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Using Neutral Singular Vectors to Study Low-Frequency Atmospheric Variability

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  • 1 Program in Atmospheres, Oceans and Climate, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

The authors explore the use of the “neutral vectors” of a linearized version of a global quasigeostrophic atmospheric model with realistic mean flow in the study of the nonlinear model's low-frequency variability. Neutral vectors are the (right) singular vectors of the linearized model's tendency matrix that have the smallest eigenvalues; they are also the patterns that exhibit the largest response to forcing perturbations in the linear model. A striking similarity is found between neutral vectors and the dominant patterns of variability (EOFs) observed in both the full nonlinear model and in the real world. The authors discuss the physical and mathematical connection between neutral vectors and EOFs.

Investigation of the “optimal forcing patterns”—the left singular vectors—proves to be less fruitful. The neutral modes have equivalent barotropic vertical structure, but their optimal forcing patterns are baroclinic and seem to be associated with low-level heating. But the horizontal patterns of the forcing patterns are not robust and are sensitive to the form of the inner product used in the singular vector decomposition analysis. Additionally, applying “optimal” forcing patterns as perturbations to the full nonlinear model does not generate the response suggested by the linear model.

Corresponding author address: Jason C. Goodman, Department of Geophysical Sciences, University of Chicago, 5734 S. Ellis Ave., Chicago, IL 60640. Email: goodmanj@uchicago.edu

Abstract

The authors explore the use of the “neutral vectors” of a linearized version of a global quasigeostrophic atmospheric model with realistic mean flow in the study of the nonlinear model's low-frequency variability. Neutral vectors are the (right) singular vectors of the linearized model's tendency matrix that have the smallest eigenvalues; they are also the patterns that exhibit the largest response to forcing perturbations in the linear model. A striking similarity is found between neutral vectors and the dominant patterns of variability (EOFs) observed in both the full nonlinear model and in the real world. The authors discuss the physical and mathematical connection between neutral vectors and EOFs.

Investigation of the “optimal forcing patterns”—the left singular vectors—proves to be less fruitful. The neutral modes have equivalent barotropic vertical structure, but their optimal forcing patterns are baroclinic and seem to be associated with low-level heating. But the horizontal patterns of the forcing patterns are not robust and are sensitive to the form of the inner product used in the singular vector decomposition analysis. Additionally, applying “optimal” forcing patterns as perturbations to the full nonlinear model does not generate the response suggested by the linear model.

Corresponding author address: Jason C. Goodman, Department of Geophysical Sciences, University of Chicago, 5734 S. Ellis Ave., Chicago, IL 60640. Email: goodmanj@uchicago.edu

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