Climate regionalization and rotation of principal components

Climate regionalization studies have made intensive use of eigenvector analysis in recent literature. This analysis provides a motivation for examination of the efficacy and validity of variations of principal component analysis (PCA) for such tasks as an eigenvector‐based regionalization. Specifically, this study applies the results of an earlier statistical comparison of rotational schemes to monthly Pennsylvanian precipitation data (1958–1978) to analyse differences among the various solutions. Unrotated, orthogonally rotated, and obliquely rotated solutions (eight in total) are compared in order to assess the model and locational consistency among and within these solutions. Model correspondence and consistency are measured by a congruence coefficient used to match (i) the principal components (PC) of the total domain for the selected benchmark pattern with PCs from the total domains of the remaining seven solutions, and (ii) each PC of the total domain with PCs of 25 randomly selected subdomain pairs (a set of 10 and 11 years of data). Locational or geographical consistency among the PC patterns is determined by quantifying the changes in area and area boundary defined by a threshold loading. The results from the Pennsylvanian data indicated that substantial differences in regionalization arose solely from the choice of a particular rotation algorithm, or lack thereof. Oblique rotations were generally found to be the most stable, whereas the orthogonally rotated and unrotated solutions were less stable. The quantitative areal differences among rotation schemes and the unrotated solution illustrate the inherent danger in blindly applying any given solution if physical interpretation of the regionalization is important. The quantitative areal and boundary differences may particularly influence PCA over global spatial domains.