Mathematics – Logic
Scientific paper
Nov 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001dps....33.1910k&link_type=abstract
American Astronomical Society, DPS Meeting #33, #19.10; Bulletin of the American Astronomical Society, Vol. 33, p.1069
Mathematics
Logic
1
Scientific paper
We present the principal components analysis (PCA) of absolutely calibrated multi-spectral images of Mars as a function of Martian season. The PCA technique is a mathematical rotation and translation of the data from a brightness/wavelength space to a vector space of principal ``traits'' that lie along the directions of maximal variance. The first of these traits, accounting for over 90% of the data variance, is overall brightness and represented by an average Mars spectrum. Interpretation of the remaining traits, which account for the remaining ~10% of the variance, is not always the same and depends upon what other components are in the scene and thus, varies with Martian season. For example, during seasons with large amounts of water ice in the scene, the second trait correlates with the ice and anti-corrlates with temperature. We will investigate the interpretation of the second, and successive important PCA traits. Although these PCA traits are orthogonal in their own vector space, it is unlikely that any one trait represents a singular, mineralogic, spectral end-member. It is more likely that there are many spectral endmembers that vary identically to within the noise level, that the PCA technique will not be able to distinguish them. Another possibility is that similar absorption features among spectral endmembers may be tied to one PCA trait, for example ''amount of 2 \micron\ absorption''. We thus attempt to extract spectral endmembers by matching linear combinations of the PCA traits to USGS, JHU, and JPL spectral libraries as aquired through the JPL Aster project. The recovered spectral endmembers are then linearly combined to model the multi-spectral image set. We present here the spectral abundance maps of the water ice/frost endmember which allow us to track Martian clouds and ground frosts. This work supported in part through NASA Planetary Astronomy Grant NAG5-6776. All data gathered at the NASA Infrared Telescope Facility in collaboration with the telescope operators and with thanks to the support staff and day crew.
Bell James Francis III
Klassen David R.
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