Troubles with teleconnections

Rotated principal component analysis (RPCA) is a commonly used tool to detect modes of low-frequency atmospheric circulation variability, also referred to as teleconnections. Teleconnections manifest themselves as distant areas of high negative or positive correlations in sea level pressure, geopotential height, or another variable describing atmospheric circulation. For outputs of RPCA to be valid representations of teleconnections, their spatial patterns (loadings) must correspond to underlying correlation / covariance structures, that is, be in agreement with autocorrelation maps.

When comparing teleconnections identified in different datasets (e.g., between reanalyses, between outputs of climate models, between different periods, between different seasons), the spatial similarity of loadings is evaluated and quantified; if it is low, the datasets are said to disagree in the representation of a particular teleconnection. However, things appear to be less straightforward: It may happen that although the loadings pertaining to the same teleconnection differ, the maps of correlations with the action centres (i.e., points with highest positive or negative loadings) are identical. This may suggest that while the autocorrelation structures are the same in the two datasets, they appear with different weight (intensity). This issue appears to be unrelated to uncertainty due to the number of principal components to rotate; it typically occurs for various reasonable numbers of components.

In our contribution, we (i) introduce the above described issue on several examples (RPCA of different reanalyses, of sliding time periods, and of sliding 93-day seasons), (ii) discuss what is a correct interpretation of such cases (should we consider the teleconnections to be equal or different when the autocorrelation maps agree but the loadings disagree?), and (iii) suggest possible ways out of it (to use oblique instead of orthogonal rotation, to return back to autocorrelation maps).