• Bender, C. M., , and S. A. Orszag, 1978: Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill, 593 pp.

  • Bracewell, R. N., 2000: The Fourier Transform and Its Applications. 3rd ed. McGraw-Hill, 640 pp.

  • Caian, M., , and J.-F. Geleyn, 1997: Some limits to the variable-mesh solution and comparison with the nested-LAM solution. Quart. J. Roy. Meteor. Soc., 123, 743766.

    • Search Google Scholar
    • Export Citation
  • Côté, J., , S. Gravel, , A. Méthot, , A. Patoine, , M. Roch, , and A. Staniforth, 1997: Preliminary results from a dry global variable-resolution primitive equations model. Numerical Methods in Atmospheric and Oceanic Modelling: The André J. Robert Memorial Volume, C. A. Lin, R. Laprise, and H. Ritchie, Eds., Canadian Meteorological and Oceanographic Society, 245–259.

    • Search Google Scholar
    • Export Citation
  • Côté, J., , S. Gravel, , A. Méthot, , A. Patoine, , M. Roch, , and A. Staniforth, 1998: The operational CMC–MRB Global Environmental Multiscale (GEM) model. Part I: Design considerations and formulation. Mon. Wea. Rev., 126, 13731395.

    • Search Google Scholar
    • Export Citation
  • Courtier, P., , and J.-F. Geleyn, 1988: A global numerical weather prediction model with variable resolution: Application to the shallow-water equations. Quart. J. Roy. Meteor. Soc., 114, 13211346.

    • Search Google Scholar
    • Export Citation
  • Déqué, M., , and J. P. Piedelièvre, 1995: High resolution climate simulation over Europe. Climate Dyn., 11, 321339.

  • 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, 29432968.

    • Search Google Scholar
    • Export Citation
  • Fox-Rabinovitz, M. S., , E. H. Berbery, , L. L. Takacs, , and R. C. Govindaraju, 2005: A multiyear ensemble simulation of the U.S. climate with a stretched-grid GCM. Mon. Wea. Rev., 133, 25052525.

    • Search Google Scholar
    • Export Citation
  • Fox-Rabinovitz, M. S., , J. Côté, , B. Dugas, , M. Déqué, , and J. L. McGregor, 2006: Variable resolution general circulation models: Stretched-Grid Model Intercomparison Project (SGMIP). J. Geophys. Res., 111, D16104, doi:10.1029/2005JD006520.

    • Search Google Scholar
    • Export Citation
  • Fox-Rabinovitz, M. S., , J. Côté, , B. Dugas, , M. Déqué, , J. L. McGregor, , and A. Belochitski, 2008: Stretched-grid Model Intercomparison Project: Decadal regional climate simulations with enhanced variable and uniform-resolution GCMs. Meteor. Atmos. Phys., 100, 159177.

    • Search Google Scholar
    • Export Citation
  • Gibelin, A. L., , and M. Déqué, 2003: Anthropogenic climate change over the Mediterranean region simulated by a global variable resolution model. Climate Dyn., 20, 327339.

    • Search Google Scholar
    • Export Citation
  • Laprise, R., 2008: Regional climate modelling. J. Comput. Phys., 227, 36413666.

  • McGregor, J. L., , K. C. Nguyen, , and J. J. Katzfey, 2002: Regional climate simulations using a stretched-grid global model. Research Activities in Atmospheric and Oceanic Modelling, WMO Tech. Doc. 1105, Rep. 32, 3.15–3.16.

    • Search Google Scholar
    • Export Citation
  • Schmidt, F., 1977: Variable fine mesh in the spectral global models. Beitr. Phys. Atmos., 50, 211217.

  • Shapiro, R., 1970: Smoothing, filtering, and boundary effects. Rev. Geophys. Space Phys., 8, 359387.

  • Surcel, D., 2005: Filtres universels pour les modèles numériques à résolution variable. M.S. thesis, Dept. of Earth and Atmospheric Sciences, Université du Québec à Montréal, 104 pp.

    • Search Google Scholar
    • Export Citation
  • Takacs, L., , W. Sawyer, , M. J. Suarez, , and M. S. Fox-Rabinovitz, 1999: Filtering techniques on a stretched grid general circulation model. NASA Tech. Memo. 104606, Vol. 16, 45 pp. [Available from Data Assimilation Office, NASA GSFC, Greenbelt, MD 20771.]

    • Search Google Scholar
    • Export Citation
  • Thatcher, M., , and J. L. McGregor, 2009: Using a scale-selective filter for dynamical downscaling with the Conformal Cubic Atmospheric Model. Mon. Wea. Rev., 137, 17421752.

    • Search Google Scholar
    • Export Citation
  • Yessad, K., , and P. Bénard, 1996: Introduction of a local mapping factor in the spectral part of the Météo-France global variable mesh numerical weather forecast model. Quart. J. Roy. Meteor. Soc., 122, 17011719.

    • Search Google Scholar
    • Export Citation
  • Zadra, A., , D. Caya, , J. Cote, , B. Dugas, , C. Jones, , R. Laprise, , K. Winger, , and L.-P. Caron, 2008: The next Canadian Regional Climate Model. Phys. Canada, 64, 7583.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 25 25 6
PDF Downloads 15 15 4

A General Filter for Stretched-Grid Models: Application in Cartesian Geometry

View More View Less
  • 1 ESCER Centre, Université du Québec à Montréal, Montréal, Québec, Canada
© Get Permissions
Restricted access

Abstract

Global climate models with variable resolution are effective means to represent regional scales over an area of interest while avoiding the nesting issues of limited-area models. The stretched-grid approach provides a dynamical downscaling approach that naturally allows two-way interactions between the regional and global scales of motion. Concentrating the resolution over a subset of the earth’s surface increases computational efficiency and reduces the computational costs compared to global uniform high-resolution models; however, it does not come free of some problems related to the variation of resolution.

To address the issues associated with the stretching and anisotropy of the computational grid, a general convolution filter with a flexible response function is developed. The main feature of this filter is to locally remove scales shorter than a user-prescribed spatially varying length scale. The filtering effectiveness and computational efficiency of the filter can be custom tailored by an appropriate compromise between the filtering response and the width of the convolution stencil. This approach has been tested in one- and two-dimensional Cartesian geometry. It is shown that an effective filter can be obtained using a limited spatial stencil for the convolution to reduce computational cost, and that an adjustable spatially variable and nearly isotropic response can be obtained for application on variable grids.

Corresponding author address: Dorina Surcel, Centre ESCER, Université du Québec à Montréal, Case postale 8888, Succursale Centre-ville, Montréal QC H3C 3P8, Canada. E-mail: colan@sca.uqam.ca

Abstract

Global climate models with variable resolution are effective means to represent regional scales over an area of interest while avoiding the nesting issues of limited-area models. The stretched-grid approach provides a dynamical downscaling approach that naturally allows two-way interactions between the regional and global scales of motion. Concentrating the resolution over a subset of the earth’s surface increases computational efficiency and reduces the computational costs compared to global uniform high-resolution models; however, it does not come free of some problems related to the variation of resolution.

To address the issues associated with the stretching and anisotropy of the computational grid, a general convolution filter with a flexible response function is developed. The main feature of this filter is to locally remove scales shorter than a user-prescribed spatially varying length scale. The filtering effectiveness and computational efficiency of the filter can be custom tailored by an appropriate compromise between the filtering response and the width of the convolution stencil. This approach has been tested in one- and two-dimensional Cartesian geometry. It is shown that an effective filter can be obtained using a limited spatial stencil for the convolution to reduce computational cost, and that an adjustable spatially variable and nearly isotropic response can be obtained for application on variable grids.

Corresponding author address: Dorina Surcel, Centre ESCER, Université du Québec à Montréal, Case postale 8888, Succursale Centre-ville, Montréal QC H3C 3P8, Canada. E-mail: colan@sca.uqam.ca
Save