Atmosphere and ocean modeling on grids of variable resolution-A 2D case study

Monthly Weather Review

Volumn 142, Issue 5, 2014, Pages 1997-2017

  Düben, Peter D ^a,b   Korn, Peter ^a  

^a MAX PLANCK INSTITUTE FOR METEOROLOGY   (Germany)

^b INTERNATIONAL MAX PLANCK RESEARCH SCHOOL ON EARTH SYSTEM MODELLING   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; ERRORS; FINITE ELEMENT METHOD; WAVE PROPAGATION;

CONVERGENCE PROPERTIES; FINITE-ELEMENT MODELS; NUMERICAL EXPERIMENTS; PARAMETERIZATION SCHEMES; REFINEMENT TECHNIQUES; SPHERICAL GEOMETRIES; THEORETICAL INVESTIGATIONS; VISCOUS SHALLOW-WATER EQUATIONS;

COMPUTER SIMULATION;

ATMOSPHERIC MODELING; FINITE ELEMENT METHOD; GENERAL CIRCULATION MODEL; NUMERICAL MODEL; PARAMETERIZATION; RESOLUTION; SHALLOW-WATER EQUATION;

EID: 84899786370     PISSN: 00270644     EISSN: 15200493     Source Type: Journal    
DOI: 10.1175/MWR-D-13-00217.1     Document Type: Article

References (30)

1. Baumgardner, J. R., and P. O. Frederickson, 1985: Icosahedral discretization of the two-sphere. SIAM J. Numer. Anal., 22, 1107-1115, doi:10.1137/0722066.
2. Behrens, J., 2006: Adaptive Atmospheric Modeling: Key Techniques in Grid Generation, Data Structures, and Numerical Operations with Applications. Springer, 214 pp.
3. Bonaventura, L., and T. Ringler, 2005: Analysis of discrete shallowwater models on geodesic Delaunay grids with C-type staggering. Mon. Wea. Rev., 133, 2351-2373, doi:10.1175/MWR2986.1.
4. Comblen, R., J. Lambrechts, J.-F. Remacle, and V. Legat, 2010: Practical evaluation of five partly discontinuous finite element pairs for the non-conservative shallow water equations. Int. J. Numer. Methods Fluids, 63, 701-724, doi: 10.1002/fld.2094.
5. Cotter, C. J., and D. A. Ham, 2011: Numerical wave propagation for the triangular P1DG-P2 finite element pair. J. Comput. Phys., 230, 2806-2820, doi:10.1016/j.jcp.2010.12.024.
6. Cotter, C. J., D. A. Ham, and C. C. Pain, 2009a:Amixed discontinuous/continuous finite element pair for shallow-water ocean modelling. Ocean Modell., 26, 86-90, doi:10.1016/j.ocemod.2008.09.002.
7. Cotter, C. J., D. A. Ham, C. C. Pain, and S. Reich, 2009b: LBB stability of a mixed Galerkin finite element pair for fluid flow simulations. J. Comput. Phys., 228, 336-348, doi:10.1016/j.jcp.2008.09.014.
8. Danilov, S., G. Kivman, and J. Schröter, 2004: A finite-element ocean model: Principles and evaluation. Ocean Modell., 6, 125-150, doi:10.1016/S1463-5003(02)00063-X.
9. Düben, P. D., P. Korn, and V. Aizinger, 2012: A discontinuous/ continuous low order finite element shallow water model on the sphere. J. Comput. Phys., 231, 2396-2413, doi:10.1016/ j.jcp.2011.11.018.
10. Griffies, S. M., 2004: Fundamentals of Ocean Climate Models. Princeton University Press, 496 pp.
11. Harris, L. M., and D. R. Durran, 2010: An idealized comparison of one-way and two-way grid nesting. Mon. Wea. Rev., 138, 2174- 2187, doi:10.1175/2010MWR3080.1.
12. Jakob, R., J. J. Hack, and D. L. Williamson, 1993: Solutions to the shallow water test set using the spectral transform method. NCAR Tech. Note TN-3881STR, NCAR, 83 pp.
13. Le Roux, D. Y., A. Staniforth, and C. A. Lin, 1998: Finite elements for shallow-water equation oceanmodels. Mon. Wea. Rev., 126, 1931-1951, doi:10.1175/1520-0493(1998)126,1931: FEFSWE.2.0.CO;2.
14. Long, D., and J. Thuburn, 2011: Numerical wave propagation on non-uniform one-dimensional staggered grids. J. Comput. Phys., 230, 2643-2659, doi:10.1016/j.jcp.2010.12.040.
15. Maddison, J., C. Cotter, and P. Farrell, 2011: Geostrophic balance preserving interpolation in mesh adaptive linearised shallowwater ocean modelling. Ocean Modell., 37, 35-48, doi:10.1016/ j.ocemod.2010.12.007.
16. McWilliams, J. C., 2006: Fundamentals of Geophysical Fluid Dynamics. Cambridge University Press, 266 pp.
17. Müller, R., and U. Schulzweida, 2010: Climate data operators, version 1.4.5.1. NOAA.
18. Pedlosky, J., 1996: Ocean Circulation Theory. Springer-Verlag, 453 pp.
19. Piggott, M. D., P. E. Farrell, C. R. Wilson, G. J. Gorman, and C. C. Pain, 2009: Anisotropic mesh adaptivity for multi-scale ocean modelling. Philos. Trans. Roy. Soc. A, 367, 4591-4611, doi:10.1098/rsta.2009.0155.
20. Piggott, M. D., C. C. Pain, G. J. Gorman, D. P. Marshall, and P. D. Killworth, 2008: Unstructured adaptive meshes for ocean modeling. Ocean Modeling in an Eddying Regime, Geophys. Monogr., Vol. 177, Amer. Geophys. Union, 383-408.
21. Ringler, T. D., and D. A. Randall, 2002: A potential enstrophy and energy conserving numerical scheme for solution of the shallow-water equations on a geodesic grid. Mon. Wea. Rev., 130, 1397-1410, doi:10.1175/1520-0493(2002)130,1397: APEAEC.2.0.CO;2.
22. Ringler, T. D., D. Jacobsen, M. Gunzburger, L. Ju, D. Michael, and W. Skamarock, 2011: Exploring a multiresolution modeling approach within the shallow-water equations. Mon. Wea. Rev., 139, 3348-3368, doi:10.1175/MWR-D-10-05049.1.
23. Ringler, T. D., M. Petersen, R. Higdon, D. Jacobsen, P. Jones, and M. Maltrud, 2013: A multiresolution approach to global ocean modeling. Ocean Modell., 69, 211-232, doi:10.1016/ j.ocemod.2013.04.010.
24. Salmon, R., 1998: Lectures on Geophysical Fluid Dynamics. Oxford University Press, 400 pp.
25. Skamarock, W. C., J. B. Klemp, M. G. Duda, L. D. Fowler, S.-H. Park, and T. D. Ringler, 2012: A multiscale nonhydrostatic atmospheric model using centroidal Voronoi tesselations and C-grid staggering. Mon. Wea. Rev., 140, 3090-3105, doi:10.1175/ MWR-D-11-00215.1.
26. 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, doi:10.1006/ jcph.1996.5554.
27. Trefethen, L. N., 1982: Group velocity in finite difference schemes. SIAM Rev., 24, 113-136.
28. Ullrich, P. A., and C. Jablonowski, 2011: An analysis of 1D finite-volume methods for geophysical problems on refined grids. J. Comput. Phys., 230, 706-725, doi:10.1016/ j.jcp.2010.10.014.
29. Vichnevetsky, R., 1987: Wave propagation and reflection in irregular grids for hyperbolic equations. Appl. Numer. Math., 3, 133-166, doi:10.1016/0168-9274(87)90009-2.
30. Williamson, D. L., 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. Comput. Phys., 102, 211-224, doi:10.1016/ S0021-9991(05)80016-6.