Kingdom)

Author keywords

Apparent gravity; Conservation properties; Coriolis force; Lagrange's equations; Primitive equations

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; VECTORS;

APPARENT GRAVITY; CONSERVATION PROPERTIES; CORIOLIS FORCE; HYDROSTATIC PRIMITIVE EQUATIONS; LAGRANGE EQUATIONS;

METEOROLOGY;

CORIOLIS FORCE; GRAVITY WAVE; HYDROSTATICS;

EID: 27644541433     PISSN: 00359009     EISSN: None     Source Type: Journal    
DOI: 10.1256/qj.04.49     Document Type: Review

References (52)

1. Barnes, R. T. H., Hide, R., White, A. A. and Wilson, C. A. 1983 Atmospheric angular momentum fluctuations, length-of-day changes and polar motion. Proc. R. Soc. London A, 387, 31-73
2. Batchelor, G. K. 1967 An introduction to fluid dynamics. First edition. Cambridge University Press, Cambridge
3. Bretherton, F. P. 1964 Low frequency oscillations trapped near the equator. Tellus, 16, 181-185
4. Colin de Verdière, A. and Schopp, R. 1994 Flows in a rotating spherical shell: the equatorial case. J. Fluid Mech., 276, 233-260
5. Cullen, M. J. P. Daley, R. 1993 The unified forecast/climate model. Meteorol. Mag., 122, 81-94
6. Daley, R. 1988 The normal modes of the spherical non-hydrostatic equations with applications to the filtering of acoustic modes. Tellus, 40A, 96-106
7. Davies, T., Cullen, M. J. P., Malcolm, A. J., Mawson, M. H., Staniforth, A., White, A. A. and Wood, N. 2005 A new dynamical core for the Met Office's global and regional modelling of the atmosphere. Q. J. R. Meteorol. Soc., 131, 1759-1782
8. Draghici, I. 1989 The hypothesis of a marginally shallow atmosphere. Sov. Meteorol. Hydrol., 19, 13-27
9. Durran, D. R. and Bretherton, C. Comments on 'The roles of the horizontal component of the Earth's angular velocity in nonhydrostatic linear models'. J. Atmos. Sci., 61, 1982-1986
10. Dutton, J. A. 1995 Dynamics of atmospheric motion. Second edition. Dover Publications, New York
11. Eckart, C. 1960 The hydrodynamics of oceans and atmospheres. Pergamon Press, Oxford
12. Egger, J. 1999 Inertial oscillations revisited. J. Atmos. Sci., 56, 2951-2954
13. Gates, W. L. 2004 Derivation of the equations of atmospheric motion in oblate spheroidal coordinates. J. Atmos. Sci., 61, 2478-2487
14. Gill, A. 1982 Atmosphere-ocean dynamics. Academic Press, London
15. Goldstein, H. 1980 Classical mechanics. Second edition. Addison-Wesley, New York
16. Holton, J. R. 1992 An introduction to dynamic meteorology. Third edition. Academic Press, New York
17. Kasahara, A. 1974 Various vertical coordinate systems used for numerical weather prediction. Mon. Weather Rev., 102, 509-522
18. Kasahara, A. 2003a On the nonhydrostatic atmospheric models with inclusion of the horizontal component of the earth's angular velocity. J. Meteorol Soc. Jpn, 81, 935-950
19. Kasahara, A. 2003b The roles of the horizontal component of the earth's angular velocity in northydrostatic linear models. J Atmos. Sci., 60, 1085-1095
20. Landau, L. D. and Lifshitz, E. M. 1976 Mechanics. Third edition. Pergamon Press, Oxford
21. Laprise, R. 1992 The Euler equations of motion with hydrostatic pressure as an independent variable. Mon. Weather Rev., 120, 197-207
22. Lorenz, E. N. 1967 The nature and theory of the general circulation of the atmosphere, WMO No. 218-TP. 115. World Meteorological Organization, Geneva
23. Marshall, J., Hill, C., Perelman, L. and Adcroft, A. 1997 Hydrostatic, quasi-hydrostatic, and non-hydrostatic ocean modeling. J. Geophys. Res., 102, 5733-5752
24. Miller, M. J. and Pearce, R. P. 1974 A three-dimensional primitive equation model of cumulonimbus convection. Q. J. R. Meteorol. Soc., 100, 133-154
25. Müller, R. 1989 A note on the relation between the 'traditional approximation' and the metric of the primitive equations. Tellus, 41A, 175-178
26. Newton, C. W. 1971 Global angular momentum balance: Earth torques and atmospheric fluxes. J. Atmos. Sci., 28, 1329-1341
27. Norbury, J. and Roulstone, I. 2002 Large-scale atmosphere-ocean dynamics I and II Cambridge University Press, Cambridge, UK
28. Oates, G. C. 1974 'Vector analysis'. Pp. 127-178 in Handbook of applied mathematics. Ed. C.E. Pearson. Van Nostrand-Reinhold, New York
29. Pedlosky, J. 1987 Geophysical fluid dynamics. Second edition. Springer-Verlag, New York
30. Phillips, N. A. 1968 Reply to 'Comments on Phillips' proposed simplification of the equations of motion for a shallow rotating atmosphere' by G. Veronis. J. Atmos. Sci., 25, 1155-1157
31. Phillips, N. A. 1973 'Principles of large-scale numerical weather prediction'. Pp. 1-96 in Dynamic meteorology. Ed. P. Morel. Reidel, Dordrecht, The Netherlands
32. Phillips, N. A. 1990 Dispersion processes in large-scale weather prediction. World Meteorological Organization Report No. 700, Geneva
33. Richardson, L. F. 1922 Weather prediction by numerical process. Cambridge University Press, Cambridge, UK
34. Roulstone, I. and Brice, S. J. 1995 On the Hamiltonian formulation of the quasi-hydrostatic equations. Q. J. R. Meteorol. Soc., 121, 927-936
35. Salmon, R. 1988 Hamiltonian fluid mechanics. Ann. Rev. Fluid Mech., 20,225-256
36. Salmon, R. 1998 Lectures on geophysical fluid dynamics. Oxford University Press, Oxford
37. Semazzi, F. H. M., Qian, J.-H. and Scroggs, J. S. 1995 A global nonhydrostatic semi-Lagrangian atmospheric model without orography. Mon. Weather Rev., 123, 2534-2550
38. Shepherd, T. G. 1990 Symmetries, conservation laws, and Hamiltonian structure in geo-physical fluid dynamics. Adv. Geophys., 32, 287-338
39. Sivadière, J. 1983 On the analogy between inertial and electromagnetic forces. Eur. J. Phys., 4, 162-164
40. Staniforth, A. 2001 'Developing efficient unified nonhydrostatic models'. Pp. 185-200 in Proceedings of Symposium on 50th Anniversary of NWP, Potsdam, Germany, 9-10 March 2000, Ed. A. Spekat. Deutsche Meteorologische Gesellschaft e.V., Berlin
41. Staniforth, A., Wood, N. and Girard, C. 2003 Energy and energy-like invariants for deep non-hydrostatic atmospheres. Q. J. R. Meteorol. Sci., 129, 3495-3499
42. Tanguay, M., Robert, A. and Laprise, R. 1990 A semi-implicit semi-Lagrangian fully compressible regional forecast model. Mon. Weather Rev., 118, 1970-1980
43. Thuburn, J., Wood, N. and Staniforth, A. 2002a Normal modes of deep atmospheres. I: Spherical geometry. Q. J. R. Meteorol. Soc., 128, 1771-1792
44. Thuburn, J., Wood, N. and Staniforth, A. 2002b Normal modes of deep atmospheres. II: f-F-plane geometry. Q. J. R. Meteorol. Soc., 128, 1793-1806
45. Tomita, H. and Satoh, M. 2004 A new dynamical framework of nonhydrostatic global model using the icosahedral grid. Fluid Dyn. Res., 34, 357-400
46. White, A. A. 1999 'Hydrostatic and quasi-hydrostatic versions of the basic 'New Dynamics' equations'. Available from National Meteorological Library and Archive, Met Office, Exeter, Devon, EX1 3PB, UK. Abstract available via www.metoffice.gov.uk/research/nwp/publications/papers/ technical_reports/index.html
47. White, A. A. 2002 'A view of the equations of meteorological dynamics and various approximations'. Pp. 1-100 in Large-scale atmosphere-ocean dynamics I, Eds. J. Norbury and I. Roulstone. Cambridge University Press, Cambridge
48. White, A. A. 2003 'Primitive equations'. Pp. 694-702 in Encyclopedia of atmospheric science, Eds. J.R. Holton et al. Academic Press, New York
49. White, A. A. and Bromley, R. A. 1995 Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force. Q. J. R. Meteorol. Soc., 121, 399-418
50. Wood, N. and Staniforth, A. 2002 The deep-atmosphere Euler equations with a mass-based vertical coordinate. Q. J. R. Meteorol. Soc., 129, 1289-1300
51. Yeh, K.-S., Coté, J., Gravel, S., Méthot, A., Patoine, A., Roch, M. and Staniforth, A. 2002 The CMC-MRB Global Environmental Multiscale (GEM) model. Part III: Nonhydrostatic formulation. Mon. Weather Rev., 130, 339-356
52. Zdunkowski, W. and Bott, A. 2003 Dynamics of the atmosphere: a course in theoretical meteorology. First edition. Cambridge University Press, Cambridge, UK