A semi-implicit semi-Lagrangian finite-element shallow-water ocean model

Monthly Weather Review

Volumn 128, Issue 5, 2000, Pages 1384-1401

  Le Roux, Daniel Y ^a,c   Lin, Charles A ^a   Staniforth, Andrew ^b,d  

^a MCGILL UNIVERSITY   (Canada)

^b ENVIRONMENT CANADA   (Canada)

^c NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

^d MET OFFICE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT ANALYSIS; LAGRANGIAN ANALYSIS; SHALLOW-WATER EQUATION;

FINITE ELEMENT METHOD; LAGRANGIAN ANALYSIS; SHALLOW-WATER EQUATION;

EID: 0033928441     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0493(2000)128<1384:ASISLF>2.0.CO;2     Document Type: Article

References (77)

1. Bares, J. R., and A. McDonald, 1982: Multiply-upstream, semi-Lagrangian advective schemes: Analysis and application to a multilevel primitive equation model. Mon. Wea. Rev., 112, 1831-1842.
2. _, F. H. M. Semazzi, R. W. Higgins, and S. R. M. Barros, 1990: Integration of the shallow-water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver. Mon. Wea. Rev., 118, 1615-1627.
3. Boyd, J. P., 1980: Equatorial solitary waves. Part I: Rossby solitons. J. Phys. Oceanogr., 10, 1699-1717.
4. _, 1985: Equatorial solitary waves. Part III: Westward-traveling modons. J. Phys. Oceanogr., 15, 46-54.
5. Brooks, D. A., 1984: Current and hydrographic variability in the northwestern Gulf of Mexico. J. Geophys. Res., 89, 8022-8032.
6. Bryan, F. O., and R. D. Smith. 1998: Modelling the North Atlantic circulation: From eddy permitting to eddy-resolving. International WOCE Newsletter 33, International Woce Project Office, Southampton, 12-13. [Available from Dr. Frank Bryan, National Center for Atmospheric Research, Boulder, CO 80307-3000.]
7. Bryan, K., 1963: A numerical investigation of a non linear model of a wind driven ocean. J. Atmos. Sci., 20, 594-606.
8. _. 1969: A numerical method for the study of the circulation of the World Ocean. J. Comput. Phys., 4, 347-376.
9. _, and M. D. Cox, 1967: A numerical investigation of the oceanic general circulation. Tellus, 19, 54-80.
10. _, and _, 1968a: A non linear model of an ocean driven by wind and differential heating. Part I: Description of the three-dimensional velocity and density fields. J. Atmos. Sci., 25, 945-967.
11. _, and _, 1968b: A non linear model of an ocean driven by wind and differential heating. Part II. An analysis of the heat, vorticity and energy balance. J. Atmos. Sci., 25, 968-978.
12. Chervin, R. M., and A. J. Semtner, 1990: An ocean modeling system for supercomputer architectures of the 1990s. Climate-Ocean Interactions, M. E. Schlesinge, Ed., Kluwer Academic, 87-95.
13. Connor, J. J., and J. D. Wang, 1974: Finite-element modeling of hydrodynamic circulation. Numerical Methods Fluid Dynamics, Pentech Press, 355-367.
14. Cox, M. D., 1970: A mathematical model of the Indian Ocean. Deep-Sea Res., 17, 47-75.
15. Dukowicz, J. K., and R. D. Smith, 1994: Implicit free-surface method for the Bryan-Cox-Semtner Ocean Model. J. Grophys. Res., 99, 7991-8014.
16. Dumas, E., C. Le Provost, and A. Poncet, 1982: Feasability of finite-element methods for oceanic general circulation modeling. Vol. 5, 4th International Conference on Finite Element in Water resources, Springer-Verlag, 43-55.
17. Elliott, B. A., 1982: Anticyclonic rings in the Gulf of Mexico. J. Phys. Oceanogr., 12, 1292-1309.
18. Engelman, M. S., R. L. Sani, and P. M. Gresho, 1982: The implementation of normal and/or tangential boundary conditions in finite-element codes for incompressible fluid flow. Int. J. Numer. Methods Fluids, 2, 225-238.
19. Fix, G. J., 1975: Finite element models for ocean circulation problems. SIAM, J. Appl. Math., 29, 371-387.
20. Fjørtoft, R., 1952: On a numerical method of integrating the barotropic vorticity equation. Tellus, 4, 179-194.
21. Gill, A. E., and K. Bryan, 1971: Effects of geometry on the circulation of a three dimensional Southern Hemisphere ocean. Deep-Sea Res., 18, 685-721.
22. Gray, W. G., 1984: On normal flow boundary conditions in finite-element codes for two-dimensional shallow-water flow. Int. J. Numer. Methods Fluids, 4, 99-104.
23. Grotkop, G., 1973: Finite-element analysis of long-period water waves. Comput. Methods Appl. Mech. Eng., 2, 147-157.
24. Haidvogel, D. B., A. R. Robinson, and E. E. Schulman. 1980: The accuracy, effiency and stability of three numerical models with application to open ocean problems. J. Comput. Phys., 34, 1-53.
25. Holland, W. R., 1971: Ocean tracer distributions. Tellus, 23, 371-392.
26. _, 1978: The role of mesoscale eddies in the general circulation of the ocean. J. Phys. Oceanogr., 8, 363-392.
27. _, and A. D. Hirschman, 1972: A numerical calculation of the circulation in the North Atlantic Ocean. J. Phys. Oceanogr., 2, 336-354.
28. _, and L. B. Lin, 1975: On the generation of mesoscale eddies and their contribution to the oceanic general circulation. J. Phys. Oceanogr., 5, 642-669.
29. Hurlburt, E. H., and J. D. Thompson, 1980: A numerical study of loop current intrusions and eddy shedding. J. Phys. Oceanogr., 10, 1611-1651.
30. Iskandarani, M., D. Haidvogel, and J. Boyd, 1995: A staggered spectral finite element model for the shallow-water equations. Int. J. Numer. Methods Fluids, 20, 393-414.
31. Kirwan, A. D., Jr., J. K. Lewis, A. W. Indest, P. Reinersman, and I. Quintero, 1988: Observed and simulated kinematic properties of loop current rings. J. Geophys. Res., 93, 1189-1198.
32. Kolmogorov, A., and S. V. Fomin, 1961: Elements of the Theory of Functions and Functional Analysis. Graylock Press.
33. LeBlond, P. H., and L. A. Mysak, 1978: Waves in the Ocean. Elsevier, 602 pp.
34. Le Provost, C., 1984: An application of finite-element methods for modeling wind driven circulations in a stratified ocean. 5th Internatinal Conference on Finite Elements in Water Resources, Springer-Verlag, 567-576.
35. _, 1986: On the use of finite-element methods for ocean modeling Advanced Physical Oceanographic Numerical Modeling NATO-ASI Series, Vol. 186, D. Reidel, 557-580.
36. _, and P. Vincent.,1991: Finite element for modeling ocean tides Tidal Hydrodynamics, B. Parker, Ed., John Wiley and Sons, 41-60.
37. _, C. Bernier, and E. Blayo, 1993: An intercomparison of two numerical methods for integrating a quasi-geostrophic multilayer model of ocean circulations. J. Comput. Phys., 110, 341-359
38. Le Roux, D. Y., C. A. Lin, and A. Staniforth, 1997: An accurate interpolating scheme for semi-Lagrangian advection on an unstructured mesh for ocean modeling. Tellus, 49, 119-138.
39. _, A. Staniforth, and C. A. Lin, 1998: Finite elements for shallow water equation ocean models. Mon. Wea. Rev., 126, 1931-1951.
40. Lewis, J. K., and A. D. Kirwan, 1987: Genesis of a Gulf of Mexico ring as determined from kinematic analyses. J. Geophys. Res., 92, 11 727-11 740.
41. Ma, H., 1993: A spectral element basin model for the shallow-water equations. J. Comput. Phys., 109, 133-149.
42. Matheron, G., 1980: Splines et krigeage: Leur équivalence formelle. Rapport N-667, 25 pp. [Available from Centre de Géostatistique, Ecole des Mines de Paris, Fontainebleau, France.]
43. McCalpin, J. D., 1988: A quantitative analysis of the dissipation inherent in semi-Lagrangian advection. Mon. Wea. Rev., 116, 2330-2336.
44. McDonald, A., 1984: Accuracy of multiply-upstream semi-Lagrangian advective schemes. Mon. Wea. Rev., 112, 1267-1275.
45. _, and J. R. Bates, 1987: Improving the estimate of the departure point position in a two-time level semi-Lagrangian and semi-implicit scheme. Mon. Wea. Rev., 115, 737-739.
46. Merrell, W. J., and J. M. Morrison, 1981: On the circulation of the western Gulf of Mexico with observations from April 1978. J. Geophys. Res., 86, 4181-4185.
47. _, and A. M. Vasquez, 1983: Observations of changing mesoscale circulation patterns in the western Gulf of Mexico. J. Geophys. Res., 88, 7721-7723.
48. Munk, W. H., 1950: On the wind driven ocean circulation. J. Meteor., 7, 79-93.
49. Ortega, J. M., and W. C. Rheinboldt, 1970: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, 572 pp.
50. Pedlosky, J., 1979: Geophysical Fluid Dynamics. Springer-Verlag, Berlin, 624 pp.
51. Pudykiewicz, J., and A. Staniforth, 1984: Some properties and comparative performance of the semi-Lagrangian method of Robert in the solution of the advection-diffusion equation. Atmos.-Ocean., 22, 283-308.
52. _, R. Benoit, and A. Staniforth, 1985: Preliminary results from a partial LRTAP model based on an existing meteorological forecast model. Atmos.-Ocean., 23, 267-303.
53. Purnell, D. K., 1976: Solution of the advective equation by upstream interpolation with a cubic spline. Mon. Wea. Rev., 104, 42-48.
54. Rasch, P., and D. Williamson, 1990: Computational aspects of moisture transport in global models of the atmosphere. Quart. J. Roy. Meteor. Soc., 116, 1071-1090.
55. Robert, A., 1969: The integration of a spectral model of the atmosphere by the implicit method. Proc. of the WMO/IUGG Symp. on Numerical Weather Prediction, Tokyo, Japan, Japan. Meteor. Agency, 19-24.
56. _, 1981: A stable numerical integration scheme for the primitive meteorological equations. Atmos.-Ocean., 19, 35-46.
57. _, 1982: A semi-Lagrangian and semi-implicit numerical integration scheme for the primitive meteorological equations. Japan Meteor. Soc., 60, 319-325.
58. _, J. Henderson, and C. Turnbull, 1972: An implicit time integration scheme for baroclinic models of the atmosphere. Mon. Wea. Rev., 100, 329-335.
59. _, T. L. Yee, and H. Ritchie, 1985: A semi-Lagrangian and semi-implicit numerical integration scheme for multilevel atmospheric models. Mon. Wea. Rev., 113, 388-394.
60. Sani, R. L., P. M. Gresho, R. L. Lee, and D. Griffiths, 1981a: The cause and cure (!) of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations. Part I. Int. J. Numer. Methods Fluids, 1, 17-43.
61. _, _, _, and _, 1981b: The cause and cure (!) of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations. Part II. Int. J. Numer. Methods. Fluids, 1, 171-204.
62. Sarkisyan, A. S., 1955: The calculation of stationary wind currents in an ocean, Izv. Akad. Nauk SSSR, Ser. Geofiz., 6, 554-561.
63. Sawyer, J. S., 1963: A semi-Lagrangian method of solving the vorticity advection equation. Tellus, 15, 336-342.
64. Semtner, A. J., and R. M. Chervin, 1988: A simulation of the global ocean with resolved eddies. J. Geophys. Res., 93, 15 502-15 522.
65. Stammer, D., R. Tokmakian, A. Semtner, and C. Wunsch, 1996: How well does a 1/4° global circulation model simulate large-scale oceanic observations? J. Geophys. Res., 101, 25 779-25 811.
66. Staniforth, A., and J. Pudykiewicz, 1985: Reply to comments on and addenda to some properties and comparative performance of the semi-Lagrangian method of Robert in the solution of the advection-diffusion equation. Atmos.-Ocean., 23, 195-200.
67. _, and J. Côté, 1991: Semi-Lagrangian integration schemes for atmospheric models: A review. Mon. Wea. Rev., 119, 2206-2223.
68. Stoer, J., and R. Bulirsch, 1993: Introduction to Numerical Analysis. Springer-Verlag, 660 pp.
69. Stommel, H. M., 1948: The westward intensification of the wind driven ocean currents. Trans. Amer. Geophys. Union, 29, 202-206.
70. Sverdrup, H. U., 1947: Wind driven currents in a barotropic ocean, with application to the equatorial currents of the Eastern Pacific. Proc. U. S. Nat. Acad. Sci. 33, 318-326.
71. Taylor, C., and J. M. Davies, 1975: Tidal propagation and dispersion in estuaries. Finite Element in Fluids, R. H. Gallagher, J. T. Oden, C. Taylor, and O. C. Zinkiewicz, Eds., John Wiley, 95-118.
72. Taylor, M., J. Tribbia, and M. Iskandarani, 1997: The spectral element method for the shallow-water equations on the sphere. J. Comput. Phys., 130, 92-108.
73. Temperton, C., and A. Staniforth. 1987: An efficient two-time level semi-Lagrangian semi-implicit integration scheme. Quart. J. Roy. Meteor. Soc., 113, 1025-1039.
74. Trochu, F., 1993: A contouring program based on dual kriging interpolation. Eng. Comput., 9, 160-177.
75. Vukovich, F. M., and B. W. Crissman, 1986: Aspects of warm rings in the Gulf of Mexico. J. Geophys. Res., 91, 2645-2660.
76. Westerink, J. J., and W. G. Gray, 1991: Progress in surface water modeling. Rev. Geophys., 29, 210-217.
77. Wiin-Nielsen, A., 1959: On the application of trajectory methods to numerical forecasting. Tellus, 11, 180-196.