A stability analysis of divergence damping on a latitude-longitude grid

Monthly Weather Review

Volumn 139, Issue 9, 2011, Pages 2976-2993

  Whitehead, Jared P ^a   Jablonowski, Christiane ^a   Rood, Richard B ^a   Lauritzen, Peter H ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

Convergence divergence; Filtering techniques; General circulation models; Grid systems

Indexed keywords

A-STABILITY; AMPLIFICATION FACTORS; ATMOSPHERIC GENERAL CIRCULATION MODELS; BAROCLINIC WAVES; COMMUNITY ATMOSPHERE MODEL; COMPUTATIONAL COSTS; COMPUTATIONAL STABILITY; CONVERGENCE/DIVERGENCE; DAMPING COEFFICIENTS; DAMPING MECHANISMS; DYNAMICAL CORE; ENSTROPHY; FILTERING TECHNIQUES; FINITE-VOLUME; FOURTH-ORDER; GENERAL CIRCULATION MODEL; GRID SYSTEMS; NUMERICAL DIFFUSION; STABILITY RESTRICTION; SUBGRID SCALE; TEST CASE; VON-NEUMANN STABILITY ANALYSIS;

DIFFUSION; EARTH ATMOSPHERE; EQUATIONS OF MOTION; STABILITY;

DAMPING;

ACCURACY ASSESSMENT; ATMOSPHERIC GENERAL CIRCULATION MODEL; BAROCLINIC WAVE; COMPUTER SIMULATION; FINITE VOLUME METHOD; GRAVITY WAVE; NUMERICAL METHOD;

EID: 80053196623     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/2011MWR3607.1     Document Type: Article

References (36)

1. Anderson, J., T. Hoar, K. Raeder, H. Liu, N. Collins, R. Torn, and A. Avellano, 2009: The data assimilation research testbed: A community facility. Bull. Amer. Meteor. Soc., 90, 1283-1296.
2. Andrews, D. G., and M. E. McIntyre, 1978: An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech., 89 (4), 609-646.
3. Arakawa, A., and V. R. Lamb, 1977: Computational design of the basic dynamical process of the UCLA general circulation model. Methods in Computational Physics, J. Chang, Ed., Academic Press, 173-265.
4. Bala, G., R. Rood, D. Bader, A. Mirin, D. Ivanova, and C. Drui, 2008: Simulated climate near steep topography: Sensitivity to numerical methods for atmospheric transport. Geophys. Res. Lett., 35, L14807, doi:10.1029/2008GL033204.
5. Bates, J. R., S. Moorthi, and R. W. Higgins, 1993: A global multilevel atmospheric model using a vector semi-Lagrangian finite difference scheme. Part I: Adiabatic formulation. Mon. Wea. Rev., 121, 244-263.
6. Boville, B. A., 1991: Sensitivity of simulated climate to model resolution. J. Climate, 4, 469-485.
7. Colella, P., and P. R. Woodward, 1984: The piecewise parabolic method (PPM) for gas-dynamical simulations. J.Comput. Phys., 54, 174-201.
8. Collins, W. D., and Coauthors, 2004: Description of the NCAR Community Atmosphere Model (CAM3.0). NCAR Tech. Note NCAR/TN-4641STR, National Center for Atmospheric Research, Boulder, CO, 226 pp.
9. Delworth, T., and Coauthors, 2006: GFDL's CM2 global coupled climate models. Part I: Formulation and simulation characteristics. J. Climate, 19, 643-674.
10. Dey, C., 1978: Noise suppression in a primitive equation prediction model. Mon. Wea. Rev., 106, 159-173.
11. Durran, D. R., 1999: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer, 465 pp.
12. Fox-Rabinovitz, M. S., G. L. Stenchikov, M. J. Suarez, and L. L. Takacs, 1997: A finite-difference GCM dynamical core with a variable-resolution stretched grid. Mon. Wea. Rev., 125, 2943-2968.
13. Haltiner, G. J., and R. T. Williams, 1980: Numerical Prediction and Dynamic Meteorology. John Wiley & Sons, 477 pp.
14. Jablonowski, C., and D. L. Williamson, 2006a: A baroclinic instabilitiy test case for atmospheric model dynamical cores. Quart. J. Roy. Meteor. Soc., 132, 2943-2975.
15. Jablonowski, C., and D. L. Williamson, 2006b: A baroclinic wave test case for dynamical cores of General Circulation Models: Model intercomparisons. NCAR Tech. Note NCAR/TN-4691STR, National Center for Atmospheric Research, Boulder, CO, 89 pp.
16. Jablonowski, C., and D. L. Williamson, 2011: Numerical methods for global atmospheric models. The Pros and Cons of Diffusion, Filters and Fixers in Atmospheric General Circulation Models, P. H. Lauritzen et al., Eds., Lecture Notes in Science and Engineering, Vol. 80, Springer, 381-493.
17. Jablonowski, C., P. H. Lauritzen, R. D. Nair, and M. A. Taylor, 2008a: Idealized test cases for the dynamical cores of Atmospheric General Circulation Models: A proposal for the NCAR ASP 2008 summer colloquium. Tech. Rep., 74 pp. [Available online at http://www-personal.umich.edu/;cjablono/NCAR_ASP_2008_idealized_testcases_29May08.pdf.]
18. Jablonowski, C., P. H. Lauritzen, M. A. Taylor, and R. D. Nair, 2008b: An intercomparison of 10 atmospheric model dynamical cores. Eos, Trans. Amer. Geophys. Union, 89 (Fall Meeting Suppl.), Abstract A33A-0214.
19. Lander, J., and B. J. Hoskins, 1997: Believable scales and parameterizations in a spectral transform model. Mon. Wea. Rev., 125, 292-303.
20. Lauritzen, P. H., 2007: A stability analysis of finite-volume advection schemes permitting long time steps. Mon. Wea. Rev., 135, 2658-2673.
21. Lauritzen, P. H., A. A. Mirin, J. Truesdale, K. Raeder, J. L. Anderson, J. Bacmeister, and R. B. Neale, 2011: Implementation of new diffusion/filtering operators in the CAM-FV dynamical core. Int. J. High Perform. Comput. Appl., doi:10.1177/1094342011410088, in press.
22. Lin, S.-J., 2004: A "vertically Lagrangian" finite-volume dynamical core for global models. Mon. Wea. Rev., 132, 2293-2307.
23. Lin, S.-J., and R. B. Rood, 1996: Multidimensional flux-form semi-Lagrangian transport scheme. Mon.Wea. Rev., 124, 2046-2070.
24. Lin, S.-J., and R. B. Rood, 1997: An explicit flux-form semi-Lagrangian shallow water model on the sphere. Quart. J. Roy. Meteor. Soc., 123, 2477-2498.
25. Lindborg, E., 1999: Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech., 388, 259-288.
26. Nastrom, G. D., and K. S. Gage, 1985: A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci., 42, 950-960.
27. Neale, R. B., and Coauthors, 2010: Description of the NCAR Community Atmosphere Model (CAM 5.0). NCAR Tech. Note NCAR/TN-XXX1STR, National Center for Atmospheric Research, Boulder, CO, in press. [Available online at http://www.cesm.ucar.edu/models/cesm1.0/cam/.]
28. Putman, W. M., and S.-J. Lin, 2009:Afinite-volume dynamical core on the cubed-sphere grid. Numerical Modeling of Space Plasma Flows: Astronum-2008, Astronomical Society of the Pacific Conference Series, Vol. 406, 268-276.
29. Rienecker, M. M., and Coauthors, 2008: The GEOS-5 data assimilation system-Documentation of versions 5.0.1, 5.1.0, and 5.2.0. Technical Report Series on Global Modeling and Data Assimilation, M. J. Suarez, Ed., NASA/TM-2008-104606, Vol. 27, NASA Goddard Space Flight Center, 118 pp. [Available online at http://gmao.gsfc.nasa.gov/pubs/docs/GEOS5_104606-Vol27.pdf.]
30. Rood, R. B., 1987: Numerical advection algorithms and their role in atmospheric transport and chemistry models. Rev. Geophys., 25, 71-100.
31. Sadourny, R., 1975: The dynamics of finite-difference models of the shallow-water equations. J. Atmos. Sci., 32, 680-689.
32. Shepherd, T. G., K. Semeniuk, and J. N. Koshyk, 1996: Sponge layer feedbacks in middle-atmosphere models. J. Geophys. Res., 101, 23 447-23 464.
33. Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132, 3019-3032.
34. Skamarock, W. C., 2008: A linear analysis of the NCAR CCSM finite-volume dynamical core. Mon. Wea. Rev., 136, 2112-2119.
35. Takahashi, Y. O., K. Hamilton, andW. Ohfuchi, 2006: Explicit global simulation of the mesoscale spectrum of atmospheric motions. Geophys. Res. Lett., 33, L12812, doi:10.1029/2006GL026429.
36. Williamson, D. L., J. G. Olson, and C. Jablonowski, 2009: Two dynamical core formulation flaws exposed by a baroclinic instability test case. Mon. Wea. Rev., 137, 790-796.