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Icarus138, 36–48 (1999)
Article ID icar.1998.6058, available online at http://www.idealibrary.com on
Infrared Spectral Imaging of Martian Clouds and Ices
David R. Klassen and James F. Bell III
Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853E-mail: [email protected]
Robert R. Howell and Paul E. Johnson
Department of Physics and Astronomy, University of Wyoming, Laramie, Wyoming 82071
and
William Golisch, Charles D. Kaminski, and David Griep
NASA Infrared Telescope Facility, Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, Hawaii 96822
Received December 16, 1997; revised August 20, 1998
Multispectral images of Mars, taken at the NASA Infrared Tele-scope Facility (IRTF) near and at the 1995 opposition, are used toidentify and track its atmospheric clouds and ground ices. Banddepth mapping is used to help distinguish between the composi-tion of volatiles and provide a check for the techniques of principalcomponents analysis (PCA) and linear mixture modeling (LMM).PCA/LMM are used to create maps that track clouds and volatiles,a technique that requires no a priori spectral information in order tocreate these maps. Band depth maps at 3.33 µm, which have beenshown to trace CO2 frosts, show some transient features which couldindicate polar CO2 clouds at the time of these observations. We showthat band depth maps at 2.25µm are good tracers of H2O frosts andthat band depth maps at 3.69 µm can distinguish between coarse-and fine-grained water frosts. These maps have allowed the detec-tion of fine-grained water frosts in the north polar region and alongthe morning and evening limb regions. From the PCA technique wefind that just two principal components can account for over 99%of the data variance. The first of these is an infrared albedo unitand the second is an ice/thermal unit. Plotting the spectral datacubes in this new vector space, we find that most of the martiandisk can be modeled by spectrally mixing three endmember spectrahaving extreme values of these principal components. The morn-ing and evening regions of Mars are composed of 40–60% of thenorth polar ice/thermal component endmember, indicating a frostcomponent there consistent with the band depth mapping results.With a combination of these techniques it is possible to not onlyidentify the extensive martian clouds, but to also determine compo-sition. These new results are particularly relevant in light of recentMars Pathfinder descent temperature profile data that indicatedupper atmosphere temperatures below the CO2 frost condensationpoint, implying that CO2 ice clouds may be an important radiativecomponent of the current martian climate. c© 1999 Academic Press
INTRODUCTION
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0019-1035/99 $30.00Copyright c© 1999 by Academic PressAll rights of reproduction in any form reserved.
Infrared spectroscopy as a means of studying the comsition of the surface and atmosphere of Mars has beensince the late 1940s. Chief among the discoveries in thisspacecraft era were that the atmosphere is composed primof CO2 (Kuiper 1947) and that the surface has a hydrated mincomponent, based on the overall low surface reflectance ar3.1µm (Sinton 1967). Spectra in the range of 1.88–6.00µmfrom the Mariner 6 and 7 spacecraft were used to show thasouthern polar cap was at least partially composed of CO2 ices(Herr and Pimentel 1969). These results prompted studieboth H2O and CO2 ice infrared spectral properties that continto this day (Kieffer 1970a,b, Fink and Sill 1982, Warren 191986, Calvin 1990, Roushet al.1990, Hansen 1997).
Viking Orbiter observations included many studies with iplications for clouds, as well as some direct studies of clofrom limb imaging. Mars Atmospheric Water Detector (MAWDobservations (Jakosky and Farmer 1982) cover about 1.5 mayears starting atLs≈ 80◦ and ending atLs≈ 245◦. A rise inthe H2O abundance occurs fromLs≈ 0◦ to 40◦ for all latitudesabove 20◦N, with the peak between 20◦ and 50◦N. The recedingcap edge at this time was at 70◦N so this peak in the water vapor should not be due to the subliming polar cap, implying tthe regolith must be the water source. Similarly, MAWD sa decrease in the low northern latitude water vapor abundabefore the formation of the seasonal ice cap, adding suppothe regolith reservoir theory. The water could be either a grofrost or water adsorbed in the soil, but neither the MAWDsults, nor various adsorption models, can account for allwater necessary for the observed vapor abundances mea(Jakosky and Farmer 1982, Jakosky and Haberle 1992).
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IR SPECTRAL IMAGI
One of the major results from the Viking Infrared ThermMapper (IRTM) was that the 20-µm brightness temperaturemeasured at the southern winter polar cap reached valuesbelow the CO2 condensation temperature of about 150 K andsome areas were as low as 125 K (Kiefferet al. 1977). Theselow atmospheric temperatures imply that CO2 clouds shouldbe condensing in the atmosphere at these times. Hunt (1showed that an optical depth (τ ) ≈0.5 CO2 cloud of 10-µmparticles over a ground with an effective temperature of 15would produce a brightness temperature at 20µm of 120–130 K,as seen in the IRTM data. More recent work on these data (Foet al. 1995) found that a precipitating CO2 cloud with particleradii larger than 10µm over CO2 snow deposits with millimetesized grains fits the 20-µm brightness temperature as well asdifference in brightness temperatures at 11 and 20µm.
In their study of polar processes in a martian general cirction model, Pollacket al.(1990) calculated atmospheric condesation rates for several different seasons as a function of latialtitude, and dust opacity. They found that airborne dust favthe condensation of CO2 in the atmosphere as clouds, raththan condensation directly on the surface. Thus, dustier cotions will produce more CO2 clouds during the formation of thnorth polar hood.
Kahn (1990) used Viking limb images to study the detachazes, or high altitude clouds,which he presumed to be cposed of water ice. He was able to measure haze base altitthicknesses, and optical depths. Using these observationcalculated that the hazes had ice concentrations of 0.0020.034 pr.µm and concluded that these hazes could be a manism for scavenging water vapor from the atmosphereparticle sizes grow, the ice would be transported down toground where it could be adsorbed into the regolith more eathan the water vapor itself. This mechanism makes a nonpsource/sink of water vapor more plausible.
A more recent study by Bellet al.(1996a) concentrated on thfeasibility of detecting martian CO2 clouds using groundbaseimaging spectroscopy. Their work concentrated on using ninfrared (NIR) measurements (1.5–4.1µm) to look for diagnos-tic CO2 and H2O absorption features. Their major conclusiwas that in the 3.33-µm wavelength region, where CO2 has amajor absorption band that distinguishes it from water ices, C2
clouds, if they exist, should be detectable.Temperature measurements from the Mars Pathfinder t
during its descent on 4 July 1997 found that at an altitudeabout 80 km the predawn atmospheric temperature was bthe CO2 condensation temperature (Schofieldet al.1997). Thisreinforces the possibility that some of the clouds seen in 191997 Hubble Space Telescope images (Jameset al.1996, Wolffet al.1997), or some of the volatiles detected in recent NIR msurements (Bellet al. 1996a,b, Klassen 1997), could be coposed of CO2.
Our study will use the relatively new technique of infrar
imaging spectroscopy to extend these previous groundbasedspacecraft results. We first describe the data set and data anaG OF MARTIAN ICES 37
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procedures used in our investigation. Then we present our reson martian clouds and volatiles. We conclude with a discussiof the implications of these results on our current understandof Mars climate variability.
THE DATA SET
The data (Fig. 1) were taken using the NSFCAM infrared aray detector (Shureet al.1994, Leggett and Denault 1996) at thNASA Infrared Telescope Facility (IRTF). The instrument usea 256× 256 InSb array detector sensitive from 1 to 5.5µm. Thecamera’s plate scale of 0.06′′/pixel was used for this work. Thisplate scale translates into a spatial scale of about 30 km/pixethe sub-Earth point, but with typical seeing at 0.6 to 0.8′′ the bestactual spatial resolution is about 325–435 km at the sub-Eapoint. For most of the data sets a circular variable filter (CVFwas stepped through several distinct wavelengths diagnosticvarious mineral and volatile absorption features. Two of the dasets were scanned through the CVFs at a full Nyquist sampliThe data were gathered on several nights around the 1995 opsition and were spaced to maximize global coverage as wellongitudinal repetition. Table I summarizes the Mars data seused in this study. In addition to the images of Mars and the soltype standard star BS4030 (Hardorp 1978, 1980, Gezariet al.1993), dome flatfields and linearity test images were taken.
The Mars and star images were then processed using the sdard infrared techniques (McCaughrean 1989) of sky-imagsubtraction (for bias, dark current, and sky flux removal), flafielding (to remove pixel-to-pixel variations), and bad pixel corection. The Mars images were calibrated by dividing them bthe integrated star brightness. Since BS4030 is a G2IV star winfrared colors differing from solar by only about 0.07 magntudes, this “scaled reflectance” differs from a true reflectanonly by some constant, namely the ratio of BS4030 to the Su
Finally, the images in each spectral scan were coregistein orthographic view to within about 0.2′′. More precise regis-tration, using map projections to remove the residual planetarotation effects, was deemed unnecessary for the specific danalyzed here. Thus, ratio images could show anomaloustections along limb and feature edges at the three pixel sca
DATA ANALYSIS PROCEDURES
Band Depth Mapping
Band depth mapping is used to study the variation of a pticular spectral feature as a function of position on Mars. Aimage from the band center is ratioed to the continuum levelthat wavelength. The continuum level is created from a linearbetween two images from local continuum levels on either siof the feature. These are defined in[
Rλb
]
lysisBDλb = (1− f )Rλ1 + f Rλ2
(1)
nd mine
38 KLASSEN ET AL.
FIG. 1. Images from 14 JAN 1995 (Ls= 45◦) compared to a visible wavelength opposition image (Ls= 63.5◦) from the Hubble Space Telescope (Jameset al.1996). The images at 1.73 and 2.25µm represent local continuum points; Mars is relatively bright with high contrast. At 2.01µm (image stretched a factor of 2more than continuum images) the limbs darken due to the atmospheric CO2 and the polar cap is dark due to CO2 and/or H2O ices. Mars darkens considerably i3.07µm (image stretched a factor of 4 more than continuum images) with much less contrast. This is due to absorptions in this spectral region by hydraterals
and water ices in the polar regions. By 3.80µm the surface brightness is back ntrast hasH
a
-
rptionevel
omend
increased; however, the polar region is still dark due to the water ices. The
with
f = λb− λ1
λ2− λ1, (2)
whereR is the scaled reflectance image at the appropriate wlength,λb is the wavelength of the desired band,λ1 is the shortwavelength continuum point, andλ2 is the long wavelength con
tinuum point. The band depth image defined here is a modified5–:23
typical H2O and CO2 ice spectra from these studies is shown in
form of the Bell and Crisp (1993) band depth map. Equation (1)TABLE IObservational Information
14 JAN 1995 01 FEB 1995
CVF scan 1 2 3 1 2 3 4Data mode 1 1 1 1 2,3 1 2,3UT time 11:57:39– 14:09:11– 15:19:18– 07:15:12– 08:03:32– 10:47:22– 11:09:4
12:17:34 14:32:40 15:40:20 07:36:24 09:10:10 11:08:50 11:57
Ls 45◦ 54◦Angular size 12.3′′ 13.6′′Sub-⊕ latitude 21.1◦ 20.2◦Sub-⊕ longitude 198◦–203◦ 231◦–236◦ 248◦–253◦ 322◦–328◦ 334◦–350◦ 14◦–19◦ 20◦–31◦Sub- latitude 18◦ 20◦Sub- longitude 223◦–228◦ 255◦–261◦ 272◦–278◦ 332◦–338◦ 344◦–1◦ 24◦–30◦ 30◦–41◦
Comments Photometric; seeing<1.0′′ Photometric; seeing<0.8′′
Fig. 2.
Note. Data modes: 1, 32-wavelength image set from 1.560 to 4.100µm; 2, 5from 3.000 to 4.164µm.
to higher values (image at same stretch as continuum images) and the coST image is presented for spatial resolution comparison.
ve-
creates an image where dark regions represent more absoand bright regions approach, or exceed, the continuum lbrightness.
The choices for the band depth map spectral regions cfrom investigations of various volatile spectra (e.g., Fink aSill 1982, Calvin 1990, Roushet al. 1990) as well as work onmartian cloud detection tests by Bellet al. (1996a). A plot of
8-wavelength image set from 1.918 to 2.477µm; 3, 48-wavelength image set
ctra are
IR SPECTRAL IMAGING OF MARTIAN ICES 39
FIG. 2. Comparison of several representative PCAe2 spectra to the spectra of possible martian volatiles. In these plots the Mars atmosphere spedust-free radiative transfer models at a spectral resolution of 1.5% (Crisp 1990, Rothmanet al.1987, Pollacket al.1993, Bellet al.1994). The CO2 frost from Finkand Sill (1982) is a laboratory-grown fine grained frost reflectance spectrum convolved to 1.5% spectral resolution. The CO2 frost from Calvin (1990) is a 1.0%spectral resolution Mariner 7 spectrum of the martian south polar cap and represents large, possibly millimeter-sized grains. The water frosts are 1.5% spectralresolution laboratory reflectance spectra from Roushet al. (1990). The fine-grained frost was grown at a temperature of 104 K and passed through a 90-µm sieve.
The coarse grained frost is actually an ice cube at 82 K. The cloud spectra (Bellet al. 1996a, M. E. Ockert-Bell, pers. commun. 1998) were modeled using thec
h
i
o
aaa
thep of
and
ver,e, itnce
n a
-r-s
ver,ther-
radiative transfer technique described in Pollacket al. (1995) and have an opti
A major distinction between CO2 and H2O appears at 3.33µm,where CO2 has a narrow absorption feature and water icea constant slope (fine grained) or shows a relative maxim(coarse grained). Another distinctive difference is the regaround 2.25µm, where water ice shows a local maximum, bthe CO2 spectrum is relatively flat. Coarse grained CO2 doesshow a local maximum near 2.25µm, but with a proper choiceof continuum points for the band depth maps it will be at ma 5% feature compared to the 30% feature of water ices.
Radiative transfer models of frost clouds (Bellet al. 1996a,M. E. Ockert-Bell, pers. commun. 1998) do not appear to shthe same characteristics as the spectra of their respectivebut as cloud optical depth increases, the characteristics docome more pronounced and approach band depth values oindividual frost spectra.
To see how well these bands will work for the data set, bdepth map tests were applied to the volatile spectra in the smanner as Bellet al. (1996a) and Klassen (1997). First, the l
ice spectra are linearly interpolated to find reflectance valuethe wavelengths of the observations. The spectral regions choal depth of 0.5 with a particle size of about 3.5µm.
asumonut
st
owices,be-
f the
ndmeb
are then divided by a linear continuum calculated betweentwo endpoints to be used in the band depth maps. The ma3.33-µm band depth, relative to a continuum between 3.273.40µm, should be a very good indicator of CO2 frost of all grainsizes. Water ice is almost undetectable in this region. Howesince water ices are all very absorbing in this spectral rangis possible that the region could show extremely low reflectadue to total absorption by water ice, making the CO2 featureundetectable. Also, if an H2O layer were lying on top of theCO2 layer, in a cloud above it, or condensed together with it ifrost mixture (Kieffer 1970a) the CO2 spectral signature couldbe hidden.
The band “depth” map at 2.25µm, relative to a continuum between 2.131 and 2.331µm, is really a measure of the spectral cuvature about this local continuum point. All of the volatile icehave a local maximum reflectance at this wavelength; howein the case of water ices, the spectra turn down rapidly on eiside of 2.25µm. The 3.69-µm band depth map, relative to a con
s atsentinuum between 3.40 and 3.80µm, provides a way of discrimi-nating between the coarse-grained water frosts, presumed to be
N
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40 KLASSE
ground ice, and the fine-grained water frosts, which could pobly be ice clouds. The value of the band depth map would bethan one in the former case and greater than one in the lattefrost grain sizes decrease, to sizes of 50, 10, or even 1µm in size,this feature becomes even more pronounced (Roushet al.1990).
Principal Components Analysis/Linear Mixture Modeling
The statistical method of principal components analysis (Ptransforms a set of data from a space of observables to a sporthonormal eigenvectors which we can try to assign to phystraits, or a combination of physical traits (Whitney 1983, Fl1988, Klett 1988, Dunteman 1989, Waddill 1994, Titus 19Klassen 1997). The main idea is to reduce the dimensionalithe data to a smaller set of coordinates that will describe mothe information in the original set. In this work, the dimensioality of each pixel is simply the number of wavelengths,n, inthat pixel’s spectrum. Thus we have a set of data that residann-dimensional wavelength space that we will transform ia p-dimensional space of eigenvectors which account for mof the data variance. The value ofp will be determined by thenumber of significant eigenvectors, i.e., the number of eigentors necessary such that the remaining variance not accofor is less than the noise level in the data.
PCA has an advantage over standard multi-variate regrein that it makes no assumptions about the interdependenthe set of variables. The technique then finds the new coordsystem by maximizing the variance/covariance matrix ofdata. Mathematically this is shown as
Ai j =n∑
l=1
[(Ri,l − Rl 〉(Rj,l − Rl 〉], (3)
where Ai j is the covariance matrix element,Ri,l is the scaledreflectance of theith pixel at wavelengthl andRl is the averagescaled reflectance over all pixels at wavelengthl . Minimization
To search for CO2 clouds and ground frosts we use the band of the matrixA leads to the eigenvalue/eigenvector equationsFIG. 3. Representative 3.33-µm band depth maps from (A) 14 JAN 95 (Ls= 45◦) and (B) 01 FEB 95 (Ls= 54◦) with continuum points at 3.27 and 3.40µm.
depth map centered on the absorption feature at 3.33µm (Fig. 3).
Variations across the disk for all scans are on the order of the noise and areabout the north polar region. This indicates either the seasonal CO2 polar cap em
ET AL.
ssi-lessr. As
A)ce oficalry6,
y oft ofn-
s intoost
ec-nted
sione ofate
he
|A − `I | = 0
and
(A − `I )en = 0, (4)
whereI is the identity matrix, is the eigenvalue, anden is theeigenvector. The eigenvectors are the new coordinate axesthe eigenvalues are representative of the amount of the varicovered by the corresponding eigenvector.
The PCA results are then used in linear mixture model(LMM). The Mars image data are plotted in the new spacethe PCA eigenvectors. From these plots, spectrally “pure” emember pixels can be chosen from pixels that map into extrvalues of the eigenvector coordinates. These endmemberthen used to model the remaining pixel spectra such that
Ri,l =m∑
k=1
= ( fi,k Ek,l )+ εi,l , (5)
where Ri,l is, again, the scaled reflectance of theith pixel atwavelengthl , Ek,l is the scaled reflectance of thekth endmember(out of a total ofm endmembers) at wavelengthl , fi,k is therelative brightness contribution that thei th pixel has of thekthendmember spectrum (i.e., the fractional abundance), andεi,l
is the residual spectrum not modeled by them endmembers(Salmon 1882, Smithet al. 1985, Boardman 1990, Tompkinet al.1994, Waddill 1994, Titus 1996, Klassen 1997).
This same PCA/LMM combination technique has been upreviously to study broadband image sets of face-on gala(Waddill 1994) and edge-on galaxies (Titus 1996). Planeapplications include Lunar Apollo images (Johnsonet al.1985)and Martian Viking lander and visible-wavelength telescoimages (Adamset al.1986, Bell 1992).
RESULTS
less than 5%. However, in the scans fromLs= 54◦ an∼ 15% feature appears in a collarerging from under cloud cover or transient CO2 polar clouds.
G
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IR SPECTRAL IMAGIN
Band depth values less than one would indicate the presena CO2 ground frost or clouds of moderate to high optical dep(τvis≥ 1). In the images from 14 JAN 95 (Ls= 45◦) there is littleto no absorption, with variations from a value of 1.00 on the orof 5% (the noise level) compared to the 40 to 60% value thregion completely covered by CO2 frost would have (Klassen1997, Bellet al. 1996a). Based on this we can say that thwere either no significant CO2 frosts observed at this time or,they did exist, they were too optically thin or were effectivemasked by other components, such as an intimate mixturewater frosts.
In the 01 FEB 95 (Ls= 54◦) images, low values of the3.33-µm band depth map lie in the northern regions. In sc1 and 3 the global values of the band depth vary from 1.00 oon the order of 5%, except in the polar regions where there iabsorption on the order of 15%. Scans 2 and 4 do not showvariations greater than the 5% noise level. The appearance oabsorption atLs= 54◦ where it was not apparent atLs= 45◦,and its transient nature, could be an indication of a CO2 cloudover the polar cap.
Water ice searches are made using the band depth mapstered on 2.25µm (Fig. 4). In most of these band depth mathe north polar region has a value of 1.40–1.50 comparethe value for a fully covered region of 1.50–1.60 as seen inband depth map tests (Klassen 1997). This indicates thatat the times when the CO2 frosts can be seen, there are ssignificant amounts of water ice. Geometric mapping of thimages shows that the water ice signature extends southwaan average latitude of 68◦N at Ls= 45◦ but has receded to aaverage latitude of 78◦N by Ls= 54◦. In HST images taken aLs= 39.7◦ (Jameset al. 1996) the polar region is circular anfeatureless, extending southward to a latitude of 66.5◦N whichwould indicate that the polar region is covered by a waterhood at this time. This polar hood could mask any possible C2
◦ ◦
spectral features in ourLs= 45 images. ByLs= 63.5 surfaceds. There i
have some information about the ice grain sizes. If the spectrale ice
features can be seen in the polar region in HST images (JamesFIG. 4. Representative 2.25-µm band depth maps from (A) 14 JAN 95 (Ls= 45◦) and (B) 01 FEB 95 (Ls= 54◦) with continuum points at 2.131 and 2.331µm.The polar cap shows up as a water ice feature with band depth values much greater than 1, but there is no real evidence of morning or evening clous
signature matches that of a coarse ice, such as the coars
also some correlation with low albedo surface features, at the∼10% level, which(Bell and Crisp 1993, Murchieet al.1993).
OF MARTIAN ICES 41
e ofth
ert a
re
yith
nslyanny
this
cen-sto
hevenllsed to
ceO
et al. 1996), indicating that the polar hood has at least modissipated and the latitude of the polar cap has receded to a75◦N. From this comparison it appears that the 2.25-µm banddepth map traces both ground frosts and clouds.
Curiously, the 2.25-µm band depth maps appear to corrlate somewhat with albedo. This implies that there may bsurface mineralogic effect influencing this spectral parameThe correlation is such that classic dark albedo regions s∼5–10% absorption features. Bell and Crisp (1993) noted wspectral variability in martian relative reflectance spectra in2.2- to 2.4-µm region with features varying by only±3–5%.They created a relative band depth map at 2.25µm using 2.21and 2.29µm as the continua (cf. 2.25-µm band using 2.131and 2.331µm as continua in Fig. 4). This band depth doshow trends (albeit small) with emission angle and airmawhich could be consistent with a weakly absorbing, spatiauniform atmospheric constituent. However, when compareother known atmospheric weak absorbers, the correlationsso weak that Bell and Crisp (1993) interpret the band depto be due to a surface constituent. They also find that isolclassic dark albedo regions have a lower than average relband depth, matching what is seen in the 2.25-µm band depthmaps here.
Murchie et al. (1993) used this wavelength region to invetigate bright region heterogeneity and discuss the possibof metal–OH bands around 2.2µm. They also note that SyrtiMajor, the only dark region in their investigation, shows a broshallow band due to the 2.0-µm pyroxene absorption dominating the spectra beyond 2.2µm, just outside the influencof the atmospheric CO2 2.0-µm absorption feature. It is cleafrom these studies that although the 2.25-µm band depth mappresented here can trace H2O frosts, it can become influenceby surface mineralogy effects.
To distinguish between clouds and ground ice it is necessa
could be due to surface mineralogy and the nearby metal–OH or pyroxene bands
ornin
42 KLASSEN ET AL.
FIG. 5. Representative 3.69-µm band depth maps from (A) 14 JAN 95 (Ls= 45◦) and (B) 01 FEB 95 (Ls= 54◦) with continuum points at 3.40 and 3.80µm.The north polar region in both has values greater than 1 consistent with a fine grained water frost composition. There is some evidence here of the mg and
evening clouds with band depth values from 1.1 to 1.2 in these regions. Although there was no evidence in the 2.25-µm band depth maps of water frosts, they.
t i
nth
,atti
ar1hthkt
ndio
the5fto.demurth
Marswithotingat-rge,or-alsoare
tralars
ageto
atile
ors
-not
ctorrs one
ater
does
could have been masked by the albedo region correlations noted in Fig. 4
spectrum of Roushet al.(1990), then it is safe to presume that ia ground frost. In the spectral region around 3.69µm, the coarsefrost is dark with little or no spectral variation, whereas the fifrosts have a rather large local maximum, with the level ofmaximum increasing for smaller grain sizes (Roushet al.1990).In modeled cloud spectra (Bellet al. 1996, M. E. Ockert-Bellpers. commun. 1998), the reflectance increases with increcloud optical depth. Thus, band depth map values greaterone would indicate fine grained ground frosts or moderate opdepth (τ ≥ 0.25) clouds.
In all the 3.69-µm band depth maps (Fig. 5) we can see clethat the north polar region has a band depth value of 1.2 toindicating a fine frost. In all the images from 14 JAN 95 tevening limb has a value from 1.2 to 1.3, thus indicatingthese regions have a large volatile rich component most licomposed of a fine water frost. In the 01 FEB 95 imagesmorning and evening limbs are not as symmetric. In Scan 1limbs do not show up well, but both limbs show up in Scawith a value of about 1.3. The morning limbs in Scans 2 anare extremely high, on the order of 1.4 to 1.5 with no indicatof absorption at the evening limbs.
When PCA is applied to our Mars spectral cubes we findthe first three eigenvectors (e1, e2, e3) account for over 99% of thdata variance.e1 accounts for 95–99% of the variance with 0.3% of the variance accounted for bye2. e3 then makes up most othe remaining variance withe4, etc., making up an insignificanpart of the variance that appears to be dominated by the nbased on the incoherence of their spectra with wavelength
The two methods used in determining the physical traitsscribed by the various eigenvectors are plotting the eigenspand creating eigenimages. The eigenspectra (Fig. 6) are asure of how much each of the particular wavelengths contribto that eigenvector. An eigenimage (Figs. 7 and 8) is a pictorepresentation of a particular eigenvector’s contribution topixels in an image, where the brighter pixels indicate hig
contribution from the eigenvector.s
eis
singhancal
ly.4,eatelyhethe34n
at
–
ise,
e-ctraea-
tesialheer
From the eigenimages it is easy to see thate1 represents the in-frared albedo. The eigenspectrum appears to be an averagespectrum and the corresponding eigenimages correlate wellMars continuum images. The eigenimages corresponding te2
have high values in the polar regions and the limbs, correlawell with the various frost band depth maps and thus indicing a frost interpretation. The dark, local noon areas have lanegative values which would be consistent with a negative crelation with temperature (see below). These eigenimagesconfirm that colder temperatures and condensed volatilesalways correlated.
Sky pixels on all these images have a weak martian specsignature, indicating that there is some amount of scattered Mlight in them, amounting to about 10% of the values of an averlow albedo region.e2 has an interesting shape that is similarthe spectrum of a fine water frost. Figure 2 showse2 from severalrepresentative spectral scans plotted relative to various volspectra.
e2 shows a strong correlation with the fine H2O frost spectraof Roushet al. (1990). Many of the features in the eigenvectspectra, such as the 2.00-µm feature, appear similar to featurein all the volatile spectra. The 2.00-µm absorption appears inthe fine water frosts, both of the CO2 frosts, and the Mars atmospheric model spectra. Based on this feature alone there isenough diagnostic information to decide what the eigenverepresents. However, the spectral shapes of the eigenvectoeither side of the 2.00-µm feature appear similar only to the finwater frost. Finally, the level of the 3.00-µm region relative tothe level in the absorption feature at 2.00µm also only appearssimilar to the reflectances of the fine water frost.
The steep drop in the eigenspectra from 3.5 through 4.1µmis interesting, as such a steep drop is not present in the wice spectra. There is a drop in the coarse CO2 frosts in thiswavelength regime, though the eigenvector spectral shapenot appear to level out as does the COspectrum. It can also
2be noted that the low 3.00-µm brightness of the eigenspectra
rurrent
of
and
IR SPECTRAL IMAGING OF MARTIAN ICES 43
FIG. 6. Representative spectra of the first three eigenvectors from the PCA.e1 has the shape of an “average” Mars spectrum.e2 traces cold, fine grained watefrost covered regions. Currently there is no physical interpretation fore3 and, as it only accounts for at most 0.5% of the data variance, is not used in the cmodeling.
FIG. 7. Representativee1 images from (A) 14 JAN 95 (Ls= 45◦) and (B) 01 FEB 95 (Ls= 54◦). These maps match well continuum wavelength imagesMars, indicating thate1 is a measure of overall regional infrared albedo.
FIG. 8. Representativee2 images from (A) 14 JAN 95 (Ls= 45◦) and (B) 01 FEB 95 (Ls= 54◦). These maps have high values in the north polar region
in the morning and evening regions. The lowest values lie in centrally located, classic low albedo regions. Based on correlations with band depth mapsand theshape of thee2 spectrum, these maps are a measure of how cold and frost covered a region is.
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FIG. 9. Mars thermal emission spectra at typical temperatures for Mat the season of the 14 JAN 95 (Ls= 45◦) images. The emission spectra wemodeled as simple blackbodies and the temperatures were taken from theLander 2 data (Hesset al.1977) or are extremes calculated from thermal inedata (Moerschet al. 1997). The emission spectra were divided by a reflecsolar spectrum from a gray surface at an albedo of 0.1, typical of martianalbedo regions. These units are then similar to the scaled reflectance unitin this paper.
is similar to coarse grained CO2, although there is a lack oa feature at 3.33µm. This would indicate that this eigenvectcould be a representation of both coarse CO2 and fine H2O frosts.
The value of this eigenvector should thus be high at the polesse v
pixels are then located by finding the extreme points in these
and limbs where the band depth maps show evidence of cloudsFIG. 10. PCA plot of the spectral image cube 01 FEB 95 (Ls= 54◦) scan 1. Extreme values ofe1 are Arabia (bright, centrally located region) at high valueand the sky at low values. Note that the sky regions in our images are not true zero points but rather have a small degree of scattered Mars light. Extremalues of
plots.
e2 are the north polar region (cold and presumably frost covered) at high valow values. PCA plots from all other scans in this work are similar and have
ET AL.
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and ground frosts. However, this would indicate that wherethere are fine H2O frosts there are also coarse CO2 frosts, and itis hard to believe that this would always be the case.
The 3.5-µm spectral shape could also be interpreted asinverse relation to surface temperature. It is in this region tthe thermal emission from the martian surface begins to comwith the solar reflected flux. Figure 9 shows modeled emissspectra with Mars–Earth distance of 0.765 AU and a Mars–Sdistance of 1.649 AU, which are equal to those at the time of14 JAN 95 observations. Thermal emission effects are negligat wavelengths shorter than about 3.5µm except at the veryhighest temperatures. The upturn at 240–250 K temperatucorresponding to local noon regions, has a factor of 8 toincrease from 3.5 to 4.1µm which is comparable to the factoof 4 to 6 downturn ine2. This inverse relation would indicatethat pixels with high values ofe2 would have colder temperatureand thus, again, would be in the polar regions and limbs whit would be cold enough to condense clouds and ground fro
The PCA by itself is quite useful in helping to interpret thspectral sets; however, it can also be used as a tool for linmixture modeling (LMM). Instead of using laboratory spectof minerals and frosts or attempting to iteratively deduce specendmembers from the image set to do the LMM, PCA canused to find endmember spectra from within the data setrepresents spectral componets on the planet. The first stefinding these endmembers is to plot the spectral cubes in the Pspace with the eigenvectors as axes (Fig. 10). The endmem
lues and Syrtis Major and Sinus Sabaeus (dark, relatively centrally located regions) atendmembers with the same physical properties as those in this plot.
60% no
IR SPECTRAL IMAGING OF MARTIAN ICES 45
FIG. 11. Representative north polar region fractional abundance maps from (A) 14 JAN 95 (Ls= 45◦) and (B) 01 FEB 95 (Ls= 54◦) with circle showing theposition of the limb of Mars. Morning and evening regions show values on the order of 0.5 to 0.6, indicating that their spectra can be modeled as 50–rth
polar region component. The north polar region component matches a fine grained water frost, indicating that these regions likely contain fine grainedwater frostsas clouds or ground ices.tho
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The goal of endmember selection is to find all those pixelshave extreme values of the chosen eigenvectors and that surrthe p-dimensional data cloud. In order to do that with this dset, five to seven endmembers would be required, as seen bnumber of extrema. In tests performed with this many endmbers, some of the fractional abundances become nonphy(e.g., negative) or approach the noise level. Slight differenin the pixel chosen as the endmember also create very diffefractional abundance results. Since LMM is by definition a lintechnique, it breaks down while trying to model extreme limareas due to the nonlinear processes of atmospheric extinand limb darkening (Klassen 1997); thus we avoid attemptinmodel these areas. Since the areas with high negative value1 correspond to the limb and sky areas we do not choosemember pixels that enclose this area. This allows the usesmaller number of endmembers, allowing a better, more robfit. The endmember pixels are chosen from the most extrvalues ofe2 and the extreme positive values ofe1. These threepoints will surround most of the data cloud, leaving only tlimb and sky pixels unmodeled. The endmembers corresponthe north polar region and a dark, centrally located region foe2
and a bright, centrally located region fore1.Once the endmember pixels are chosen from the PCA p
the spectra of those pixels are used to model the spectra othe other pixels as a linear combination of those three endmbers. Maps of these fractional abundances are then madeFig. 11).
The bright region fractional abundance maps show highues in the classical bright regions and low values in the limand low albedo regions, as expected. The images do showthe outlying areas of low albedo regions have a 10 to 20% brendmember composition. This is consistent with the resultSingeret al. (1979), who described a simple additive modwhich found that a typical dark region spectrum could be co
posed of at most 30% of a typical bright region endmember. B(1992) performed a similar two endmember spectral mixture aatund
tathe
m-icalesentarbtiontos ofnd-f ast,
me
ed to
ts,f allm-
e.g.,
al-bsthathtofl-
found that at visible to NIR wavelengths the dark regions cont10 to 40% of the brightest image endmember spectrum.
The dark region fractional abundance maps show all thealbedo regions having values of 60 to 100% dark endmemcomposition. The images also show typical bright regionshaving 10 to 15% dark endmember composition, implying thmany of the intermediate albedo regions are similar to the dregions but are mixed with a bright component. Similarly, B(1992) in his simple two endmember spectral mixture analyfound that 5 to 10% of the bright region visible-NIR spectrucould be accounted for by a dark region endmember spectr
The north polar region fractional abundance maps (Fig.show high values of this endmember not only at the polargion, as expected, but also along the morning and evening hespheres, with values of 50% and higher. This would indicate tthere are volatiles in these regions perhaps in the form of cloor ground frosts. In his visible to NIR wavelength studies, B(1992) added a frost spectrum to his mixture model and fouthat the morning limb and north polar cap had substantial frtions of this endmember. It must be pointed out that the frspectrum used in the Bell (1992) model was a CO2 frost, andthus the south polar cap had the highest fractions of this emember. However, at the wavelengths used in his study it ispossible to discriminate between water and CO2 ices.
DISCUSSION AND IMPLICATIONS
The conclusion from the band depth maps is that significand diagnostic volatile signatures at the north pole, and to sodegree at the limb, can be detected using NIR mapping teniques. The signatures observed in the data shown here aremostly to the effect of water ices and surface mineralogy, ratthan CO2 ices. The north polar region during early 1995 (earmartian northern spring) was apparently covered by water i
ellndthat obscured any possible CO2 signatures. As the season pro-gressed the water ices receded or thinned enough to detect the
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CO2 ice. One interpretation could be that the water ices wepolar hood that thinned, allowing CO2 ground frosts in the polacap to become visible. Another is that the CO2 frosts were cloudsabove a polar cap that was composed of at least enough watto mask any CO2 ground frost signatures. We are currently eploring more detailed spectral methods of distinguishing clofrom ground frosts in order to resolve this ambiguity.
Hubble Space Telescope images from the same time peas our IRTF data (Jameset al.1996) show many clouds locatein a belt around the northern tropics. Their calculated cloopacity of this belt is generally about 0.25–0.35 at 410 nm,though areas near the limbs can reach values of 0.4 to 0.5. Clet al.(1996a,b) modeled images from previous HST near-apion oppositions in 1990–1991 and 1993 and found that the etorial belt has an ultraviolet opacity of about 0.2. Since thetections in this paper found fine water frosts in the same regas the HST detected clouds, we conclude that the 2.25-µm banddepth map is a good method of detecting and uniquely idening these clouds as water ices.
The physical location of the water frosts (surface vs atmspheric) in the north polar region is unclear, although a pohood cloud during theLs= 45◦ observations would be consistewith the HST images (Jameset al.1996, Clancyet al.1996a,b).The clouds seen in the HST images (Jameset al. 1996) mayalso indicate that the recent martian near-aphelion atmospis colder than during the times of the typical Viking era mesurements. Microwave measurements of water vapor saturaltitudes (Clancyet al. 1992, 1996a) also measure a martiatmosphere that, when relatively dust-free, is 15–20 K cothan typical Viking data, with absolute column abundanceswater vapor around 8–l1 pr.µm as compared to the 12–14 pr.µmmeasured at comparable seasons by the Viking MAWD.
The results of the frost fractional abundance maps, as wethee2 eigenimages, correlate well in the north polar regions wthe results from the band depth maps, but with two major advtages. The first is that there was no a priori knowledge needesearch for the volatile signatures. The north polar region coout as an endmember based only on the PCA transformatThe second advantage is that there is little to no correlatiothese fractional abundance maps with albedo. The variousdepth maps do show this correlation due to surface mineraand the fact that the map is dependent on only one absorpfeature. The PCA/LMM-based fractional abundance mapsmeasuring the amount of a particular endmember spectrueach pixel, making it a more robust technique for finding regiwith frost components. This is why the morning and evenclouds can be seen in the frost fractional abundance mapsnot in the band depth maps.
If the atmosphere is so much colder than typical Viking coditions for this season, then why is there not stronger evidencnorth polar CO2 ice clouds in the data used in this paper? Kief(1970a) showed that even small amounts of H2O frosts inti-
mately mixed with CO2 frosts can completely dominate the reflectance spectra beyond 3.0µm. At particle scales of 5–50µm,ET AL.
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the mixing ratio that can hide the CO2 spectral features is only0.1. At larger scales of 20–100µm, this mixing ratio drops to0.008, so we could have a case of CO2 being hidden by the H2O.
Pollacket al.(1990) showed that there is a correlation betwethe dust opacity and the amount of CO2 condensation within theatmosphere. As the dust opacity increases, so would the C2
cloud formation. If the northern autumn processes are symmeto those in the spring, then the lack of CO2 clouds could beexplained by the relatively dust-free environment on Marsthe time of these observations (Jameset al.1996, Clancyet al.1996b).
If the detected water ice is a ground frost, then it is unclewhy the CO2 frost feature is missing in theLs= 45◦ images butappears in the laterLs= 54◦ images. Since the CO2 is not in theearlier, seasonally colder, images and then appears in the lpresumably warmer, images then it may be concluded thatfine water frosts are a dissipating polar hood.
The data used in this paper make up a fraction of a failarge data set that includes images from nights before andter those presented here, spanning the entire martian nortspring season (Ls≈ 356◦–79◦). Future work will include ana-lyzing the rest of the image sets using these techniques, asas folding in additional observations taken later in the martiseasonal cycle during 1996–1997 (Ls≈ 48◦–148◦) (Bell et al.1997). Earlier image sets may show even colder atmosphconditions, with a higher probability of seeing CO2 clouds. Thethickness of the polar hood may be changing and thinninglater image sets, allowing better viewing of the seasonal polarcap.
ACKNOWLEDGMENTS
We thank the day crew and support staff of the NASA IRTF, without whothe observations could not have been made. We are grateful to Ted Roushan anonymous reviewer for their review of the original manuscript and Tefurther discussion of water ices and clouds. Invaluable assistance was provby Maureen Ockert-Bell with the model cloud spectra—many thanks. This wwas supported by grants from the NASA Planetary Astronomy Program (NAG4721 and NAGW-5117).
REFERENCES
Adams, J. B., M. O. Smith, and P. E. Johnson 1986. Spectral mixture modelA new analysis of rock and soil types at the Viking 1 site.J. Geophys. Res.91, 8098–8112.
Bell, J. F. III 1992. Charge-coupled device imaging spectroscopy of MarsResults and implications for martian ferric mineralogy.Icarus100, 575–597.
Bell, J. F., III, and D. Crisp 1993. Groundbased imaging spectroscopy of Min the near-infrared: Preliminary results.Icarus104, 2–19.
Bell, J. F., III, W. M. Calvin, M. E. Ockert-Bell, D. Crisp, J. B. Pollack, andJ. Spencer 1996a. Detection and monitoring of H2O and CO2 ice clouds onMars.J. Geophys. Res.101, 9227–9237.
Bell, J. F., III, R. N. Clark, S. Sagan, D. R. Klassen, T. L. Roush, D. Cris
- W. F. Golisch, D. M. Griep, and C. D. Kaminski 1996b. Imaging spectroscopyof Mars from 3 to 4µm. Bull. Am. Astron. Soc.28, 1063.
p
T
o
s
a
N
t
9M
,
iles
e
t
a
r
r
7
a
s
o
is of
.
nding
ro
gingop
, and
vari-
risp,3.
f the
ge
M.on,86
sonectra.
ns.
J. R.ment
94.pe
ninary.
IR SPECTRAL IMAGIN
Bell, J. F., III, D. R. Klassen, J. E. Moersch, W. F. Golisch, D. M. GrieC. D. Kaminski, P. Martin, C. Dumas, R. N. Clark, and E. A. Cloutis 199High spatial resolution near-IR imaging spectroscopy of Mars from the IRduring 1996–97.Bull. Am. Astron. Soc.29, 913.
Bell, J. F., III, J. B. Pollack, T. R. Geballe, D. P. Cruikshank, and R. Freedm1994. Spectroscopy of Mars from 2.04 to 2.44µm during the 1993 Opposi-tion: Absolute calibration and atmospheric vs mineralogic origin of narrabsorption features.Icarus111, 106–123.
Boardman, J. W. 1990. Inversion of high spectral resolution data.SPIE1298,222–233.
Calvin, W. M. 1990. Additions and corrections to the absorption coefficientCO2 ice: Applications to the martian south polar cap.J. Geophys. Res.95,14743–14750.
Clancy, R. T., A. W. Grossman, and D. O. Muhleman 1992. Mapping Mars wvapor with the very large array.Icarus100, 48–59.
Clancy, R. T., A. W. Grossman, M. J. Wolff, P. B. James, D. J. Rudy, Y.Billawala, B. J. Sandor, S. W. Lee, and D. O. Mubleman 1996a. Water vasaturation at low altitudes around Mars aphelion: A key to Mars climaIcarus122, 36–62.
Clancy, R. T., M. J. Wolff, B. J. Sandor, P. B. James, and S. W. Lee 191995–96 Observations of atmospheric dust/water ice relationships in theclimate.Bull. Am. Astron. Soc.28, 1065.
Crisp, D. 1990. Infrared radiative transfer in the dust-free martian atmosphJ. Geophys. Res.95, 14577–14588.
Dunteman, G. H. 1989.Principal Components Analysis.Sage, Newbury ParkCA.
Fink, U., and G. T. Sill 1982. The infrared spectral properties of frozen volatIn Comets(L. L. Wilkening, Ed.), pp. 164–202. Univ. of Arizona PresTucson.
Flury, B. 1988.Common principal components and related multivariate modWiley, New York.
Forget, F., G. B. Hansen, and J. B. Pollack 1995. Low brightness temperaof martian polar caps: CO2 Clouds or low surface emissivity?J. Geophys.Res.100, 21219–21234.
Gezari, D. Y., M. Schmitz, P. S. Pitts, and J. M. Mead 1993.Catalog of InfraredObservations, NASA Public Reference 1294.
Hansen, G. B. 1997. The infrared absorption spectrum of carbon dioxidefrom 1.8 to 333µm. J. Geophys. Res.102, 21569.
Hardorp, J. 1978. The Sun among the stars. I. A search for solar spectral anAstron. Astrophys.63, 383–390.
Hardorp, J. 1980. The Sun among the stars. III. Energy distributions fonorthern G-type stars and the solar flux calibration.Astron. Astrophys.91,221–232.
Herr, K. C., and G. C. Pimental 1969. Infrared absorptions near three micrecorded over the polar cap of mars.Science166, 496–499.
Hess, S. L., R. M. Henry, C. B. Levoy, J. A. Ryan, and J. E. Tillman 19Meteorological results from the surface of Mars: Viking 1 and 2.J. Geophys.Res.82, 4559–4574.
Hunt, G. E. 1980. On the infrared radiative properties of CO2 ice clouds: Ap-plications to Mars.Geophys. Res. Lett.7, 481–484.
Jakosky, B. M., and C. B. Farmer 1982. The seasonal and global behof water vapor in the Mars atmosphere: Complete global results ofViking atmospheric water detector experiment.J. Geophys. Res.87, 2999–3019.
Jakosky, B. M., and R. M. Haberle 1992. The seasonal behavior of water on MIn Mars (H. H. Kieffer, B. M. Jakosky, C. W. Snyder, and M. S. MatthewEds.), pp. 969–1016. Univ. of Arizona Press, Tucson.
James, P. B., J. F. Bell III, R. T. Clancy, S. W. Lee, L. J. Martin, and M. J. W
1996. Global imaging of Mars by Hubble Space Telescope during the 19opposition.J. Geophys Res.101, 18883–18890.G OF MARTIAN ICES 47
,7.
F
an
w
of
ter
.pore?
6b.ars
ere.
s.,
ls.
ures
ice
logs.
16
ons
7.
viorthe
ars.,
lff
Johnson, P. E., M. O. Smith, and J. B. Adams 1985. Quantitative analysplanetary reflectance spectra with principal components analysis.J. Geophys.Res. Suppl.90, C805–C810.
Kahn, R. 1990. Ice haze, snow, and the Mars water cycle.J. Geophys. Res.95,14677–14693.
Kieffer, H. H. 1970a. Spectral reflectance of CO2–H2O Frosts.J. Geophys. Res75, 501–509.
Kieffer, H. H. 1970b. Interpretation of the martian polar cap spectra.J. Geophys.Res.75, 510–514.
Kieffer, H. H., T. Z. Martin, A. R. Peterfreund, B. M. Jakosky, E. D. Miner, aF. D. Palluconi 1977. Thermal and albedo mapping of Mars during the Vikprimary mission.J. Geophys. Res.82, 4249–4291.
Klassen, D. R. 1997.Infrared Imaging Spectroscopy of Martian Volatiles.Ph.Ddissertation, Univ. of Wyoming.
Klett, K. K. 1988. A Principal Components Analysis of Three Herbig-HaObjects.Master’s thesis, Univ. of Wyoming.
Kuiper, G. P. 1947. Planetary atmospheres and their origin. InThe Atmo-spheres of the Earth and Planets(G. P. Kuiper, Ed.), Univ. of ChicagoPress.
Leggett, S., and T. Denault 1996.NSFCAM 256× 256 InSb Infrared ArrayCamera User’s Guide.NASA Infrared Telescope Facility.
McCaughrean M. 1989. Reduction and analysis techniques for infrared imadata. InProceedings of the Third Infrared Detector Technology Worksh,NASA TM-102209, pp. 201–219.
Moersch, J. E., T. L. Hayward, P. D. Nicholson, S. W. Squyres, J. Van CleveP. R. Christensen 1977. Identification of a 10-µm silicate absorption featurein the Acidalia region of Mars.Icarus126, 183–196.
Murchie, S., J. Mustard, J. Bishop, J. Head, and C. Pieters 1993. Spatialations in the spectral properties of bright regions on Mars.Icarus105, 454–468.
Pollack, J. B., J. B. Dalton, D. Grinspoon, R. B. Wattson, R. Freedman, D. CD. A. Allen, B. Bezard, C. DeBergh, L. P. Biver, Q. Ma, and R. Tipping 199Near-infrared light from Venus’ nightside: A spectroscopic analysis.Icarus103, 1–42.
Pollack, J. B., R. M. Haberle, J. Schaeffer, and H. Lee 1990. Simulations ogeneral circulation of the martian atmosphere 1. Polar processes.J. Geophys.Res.95, 1447–1473.
Pollack, J. B., M. E. Ockert-Bell, and M. K. Shepard 1995. Viking lander imaanalysis of martian atmospheric dust.J. Geophys. Res.100, 5235–5250.
Rothman, L. S., R. R. Gamache, A. Goldman, L. R. Brown, R. A. Toth, H.Pickett, R. L. Poynter, J.-M. Flaud, C. Camy-Peyret, A. Barbe, N. HussC. P. Rinsland, and M. A. H. Smith 1987. The HITRAN database: 19Edition.Appl. Opt.26, 4058–4097.
Roush, T. L., J. B. Pollack, F. C. Witteborn, J. D. Bregman, and J. P. Simp1990. Ice and minerals on Callisto: A reassessment of the reflectance spIcarus86, 355–382.
Salmon, G. 1882.Treatise on the Analytic Geometry of Three DimensioHodges, Figgis, Dublin.
Schofield, J. T., D. Crisp, J. R. Barnes, R. Haberle, J. A. Magalhaes,Murphy, A. Seiff, C. LaBraw, and G. R. Wilson 1997. Preliminary results frothe Pathfinder Atmospheric Structure Investigation/Meteorology Experim(ASI/MET). Science, 278, 1752–1758.
Shure, M., D. W. Toomey, J. T. Rayner, P. M. Onaka, and A. T. Denault 19NSFCAM: A new infrared array camera for the NASA infrared telescofacility. SPIE2198, 614–622.
Singer, R. B., T. B. McCord, R. N. Clark, J. D. Adams, and R. L. Hugue1979. Mars surface composition from reflectance spectroscopy: A summJ. Geophys. Res.84, 8415–8426.
95Sinton, W. M. 1967. On the composition of martian surface materials.Icarus6, 222–228.
N
an
,
.io
i-
od-
s
48 KLASSE
Smith, M. O., P. E. Johnson, and J. B. Adams 1985. Quantitative determinof mineral types and abundances from reflectance spectra using pricomponents analysis.J. Geophys. Res. Suppl.80, C797–C804.
Titus, T. N. 1996.Multivariate Analysis of Galaxian Spectra.Ph.D dissertationUniv. of Wyoming.
Tompkins, S., C. M. Pieters, J. F. Mustard, P. Pinet, and S. D. Chevrel 1994tribution of materials excavated by the lunar crater Bullialdus and implicatfor the geologic history of the Nubium region.Icarus110, 261–274.
Waddill, D. M. 1994.Mixture Modeling of the Galaxy M51.Master’s thesis,Univ. of Wyoming.
ET AL.
tioncipal
Dis-ns
Warren, S. G. 1984. Optical constants of ice from the ultraviolet to the mcrowave.Appl. Opt.23, 1206–1225.
Warren, S. G. 1986. Optical constants of carbon dioxide ice.Appl. Opt.25,2650–2674.
Whitney, C. A. 1983. Principal components analysis of spectral data. I. Methology for spectral classification.Astron. Astrophys. Suppl. Ser.51, 443–461.
Wolff, M. J., S. W. Lee, R. T. Clancy, L. J. Martin, J. F. Bell III, and P. B. Jame
1997. 1995 Observations of martian dust storms using the Hubble SpaceTelescope.J. Geophys. Res.102, 1679–1692.
