Using singular vectors to study low-frequency atmospheric variability

In this work, we attempt to identify dynamical modes in the atmosphere that exhibit prominent low-frequency variability, and which may be implicated in atmosphere-ocean coupled interaction.

We study the "neutral vectors" of a linearized version of a 3-layer quasi-geostrophic model with realistic mean flow. 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. We find a striking similarity between neutral vectors and the dominant patterns of variability (EOFs) observed in both the full nonlinear model and in the real world. We provide a mathematical explanation for this connection.

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 SVD analysis. Additionally, applying "optimal" forcing patterns as perturbations to the full nonlinear model does not generate the response suggested by the linear model.