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Chapter 4 - Extracted Spectra Results

The Regional Spectra

Presented here are spectra extracted from the registered spectral cubes to show the variations in scaled reflectance from various regions.  Regions were chosen to cover many different cases such as differing albedo and distance from the limb.  The spectra were created by choosing a desired region and averaging the scaled reflectance of some number of the pixels within that region, making sure that the number of pixels covered an area on the order of the seeing disk (0.8" to 1.0").  Error bars on the reflectance are the standard deviation of the mean of the scaled reflectances of the pixels in the area.  The graphs in Figures 4.1 through 4.7 show the spectra from each of the seven data cubes.

Common Spectral Features

These spectra contain a variety of absorption features, only some of which are useful for volatile analysis.  The most prominent spectral feature is the deep, broad band at 3.0µm which rises almost continuously through longer wavelengths due to bound water in Martian minerals or in the form of ice (Sinton 1967, Houck et al. 1973).  The spectral slope from 3.25µm to 3.75µm is greater, and shows less absorption, in the bright regions than in the dark regions, with some variation among the regions of similar albedo.  This may indicate differences in the hydrated mineralogy between bright and dark albedo regions, although to truly make any conclusions concerning these 3.00µm band differences would require a more detailed band integration technique (Calvin 1997) which is beyond the scope of this work.  The spectral slope is smallest, almost leveling out, in the spectra of the north polar regions.  This is due presumably to water ices which are quite dark at the longer wavelengths as well as the colder temperatures.

The other feature common to all spectra is the broad, relatively deep absorption at 2.01µm.  This feature is due mainly to the Martian atmospheric CO2 (Kuiper 1947).  The band is broader and deeper in the north polar region spectra due to frosts and ices in this region as both CO2 and H2O frosts absorb here as well (Kieffer 1970a).  There is also a correlation due to atmospheric pathlength, from both local topography and nearness to the limb.  This correlation is more apparent in band depth maps than in the regions extracted here.  Due to the number of volatiles which absorb in this band it is not vary diagnostic for discriminating between the species.

There are also features throughout the L band with shapes that appear to correlate with albedo and thus are presumably due to surface mineralogy.  Most notable are features around 3.4 and 3.58µm.  There are also differences in spectral slope beyond 3.5µm.  All of these effects are beyond the scope of this dissertation but are works in progress (Bell et al. 1995, 1996b) or directions for future work.

CO2 Cloud Modeling

In some of the spectra there appears to be some structure around 3.33µm which could be indicative of CO2 frosts either as a ground ice or a condensate cloud.  This feature is deeper and narrower for smaller grained frosts, due mainly to the overall reduction of the 3.0 to 3.5µm reflectance as grain size increases (Calvin 1990).  There really is no expectation that there will be CO2 clouds anywhere but perhaps in the north polar hood.  Clouds seen over the Tharsis volcanoes in Mariner 9 images are shown to be composed of H2O ices particles with a mode radius of 2.0µm and a column amount of about 226µg/cm2, which corresponds to 2.26pr.µm based on models of the Mariner 9 infrared spectra (Curren et al. 1973).  Similar modeling to Viking spectra of the north polar hazes find clouds with the same properties (Christensen and Zurek 1984).  There are also major tropical cloud systems seen in HST images from the same time period as the data presented in this dissertation which are presumed to be composed of water ices based upon microwave measurements around the same time (James et al. 1996, Clancy et al. 1996).  However there are times and places where it CO2 ice clouds are expected, most notably in the polar hoods during the winter season (Pollack et al. 1990) and perhaps in the high atmosphere during a time when Mars is colder than during the Viking age.  We therefore investigate the possibilities of CO2 clouds using the apparent 3.33µm absorption feature.

A modeling analysis of this region was performed to determine the quantity of CO2 frost that could be consistent with the observed spectra.  The test is a simple Beer's law model where the observed intensity is given by the relation where a(l) is the absorption coefficient of the intervening material, defined as , where k(l) is the imaginary index of refraction (values from Warren 1986, Hansen 1996) of the material and x is the thickness of the frost in the optical path.  To simplify the model, it completely ignores the effects of scattering, although we will come back to this issue as it turns out to be very important.

The modeling program simulates light passing through a Martian CO2 cloud, reflecting from a grey Martian surface and passing a second time through the cloud.  The adjustable parameters for the fit were thickness of the frost layer, the slope of the incoming light, and average level of the final spectrum.  The slope parameter is designed to fit the data spectral slope and the average level of the final spectrum should come out to be close to a value of 1.0 as the data were normalized before running them through the model.  The parameters were allowed to vary until the c2 between the model and the data was minimized.

The model was run over a five point spectrum centered on 3.33µm extracted from all the above presented regional spectra resulting in a frost thicknesses of 34µm with a sample standard deviation of 110µm, when averaged over all but the north polar regions.  Over the north polar regions the value ranged from about 180-500µm thickness.  Using the relation that optical depth is the integral of the absorption coefficient over the thickness, these average frost thicknesses become IR optical depths of 0.0063 for non-polar regions and 0.064 for polar regions.  These numbers thus represent an average value of how much CO2 frost that could be in the optical path. Figures 4.8 through 4.10 show some of the representative model and data spectra.



The question then becomes: How reasonable are these thicknesses?  Previously studied Tharsis clouds (Curren et al. 1973) and north polar hazes (Christensen and Zurek 1984) find that water ice clouds that fit the 8-50µm spectra need only 2.0pr.µm to make a cloud with visible opacity of 1.0.  In the visible wavelengths (0.5µm) the ratio of the real to the imaginary index of refraction (Warren 1984) is on the order of 109, indicating that scattering processes are far more important than absorption processes.  Similarly, for CO2 ices the ratio of real to imaginary index of refraction (Hansen 1996) is on the order of 107, again indicating that scattering is the more important to total extinction than absorption.  The real indices of refraction for H2O and CO2 are 1.31 and 1.42 respectively (Warren 1984,1986) and so their scattering properties, at least to 0th order, will be similar.  This would mean that a CO2 frost thickness of 34µm obviously creates a cloud with tvisible « 1.0.  Using the relation , where Mc is the column amount, rm is the mode radius or 2µm, and tvisible is the visible wavelength optical depth (Christensen and Zurek 1984), 34pr.µm gives tvisible  ~ 26.  This indicates that something in the initial assumptions of the model is incorrect.

The major assumption which allowed us to do the "slab" model was that the effects of scattering relative to the total extinction at 3.33µm was negligible for CO2 ices.  This is true for H2O ice but not for CO2 ice.  For H2O ice the ratio of the real to imaginary index of refraction in the 3µm band is on the order of 20 (Warren 1984).  Compared to the value of 109 calculated above at 0.5µm, it is evident that absorption becomes very important.  For CO2 this ratio is on the order of 105, indicating that although absorption is far more important at 3.33µm than at 0.5µm, where the ratio was on the order of 107, it is certainly not as important as it is for water ice and thus a pure absorption model fails.

Given that scattering dominates even at 3.33µm, the 34µm frost thickness calculated from this model is not a measure of the amount of pr.µm of CO2, but rather some measure of the total optical pathlength a photon must travel to create the structure seen.  With a mode particle diameter of 4µm, this pathlength indicates that a photon interacts with about 10 or so cloud particles making it an optically thick cloud.  This would mean that the sensitivity of this technique for finding CO2 ice clouds is limited to clouds with an optical depth of 1.0 or greater.

We can compare the above sensitivity to the results from a model that truly address many of the details, calculated by Bell et al. (1996a) which was performed to test band depth contrast. The model used a full radiative transfer technique including a Hapke (1981a,b) representation of the surface and a Mie particle scattering representation of the clouds.  Cloud particles were assumed to be spherical and composed of a dust core surrounded by a CO2 ice shell of varying volume fractions of 30, 60 and 90%, creating particles of sizes ranging from 1.8µm (no ice) to 3.5µm (90% ice shell).  Their results indicate that cloud optical depths at 2.00µm on the order of 1.0 are necessary for the cloud to be detectable in a 3.33µm band depth map and thus also in the five-point spectra used in the simple Beer's Law model above.  Thus it is unlikely that the absorption features seen in the non-polar regional spectra are due to CO2 clouds.

But what about the north polar region extracted regional spectra?  It is still safe to say that the model does not indicate a CO2 cloud detection for all the above reasons, however there does appear to be some kind of detection at 3.33µm.  As will be shown in the band depth mapping results, there does appear to be a detection of CO2 in a collar around the north pole indicating the seasonal north polar cap showing through the receding north polar hood.

We can compare these values to typical visible wavelength optical depths from other studies.  The high, thin hazes seen in Viking limb images, and assumed to be composed of water ice, (Kahn 1990) range in optical depth from about 0.015 to 0.04.  The polar hood as viewed in 1986 (Akabane et al. 1995) ranged from an optical depth of greater than one in the morning to about 0.5 in the afternoon with a mean optical depth of 0.6±0.2.  Hubble Space Telescope images taken during the 1995 opposition show a belt of  tropical clouds with an optical depth ranging from 0.2 to 0.6 which are assumed to be composed of water ice based on temperature measurements (Clancy et al. 1996a).

In all of the above detected clouds, none of them has measured optical depths greater than 1.0 and thus if they were composed of CO2, would not be detectable using a spectral modeling technique with the current sensitivity.  In future work we will look for CO2 clouds in the north polar hood in images from earlier in the spring season where temperatures are presumably colder.

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