A semi-Lagrangian double Fourier method for the shallow water equations on the sphere

Journal of Computational Physics

Volumn 189, Issue 1, 2003, Pages 180-196

  Layton, Anita T ^a   Spotz, William F ^b  

^a University of North Carolina at Chapel Hill   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Double Fourier series; Numerical weather prediction; Semi implicit scheme; Semi Lagrangian scheme; Shallow water equations; Spectral methods; Spherical coordinates

Indexed keywords

COMPUTATIONAL COMPLEXITY; DISCRETE EVENT SIMULATION; EQUATIONS OF MOTION; FOURIER SERIES; LAGRANGE MULTIPLIERS; NUMERICAL METHODS; SPHERES; WEATHER FORECASTING;

DOUBLE FOURIER SERIES; FOURIER METHODS; NUMERICAL WEATHER PREDICTION; SEMI-IMPLICIT SCHEME; SEMI-LAGRANGIAN; SEMI-LAGRANGIAN SCHEME; SHALLOW WATER EQUATIONS; SPECTRAL METHODS; SPECTRAL TRANSFORM METHOD; SPHERICAL COORDINATES;

FAST FOURIER TRANSFORMS;

EID: 0038454598     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00207-9     Document Type: Article

References (30)

1. R.A. Asselin, Frequency filter for time integration, Mon, Weather Rev. 100 (1972) 487-490.
2. J.R. Bates, A. McDonald, Multiply-upstream, semi-Lagrangian advection schemes: analysis and application to a multi-level primitive equation model, Mon. Weather Rev. 110 (December) (1982) 1831-1842.
3. H.-B. Cheong, Application of double Fourier series to the shallow-water equations on a sphere, J. Comput. Phys. 165 (2000) 261-287, doi:10.1006/jcp.2000.6615.
4. H.-B. Cheong, Double Fourier series on a sphere: application to elliptic and vorticity equations, J. Comput. Phys. 157 (2000) 327-349, doi:10.1006/jcp.1999.6385.
5. J. Côté, A. Staniforth, A two-time-level semi-Lagrangian semi-implicit scheme for spectral models, Mon. Weather Rev. 116. (October) (1988) 2003-2012.
6. J. Côté, A. Staniforth, An accurate and efficient finite-element global model of the shallow water equations, Mon. Weather Rev. 118 (December) (1990) 2707-2717.
7. B. Haurwitz, The motion of atmospheric disturbances at the spherical earth, J. Mar. Res. (1940) 254-267.
8. M. Hortal, Aspects of numerics of the ECMWF model. In: Proceedings of a Seminar Held at ECMWF on Recent Developments in Numerical Methods for Atmospheric Modeling, European Centre for Medium-Range Weather Forecasts, 1999.
9. R. Jakob, J.J. Hack, and D.L. Williamson, Solutions to the shallow water test set using the spectral transform method, Technical report, National Center for Atmospheric Research, 1993, NCAR/TN-388+STR.
10. A.T. Layton, Cubic spline collocation method for the shallow water equations on the sphere, J. Comput. Phys. 179 (2002) 1-15, doi:10.1006/jcp.2002.7075..
11. P.E. Merilees, The pseudospectral approximation applied to the shallow water equations on the sphere, Atmosphere 11 (1) (1973) 13-20.
12. S.A. Orszag, Fourier series on spheres, Mon. Weather Rev. 102 (January) (1974) 56-75.
13. H. Ritchie, Application of the semi-Lagrangian method on a spectral model of the shallow water equations, Mon. Weather Rev. 116 (1988) 1587-1598.
14. A. Robert, The integration of a low order spectral form of the primitive meteorological equations, J. Meteor. Soc. Jpn. 44 (2) (1966) 237-245.
15. A. Robert, The integration of a spectral model of the atmosphere by the implicit method. In: Proceedings of the WMO/IUGG Symposium on NWP in Tokyo, Jap. Met. Agency, 1969, pp. VII.19-VII.24.
16. A. Robert, A semi-Lagrangian, semi-implicit numerical integration scheme for the primitive meteorological equations, Atmos. Ocean 19 (1981) 35-46.
17. A. Robert, A stable numerical integration scheme for the primitive meteorological equations, Atmos. Ocean 19 (1) (1981) 35-46.
18. A. Robert, J. Henderson, C. Turnbull, An implicit time integration scheme for barochlinic models of the atmosphere, Mon. Weather Rev. 100 (1972) 329-335.
19. W.F. Spotz, P.N. Swarztrauber, A performance comparison of associated Legendre projections, J. Comput. Phys. 168 (2001) 330-355.
20. W.F. Spotz, M.A. Taylor, P.N. Swarztrauber, Fast shallow-water equation solvers in latitude-longitude coordinates, J. Comput. Phys. 145 (1998) 432-444.
21. A. Staniforth, J. Côté, Semi-Lagrangian integration schemes for atmospheric models - a review, Mon. Weather Rev. 119 (September) (1991) 2206-2223.
22. P.N. Swarztrauber, Spectral transform methods for solving the shallow-water equations on the sphere, Mon. Weather Rev. 124 (April) (1996) 730-743.
23. S. Thomas, J. Côté, and A. Staniforth, A semi-implicit semi-Lagrangian shallow-water model for massively parallel processors. ECMWF Workshop on the Use of Parallel Processors in Meteorology, 1993.
24. S.J. Thomas, J. Côté, Massively parallel semi-Lagrangian advection, J. Sim. Theory and Practice 3 (1995) 223-238.
25. M.A. Tolstykh, Vorticity-divergence semi-Lagrangian shallow-water model on the sphere based on compact finite differences, J. Comput. Phys. 179 (2002) 180-200.
26. D.L. Williamson, G.L. Browning, Comparison of grids and difference approximations for numerical weather prediction over a sphere, J. Appl. Meteorol. 12 (1973) 264-274.
27. D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, P.N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1) (1992) 211-224.
28. D.L. Williamson, J.G. Olson, Climate simulations with a semi-Lagrangian version of the NCAR Community Climate model, Mon. Weather Rev. 122 (1993) 1594-1610.
29. S.Y.K. Yee, Studies on Fourier series on spheres, Mon. Weather Rev. 108 (May) (1980) 676-678.
30. S.Y.K. Yee, Solution of Poisson's equation on a sphere by truncated double Fourier series, Mon. Weather Rev. 109 (1981) 501-505.