Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

4.3. Spatial and Temporal Variation in Atmospheric Science 71Interpretations of the first 11 PCs for the two age groups are given inTable 4.4, together with the percentage of total variation accounted for byeach PC. The variances of corresponding PCs for the two age groups differvery little, and there are similar interpretations for several pairs of PCs, forexample the first, second, sixth and eighth. In other cases there are groupsof PCs involving the same variables, but in different combinations for thetwo age groups, for example the third, fourth and fifth PCs. Similarly, theninth and tenth PCs involve the same variables for the two age groups, butthe order of the PCs is reversed.Principal component analysis has also been found useful in other demographicstudies, one of the earliest being that described by Moser andScott (1961). In this study, there were 57 demographic variables measuredfor 157 British towns. A PCA of these data showed that, unlike the elderlydata, dimensionality could be vastly reduced; there are 57 variables, butas few as four PCs account for 63% of the total variation. These PCs alsohave ready interpretations as measures of social class, population growthfrom 1931 to 1951, population growth after 1951, and overcrowding.Similar studies have been done on local authority areas in the UK byImber (1977) and Webber and Craig (1978) (see also Jolliffe et al. (1986)).In each of these studies, as well as Moser and Scott (1961) and the ‘elderly athome’ project, the main objective was to classify the local authorities, townsor elderly individuals, and the PCA was done as a prelude to, or as partof, cluster analysis. The use of PCA in cluster analysis is discussed furtherin Section 9.2, but the PCA in each study mentioned here provided usefulinformation, separate from the results of the cluster analysis, For example,Webber and Craig (1978) used 40 variables, and they were able to interpretthe first four PCs as measuring social dependence, family structure, agestructure and industrial employment opportunity. These four componentsaccounted for 29.5%, 22.7%, 12.0% and 7.4% of total variation, respectively,so that 71.6% of the total variation is accounted for in four interpretabledimensions.4.3 Spatial and Temporal Variation inAtmospheric SciencePrincipal component analysis provides a widely used method of describingpatterns of pressure, temperature, or other meteorological variables over alarge spatial area. For example, Richman (1983) stated that, over the previous3 years, more than 60 applications of PCA, or similar techniques, hadappeared in meteorological/climatological journals. More recently, 53 outof 215 articles in the 1999 and 2000 volumes of the International Journal ofClimatology used PCA in some form. No other statistical technique cameclose to this 25% rate of usage. The example considered in detail in this