Abstract
Given the complexity of climate systems, trends are generally expected to have both global and local features. The use of Empirical Orthogonal Function (EOF) analysis to decompose these different trends has been brought into question. In this paper we show that for land regions of the order of size of most countries the first Principal Component (PC) obtained by EOF analysis in fact captures the entire trend of the time series. We demonstrate a simple linear relation relating the amount of variance described by PCs and the size of the system. We provide a novel normalisation and ordering of the PCs, and show that this provides important insight for larger more complex regions where several PCs are added. We apply this framework along with a recently introduced method to deal with long range correlations to the study of warming trends in the polar regions between 1979 and 2023. We find a significant Arctic warming trend of K/dec. In the case of Antarctica we find insignificant trends both for West Antarctica and East Antarctica (including ice sheets) of K/dec. and K/dec. respectively.