The Robustness of Barotropic Unstable Modes in a Zonally Varying Atmosphere

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  • 1 Climate Analysis Center/NMC, Washington, D.C.
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Abstract

The unstable normal modes of the barotropic vorticity equation, linearized around an observed zonally varying atmospheric flow, have been related to patterns of observed low-frequency variability. The sensitivity of this problem to changes in the model truncation and diffusion and to details of the basic state flow are examined. Normal modes that are highly sensitive to these changes are found to be of minimal relevance to the low-frequency variability of the atmosphere.

A new numerical method capable of efficiently finding a number of the most unstable modes of large eigenvalue problems is used to examine the effects of model truncation on the instability problem. Most previous studies are found to have utilized models of insufficiently high resolution. A small subset of unstable modes is found to be robust to changes in truncation. Sensitivity to changes in diffusion in a low-resolution model can partially reproduce the truncation results.

Sensitivity to the basic state is examined using a matrix method and by examining the normal modes of perturbed basic states. Again, a small subset of unstable normal modes is found to be robust. These modes appear to agree better with observed patterns of low-frequency variability than do less robust unstable modes.

Abstract

The unstable normal modes of the barotropic vorticity equation, linearized around an observed zonally varying atmospheric flow, have been related to patterns of observed low-frequency variability. The sensitivity of this problem to changes in the model truncation and diffusion and to details of the basic state flow are examined. Normal modes that are highly sensitive to these changes are found to be of minimal relevance to the low-frequency variability of the atmosphere.

A new numerical method capable of efficiently finding a number of the most unstable modes of large eigenvalue problems is used to examine the effects of model truncation on the instability problem. Most previous studies are found to have utilized models of insufficiently high resolution. A small subset of unstable modes is found to be robust to changes in truncation. Sensitivity to changes in diffusion in a low-resolution model can partially reproduce the truncation results.

Sensitivity to the basic state is examined using a matrix method and by examining the normal modes of perturbed basic states. Again, a small subset of unstable normal modes is found to be robust. These modes appear to agree better with observed patterns of low-frequency variability than do less robust unstable modes.

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