A finite-element scheme for the vertical discretization of the semi-Lagrangian version of the ECMWF forecast model

Quarterly Journal of the Royal Meteorological Society

Volumn 130, Issue 599 PART B, 2004, Pages 1505-1530

  Untch, A ^a   Hortal, M ^a  

^a EUROPEAN CENTRE FOR MEDIUM RANGE WEATHER FORECASTS   (United Kingdom)

Author keywords

B splines; Charney Phillips staggering; Eigenmodes; Galerkin method; Hat functions; Integral operator; Lorenz staggering

Indexed keywords

COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; GRAVITY WAVES; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; UPPER ATMOSPHERE;

LINEAR GRAVITY WAVES; LORENZ STAGGERING;

WEATHER FORECASTING;

FINITE ELEMENT METHOD; FORECASTING METHOD; MATHEMATICAL ANALYSIS; WEATHER FORECASTING;

EID: 2942522394     PISSN: 00359009     EISSN: None     Source Type: Journal    
DOI: 10.1256/qj.03.173     Document Type: Article

References (22)

1. Arakawa, A. and Konor, C. S. 1996 Vertical differencing of the primitive equations based on the Charney-Phillips grid in hybrid vertical coordinates. Mon. Weather Rev., 124, 511-528
2. Becker, E. B., Carey, G. F. and Oden, J. T. 1981 Finite elements: An introduction. Volume 1. Prentice-Hall Inc., Englewood Cliffs, New Jersey, USA
3. Beland, M., Cote, J. and Staniforth, A. 1983 The accuracy of a finite-element vertical discretization scheme for primitive equation models: Comparison with a finite difference scheme. Mon. Weather Rev., 111, 2298-2318
4. Burridge, D. M., Steppeler, J. and Strüffing, R. 1986 'Finite element schemes for the vertical discretization of the ECMWF forecast model using linear elements'. Technical Report No. 54. ECMWF, Shinfield Park, Reading, UK
5. Charney, J. G. and Phillips, N. A. 1953 Numerical integration of the quasi-geostrophic equations for barotropic and simple baroclinic flows. J. Meteorol., 10, 71-99
6. Cullen, M. J. P. 2002 'Use of potential vorticity as a control variable within a 4D variational data assimilation system'. Technical Memorandum 358. ECMWF, Shinfield Park, Reading, UK
7. Francis, P. E. 1972 The possible use of Laguerre polynomials for representing the vertical structure of numerical models of the atmosphere. Q. J. R. Meteorol. Soc., 98, 662-667
8. Gibson, J. K., Fiorino, M., Hernandez, A., Kållberg, P., Li, X., Onogi, K., Saarinen, S. and Uppala, S. 1999 'The ECMWF 40-Year Re-Analysis (ERA-40) Project-Plans and current status'. Pp. 369-372 of Proceedings of the tenth symposium on global change. American Meteorological Society. Boston, USA
9. Hollingsworth, A. 1995 'A spurious mode in the 'Lorenz' arrangement of φ and T which does not exist in the 'Charney-Phillips' arrangement'. Technical Memorandum 211. ECMWF, Shinfield Park, Reading, UK
10. Hoskins, B. 1973 Comments on 'The possible use of Laguerre polynomials for representing the vertical structure of numerical models of the atmosphere' by P. E. Francis, Q. J. R. Meteorol. Soc., 99, 571-572
11. Lorenz, E. N. 1960 Energy and numerical weather prediction. Tellus, 12, 364-373
12. Machenhauer, B. and Daley, R. 1972 'A baroclinic primitive equation model with a spectral representation in three dimensions'. Report 4, Institut for Teoretisk Meteorologi, University of Copenhagen, Denmark
13. Oden, J. T. and Reddy, J. N. 1976 An introduction to the mathematical theory of finite elements. Springer-Verlag, Berlin, Germany
14. Prenter, P. M. 1975 Splines and variational methods. John Wiley and Sons. New York, USA
15. Ritchie, H., Temperton, C., Simmons, A. J., Hortal, M., Davies, T., Dent, D. and Hamrud, M. 1995 Implementation of the semi-Lagrangian method in a high-resolution version of the ECMWF forecast model. Mon. Weather Rev., 123, 489-514
16. Simmons, A. J. and Burridge, D. M. 1981 An energy and angular momentum conserving vertical finite difference scheme and hybrid vertical coordinates. Mon. Weather Rev., 109, 758-766
17. Simmons, A. J. and Strüfing, R. 1983 Numerical forecasts of stratospheric warming events using a model with hybrid vertical coordinates. Q. J. R. Meteorol. Soc., 109, 81-111
18. Simmons, A. J. and Temperton, C. 1997 Stability of a two-time-level semi-implicit integration scheme for gravity wave motion. Mon. Weather Rev., 125, 600-615
19. Staniforth, A. N. and Daley, R. W. 1977 A finite-element formulation for the vertical discretization of sigma-coordinate primitive equation models. Mon. Weather Rev., 105, 1108-1118
20. Steppeler, J. 1986 'Finite elements scheme for the vertical discretization of the ECMWF forecast model using quadratic and cubic elements'. Technical Report No. 55. ECMWF, Shinfield Park, Reading, UK
21. Steppeler, J. 1987 Quadratic Galerkin finite element schemes for the vertical discretization of numerical models. Mon. Weather Rev., 115, 1575-1588
22. Tokioka, T. 1978 Some considerations on vertical differencing. J. Meteorol. Soc. Jpn. 56, 89-111