## 5 Discussion
While difficult to estimate, the question of dimensionality is important because it places in context the aggregate landscape-scale measurements of a sensor. The observation of the similarity of the multispectral and hyperspectral feature spaces suggests that, even with hyperspectral observations, the shape and amplitude of the spectral continuum dominates the variance structure of the data, but does not fully determine its information content. It is upon the structure of this low-order spectral feature space that the narrowband absorptions and other fine spectral features are superposed. Our results suggest that these information-rich fine spectral features do not appreciably change the fundamental low-order structure of the feature space. This finding has potential implications for the future synergistic use of multispectral and hyperspectral data. Figure 9 shows an additional way of visualizing information content present in these fine spectral features. In this figure, each of the NIR, SWIR 1, and SWIR 2 Landsat bands are shown individually for a single spatial domain. Because there is only one band for each of these spectral regimes, the Landsat dimensionality for each spectral subset is 1 and must be shown as a grayscale image. However, over 40 AVIRIS channels are present for each of these spectral regimes. Adjacent to each Landsat band is a tricolor composite showing the three low order PC images for the AVIRIS spectral subset corresponding to each spectral regime. Substantially greater information is obviously present in each spectral regime for the hyperspectral cube than the multispectral dataset. The dimensionality of AVIRIS is clearly at least two in each of these spectral regimes, yielding intraband feature spaces with a considerable structure and physically meaningful EMs. The results of this study do not imply that the AVIRIS data cube only images three or four spectrally distinct quantities, nor that the information contained in the hyperspectral cube can be captured by a multispectral instrument. Rather, they demonstrate that, when decomposed linearly using the PC transform, the variance of both datasets is partitioned into a nearly identical number of fundamental dimensions and the relationship between the spectra follows a similar geometric relationship. It might have been expected that substantially different EMs would arise from the differences in spatial and spectral resolutions of the sensors. This was not the case. Furthermore, it might have been expected that a low-order dimension would emerge in the hyperspectral dataset which differed substantially from the multispectral dataset. This was not the case either. Rather, despite the significant variations in absorption features-most notably in the plane of substrates-the EMs were arranged in a nearly identical configuration. The implications of this result for multitemporal analyses are substantial, as they suggest that pixel trajectories in multispectral feature space correspond to nearly identical trajectories in low-order hyperspectral feature space. The second question of this study is addressed quantitatively through the partitions of variance in Figure 4 and qualitatively by the feature spaces in Figures 5 and 6. Both the hyperspectral and multispectral partitions of variance, feature spaces, and EMs found in this study are remarkably similar to those found in previous analyses of Landsat data sampling much more spatially extensive regions. These results suggest that a substantial fraction of global multispectral diversity can be sampled in a local spatial extent. Notably, the entire area used in this analysis, 9800 km\({}^{2}\), is roughly 1/3 of the 34,000 km\({}^{2}\) area covered by a single Landsat scene and less than 0.01% of the ice-free global land area.