Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
https://doi.org/10.5194/gmd-2017-234
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Methods for assessment of models
22 Dec 2017
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Geoscientific Model Development (GMD).
Impacts of the Horizontal and Vertical Grids on the Numerical Solutions of the Dynamical Equations. Part I: Nonhydrostatic Inertia-Gravity Modes
Celal S Konor and David A. Randall Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado, 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 wave number 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 for cloud-resolving resolutions (with high horizontal wavenumbers) the Z and C grids become overall more accurate than for the cyclone-resolving scales, aided by nonhydrostatic effects.

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


Citation: Konor, C. S. and Randall, D. A.: Impacts of the Horizontal and Vertical Grids on the Numerical Solutions of the Dynamical Equations. Part I: Nonhydrostatic Inertia-Gravity Modes, Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2017-234, in review, 2017.
Celal S Konor and David A. Randall
Celal S Konor and David A. Randall
Celal S Konor and David A. Randall

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Short summary
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 the L and CP vertical grids, with an emphasis on middle-latitude inertia-gravity waves. The Z and C grids are 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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