Previous: Methodology Next: Conclusions Up: Ext. Abst.

Results

• The dimensionality of the analysis can not be accurately gauged by looking at the eigenvalues. There are more interpretable eigenvectors than would be found by application of typical eigenvalue magnitude and spacing techniques, such as the Scree test, LEV test or North et al. test. This suggests that those eigenvectors with variability indistinguishable from white noise have physical signal embedded within them. Developing new tests, based on the spatial structure of the variability, rather than the magnitude of the variability, should be given priority.
• Random targets can be applied by Procrustes with relatively poor fits (e.g., correlations between the target and the fit were typically 0.20), suggesting that the MSU channel 4 temporal fluctuations are not random. However, the PC scores based on the random fits present a shocking picture, that of robust appearing dipoles, mainly wave number 1 and occasionally wave number 2, centered around Antarctica. Undoubtedly, if such patterns were presented to analysts, they would interpret them as physically relevant. However, the Procrustes analysis has a safeguard built into the technique and one can quickly determine that 95 percent of the target is not fit. Therefore, the perceptive analyst can ignore such spatial modes.
• The unrotated PC scores exhibit wave number 1 to wave number 4 patterns with most variability in the middle and high latitudes, although two patterns (PCs 4 and5) had some tropical signal. The higher wave number patterns are associated with about one-half the variance as the larger scales. The PC loadings might be used to track the temporal behavior of the PC scores if the patterns are relatively simple. As the wave number increases, the probability of obtaining a high spatial match to the PC scores decreases.

However, the loadings of PC 3 had a decreasing trend with time and those for PC 5 had an increasing trend.

• The orthogonal rotations (Varimax and Quartimax) had virtually identical PC loadings.

This suggests that the MSU data can be simplified by PC loading number/column (Varimax) or by time/row (Quartimax) with little difference. The PC scores for the two rotations are nearly indistinguishable. It also suggests, for these data, that the solution is insensitive to the choice of orthogonal rotation ? the temporal configuration of temperature anomalies can be well simplified. The PC scores suggested that wave numbers ranged primarily from 1 to 3 with the exception of a high wave number on Varimax/Quartimax PC 6.

• The oblique rotation used (Covarimin) indicated a fairly high correspondence to the orthogonal ones in both loadings and scores, particularly for PC 2, 4, 5 and 6. There were some phase shifts in PCs1 and 3. The average absolute correlation among PC scores (maps) was less than 0.09 whereas the highest correlation was less than 0.22, indicating the underlying modes are close to uncorrelated in space.
• When an increasing trend was fit to the time series using Procrustes analysis, the best fit was a 0.34 correlation to a linear target and slightly lower (0.30) for a monotonic increasing sigmoidal trend. The scores of the Procrustes trend analysis indicated low temperature anomalies from Antarctica into southern Argentina and high anomalies south of Australia.