Spectral transform methods for solving the shallow-water equations on the sphere

Monthly Weather Review

Volumn 124, Issue 4, 1996, Pages 730-744

  Swarztrauber, Paul N ^a  

^a NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001366216     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0493(1996)124<0730:STMFST>2.0.CO;2     Document Type: Article

References (19)

1. Baede, A. P. M., M. Jarraud, and U. Cubasch, 1979: Adiabatic formulation and organization of ECMWF's model. ECMWF Tech. Rep. No. 15, 40 pp. [Available from ECMWF, Shinfield Park, Reading, Berkshire, RG2 9AX, England.]
2. Bourke, W., 1972: An efficient, one-level, primitive-equation spectral model. Mon. Wea. Rev., 100, 683-698
3. _, B. McAvaney, K. Puri, and R. Thurling, 1977: Global modeling of atmospheric flow by spectral methods. General Circulation Models of the Atmosphere, Methods of Computational Physics, Academic Press, 268-324.
4. Browning, G. L., J. J. Hack, and P. N. Swarztrauber, 1989: A comparison of three numerical methods for solving differential equations on the sphere. Mon. Wea. Rev., 117, 1058-1075.
5. Eliasen, E., B. Machenhauer, and E. Rasmussen, 1970: On a numerical method for integration of the hydrodynamical equations with a spectral representation of the horizontal fields. Rep. No. 2, Institut for Teoretisk Meteorologi, Kobenhavns Universitet, Denmark, 37 pp.
6. Hack, J. J., and R. Jakob, 1992: Description of a global shallow water model based on the spectral transform method. NCAR/TN-343+STR, National Center for Atmospheric Research, Boulder, CO, 39 pp.
7. Kasahara, A., 1980: Effect of zonal flows on the free oscillations of a barotropic atmosphere. J. Atmos. Sci., 37, 917-929.
8. Machenhauer, B., 1979: The spectral method. Numerical Methods Used in Atmospheric Models, GARP Publication Series, Vol. 17, World Meteor. Org., 121-275.
9. _, and R. Daley, 1972: A baroclinic primitive equation model with spectral representation in three dimensions. Rep. No. 4, Institut for Teoretisk Meteorologi, Kobenhavns Universitet, Denmark, 63 pp.
10. _, and E. Rasmussen, 1972: On the integration of the spectral hydrodynamical equations by a transform method. Rep. No. 3, Institut for Teoretisk Meteorologi, Kobenhavns Universitet, Denmark, 44 pp.
11. Orszag, S. A., 1970: Transform method for the calculation of vector coupled sums: Application to the spectral form of the vorticity equation. J. Atmos. Sci., 27, 890-895.
12. Ritchie, H., 1988: Application of the semi-Lagrangian method to a spectral model of the shallow water equations. Mon. Wea. Rev., 116, 1587-1598.
13. Robert, A. J., 1966: The integration of a low order spectral form of the primitive meteorological equations. J. Meteor. Soc. Japan, 44, 237-245.
14. Swarztrauber, P. N., 1979: On the spectral approximation of discrete scalar and vector functions on the sphere. SIAM J. Numer. Anal., 16, 934-949.
15. _, 1981: The approximation of vector functions and their derivatives on the sphere. SIAM J. Numer. Anal., 18, 191-210.
16. _, 1993: The vector harmonic transform method for solving partial differential equations in spherical geometry. Mon. Wea. Rev., 121, 3415-3437.
17. Temperton, C., 1991: On scalar and vector transform methods for global spectral models. Mon. Wea. Rev., 119, 1303-1307
18. Williamson, D. L., J. T. Kiehl, V. Ramanathan, R. E. Dickinson, and J. J. Hack, 1987: Description of NCAR Community Climate Model (CCM1), NCAR Tech. Rep. TN-285+STR, National Center for Atmospheric Research, Boulder, CO, 112 pp.
19. _, J. B. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, 1992: A standard test set for numerical approximations to the shallow water equations in spherical geometry. J. Comp. Phys., 102, 211-224.