A New Treatment of the Coriolis Terms in C-Grid Models at Both High and Low Resolutions

A. J. Adcroft Department of Earth, Atmospheres and Planetary Science, Massachusetts Institute of Technology, Cambridge, Massachusetts

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C. N. Hill Department of Earth, Atmospheres and Planetary Science, Massachusetts Institute of Technology, Cambridge, Massachusetts

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J. C. Marshall Department of Earth, Atmospheres and Planetary Science, Massachusetts Institute of Technology, Cambridge, Massachusetts

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Abstract

Numerical models of the ocean typically employ gridpoint techniques in which the dynamical variables defining the state of the ocean are held on a staggered grid. One common arrangement of the variables, known as the Arakawa C-grid, is particularly prone to gridscale noise that is due to spatial averaging of Coriolis terms and that is manifest when the grid resolution is coarse with respect to the deformation radius. Here, the authors analyze the problem in the context of linear inertia–gravity waves and discuss the reason for the prevalence of noise. They suggest a solution to the problem in which the C-grid model variables are augmented with D-grid velocity variables. An analysis of the resulting C–D grid indicates favorable behavior and numerical results are presented to demonstrate this. Finally, they discuss the similarity in nature between the C–D grid and the Z-grid, to explain why the C–D grid works well at both high and low resolution.

Corresponding author address: Dr. Alistair J. Adcroft, MIT 54-1523, 77 Massachusetts Ave., Cambridge, MA 02139.

Email: adcroft@mit.edu

Abstract

Numerical models of the ocean typically employ gridpoint techniques in which the dynamical variables defining the state of the ocean are held on a staggered grid. One common arrangement of the variables, known as the Arakawa C-grid, is particularly prone to gridscale noise that is due to spatial averaging of Coriolis terms and that is manifest when the grid resolution is coarse with respect to the deformation radius. Here, the authors analyze the problem in the context of linear inertia–gravity waves and discuss the reason for the prevalence of noise. They suggest a solution to the problem in which the C-grid model variables are augmented with D-grid velocity variables. An analysis of the resulting C–D grid indicates favorable behavior and numerical results are presented to demonstrate this. Finally, they discuss the similarity in nature between the C–D grid and the Z-grid, to explain why the C–D grid works well at both high and low resolution.

Corresponding author address: Dr. Alistair J. Adcroft, MIT 54-1523, 77 Massachusetts Ave., Cambridge, MA 02139.

Email: adcroft@mit.edu

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