THE EFFECT OF DOMAIN SHAPE ON PRINCIPAL COMPONENTS ANALYSES

In a recent article, Richman criticized principal components analysis for not reflecting the spatial covariance structure observed in the data owing to an overdependence on the shape of the domain. This assertion, originally posited by Buell, is re-examined using Buell's correlation functions and the geophysically based studies cited by Richman. Two examples-gauge-corrected, global precipitation and global surface air temperature-are given to illustrate that even though both fields are from the same domain, maps of the spatial distribution of the loadings on the first four principal components are highly dissimilar. These fields are mapped using a rectangular (cylindrical equal-area) projection and compared with other geophysically based studies that have employed rectangularly shaped domains as well as the rectangular domain mapping of Buell's correlation functions. Results indicate that component loading patterns are mainly determined by the structure exhibited in the dispersion matrix and only influenced by the domain shape (through spatial autocorrelation) to a limited degree.