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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Volume 11, issue 5 | Copyright
Geosci. Model Dev., 11, 1753-1784, 2018
https://doi.org/10.5194/gmd-11-1753-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Methods for assessment of models 08 May 2018

Methods for assessment of models | 08 May 2018

Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 1: Nonhydrostatic inertia–gravity modes

Celal S. Konor and David A. Randall Celal S. Konor and David A. Randall
  • Department of Atmospheric Science, Colorado State University, Fort Collins, CO 80523, USA

Abstract. We have used a normal-mode analysis to investigate the impacts of the horizontal and vertical discretizations on the numerical solutions of the nonhydrostatic anelastic inertia–gravity modes on a midlatitude f plane. The dispersion equations are derived from the linearized anelastic equations that are 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 both horizontal grid spacing and vertical wavenumber are analyzed, and the role of nonhydrostatic effects is discussed. We also compare the results of the normal-mode analyses with numerical solutions obtained by running linearized numerical models based on the various horizontal grids. The sources and behaviors of the computational modes in the numerical simulations are also examined.

Our normal-mode analyses with the Z, C, D, A, E and B grids generally confirm the conclusions of previous shallow-water studies for the cyclone-resolving scales (with low horizontal wavenumbers). We conclude that, aided by nonhydrostatic effects, the Z and C grids become overall more accurate for cloud-resolving resolutions (with high horizontal wavenumbers) than for the cyclone-resolving scales.

A companion paper, Part 2, discusses the impacts of the discretization on the Rossby modes on a midlatitude β plane.

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We have discussed the discretizations of the three-dimensional nonhydrostatic linearized anelastic equations on the A, B, C, CD, (DC), D, E and Z horizontal grids, and on the L and CP vertical grids, with an emphasis on midlatitude inertia–gravity waves. The Z and C grids show the most accurate dispersion among the seven horizontal grids. The inertia–gravity mode solutions with the D and CD grids are almost identical. The A, B and E grids suffer from the multiple (or non-unique) physical modes.
We have discussed the discretizations of the three-dimensional nonhydrostatic linearized...
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