Representation of Modes of Atmospheric Circulation Variability by Self‐Organizing Maps: A Study Using Synthetic Data

Abstract Self‐organizing maps (SOMs) represent a popular tool for classifying atmospheric circulation patterns. One of their traditional applications has been to link typical synoptic‐scale patterns to large‐scale teleconnections, or modes of low‐frequency circulation variability. However, recently there have been attempts to interpret an array of SOM nodes directly as a continuum of teleconnections, grounded in SOMs' ability to combine two otherwise distinct approaches to data analysis, that is, exploratory projection (or, dimensionality reduction) and classification. This conceptual shift calls for methodological studies that would improve our understanding of how orthogonal modes of variability, typically used to describe teleconnections, relate to SOM outputs. Here, we define three idealized modes of variability and use their various combinations to generate synthetic data sets. Many variants of SOMs are generated for SOMs of various shapes and sizes. The results show that projection of modes on a SOM array is sensitive not only to data structure, but also to various SOM parameters. The leading mode of variability projects rather strongly on SOMs if its explained variance is markedly higher than that of the second‐order mode; the remaining modes project considerably more weakly, and all modes tend to blend when their explained variance is similar, which leads to underrepresentation of some phases of modes and/or combinations of modes among the SOM patterns. Furthermore, we show that some features of SOM topology that were previously considered a proof of data nonlinearity appear even if the underlying modes of variability are strictly linear.