# Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes

## 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.

- Authors:

- Publication Date:

- Research Org.:
- Colorado State Univ., Fort Collins, CO (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23); National Science Foundation (NSF)

- OSTI Identifier:
- 1436358

- Alternate Identifier(s):
- OSTI ID: 1505825

- Grant/Contract Number:
- SC0016273; SC0007050; SC0016305; AGS-1500187

- Resource Type:
- Published Article

- Journal Name:
- Geoscientific Model Development (Online)

- Additional Journal Information:
- Journal Name: Geoscientific Model Development (Online) Journal Volume: 11 Journal Issue: 5; Journal ID: ISSN 1991-9603

- Publisher:
- European Geosciences Union

- Country of Publication:
- Germany

- Language:
- English

- Subject:
- 58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Konor, Celal S., and Randall, David A. Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes. Germany: N. p., 2018.
Web. doi:10.5194/gmd-11-1785-2018.
```

```
Konor, Celal S., & Randall, David A. Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes. Germany. doi:10.5194/gmd-11-1785-2018.
```

```
Konor, Celal S., and Randall, David A. Tue .
"Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes". Germany. doi:10.5194/gmd-11-1785-2018.
```

```
@article{osti_1436358,
```

title = {Impacts of the horizontal and vertical grids on the numerical solutions of the dynamical equations – Part 2: Quasi-geostrophic Rossby modes},

author = {Konor, Celal S. and Randall, David A.},

abstractNote = {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.},

doi = {10.5194/gmd-11-1785-2018},

journal = {Geoscientific Model Development (Online)},

number = 5,

volume = 11,

place = {Germany},

year = {2018},

month = {5}

}

DOI: 10.5194/gmd-11-1785-2018

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

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

journal, January 2018

- Konor, Celal S.; Randall, David A.
- Geoscientific Model Development, Vol. 11, Issue 5