Computational Dispersion Properties of Horizontal Staggered Grids for Atmospheric and Ocean Models

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  • 1 Laboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, Maryland
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Abstract

The computational dispersion properties of horizontally and time-horizontally staggered grids using corresponding centered-difference schemes for approximation of the Adjustment, or gravity wave equation, are analyzed in terms of their group velocity characteristics. Results are obtained for atmospheric and oceanic models, the latter being characterized by a much smaller Rossby radius of deformation. Three best time-horizontally staggered grids have practically the same advantageous computational dispersion properties as the Arakawa C grid for both atmospheric and oceanic models—namely, the time-staggered D (or Eliassen) and time-staggered C (only with a semi-implicit scheme) grids—and to a certain extent the Lilly grid. Both, the Arakawa B and the time-staggered A grids for atmospheric and oceanic models, along with the Arakawa E and the time-staggered E grids only for atmospheric models (although having worse dispersion properties) also may be used as additional practical options. For all grids considered some additional filtering is needed to control and even eliminate waves with poor computational dispersion characteristics.

Note that along with the B grid widely used in ocean models, the Arakawa C grid, the time-staggered A grid, and especially the time-staggered D (or Eliassen) and C (only with a semi-implicit scheme) grids can be recommended for practical use. The two latter grids have the best dispersion characteristics for ocean models among all staggered grids considered.

Due to the staggering procedure, the grids have enhanced effective resolution that corresponds to the regular Arakawa A grid with half horizontal intervals. Approximate comparative estimates of computation time requirements for different staggered grids versus that of a regular grid are presented for advection and adjustment terms.

Computational dispersion properties along with other computational characteristics and requirements provide some guidance for an optimal choice of an appropriate grid for an atmospheric or ocean model.

Abstract

The computational dispersion properties of horizontally and time-horizontally staggered grids using corresponding centered-difference schemes for approximation of the Adjustment, or gravity wave equation, are analyzed in terms of their group velocity characteristics. Results are obtained for atmospheric and oceanic models, the latter being characterized by a much smaller Rossby radius of deformation. Three best time-horizontally staggered grids have practically the same advantageous computational dispersion properties as the Arakawa C grid for both atmospheric and oceanic models—namely, the time-staggered D (or Eliassen) and time-staggered C (only with a semi-implicit scheme) grids—and to a certain extent the Lilly grid. Both, the Arakawa B and the time-staggered A grids for atmospheric and oceanic models, along with the Arakawa E and the time-staggered E grids only for atmospheric models (although having worse dispersion properties) also may be used as additional practical options. For all grids considered some additional filtering is needed to control and even eliminate waves with poor computational dispersion characteristics.

Note that along with the B grid widely used in ocean models, the Arakawa C grid, the time-staggered A grid, and especially the time-staggered D (or Eliassen) and C (only with a semi-implicit scheme) grids can be recommended for practical use. The two latter grids have the best dispersion characteristics for ocean models among all staggered grids considered.

Due to the staggering procedure, the grids have enhanced effective resolution that corresponds to the regular Arakawa A grid with half horizontal intervals. Approximate comparative estimates of computation time requirements for different staggered grids versus that of a regular grid are presented for advection and adjustment terms.

Computational dispersion properties along with other computational characteristics and requirements provide some guidance for an optimal choice of an appropriate grid for an atmospheric or ocean model.

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