We have applied the PCA method, as did on Chapter 5, section 5.1.1, in a more explicit and sophisticated way than in the previous section. Hence, we applied the method to the three study areas; Hotei Regio, Tui Regio and Sotra Patera, but this time by taking into account the eigenvalues, eigenvectors and the visual results as seen in the PCA images. I have presented some examples of the steps taken during that method on Chapter 5. Moreover, we are using the bands 97 to 352 that correspond only to the infrared channel.
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The eigenvalue information for the case of Hotei Regio (Fig. 6.12) indicates that the first PC contains most of the information present in the dataset but the second and third could be useful as well. For the datacube details see Chapter 3, Table 3.4, #3.
Fig. 6.12. Eigenvalues plot for Hotei Regio datacube #3 (Table 3.4, Chapter 3). The variability is accounted mostly for the 1st PC and 2nd PC, while PC3 is also of interest. After that, the flatenning indicates the absence of variability in the PCs.
Moreover, from the eigenvectors seen hereafter (Fig. 6.13), PC1 and PC2 seem to correspond to the surface, with signals in the short wavelengths, the 2.69-2.79 double window and the 5 μm one, while PC3 and PC4 present a light signal at 5 μm. However, at PC4, noise is also present. After that the PCs are dominated by noise.
Fig. 6.13 - Calculated eigenvectors from the Hotei Regio datacube. It appears that only PCs #1,2,3 are compatible with surface spectra.
For the production of the PCA image we use PCs 1, 2 and 3 (R:PC1, G:PC2, B:PC3). We distinguish three major spectral units (red, green, yellow) (Fig. 6.16).
All Tui Regio datacube’s (see Chapter 3, Table 3.4, #4) results, regarding the eigenvalues, the eigenvectors and the PCs, can be found on Chapter 5, section 5.1.1.2.
Sotra Patera
In the case of Sotra Patera, the PCA eigenvalues yield that the 1st PC contains the largest information present in the dataset (Fig. 6.14). Nevertheless, the 2nd and 3rd are also of good use while after that only noise is present.
Fig. 6.14. Eigenvalues plot for Sotra Patera datacube #5 (Table 3.4, Chapter 3). The variability is accounted most for the 1st PC and 2nd PC, while PC3 is also of interest.
From the eigenvector investigation, it appears that PC1 and 2, and slightly 3, reflect the surface. The rest PCs are dominated by noise (Fig. 6.15).
Fig. 6.15 - Calculated eigenvectors from the Sotra Patera datacube. It appears that only the first three PCs are compatible with surface spectra. Hence, we use PCs #1,2,3 to create the PCA image and extract the surface information concerning the heterogeneities of the regions.
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Since PCA is not sensitive to brightness, we use certain color identification so that the brightest units appear in red and the darkest units in green or blue following the rationale described in section 5.1.1.2 of Chapter 5. With such a representation, it is easy to identify a number of RoIs that indicate the most diverse spectral response and possibly different chemical composition. We select two small RoIs, as close as possible to each other in the area, so that we can safely assume that, - although the RT code attempts to take this into account - the atmospheric contribution and the observational geometry is similar so that any changes in reflectivity are due mainly to the surface (Figs. 6.16c1; c2; c3).
Fig. 6.16 - VIMS images for Hotei Regio (vertical left), Tui Regio (vertical middle) and Sotra Patera (vertical right) showing the spectral units of these areas. Upper panel: 2.03 μm band. Middle panel: RGB composite of the same spectro-images (with R: 5 μm; G: 2.03 μm; B: 1.08 μm). Lower panel: RGB composition of the PCs showing most of the surface contribution for the three areas. The white box includes the pixel selections of the ‘bright’ RoI and the black the ‘dark’.
In conclusion, it appears that the combination of PCs, their eigenvectors and eigenvalues in the outcome image, and the RoI selection, is the best approximation and gives us confidence of the results. However, the selection of appropriate channels from the original
dataset is of significant importance as well. Before engaging the PCA method as an investigation, concentrated only to the infrared spectrum of the datasets, I have used it in an alternative way by using the seven narrow methane spectral windows centred at 0.93, 1.08, 1.27, 1.59, 2.03, 2.79, and 5.00 μm, wavelengths in which the methane absorption is weak, giving access to Titan’s lower atmosphere and surface and in their adjacent bands. This caused error to our results since, for instance, in the Tui Regio case, the 0.93 channel and its two adjacent ones overlap between the visual spectrum of VIMS (Visual) and the infrared (IR), causing issues to the projection of the PCs and PCA image. Spotting and understanding the nature of this problem urged us to use only the IR spectrum, thus 256 channels from the original VIMS dataset. Figure 6.17 shows the PCA result images from the previous approximation in comparison to the new –more suitable one.
Fig. 6.17 – PCA images using 21 channels of both Visual and IR spectrum (left column) and 256 IR (right column).
It seems that, more or less, the method distinguishes the same spectral units among the datacubes as before, although with (at some cases) differences in their limits. For instance, at Hotei Regio the red spectral unit that corresponds to the actual Hotei feature is less extended to the west with respect to the old PCA image.
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Additionally, for a follow up work that I present on Chapter 7, I have used the bright RoIs of each area (Hotei Regio, Tui Regio and Sotra Facula) for the study of the temporal variation of the areas. Figure 6.18 shows that the bright RoI is the same at all datacubes in the temporal investigation (2005-2009) of Tui Regio (Solomonidou et al. 2013c).
Fig. 6.18 - (upper row) Tui Regio from five VIMS datacubes (T8, T12, T44, T46, T50) at 2.03 μm using geometric projection (i.e. same projection parameters: spatial resolution, projection center, resampling method). (lower row) Same datacubes after PCA application. The PCA images distinguish 2-3 spectrally different areas (depending on the spatial resolution) identifying the bright region (RoI) in the Tui Regio area in red color as in Solomonidou et al. 2013b.
Finally, as mentioned earlier, I use the RoIs selections (Fig. 6.16) with RT code analysis to simulate the spectra and retrieve the surface albedo (see section 6.4).