You’re right. Data decomposition and reconstruction by principal components goes badly awry whenever the premises of the Karhunen-Loeve expansion, which underlies all PC methods, are forgotten. The most fundamental premise is some well-defined spatio-temporal frame over which there are multiple data sets. The whole purpose of the KH expansion was to reduce these data sets to more economical, more-easily intelligible metrics.

It is one thing to obtain the natural eigenmodes of tidal oscillation of some basin such as the Black Sea from partially incomplete data. It is quite another to try to determine the temperature record throughout Antartica, which is not spatially homogeneous, has no natural time frame apart from the diurnal and annual, and lacks adequate data, to begin with. Sadly, the mistaken idea that PC methods cure all data deficiencies has taken hold in some quarters and often leads to the travesty of highly arbitrary results so clearly displayed by Ryan’s tiles.

Whenever PCs are used as a time-series analysis tool over time-frames that are not naturally defined, it should arouse the suspicion that someone is trying to claim more information than is truly available in the data.

It’s getting to where a new variation of Climate Science is being born, that of Statistical Climate Sciences. It’s being proven, again and again, that the choice of PC’s and regpars have an effect on the results, causing drastic changes with the same data being used.

Considering that the “Team” has stated they’re not statisticians, and have refused help from mainstream statisticians, then some statisticians need to step forward and post articles in their OWN peer-reviewed journals. They’re not being heard in the “climate” journals…