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Principal Components Analysis of Martian Spectral Images
as presented at the 28th Annual Meeting of the Division
for Planetary Sciences of the American Astronomical Society in Tucson,Arizona
D. R. Klassen
R. R. Howell, P. Johnson
(Univ. of Wyoming)
J. F. Bell
We present preliminary Principal Components Analysis (PCA) results from the 1995 infrared
spectral imaging sets of Mars taken at the NASA Infrared Telescope Facility (IRTF) using
NSFCAM. The PCA technique transforms the data set into a new multi-dimensional space the
axes of which lie along the dimensions of greatest variance in the data set. We find that the first
principal component corresponds to surface albedo which accounts for over 98% of the data
variance and the second component has a spectral shape consistent with a fine-grained water ice.
Three endmember spectra are then chosen from pixels representing the extreme values of the
principal components and the image set is modeled as linear combinations of these spectra. The
resulting fractional abundance map of the second principal component endmember (the North
Polar Hood) has high values along the polar region, the evening limb and the morning hemisphere.
We interpret this map to represent water ice cloud cover. This interpretation correlates well with
previously presented band-depth maps of water ice absorption features as well as Hubble images of
the same time.
Analysis of these spectral sets alone has so far detected no evidence for CO2 ice on the planet.
This suggests that all of the cloud structures seen at mid- to low latitudes by HST are composed
only of water ice. The apparent absence of any CO2 ice in the polar region may be due to the
thickness of the North Polar Hood since the primary CO2 band at 3.33µm could be obscured by a
saturated water band throughout the 3-4µm region.
Data Reduction and Processing
The data presented here were taken on 01 FEB 95 UT and are part of a much larger set of data
taken over several months during the last Mars opposition. On this night Mars was imaged through
two of the three circular variable filters (CVF) in NSFCAM over a spectral range from 1.56 to
4.10µm. The first and third spectral sets were taken at 32 colors chosen to lie in and around
various volatile and mineral spectral features. The second and fourth sets were taken at 105 colors
and are Nyquist sampled throughout the two CVF wavelength regions. The standard star BS4030
(35 Leo) was also imaged in a similar manner in order to provide a means to absolutely calibrate
the Mars images.
The data were reduced in the manner standard with infrared imaging, i.e. linearization, sky-subtraction and flat-fielding. The Mars images were then divided by the total integrated stellar flux
at each wavelength. Since 35 Leo is a G2IV star with an infrared spectrum nearly identical to the
sun's (a G2V star) these divided Mars images represent scaled reflectance measurements. All
spectra and images presented here are in these scaled reflectance units.
Principal Components Analysis
PCA is a statistical technique to linearly transform a set of variables into a new space of
orthogonal variables. The first of these variables lies along the axis of greatest variation in the data
set. The next coordinate, orthogonal to the first, lies along the axis of second greatest variation,
and so on through all dimensions of the data set. Since at some point noise is the only variation,
this technique serves to reduce the dimensionality of the original data set to a much smaller set of
variables that contains all the information of the original set.
The images are then searched for pixels that act as endmembers for these new coordinates;
pixels that have the highest or lowest value of the principal coordinates in question. These
endmember spectra are then used in a linear mixture modeling technique to describe all the other
pixels in the image set. This then allows every pixel in the spectral set to be described as a linear
combination of a very small set of individual spectra.
The method of PCA reduces to a multi-variable eigenvector problem where the eigenvectors
are the new principal components and the eigenvalues are proportional to the amount of the total
variance that component covers. The first three eigenvectors from scans one and two are presented
in figures 1 and 2. The eigenvectors for scans three and four are similar to these. The 0th
eigenvector has a spectral shape similar to an average Mars spectrum and is a measure of the
overall brightness level of a pixel. This eigenvector accounts for about 98% of the total image set
variance. The 1st eigenvector (figure 3) shows a deep absorption at about 2.00µm and a very low
reflectance from 3.00-4.00µm. The 2nd eigenvector (figure 4) does not have as much similarity
between scans as the other two however it does show an overall increasing slope from about 3.8 to
As can be seen in figure 3 the 1st eigenvector appears to have a connection to Martian volatiles
and the Martian atmosphere. Based on this graph it appears to be a combination of a fine H2O frost
and the CO2 atmosphere. The atmospheric contribution is mostly in the longest wavelengths as the
eigenvector spectrum begins to dive into a broad, deep absorption. The ice contribution is seen
mainly in the low 3-4µm values of the eigenvector spectrum and the downturn between
In order to choose endmember spectra the image pixels are plotted in the PCA space.
Normally plotting the pixels in the space of the 1st vs the 0th eigenvector will provide enough of a
distribution to pick out the eigenvector endmember pixels. These plots for the first and second
scans are shown in figures 5 and 6. The 0th eigenvector is a measure of overall pixel brightness and
thus its endmembers are pixels in the brightest and darkest image regions. The 1st endmember has
its highest values in the northern polar regions but its low value endmember is somewhat
broadened as it merges into the cloud of the 0th eigenvector pixels.
The endmember pixels chosen for the first pass through the mixture modeling were pixels that
all lie in the disk of Mars. In the case of scan one they were pixels in the regions of Arabia, Syrtis
Major, and the north polar region (NPR). For scan two the first three endmembers were pixels in
the regions of Arabia, Sinus Meridianii, and the NPR. After running all pixels through the
mixture modeling we can create fractional abundance maps showing the amount of each
endmember spectrum within each pixel. The fractional abundance maps are then used, along with
the endmember spectra to create theoretical images which are differenced from the actual images.
The residual flux is then compared to an estimate of the image noise. Those pixels which have a
remaining flux greater than twice this noise level are rerun through the PCA and a second set of
endmembers are chosen. For all four scans these remaining endmembers cover mostly limb effects
and sky pixels and will not be treated in this paper.
Results and Future Work
Figure 7 shows the results of the first mixture modeling for each scan. Each image is a
fractional abundance map showing how much of that endmember spectrum is in each pixel. Only
pixels which were modeled such that the residual flux was less than 2, where is an estimate of
the noise, are shown. The first and second endmember fractional abundance maps are all very
predictable. The first maps show highest values in the bright regions such as Arabia, Moab, and
Xanthe, falling off as the albedo drops. The second maps show the reverse pattern, with high
values in dark regions such as Sinus Meridianii, Sinus Sabaeus, Acidalia, Niliacus, and Syrtis
Major falling off as albedo increases.
The most interesting maps are the NPR fractional abundances which corresponds to the high
value end of the 1st principal component. It shows highest values in the north polar region but also
shows high values along not only the morning and evening limbs, but even into the morning and
evening hemispheres. The pixels in these areas are modeled as having up to 50% of the flux being
due to the NPR endmember. These areas correspond to the clouded regions seen in Hubble images
taken at about the same time and seen in figure 8.
We conclude that the PCA technique can be used to identify and track the Martian clouds.
Since the second eigenvector does not show any features which can be identified as CO2 ices we
can also conclude that these cloud formations are H2O ice. This determination does not take into
account that the CO2 ice absorption feature may be buried in a saturated water ice feature. Also,
CO2 ice may start to show up in the second PCA pass of the limb, specifically the northern limb,
Future work will concentrate on trying to find any evidence of the apparent missing CO2 in the
northern regions. One method we will try is to run PCA on only those pixels or spatial regions of
the images that we would expect to contain such ices.
Figure 1. Spectral plots of the first three principal components from the PCA of the first CVF scan
- a 32 color spectral scan.
Figure 2. Spectral plots of the first three principal components from the PCA of the second CVF
scan - a 105 color Nyquist sampled scan.
Figure 3. Comparison graph of the 1st principal component with various volatile spectra as well as
a synthetic Mars atmosphere spectrum. The CO2 frost spectrum is from Fink and Sill (1982) and
the H2O spectra are from Roush, et al. (1990). The eigenvector shows a 2µm absorption similar to
all the volatiles but has low values in the 3.00 to 3.75µm region indicative of H2O ice. The 2.00 to
2.25µm ratios shows a correlation to the fine frost rather than the coarse frost. The drop from 3.75
to 4.1µm appears to indicate a correlation with the Mars atmosphere.
Figure 4. Comparison graph of the negative of the 2nd principal component with various volatile
spectra as well as a synthetic Mars atmosphere spectrum. The CO2 frost spectrum is from Fink and
Sill (1982) and the H2O spectra are from Roush, et al. (1990). In the K-band this eigenvector show
either a correlation or anti-correlation in the 2.00µm absorption feature. The various features in the
L-band are still under investigation but all eigenvectors show a correlation with the 3.75 to 4.1µm
Mars atmospheric absorption feature.
Postscript file plot
Figure 5. Image pixels of scan one plotted in the PCA space spanned by the 0th and 1st
Postscript file plot
Figure 6. Image pixels of scan two plotted in the PCA space spanned by the 0th and 1st
Figure 7. The endmember fractional abundance maps. The rows correspond to maps from the
same spectral scan with scan 1 on the top and scan 4 on the bottom. The first column is the
bright region endmember and the second column is the dark region endmember. The third column
is the north polar region endmember.
Figure 8. Hubble images of Mars in the visible band showing the thick clouds along the limbs and
into the morning evening hemispheres.
Fink, U., G. T. Sill (1982). "The Infrared Spectral Properties of Frozen Volatiles", in Comets
(edited by L. L. Wilkening, University of Arizona Press), pp. 164-202.
Klassen, D. R., J. F. Bell, III, R. R. Howell (1995). "Infrared Imaging Spectroscopy of Martian
Clouds and Volatiles", Bull. Am. Astron. Soc., 27, 1061
Roush, T. L., J. B. Pollack, F. C. Witteborn, J. D. Bregman, J. P. Simpson (1990). "Ice and
Minerals on Callisto: A Reassessment of the Reflectance Spectra", Icarus, 86, 355-382
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