Can principal component analysis provide atmospheric circulation or teleconnection patterns?

Abstract

This investigation examines principal component (PC) methodology and the interpretation of the displays, such as eigenvalue magnitude, loadings and scores, which the methodology provides. The key question posed is, to what extent can S-and T-mode decompositions of a dispersion matrix yield the kinds of interpretations placed on them typically? In particular, a series of experiments are designed based on various amalgamations of three distinct synoptic flow patterns. Since these flow patterns are known, a priori, this allows testing via subtle alterations of the methodology to determine whether there is equivalence between the S-and T-mode decompositions, the degree to which the flow patterns or teleconnections can be recovered by each mode, and the interpretation of each mode.The findings are examined in two contexts: how well they classify the flow patterns, and how well they provide meaningful teleconnections. Both correlation and covariance dispersion matrices are used to determine differences that arise from the standardization. Additionally, unrotated and rotated results are included. By examining a variety of commonly applied methodologies, the results hold for a wider range of studies. Key findings are that eigenvalue degeneracy can influence one mode (but not the other) or both modes for any set of flow patterns resulting in pattern intermixing at times. Similarly, such degeneracy is found in one or both dispersion matrices. Congruence coefficients are used to provide a measure of validity by matching the PC loadings to the parent correlations and covariances. This matching is vital as the loadings exhibit dipoles that have been interpreted historically as physically meaningful, but the present work indicates they may arise purely through the methodology. Overall, we observe that S-mode results can be interpreted as teleconnection patterns and T-mode as flow patterns for well-designed analyses that are meticulously scrutinized for methodological problems.

Annual and seasonal precipitation over Italy from 1961 to 2006

“…In this work, we performed an Smode PCA (Richman, 1986), which 'clusters the stations with similar time behaviour' (Compagnucci and Richman, 2008). In other words, the monthly time series of each station were chosen as input variables for the analysis, so that each column of the data matrix represents a station.…”

Analysis of atmospheric conditions associated to CHACO events of the Low Level Jet East of the Andes and their implications for regional transport

“…A similar approach was applied by Compagnucci and Salles (1997), Salles et al (2001), Compagnucci et al (2001) and Compagnucci and Richman (2008). In this paper, the domain selected to apply the PCA stretches from 10 ∘ N to 60 ∘ S in latitude and from 1.25 ∘ W to 100 ∘ W in longitude and includes 5016 grid points.…”

Identification of Intraseasonal Modes of Variability Using Rotated Principal Components

“…Because positive values exceeding ~ +0.25 correspond to ridges (Richman & Gong, 1999), negative values of ~ -0.25 correspond to troughs, multiplication by -1 reverses the interpretation of the troughs and ridges. Furthermore, the sign of the PC score is multiplied by the sign of the PC loading to obtain a physical interpretation of any monthly map (Compagnucci & Richman, 2008). For example, a negative anomaly in a PC loading map multiplied by a negative PC score gives the interpretation of a positive height anomaly.…”