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On the Adequacy of Meridional Resolution of Linear and Quasi-Linear Barotropic Models

Sumant NigamDepartment of Earth, Atmospheric, and Planetary Sciences, MIT, Cambridge, MA 02139

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Abstract

The minimum meridional resolution needed for an adequate numerical simulation of the linear and “quasi-linear” baroscopic vorticity dynamics in the vicinity of a critical latitude is determined by using a semi-spectral nondivergent barotropic model on a sphere. The high resolution barotropic calculations of Nigam and Held in which the stationary waves are forced by the earth's orography are repeated with several lower meridional resolutions. Comparison of the lower resolution simulations with the higher resolution ones (the “true solutions”) shows the quality of both the linear and the quasi-linear simulations to deteriorate with decreasing meridional resolution.

An unresolved critical latitude results in spurious sensitivity of the steady linear response to the tropical zonal wind structure, whereas a critical latitude resolved using a strong damping coefficient rather than a fine latitudinal grid may result in the attenuation of any genuinely reflected wave at the critical latitude. For a Rayleigh damping coefficient of (13.5 days)−1, a latitudinal resolution of Δθ <3° is found to be sufficient for an adequate simulation of planetary waves in the quasi-linear model; the linear model, for a commensurate quality of simulation, needs a Δθ< 2°. While this choice of the damping coefficient is arbitrary to some extent, the obtained solutions do have structure similar to that seen in the observed wintertime stationary planetary waves.

Abstract

The minimum meridional resolution needed for an adequate numerical simulation of the linear and “quasi-linear” baroscopic vorticity dynamics in the vicinity of a critical latitude is determined by using a semi-spectral nondivergent barotropic model on a sphere. The high resolution barotropic calculations of Nigam and Held in which the stationary waves are forced by the earth's orography are repeated with several lower meridional resolutions. Comparison of the lower resolution simulations with the higher resolution ones (the “true solutions”) shows the quality of both the linear and the quasi-linear simulations to deteriorate with decreasing meridional resolution.

An unresolved critical latitude results in spurious sensitivity of the steady linear response to the tropical zonal wind structure, whereas a critical latitude resolved using a strong damping coefficient rather than a fine latitudinal grid may result in the attenuation of any genuinely reflected wave at the critical latitude. For a Rayleigh damping coefficient of (13.5 days)−1, a latitudinal resolution of Δθ <3° is found to be sufficient for an adequate simulation of planetary waves in the quasi-linear model; the linear model, for a commensurate quality of simulation, needs a Δθ< 2°. While this choice of the damping coefficient is arbitrary to some extent, the obtained solutions do have structure similar to that seen in the observed wintertime stationary planetary waves.

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