• Asselin, R. A., 1972: Frequency filter for time integrations. Mon. Wea. Rev., 100 , 487490.

  • Bénard, P., 2003: Stability of semi-implicit and iterative centered-implicit time discretizations for various equation systems used in NWP. Mon. Wea. Rev., 131 , 24792491.

    • Search Google Scholar
    • Export Citation
  • Benoit, R., , M. Desgagné, , P. Pellerin, , Y. Chartier, , and S. Desjardins, 1997: The Canadian MC2: A semi-Lagrangian, semi-implicit wideband atmospheric model suited for finescale process studies and simulation. Mon. Wea. Rev., 125 , 23822415.

    • Search Google Scholar
    • Export Citation
  • Benoit, R., and Coauthors, 2002a: The real-time ultrafinescale forecast support during the special observing period of the MAP. Bull. Amer. Meteor. Soc., 83 , 85109.

    • Search Google Scholar
    • Export Citation
  • Benoit, R., , C. Girard, , M. Desgagné, , S. Chamberland, , and W. Yu, 2002b: Finescale orography and the MC2 dynamics kernel. Preprints, 10th Conf. on Mountain Meteorology, Park City, UT, Amer. Meteor. Soc., 219–222.

  • Caya, D., , and R. Laprise, 1999: A semi-implicit semi-Lagrangian regional climate model: The Canadian RCM. Mon. Wea. Rev., 127 , 341362.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G., , and N. A. Phillips, 1953: Numerical integration of the quasi-geostrophic equations for barotropic and simple baroclinic flows. J. Meteor., 10 , 7199.

    • Search Google Scholar
    • Export Citation
  • Denis, B., 1990: Introduction de la topographie dans un modèle atmosphérique non-hydrostatique. M.S. thesis, UQAM, 121 pp. [Available from R. Laprise, Département de physique, UQAM, P.O. Box 8888, Stn “Downtown,” Montréal, Québec H3C 3P8, Canada.].

  • Denis, B., , J. Côté, , and R. Laprise, 2002: Spectra decomposition of two-dimensional atmospheric fields on limited-area domains using the discrete cosine transform (DCT). Mon. Wea. Rev., 130 , 18121829.

    • Search Google Scholar
    • Export Citation
  • Eckart, C., 1960: Hydrodynamics of Oceans and Atmospheres. Pergamon, 290 pp.

  • Gal-Chen, T., , and R. C. Somerville, 1975: On the use of a coordinate transformation for the solution of Navier–Stokes equations. J. Comput. Phys., 17 , 209228.

    • Search Google Scholar
    • Export Citation
  • Girard, C., , and M. Desgagné, 2004: An unstable semi-implicit scheme made stable. Preprints, 38th CMOS Congress, Edmonton, AB, Canada, Canadian Meteorological and Oceanographic Society, 120.

  • Héreil, P., , and R. Laprise, 1996: Sensitivity of internal gravity waves solutions to the time step of a semi-implicit semi-Lagrangian nonhydrostatic model. Mon. Wea. Rev., 124 , 972999.

    • Search Google Scholar
    • Export Citation
  • Kasahara, A., 1974: Various vertical coordinate systems used for numerical weather prediction. Mon. Wea. Rev., 102 , 507522.

  • Klemp, J. B., , W. C. Skamarock, , and O. Fuhrer, 2003: Numerical consistency of finite differencing in terrain-following coordinates. Mon. Wea. Rev., 131 , 12291239.

    • Search Google Scholar
    • Export Citation
  • Kwizak, M., , and A. Robert, 1971: A semi-implicit scheme for grid point atmospheric models of the primitive equations. Mon. Wea. Rev., 99 , 3236.

    • Search Google Scholar
    • Export Citation
  • Laprise, R., , and C. Girard, 1990: A spectral general circulation model using piecewise-constant finite-element representation on a hybrid vertical coordinate system. J. Climate, 3 , 3252.

    • Search Google Scholar
    • Export Citation
  • Laprise, R., , D. Caya, , G. Bergeron, , and M. Giguère, 1997: The formulation of the André Robert MC2 (Mesoscale Compressible Community) model. Numerical Methods in Atmospheric and Oceanic Modeling Atmosphere-Ocean: The Andre J. Robert Memorial Volume, C. A. Lin, R. Laprise, and H. Ritchie, Eds., Canadian Meteorological and Oceanographic Society/NRC Research Press, 195–220.

    • Search Google Scholar
    • Export Citation
  • Pinty, J-P., , R. Benoit, , E. Richard, , and R. Laprise, 1995: Simple tests of a semi-implicit semi-Lagrangian model in 2D mountain wave problems. Mon. Wea. Rev., 123 , 30423058.

    • Search Google Scholar
    • Export Citation
  • Robert, A., 1966: The integration of a low order spectral form of the primitive meteorological equations. J. Meteor. Soc. Japan, 44 , 237244.

    • Search Google Scholar
    • Export Citation
  • Robert, A., 1969: The integration of a spectral model of the atmosphere by the implicit method. Proc. WMO/IUGG Symp. on NWP, Tokyo, Japan, Japan Meteorological Agency, 19–24.

  • Robert, A., 1981: A stable numerical integration scheme for the primitive meteorological equations. Atmos.–Ocean, 19 , 3546.

  • Robert, A., 1982: A semi-Lagrangian and semi-implicit numerical integration scheme for the primitive meteorological equations. J. Meteor. Soc. Japan, 60 , 319325.

    • Search Google Scholar
    • Export Citation
  • Robert, A., , J. Henderson, , and C. Turnbull, 1972: An implicit time integration scheme for baroclinic models of the atmosphere. Mon. Wea. Rev., 100 , 329335.

    • Search Google Scholar
    • Export Citation
  • Robert, A., , T. L. Yee, , and H. Ritchie, 1985: A semi-Lagrangian and semi-implicit numerical integration scheme for multilevel atmospheric models. Mon. Wea. Rev., 113 , 388394.

    • Search Google Scholar
    • Export Citation
  • Schär, C., , D. Leuenberger, , O. Fuhrer, , D. Lüthi, , and C. Girard, 2002: A new terrain-following vertical coordinate formulation for high-resolution numerical weather prediction models. Mon. Wea. Rev., 130 , 24592480.

    • Search Google Scholar
    • Export Citation
  • Simmons, A. J., , B. J. Hoskins, , and D. M. Burridge, 1978: Stability of the semi-implicit method of time integration. Mon. Wea. Rev., 106 , 405412.

    • Search Google Scholar
    • Export Citation
  • Tanguay, M., , A. Robert, , and R. Laprise, 1990: A semi-implicit semi-Lagrangian fully compressible regional forecast model. Mon. Wea. Rev., 118 , 19701980.

    • Search Google Scholar
    • Export Citation
  • Tanguay, M., , E. Yakimiw, , H. Ritchie, , and A. Robert, 1992: Advantages of spatial averaging in semi-implicit semi-Lagrangian schemes. Mon. Wea. Rev., 120 , 113123.

    • Search Google Scholar
    • Export Citation
  • Thomas, S. J., , A. V. Malevsky, , M. Desgagné, , R. Benoit, , P. Pellerin, , and M. Valin, 1997: Massively parallel implementation of the mesoscale compressible community model. Parallel Comput., 23 , 21432160.

    • Search Google Scholar
    • Export Citation
  • Thomas, S. J., , C. Girard, , R. Benoit, , M. Desgagné, , and P. Pellerin, 1998: A new adiabatic kernel for the MC2 model. Atmos.–Ocean, 36 , 241270.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 26 26 1
PDF Downloads 18 18 0

Finescale Topography and the MC2 Dynamics Kernel

View More View Less
  • 1 Recherche en Prévision Numérique, Meteorological Service of Canada, Dorval, Quebec, Canada
© Get Permissions
Restricted access

Abstract

The Canadian Mesoscale Compressible Community (MC2) model provided daily forecasts across the Alps at 3-km resolution during the Mesoscale Alpine Programme (MAP) field phase of 1999. Among the results of this endeavor, some have had an immediate impact on MC2 itself as it increasingly became evident that the model was spuriously too sensitive to finescale orographic forcing. The model solves the Euler equations of motion using a semi-implicit semi-Lagrangian scheme in an oblique terrain-following coordinate. To improve model behavior, typical approaches were tried at first. These included a generalization of the coordinate transformation to make the terrain influence decay much more quickly with height as well as the introduction of nonisothermal basic states to diminish the amplitude of numerical truncation errors. The concept of piecewise-constant finite elements was invoked to reduce coding arbitrariness. But it was later pointed out that the problem was very specific and due to a numerical inconsistency. The true height of model grid points is fixed and known in height-based coordinates. Nevertheless, it was discovered that for this semi-Lagrangian scheme to be consistent, the departure height is an unknown that must be obtained in the same manner as the other unknowns.

Corresponding author address: Claude Girard, Recherche en Prévision Numérique, 2121 Trans-Canada Highway, Room 500, Dorval QC H9P 1J3, Canada. Email: claude.girard@ec.gc.ca

Abstract

The Canadian Mesoscale Compressible Community (MC2) model provided daily forecasts across the Alps at 3-km resolution during the Mesoscale Alpine Programme (MAP) field phase of 1999. Among the results of this endeavor, some have had an immediate impact on MC2 itself as it increasingly became evident that the model was spuriously too sensitive to finescale orographic forcing. The model solves the Euler equations of motion using a semi-implicit semi-Lagrangian scheme in an oblique terrain-following coordinate. To improve model behavior, typical approaches were tried at first. These included a generalization of the coordinate transformation to make the terrain influence decay much more quickly with height as well as the introduction of nonisothermal basic states to diminish the amplitude of numerical truncation errors. The concept of piecewise-constant finite elements was invoked to reduce coding arbitrariness. But it was later pointed out that the problem was very specific and due to a numerical inconsistency. The true height of model grid points is fixed and known in height-based coordinates. Nevertheless, it was discovered that for this semi-Lagrangian scheme to be consistent, the departure height is an unknown that must be obtained in the same manner as the other unknowns.

Corresponding author address: Claude Girard, Recherche en Prévision Numérique, 2121 Trans-Canada Highway, Room 500, Dorval QC H9P 1J3, Canada. Email: claude.girard@ec.gc.ca

Save