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Geosci. Model Dev., 11, 1785-1797, 2018
https://doi.org/10.5194/gmd-11-1785-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Methods for assessment of models
08 May 2018
Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes
Celal S. Konor and David A. Randall Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523, USA
Abstract. We use a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the quasi-geostrophic anelastic baroclinic and barotropic Rossby modes on a midlatitude β plane. The dispersion equations are derived for the linearized anelastic system, discretized on the Z, C, D, CD, (DC), A, E and B horizontal grids, and on the L and CP vertical grids. The effects of various horizontal grid spacings and vertical wavenumbers are discussed. A companion paper, Part 1, discusses the impacts of the discretization on the inertia–gravity modes on a midlatitude f plane.

The results of our normal-mode analyses for the Rossby waves overall support the conclusions of the previous studies obtained with the shallow-water equations. We identify an area of disagreement with the E-grid solution.

Citation: Konor, C. S. and Randall, D. A.: Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes, Geosci. Model Dev., 11, 1785-1797, https://doi.org/10.5194/gmd-11-1785-2018, 2018.
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Short summary
We have discussed the effects of discretization on dispersion of midlatitude Rossby waves on the A, B, C, CD, (DC), D, E and Z horizontal grids, and the L and CP vertical grids. The Z, C, D and CD (DC) grids generate similar dispersion of the baroclinic and barotropic Rossby modes. The A, E and B grids generate multiple (non-unique) solutions. The modes with the smallest resolvable vertical scale on the L grid do not retrograde. The CP-grid solutions are much more accurate than the L grid.
We have discussed the effects of discretization on dispersion of midlatitude Rossby waves on the...
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