Empirical Normal-Mode Analysis of Atmospheric Data

Abstract

Abstract The theory of empirical orthogonal functions (EOFs) is generalized in the context of normal modes on unidirectional sheared flows, at first using small disturbance to a monotonic potential vorticity basic state. A wave function is introduced (so called because of a partial analogy with quantum mechanical wave function), via the pseudomomentum, and is used to define the covariance matrix needed in an EOF analysis. The resulting new formalism comprises a fundamental, simpler and more physically insightful, version of EOF theory: it allows empirical reconstruction of the normal modes excited in an atmospheric time series, their respective variances, and phase speed relationship. This new approach permits quantitative and qualitative discussions of the underlying wave mechanisms present in a sheared flow. The theory is given for a hierarchy of models starting with the linearized quasigeostrophic equations. The extent to which these concepts carry over to nonlinear finite-amplitude disturbance is inve...