Principal oscillation pattern analysis of the 30‐ to 60‐day oscillation in general circulation model equatorial troposphere

Abstract

A new technique is described for identifying time-dependent patterns (i.e., "principal oscillation patterns," or POPs) in a set of geophysical time series. POPs are defined as the normal modes of a linear dynamical representation of the data in terms of a first-order autoregressive vector process with residual noise forcing. POPs associated with real eigenvalues represent nonpropagating, nonoscillatory patterns which decay exponentially. POPs associated with complex eigenvalues occur in complex conjugate pairs and can represent standing wave structures (if one pattern is much stronger than the other), propagating waves (if both patterns are periodic and have the same structure except for a quarter-wavelength shift) or, in general, an arbitrary amphidromal oscillation. After the POPs have been defined for a selected set of primary variables, associated correlation or composite patterns may be derived for additional secondary fields to gain further insight into the structure of the interaction mechanisms. Principal Oscillation Pattern AnalysisIn this paper we describe and apply a new technique for analyzing spatial and temporal variability in a multicomponent data set. The "principal oscillation pattern" (POP) analysis identifies coherent migrating, standing, or otherwise changing patterns of the system without prior knowledge of the system dynamics. The basic approach is to represent the vector time series as the output of a multivariate first-order autoregressive process forced by residual noise (not necessarily white noise). The process matrix is estimated from the data. The POPs are defined as the real or complex eigenvectors of the process matrix, with associated real or complex eigenvalues. Complex POPs occur in complex conjugate pairs and represent damped amphidromal oscillations (including propagating and standing waves as special cases), while real POPs occur as singlets and describe nonpropagating, nonoscillating, damped patterns. In the continuous case the POP analysis corresponds to the normal-mode analysis of a linear system of differential equations.Copyright 1988 by the American Geophysical Union. Paper number 8D0305.0148-0227/88/008D-0305505.00The method described here represents the linearized form of the more general "principal interaction pattern" (PIP) technique for constructing simplified dynamical models to approximate complex nonlinear systems with many degrees of freedom [cf. Hasselmann, this issue]. In the present application, however, we emphasize the diagnostic rather than the dynamical aspects of the method. Thus we introduce a further simplification of the general technique in addition to the linearization. Rather than simultaneously seeking both the optimal linear model (i.e., the Markov system matrix) and the optimal vector subspace in which the model is to be constructed, in accordance with the general PIPs and POPs philosophy, we regard the vector subspace as given. We carry out a standard reduction of the number of variables by using a relatively small set of empirical orthogonal...

A delayed oscillator model for the quasi-periodic multidecadal variability of the NAO

“…Principal Oscillation Pattern (POP) analysis (von Storch et al 1988) was applied to investigate the dominant SST patterns of the oscillatory multidecadal variability. In contrast to Empirical Orthogonal Function (EOF) analysis, which considers only the spatial co-variability in a dataset, the POP method considers the full spatiotemporal structure.…”

Spatio-temporal statistical models with application to atmospheric processes

“…POPs were reformulated by von Storch et al (1988) and extended to complex fields by Biirger (1993). Recent years have seen a substantial increase in the number of POP applications in the literature.…”

“…After filtering, it is hoped that the spatial patterns of the empirical normal modes can illustrate the spatial structure of the phenomenon of interest as it evolves in time. For example, von Storch et al (1988) used POPs to consider the equatorial 30-60 day oscillation (Madden and Julian 1971).…”

“…EOFs (e.g., Preisendorfer 1988), spatio-temporal Canonical Correlation Analysis or CCA (e.g., , and Principal Oscillation Patterns or POPs (e.g., von Storch et al 1988von Storch et al ,1994. These are excellent tools with which to summarize data and have, to a lesser extent, sometimes been considered for prediction..…”

“…For example, in climatology we are typically interested in the time evolution of certain atmospheric parame ters (e.g., wind, temperature, precipitation) over specified spatial domains. In the atmospheric sciences, many methods have been developed to examine such spatio-temporal variability: Em pirical Orthogonal Functions or EOFs (e.g., Preisendorfer 1988), spatio-tempora:l Canonical Correlation Analysis or CCA (e.g., , and Prin cipal Oscillation Patterns or POPs (e.g., von Storch et al 1988von Storch et al ,1994.…”