Component extraction techniques are used widely in the analysis and interpretation of high-dimensional climate datasets such as global sea surface temperatures (SSTs). Principal component analysis (PCA), a frequently used component extraction technique, provides an orthogonal representation of the multivariate dataset and maximizes the variance explained by successive components. A disadvantage of PCA, however, is that the interpretability of the second and higher components may be limited. For this reason, a Varimax rotation is often applied to the PCA solution to enhance the interpretability of the components by maximizing a simple structure. An alternative rotational approach is known as independent component analysis (ICA), which finds a set of underlying 'source signals' which drive the multivariate 'mixed' dataset. Here we compare the capacity of PCA, the Varimax rotation and ICA in explaining climate variability present in globally distributed SST anomaly (SSTA) data. We find that phenomena which are global in extent, such as the global warming trend and the El Niño-Southern Oscillation (ENSO), are well represented using PCA. In contrast, the Varimax rotation provides distinct advantages in interpreting more localized phenomena such as variability in the tropical Atlantic. Finally, our analysis suggests that the interpretability of independent components (ICs) appears to be low. This does not diminish the statistical advantages of deriving components that are mutually independent, with potential applications ranging from synthetically generating multivariate datasets, developing statistical forecasts, and reconstructing spatial datasets from patchy observations at multiple point locations.