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

Konor, Celal S.; Randall, David A.

doi:10.5194/gmd-11-1785-2018

Cited by 3 publications

(3 citation statements)

References 5 publications

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“…However, the Qń Λ k family has a significant spectral gap in the shortest wavelength part of the spectrum that the M GD n family avoids. It is unclear which of the two families will perform better in practice, and it seems likely that both will do poorly, just like C-grid finite difference models with a poorly resolved Rossby radius [17,18,30,32,36].…”

Section: Dispersion Relationshipsmentioning

confidence: 99%

Dispersion analysis of compatible Galerkin schemes on quadrilaterals for shallow water models

Eldred

Roux

2019

Journal of Computational Physics

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Compatible Galerkin methods (the Galerkin analogue of an Arakawa C-Grid) are growing in popularity for simulating geophysical fluid flows, due to their desirable characteristics, including but not limited to: energy conservation, higher-order accuracy, steady geostrophic modes and the absence of spurious stationary modes, such as pressure modes. However, these characteristics still do not guarantee good wave dispersion properties. In this work, we study the dispersion properties of two compatible Galerkin families for the 2D linear rotating shallow water equations on quadrilaterals: the Qń Λ k family from finite element exterior calculus and the newly developed M GD n family. These families are the extensions to quadrilaterals of the P C n´P DG n´1 and GD n´D GD n´1 pairs, respectively, studied for the 1D linear shallow water equations in [13]. A major finding from that paper was that the P C n´P DG n´1 pair has spectral gaps for n ě 2 and the GD n´D GD n´1 does not. These spectral gaps are non-dimensional wavenumbers where the dispersion relationship is double-valued, and lead to anomalous dispersion and noise in numerical simulations. On quadrilaterals, previous work [24, 26] on the Qń Λ k family for inertia waves with n " 2 and for gravity waves for arbitrary n has indicated the presence of spectral gaps, in the form of line discontinuities. The investigation of these gaps for the Qń Λ k family is extended in this paper to inertiagravity waves for arbitrary n, including plots of the dispersion relationship for n " 2 when using the lumping developed in [26, 35] that eliminates the spectral gaps. Additionally, the M GD n family is studied (including the use of reduced quadrature), which is found to be free of spectral gaps. For both families asymptotic convergence rates are established, effective resolutions determined and plots of the dispersion relationships for a range of n and Rossby radii are shown. Finally, a pair of numerical simulations are run to investigate the consequences of the spectral gaps and highlight the main differences between the two families.

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Section: Dispersion Relationshipsmentioning

confidence: 99%

Dispersion analysis of compatible Galerkin schemes on quadrilaterals for shallow water models

Eldred

Roux

2019

Journal of Computational Physics

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“…Part 2 (Konor and Randall, 2018) discusses the dispersion of the middle-latitude Rossby waves for all the horizontal grids.…”

Section: Numerical Simulations Of Waves That Are Forced By Noisy Heatmentioning

confidence: 99%

“…Additional details are given in the Supplement. Finally, Part 2 (Konor and Randall, 2018) discusses the dispersion of Rossby modes on a midlatitude β plane.…”

Section: Introductionmentioning

confidence: 99%

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

Konor

Randall

2018

Geosci. Model Dev.

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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 shallowwater 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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Numerical uncertainties in discretization of the shallow-water equations for weather predication models

Wang

2021

Uncertainties in Numerical Weather Prediction

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

Cited by 3 publications

References 5 publications

Dispersion analysis of compatible Galerkin schemes on quadrilaterals for shallow water models

Dispersion analysis of compatible Galerkin schemes on quadrilaterals for shallow water models

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

Numerical uncertainties in discretization of the shallow-water equations for weather predication models

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