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Semi-implicit semi-Lagrangian modelling of the atmosphere: a Met Office perspective Cover

Semi-implicit semi-Lagrangian modelling of the atmosphere: a Met Office perspective

By: Tommaso Benacchio and  Nigel Wood  
Open Access
|Oct 2016

References

  1. 1. C. Temperton, M. Hortal, and A. J. Simmons, A two-time-level semi- Lagrangian global spectral model, Quarterly Journal of the Royal Meteorological Society, vol. 127, pp. 111-126, 2001.10.1002/qj.49712757107
  2. 2. P. Courtier, C. Freydier, J. F. Geleyn, F. Rabier, and M. Rochas, The ARPEGE project at Météo-France, in ECMWF Workshop on Numerical Methods in Atmospheric Modelling, Vol. II, 2, pp. 193-231, 1991.
  3. 3. J. Côté, S. Gravel, A. Méthot, A. Patoine, M. Roch, and A. Staniforth, The operational CMC-MRB global environmental multiscale (GEM) model. Part I: Design considerations and formulation, Monthly Weather Review, vol. 126, pp. 1373-1395, 1998.
  4. 4. D. Chen, J. Xue, X. Yang, H. Zhang, X. Shen, J. Hu, Y. Wang, L. Ji, and J. Chen, New generation of multi-scale NWP system (GRAPES): general scientific design, Chinese Science Bulletin, vol. 53, pp. 3433- 3445, 2008.
  5. 5. Y. Takeuchi and Others, Outline of the operational numerical weather prediction at the Japan Meteorological Agency. Appendix to WMO Technical Progress Report on the Global Data-processing and Forecasting System (GDPFS) and Numerical Weather Prediction (NWP) Research, tech. rep., JMA, 2013. Available at: http://www.jma.go.jp/jma/jma-eng/jma-center/nwp/outline2013-nwp/pdf/outline2013_all.pdf (Last access: 8 May 2015).
  6. 6. M. Tolstykh, Variable resolution global semi-Lagrangian atmospheric model, Russian Journal of Numerical Analysis and Mathematical Modelling, vol. 18, pp. 347-361, 2003.10.1515/156939803769210993
  7. 7. M. Zhao, I. Held, S. Lin, and G. Vecchi, Simulations of global hurricane climatology, inter-annual variability, and response to global warming using a 50-km resolution gcm., Journal of Climate, vol. 22, pp. 6653-6678, 2009.
  8. 8. R. B. Neale and Others, Description of the NCAR Community Atmosphere Model (CAM5.0), tech. rep., NCAR, 2012. Available at: http://www.cesm.ucar.edu/models/cesm1.0/cam/docs/description/cam5_desc.pdf (Last access: 17 August 2015).
  9. 9. A. Brown, S. Milton, M. Cullen, B. Golding, J. Mitchell, and A. Shelly, Unified modeling and prediction of weather and climate: A 25-year journey, Bulletin of the American Meteorological Society, vol. 93, pp. 1865-1877, 2012.
  10. 10. A. Staniforth and J. Côté, Semi-Lagrangian integration schemes for atmospheric models - a review, Monthly Weather Review, vol. 119, pp. 2206-2223, 1991.
  11. 11. P. Bénard, Stability of semi-implicit and iterative centered-implicit time discretizations for various equation systems used in NWP, Monthly Weather Review, vol. 131, pp. 2479-2491, 2003.
  12. 12. A. Staniforth and J. Thuburn, Horizontal grids for global weather prediction and climate models: a review, Quarterly Journal of the Royal Meteorological Society, vol. 138, pp. 1-26, 2012.10.1002/qj.958
  13. 13. M. J. P. Cullen, Modelling atmospheric ows, Acta Numerica, vol. 16, pp. 67-154, 2007.10.1017/S0962492906290019
  14. 14. M. J. P. Cullen, T. Davies, M. H. Mawson, J. A. James, S. C. Coulter, and A. Malcolm, An overview of numerical methods for the next genera-tion UK NWP and climate model, in Numerical Methods in Atmospheric Modelling, The André Robert memorial volume (C. Lin, R. Laprise, and H. Ritchie, eds.), (Ottawa, Canada), pp. 425-444, Canadian Meteoro-logical and Oceanographical Society, 1997.10.1080/07055900.1997.9687359
  15. 15. M. C. Tapp and P. W. White, A non-hydrostatic mesoscale model, Quarterly Journal of the Royal Meteorological Society, vol. 102, pp. 277-296, 1992.10.1002/qj.49710243202
  16. 16. T. Davies, M. J. P. Cullen, A. J. Malcolm, M. H. Mawson, A. Staniforth, A. White, and N. Wood, A new dynamical core for the Met Office's global and regional modelling of the atmosphere, Quarterly Journal of the Royal Meteorological Society, vol. 131, pp. 1759-1782, 2005.
  17. 17. A. A. White and R. A. Bromley, Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force, Quarterly Journal of the Royal Meteorological Society, vol. 121, pp. 399-418, 1995.10.1002/qj.49712152208
  18. 18. A. A. White, B. J. Hoskins, I. Roulstone, and A. Staniforth, Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic, Quarterly Journal of the Royal Meteorological Society, vol. 131, pp. 2081-2107, 2005.
  19. 19. R. Laprise, The Euler equations of motion with hydrostatic pressure as an independent variable, Monthly Weather Review, vol. 120, pp. 197-207, 1992.10.1175/1520-0493(1992)120<;0197:TEEOMW>2.0.CO;2
  20. 20. N. Wood and A. Staniforth, The deep-atmosphere Euler equations with a mass-based vertical coordinate, Quarterly Journal of the Royal Meteorological Society, vol. 129, pp. 1289-1300, 2003.
  21. 21. P. R. Bannon, C. H. Bishop, and J. B. Kerr, Does the surface pressure equal the weight per unit area of a hydrostatic atmosphere?, Bulletin of the American Meteorological Society, vol. 78, pp. 2637-2642, 1997.
  22. 22. M. Zerroukat, N. Wood, and A. Staniforth, SLICE-S: A Semi-Lagrangian Inherently Conserving and Efficient scheme for transport problems on the sphere, Quarterly Journal of the Royal Meteorological Society, vol. 130, pp. 2649-2664, 2004.
  23. 23. N. Wood, A. Staniforth, A. White, T. Allen, M. Diamantakis, M. Gross, T. Melvin, C. Smith, S. Vosper, M. Zerroukat, and J. Thuburn, An inherently mass-conserving semi-implicit semi-Lagrangian discretization of the deep-atmosphere global non-hydrostatic equations, Quarterly Journal of the Royal Meteorological Society, vol. 140, pp. 1505-1520, 2014.
  24. 24. K.-S. Yeh, J. Côté, S. Gravel, A. Méthot, A. Patoine, M. Roch, and A. Staniforth, The CMC-MRB Global Environmental Multiscale (GEM) model. Part III: Nonhydrostatic formulation, Monthly Weather Review, vol. 130, pp. 339-356, 2002.10.1175/1520-0493(2002)130<;0339:TCMGEM>2.0.CO;2
  25. 25. M. J. P. Cullen, Alternative implementations of the semi-Lagrangian semi-implicit schemes in the ECMWF model, Quarterly Journal of the Royal Meteorological Society, vol. 127, pp. 2787-2802, 2001.
  26. 26. M. Diamantakis, T. Davies, and N. Wood, An iterative time-stepping scheme for the Met Ofice's semi-implicit semi-Lagrangian non-hydrostatic model, Quarterly Journal of the Royal Meteorological Society, vol. 133, pp. 997-1011, 2007.10.1002/qj.59
  27. 27. A. J. Simmons, B. J. Hoskins, and D. M. Burridge, Stability of the semi-implicit method of time integration, Monthly Weather Review, vol. 106, pp. 405-412, 1978.10.1175/1520-0493(1978)106<;0405:SOTSIM>2.0.CO;2
  28. 28. A. J. Simmons and C. Temperton, Stability of a two-time-level semi- implicit integration scheme for gravity wave motion, Monthly Weather Review, vol. 125, pp. 600-615, 1997.10.1175/1520-0493(1997)125<;0600:SOATTL>2.0.CO;2
  29. 29. J. Thuburn, Vertical discretizations giving optimal representation of normal modes: Sensitivity to the form of the pressure-gradient term, Quarterly Journal of the Royal Meteorological Society, vol. 132, pp. 2809-2825, 2006.
  30. 30. J. Thuburn, M. Zerroukat, N. Wood, and A. Staniforth, Coupling amass-conserving semi-Lagrangian scheme (SLICE) to a semi-implicit discretisation of the shallow-water equations: minimizing the dependence on a reference atmosphere, Quarterly Journal of the Royal Mete-orological Society, vol. 136, pp. 146-154, 2010.10.1002/qj.517
  31. 31. A. Staniforth, A. White, and N. Wood, Analysis of semi-Lagrangian trajectory computations, Quarterly Journal of the Royal Meteorological Society, vol. 129, pp. 2065-2085, 2003.
  32. 32. N.Wood, A. A. White, and A. Staniforth, Treatment of vector equations in deep-atmosphere, semi-Lagrangian models. II: Kinematic equation, Quarterly Journal of the Royal Meteorological Society, vol. 136, pp. 507-516, 2010.10.1002/qj.565
  33. 33. E. Cordero, N. Wood, and A. Staniforth, Impact of semi-Lagrangian trajectories on the discrete normal modes of a non-hydrostatic vertical-column model, Quarterly Journal of the Royal Meteorological Society, vol. 131, pp. 93-108, 2005.10.1256/qj.04/34
  34. 34. E. Cordero, A. Staniforth, and N. Wood, Normal mode analysis of the New Dynamics, tech. rep., FR Technical Report No. 393, 2002. Available at: http://www.metofice.gov.uk/media/pdf/c/9/FRTR393-wontconvert.pdf (Last access 13 May 2015).
  35. 35. J. Thuburn, N. Wood, and A. Staniforth, Normal modes of deep atmo-spheres. I: Spherical geometry, Quarterly Journal of the Royal Meteorological Society, vol. 128, pp. 1771-1792, 2002.
  36. 36. T. Davies, A. Staniforth, N.Wood, and J. Thuburn, Validity of anelastic and other equation sets as inferred from normal-mode analysis, Quarterly Journal of the Royal Meteorological Society, vol. 129, pp. 2761-2775, 2003.
  37. 37. A. Arakawa and C. S. Konor, Uni cation of the anelastic and quasihydrostatic systems of equations, Monthly Weather Review, vol. 137, pp. 710-726, 2009.10.1175/2008MWR2520.1
  38. 38. J. K. Dukowicz, Evaluation of various approximations in ocean and atmospheric modeling based on an exact treatment of gravity wave dispersion, Monthly Weather Review, vol. 141, pp. 4487-4506, 2013.
  39. 39. T. Dubos and F. Voitus, A semihydrostatic theory of gravity-dominated compressible ow, Journal of the Atmospheric Sciences, vol. 71,pp. 4621-4638, 2014.
  40. 40. D. Walters, N. Wood, S. Vosper, and S. Milton, ENDGame: A new dynamical core for seamless atmospheric prediction, tech. rep., Met Office, 2014. Available at: http://www.metoffice.gov.uk/media/pdf/s/h/ENDGameGOVSciv2.0.pdf (Last access: 13 May 2015).
Language: English
Page range: 4 - 25
Submitted on: Jun 15, 2015
Accepted on: Aug 2, 2015
Published on: Oct 1, 2016
Published by: Italian Society for Applied and Industrial Mathemathics
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2016 Tommaso Benacchio, Nigel Wood, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.