Mapping the Martian Polar Ice Caps: Applications of Terrestrial Optical

JOURNAL OF GEOPHYSICALRESEARCH, VOL. 103,NO. Ell, PAGES25,851-25,864, OCTOBER 25, 1998

Mapping the Martian polar ice caps' Applications of terrestrial optical remote sensing methods

Anne W. Nolin National Snow and Ice Data Center, Universityof Colorado,Boulder

Abstract. With improvementsin bothinstrumentation and algorithms,methods formapping terrestrial snow cover using optical remote sensing data have progressed significantlyover the past decade. Multispectral data can now be used to determine notonly the presence or absenceof snowbut the fraction of snowcover in a pixel. Radiativetransfer models have been used to quantifythe nonlinearrelationship betweensurface reflectance and grainsize thereby providing the basisfor mapping snowgrain size from surface reflectance images. Model-derived characterization of the bidirectionalreflectance distribution function provides the meansfor converting measuredbidirectional reflectance to directionM-hemisphericMalbedo. In recent work,this approach has allowed climatologists to examine the large scale seasonal variabilityof albedoon the Greenlandice sheet. This seasonal albedo variability resultsfrom increasesin snowgrain size and exposureof the underlyingice cap •s the se•sonMsnow cover •bl•tes •w•y. With the currentM•rs GlobM Surveyor and future missionsto Mars, it will soonbe possibleto apply someof these terrestrialmapping methods to learnmore about Martian ice properties,extent, andvariability. Distinct differences exist between Mars and Earth ice mapping conditions,including surface temperature, ice type,ice-minerM mixtures, and atmosphericproperties, so a directapplication of terrestrialsnow and ice mapping methodsmay not be possible.However, expertise in mappingand interpreting terrestrialsnow and ice will contributeto the inventoryof techniquesfor mapping planetaryices. Furthermore, adaptation ofterrestrial methods will provide a basis for comparisonof terrestrialand planetary cryospheric components.

1. ComparisonBetween Ices on Earth temperatureregimes, ice on Earth exists in a statethat is closeto the meltingpoint. Seasonalinsolation dif- and Mars ferences lead to substantial variability of snow cover, In comparativeplanetology, we often look at similar- seaice, and ice sheet conditions extent over the course ities betweenEarth and Mars. One of the most striking of a year. OverEarth's northern hemisphere, seasonal featuresof both planets,with criticallinkages to cli- extremes of snow and ice cover range from a January mate changeand hydrology,is the existenceof large maximumof about23% to an Augustminimum of 3% icecaps in their polarregions. Earth's cryosphere can, [Barry,1985], with significant regional and interannual in someways, serve as an analogfor the Martianice. variabilityin mostmonths [Robinson and Dewey, 1990]. Comparedwith Earth,we have only a limitedset of re- It is this combinationof spectral,spatial, and temporal motesensing observations for the Martian polar caps. variabilitythat makessnow and ice the mostdynamic Future Mars missionsand continuedadvancements in of Earth's surface cover types. instrumentationand algorithmswill enhanceour abili- Althoughsurface temperatures are typicallycolder tiesto compareand understand terrestrial and Martian than thosefound on Earth, the polar regionsof Mars polar regions. still experiencechanges in frost-coveredarea, surface While we know terrestrialsnow to be highly reflecting albedoand sublimation rates [Kieffer e! al., 1976;Farmer in thevisible, part to the spectrum, in the neaf-infrared et al., 1976;Paige and Ingersoll,1985; Haberle and wavelengthsits albedoranges from about0.8 to near Jakosky,1990]. On Mars, the extentof ice is less zero(see Fig. 1). Unlikemost other surface cover well-knownand may extend into the lower latitudes types,snow and ice haveextreme spectral variability asground ice [Paige, 1992; Mellon and Jakosky, 1995]. overa spanof only 2/•m. In comparisonto Martian Mellon and Jakosky,[1995] showed that groundice is stableon Mars at latitudesgreater than 600 and that icemay be presentnear the surface.Thermal models Copyright1998 by the AmericanGeophysical Union. and observationsof polygonalfeatures also show that Paper number 98JE02082. groundice may be presentat lowerlatitudes during 0148-0227/ 98 / 98JE-02082,09. O0 periodsof highobliquity of the Martianorbit [Mel- 25,851 25,852 NOLIN: MAPPING THE MARTIAN POLAR ICE CAPS

i r = 50gm

200gm

500 gm

1000gm

0.5 I

R (oo)at 60ø

illuminationangle

0.5 1 1.5 2 2.5 wavelength,gm Figure 1. Modeled directional-hemisphericalspectral reflectances of snowfor different optically equivalent grain radii.

lonet al., 1997]. Studiesof terrestrial permafrostmay the layered terrains and unknown quantity of dust in shedlight on the dynamicsand distributionof Martian the north polar cap [Kieffer, 1990]. Clark and McCord, ground ice. [1982]modeled the reflectancespectrum of the polar cap As with Earth's fresh water, most Martian water re- surfaceusing a linear mixture of 60% medium-grained sidesin the polar regionsin the form of ice caps. While water frost and 40% clay minerals. They estimatedthat both the northern and southern Mars polar caps are the permanent cap could contain 10-40% by weight of bright comparedwith non-icecovered regions, the com- mineral particulates. The seasonalcycle of CO2 depo- positions of the ice caps differ. The more extensive sition is also affected by Martian dust. Atmospheric north polar cap consists of H20 ice and the smaller dust is removed as CO2 condenseson dust particles south polar cap is thought to be mostly or entirely CO2 and precipitates onto the ice cap surface. These dust ice [Kieffer et al., 1976;Farmer et al., 1976]. Modeling particles remain in the seasonalsurface deposits and and observational evidence support the idea of little, if are thought to control both surface albedo and subli- any, CO2 in the northern hemispherepermanent ice cap mation rates [Pollack et al., 1990]. This is a different [Mellon,1996; Clark and McCord,1982]. case than for Earth's polar caps that are nearly pure Polar and ground ice are thought to be important ice with generallyless than 0.5 ng/g elementalcarbon componentsof the Martian hydrologiccycle where sub- [Warren and Clarke,1990] and lessthan 26 ng/g dust limation processesdominate the ice-atmosphereinterac- [Kumai, 1976; Royer et al., 1983]. Changesin surface tions [Haberleand Jakosky,1990, Mellon and Jakosky, albedo and energy balance for terrestrial ice sheetsare 1995]. Measurementsof Martian atmosphericwater va- primarily driven by changesin surfacesnow grain size por showlarge changes in water vaporamounts through [Nolin and Stroeve,1997]. Thus comparisonsbetween the courseof a year [Jakoskyand Farmer, 1982] and Earth and Martian ice-atmosphereinteractions are not that the north polar cap is a likely source[Haberle and straightforward. Jakosky,1990]. A significant differencebetween Martian and terres- 2. Some Relevant Martian Ice Mapping trial ices is the amount of light absorbingparticulates in the Martian polar ice caps and seasonalfrost de- Questions posits. Dust is a significantcomponent of Martian ice, What is similar between Earth and Mars is that their with roughly equal parts of dust and water present in extensiveice capsappear •o record,respond to, andper- NOLIN: MAPPING THE MARTIAN POLAR ICE CAPS 25,853 turb climate change.On Earth, polar ice coringefforts 3. Terrestrial Snow Mapping Using have generateda climate time seriesextending back Optical Remote Sensing over 110,000 years. These data document changesin Earth climate driven by periodic variability in Earth- In this section,selected snow/ice mapping methods Sun geometry[Johnsen et al., 1997; Yang et al., 1997] are described. These optical remote sensingmethods as well as other, shorter-termfluctuations [Barlow et addressmapping snow/ice extent, grainsize and albedo al., 1993; White et al., 1997]. Other ongoingpolar and thus are considered candidates for adaptation to climatological investigationsare examining changesin Martian ice cap mappingendeavors. It shouldbe noted ice sheet elevation, ice flow, calving rates, surface en- that passivemicrowave and radar techniquesare widely ergy balance,and snowaccumulation rates over the ice used to map snow and ice on Earth. However,because sheets. These short-timescale variations, involving ice- such instrumentation has not been used in Mars map- Ocean-atmosphereinteractions, are not well-quantified.ping, and are not currentlyplanned, the focusof this The salient questions on Mars are in some ways article is on the use of optical remote sensingmethods. more exploratory in nature. For instance, although the As background,a brief overviewof the optical prop- Mariner 9 and Viking Orbiter 2 have provided imagesof ertiesof snowis given. However,for more detail on this Mars' polar regions,the exact compositionof eachpolar subject, the reader is referred to the more comprehen- cap remains somewhat obscured. Changesin ice extent sivework of Warren, [1982]. have been difficult to quantify becauseof lack of multispectral image data. Mapping ice extent and polar lay- 3.1. Optical Properties of Snow ered depositsis key to understandinglong term changes It is well known that the optical properties of ice can in Martian climate that are thought to be driven by be directly related to snowpackphysical properties such quasi-periodicorbital variations[Howard et al., 1982]. as grain size and albedo. An aggregationof ice particles On shorter timescales,the spatial extent and tempo- will reflect nearly all energy in the visible wavelengths ral variability of CO2 frost depositionand sublimation (0.4- 0.7/•m) [Wiscombeand Warren,1980]. In thevis- on the polar capsare not well-characterized.A 25% de- ible, ice particles reflect predominantly into the forward creasein apparentalbedo (uncorrected for anisotropic direction.When light absorbingparticulates (e.g. dust) scattering)most likely indicatesthe seasonalremoval are mixed with snow, reflectance decreases and becomes of the CO2 surface frost from the north polar ice cap more isotropic[Warren and Wiscombe,1980]. In the [Paigeand Ingersoll, 1985]. The CO2 frost sublimation near-infraredregion (0.7 - 2.5/•m), ice is still forward dynamics need to be quantified, since the latent heat scatteringbut the property controllingthe magnitudeof of CO2 frost sublimation is a significant componentin albedois the particlesize [Wiscombe and Warren,1980; the heat budgetfor the polar caps[Paige and Ingersoll, Warren, 1982]. In Figure 1, resultsof a two-streamra- 1985]. Determinationof surfacefrost grain sizesand diative transfer model demonstrate the relationship be- grain size metamorphismrates would provide cluesto tween spectral albedo and snow grain radius. Because the thermo'dynamicsof that process[Clark et al., 1983]. a significantproportion of incidentsolar radiation is in Without more quantifiable information on ice extent, the near-infrared region, grain-size-inducedchanges in surface albedo, surface grain size, and dust content, it albedo have important consequencesfor the surface ra- is difficult to characterize the interactions between the diation balance and top-of-atmospherefluxes. dusty Martian atmosphereand the polar ice caps. Martian ground ice, while an important element of 3.2. Optical Remote Sensing of Snow on Earth the global hydrologic cycle, is less amenable to di- Instrumentation available to map snow and ice on rect observation by remote sensing instruments. In Earth differsgreatly from the few instrumentsavailable most cases,the overlying ice-free regolith obscuresthe for Mars. While optical remote sensingof Martian ice buried soil layers, whosepores contain water ice. How- is currently limited, the followingdescriptions of terres- ever, indirect evidence can be obtained through map- trial optical remote sensingtechniques and instrumen- ping polygonalfeatures thought to be associatedwith tation are meant to provide backgroundand impetus for seasonallydriven frost heaving[Mellon, 1997]. These potential applicationsof terrestrialmethods. While not polygonalfeatures may not representpresent ground exhaustive, this section provides a brief overview of the ice distributions,since they can persistfor long periods. most widely usedoptical instruments for snow/icemap- Although attempts to directly map Martian ground ice ping as well as selectedmethods that potentially could with remotely senseddata have not provenhighly use- be used for mapping Martian ice cap surface character- ful, geomorphicmapping at higher image resolution istics. should help in their characterization. The LandsatThematic Mapper (TM), with 30m spa- To assessthe applicability of optical remote sens- tial resolution and six channels in the visible and near- ing techniquesto Martian ice mapping problems, an infrared, provideseffective multispectral snowmapping overview of these terrestrial methods is presented. This capabilities(see Table 1) [Dozier, 1989a; Hall et al., is followed by a discussionof how such methods might 1995; Rosenthal and Dozier, 1996]. The Advanced be applied to help answersome of the relevant questions Very High ResolutionRadiometer (AVHRR) has visi- about Martian ice. ble, near-infrared, and thermal channelsand spatial res- 25,854 NOLIN: MAPPING THE MARTIAN POLAR ICE CAPS

Table 1. Landsat Thematic Mapper age. Dozier and Marks, [1987] developedan index- Spectral Bands basedmethod to map snowin the Sierra Nevadaof Cal- ifornia usingLandsat (TM) bands2 and 5 (seeTable Band Number SpectrM Range, /•m 1). Dozier, [1989a]found that a thresholdvalue of 0.4 1 0.45- 0.52 could discriminate snow from non-snow-coveredpixels 2 0.52- 0.60 3 0.63- 0.69 and most cloud-coveredpixels. They also found that, 4 0.76- 0.90 by usinga reflectancethreshold of 11%in TM band4, 5 1.55 - 1.75 snowand open water could be separated. 6 10.40- 12.50 Thoughits simplicityis appealingfor computational 7 2.08- 2.35 reasons,several problems have plaguedthis two-band Band 1 was not used in this analysis classification method. Index-based methods typically because it tends to saturate over snow. have difficulty distinguishingbetween snow and cirrus Band 6 was not used becauseit is outside cloudsbecause of their similar optical propertiesin both of the optical region. the visible and near-infrared. A separate cloud mask can be used that incorporatesa spectral band centered at 1.6 Jam(useful for mappingvery smallice particles olutionsof 1 km and 4 km. The visible(0.58 - 0.68Jam) suchas thosein cirrusclouds). Shadowed snow is often misclassified as non-snow covered. Partially snow cov- andnear-infrared (0.725- 1.10jam) channels have been successfullyused for mapping snow albedo over the eredpixels can alsobe difficultto classifyusing a binary classification. It remains unclear what fraction, depth, Greenlandice sheet [Stroeve et al., 1997].With the up- and pattern of partial snowcover is neededin orderfor cominglaunch of NASA'sEOS AM-1 satellite,the Mod- erateResolution Imaging Spectroradiometer (MODIS) a pixel to be mapped as snow. sensor will have 19 channels in the visible and near- 3.3.2. "Subpixel" snow mapping. The field of view of a sensor often contains more than one land sur- infrared(36 channelstotal) and a spatialresolution rangingfrom 250m to 1kin. In additionto theseex- face covertype, causing"mixed pixels." For instance,in isting and plannedsatellite-based optical sensors, air- many regions,snow is typically spatially associatedwith borne opticalmapping delivers high spatial resolution rock and vegetation. Melting snow, even in topograph- and, in many cases,offers sensor types not yet avail- ically uniformregions, tends to be patchy[Shook et al., able on satelliteplatforms. For example,the Airborne 1993]revealing the underlyingvegetation and soil. For Visible/InfraredImaging Spectrometer (AVIRIS) is an hydrologic purposesand for estimating the thermody- airborneimaging spectrometer with 224spectral bands namic state of the snowpack, we require knowledgeof from 0.4 to 2.45 Jamwith a nominalsampling interval only the snow properties but not those of the other components that may be present in the pixel. We also re- andspectral response function (full width at half max- quire an accurate estimate of the fraction of a pixel that imum)of 10 nm. This instrumentprovides us with is covered by snow as a validation and calibration for the appropriateband locations and spectralresolution the more widely used binary classificationmethods. for sensitivityto ice absorptionfeatures in the near- infraredwavelengths. In the followingsections, meth- Spectralmixture analysis(SMA) is a multispectral ods usingthese optical instruments are describedfor method that is currently used for determiningthe frac- mappingsnow-covered area, snow grain size, and snow tion of snow coverin a pixel. This fractional snowmap- albedo. ping approachis termed "subpixel"mapping becauseit provides information on snow content in a pixel. This approach does not map the distribution of snow cover 3.3. Mapping Snow Covered Area within a pixel, rather the contribution of the snow to 3.3.1. Binary snow/ice mapping. A binary the multispectral reflectance of the whole pixel. SMA classificationis one in which each image pixel is des- evolved out of earlier research that relied on principal ignatedas either 100% or 0% of a particularland cover componentsanalysis (PCA) to quantifythe amountsof component,in this case,snow. Such index-based classi- variousconstituents in chemicalmixtures [Lawtonand fication methods are commonly used for mapping snow- Sylvestre,1971]. Mixture analysiswas developedto an- coveredarea with multispectraloptical remotesensing alyze linear combinationsof land surfacecovers having data. For instance, the Normalized Difference Snow a adjacent (rather than a layered) spatial distribution Index (NDSI) has been chosenfor the MODIS snow [Adamset al., 1986]. When incidentphotons interact mappingalgorithm [Hall et al., 1995]. Unlikemost with a single constituent before scattering, the spec- land surfacecovers, snow is highly reflectingin the vis- tral mixing processis describedas predominantly linear. ible and only moderatelyreflecting in the near-infrared When light interacts with two or more materials before wavelengths.The NDSI usesa visiblechannel (0.52- being reflectedfrom the surface,this resultsin nonlinear 0.60Jam) and a near-infraredchannel (1.55- 1.75Jam) spectral mixing. If the nature of the nonlinearity can be in the followingrelationship: characterized[Roberts et al., 1993]or if their properties NDSI= (Vis- NIR)/(Vis+ NIR) (1) can be linearized by using the singlescattering albedo insteadof singleconstituent reflectances [Mustard and The normalizationprocess is highly effectivein reduc- Pieters, 1989; Ulark and Roush,1984], nonlinearmix- ing differencesin irradianceconditions across an im- ing doesnot presenta problem. Sourcesof nonlinearity NOLIN: MAPPING THE MARTIAN POLAR ICE CAPS 25,855 include intimate mixtures of mineral particulates and problems require detection using imaging spectrometer ice, optically thin snow, a wide range of mean snow data followed by pixel-by-pixel atmosphericcorrection. grain size acrossthe surfaceof a pixel, and changesin What is critical for this mapping method is that the the spectral compositionof irradiance over a pixel. The end-membersbe spectrally unique, and present in suffi- first of thesenonlinear effectswould have the largestef- cient amounts to be detectable and that the sensor has fect for Martian frost/ice remotesensing. Though dust the spectral and radiometric resolution needed to dis- amounts in Earth snow are generally low, Clark and tinguishbetween the end-members[Sahol et al., 1992]. œucey,[1984] have shown that higherdust particlecon- Selection of end-members is the most important step centrations,such as those that would be found on Mars, in the processof spectral unmixing. End-membersmay nonlinearly affect reflectanceof mixtures. be chosenfrom libraries of mineral and vegetationspec- The reflectanceof an image pixel holds information tra [Clarket al., 1993;Grove et al., 1992]or theymay be about the number of constituentsin a pixel, their spec- derived from the image data itself. For the latter case, tral signatures, and their relative abundances. Such there is typically no a priori knowledgeof the number image constituentsare termed "end-members"and each of end-membersnor of the location of the purest pixels end-member is consideredto be a pure representation representingeach end-member. It is advantageousto of a surfacecover type in the image(such as snow, rock, perform somenoise reduction preprocessing to improve or vegetation).Each imagecan be well-representedby image end-member selection. For this, the minimum a finite and small set of spectrally-unique end-members noisefraction (MNF) transform[Green et al., 1988]is that describesthe dimensionalityof the data [Gillespie used in a multistep PCA to identify noise-dominated et al., 1990]. For a multispectralimage, a linear mix- eigenimages.These noise componentscan be removed ture of the end-membersis calculatedusing the follow- and the data then transformed back to the original ing mixing rule [Adamset al., 1986]: data space. Iterative statistical analysis of the noise-

N reduceddata is performed to identify thosepixels in the + multispectral image data that best represent spectrally i=1 pure pixels [Boardmanet al., 1995]. These automated where, Rc is the apparent reflectance, at-sensor radi- techniquesprovide the information needed to identify ance,or digitalnumber (DN) (dependingon the data- the end-membersfrom image data but, the final end- type) in sensorchannel c; Fi is the fraction of end- member selection remains a subjective process. Figure memberi, Ri,c is the radiance,reflectance or DN of 2 shows reflectance data in Landsat TM channels 2 and end-member i in channel c; N is the number of spectral 7. These imagesare an exampleof how additional spec- end-members, and E• is the error for channel c of the tral data can provide much neededinformation for scene fit of N spectral end-members. Apparent reflectance interpretation. This scene, acquired on March 6, 1994, is the atmosphericallycorrected surface reflectancefor over Glacier National Park, Montana, has dimensions eachpixel, uncorrectedfor illumination differences.The of 75 kmby 75 km. On the left, the band 2 image shows fit of the linear mixture model to the spectral data in bright snow cover in the mountainous region. In the each pixel is measuredby the error term E•. Unlike the band 7 image, on the right, one can see that much of binary classificationmethod, SMA providesa quantita- the image is influencedby cloud cover. Clouds and snow tive estimate of how well the model describes the mul- increase in contrast at longer wavelengthsbecause of tispectral image data. differencesin their particlesizes [Dozier, 1989a]. With- The ability of the SMA model to accurately map out sufficientspectral information, snow and cloudscan snow cover in mountainousregions has been demon- be impossibleto distinguish. Figure 3 showsthe re- strated by Nolin et al., [1993a], using AVIRIS data, sults of snow detection using the index-based binary and also by Rosenthaland Dozier, [1993] who used classification and the SMA method. The binary clas- Landsat TM data. In both cases, the SMA technique sificationhas difficulty distinguishingclouds from snow was found to be as accurate in mapping snow covered and appears to overestimatethe total snow in the im- area as high resolutionaerial photographsfor discern- age. With SMA, end-memberswere derivedfrom the ing snow cover. Nolin, [1993] also demonstratedthat image using MNF for noise reduction and pixel purity the SMA method for snow cover mapping is relatively identification to map the purest end-member pixels in insensitive to illumination effects because it relies on the image. Rosenthaland Dozier, [1996]showed that the shape of the spectral signature of snow and other multiple snow end-members were needed when illumi- image components,rather than the magnitude of the nation conditionsvaried widely. Painter et al., [1998] snow signal. While this method has been found to be demonstrated that when snow grain size varies over an more accurate when surface reflectancesare used, under image, the use of multiple snow end-memberssignifi- most conditions, atmospheric correction is not required, cantly reduces RMS error and provides a more accu- and the unmixing can be performedusing at-sensorra- rate representation of snow cover. Becauseof the wide diances. Without atmospheric correction, each image disparity of snow illumination conditionsin the Glacier end-member is assumedto incorporate all atmospheric National Park TM scene, two snow end-members were effects into its spectral signature. Errors may result needed: one which represented snow with a small solar when the overlying atmosphere has significant spatial illumination angle and one for snow with a large solar inhomogeneitiessuch as large changesin optical depth illumination angle. Other end-membersincluded veg- from atmospheric water vapor or dust plumes. Such etation, cloud, and deep shade. In this analysis, TM 25,856 NOLIN- MAPPING THE MARTIAN POLAR ICE CAPS

Glacier NP, M,rch 6, 19,,,

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Figure 2. March 6, 1994, LandsatThematic Mapper bands2 (left) and 7 (right) of Glacier National Park, Montana. The image coversan area of 75 kmby 75 km. North is to the top of the image. TM band 2 appearsto show extensivesnow coverover the mountainousregion but in TM band 7, one can seemore clearly that thin cloudsextend acrossmuch of the image.

bands 2-5 and 7 were used. TM band 1 was not used The effects of instrumental noise and calibration er- because it tends to saturate over snow and TM band 6 rors are known to influence SMA results in severalways. was not used becauseit is in the thermal region. [Sabolet al., 1992]showed that the subpixelfraction es- The SMA results show very good representationof timates are less impacted by noise as the number of the distribution of snow cover. Some cloudy pixels are bands increases. As with noise, calibration errors have mapped as snow but not nearly as many as the binary a decreased effect when more bands are used. This is classificationmethod. With both methods, slopes in becauseeach noisy measurementhas lesssignificance as deep shadow are not mapped as snow because they the total number of measurementsincreases (assuming do not produce a sufficientsignal. Also, south-facing the band-to-bandspectral information is uncorrelated). slopesare generally mapped as having less snow than Thus, from the standpointof noise/calibration-induced the north-facing slopes. This may be the result of in- error, results derived from an imaging spectrometerwill completespectral characterization(the two snowend- be less impacted by noise than those derived from a membersmay not representthis type of snow). How- multispectral instrument such as Landsat TM. As de- ever, it is also likely that there is lesssnow on the south- scribedearlier, when using either imaging spectrometer facing slopesbecause of their higher insolation. data or multispectral data, noise reduction using the The relative accuracy of binary versussubpixel clas- MNF transform can effectively remove noise and is a sification methods dependson the spatial resolution of recommendedstep in the unmixing process. the image. For coarse-resolutionimages in which the Results for any land cover mapping method are dif- snow cover is heterogeneous,the SMA method is su- ficult to validate and no direct measurements of snow perior to the binary method. The binary classification coveror snowdepth were availablefor this region at the uses a single threshold for all sensorresolutions and time of the overpass. However, in similar studies us- snow cover conditions. There is no physically based ing spectral mixture analysisover the California Sierra means of determiningsuch a threshold. When image Nevada, the SMA results using imaging spectrometer data with high spatialresolution is usedand/or the sur- and Landsat TM data compared very closely to esti- face becomesmore homogeneous,the two methods will mates from high-resolutionaerial photographswith a have similar levels of accuracy in snow-covered-areare- nearly 1:1 relationship [Nolin, 1994; Rosenthal,1996; trievals. Rosenthaland Dozier, 1996]. NOLIN: MAPPING THE MARTIAN POLAR ICE CAPS 25,857

Covcrcd A'ca Ma,. pina f--ott Lat(tsat M

Biary Classifica Spcc...tral Mixt. ur.c Analysis

Figure 3. Multispectral snowmapping resultsfrom two differentmethods. The left image is the result of the binary NDSI index-basedmethod. Cloudy regionshave been mistakenly mapped as snow, and patchy snow areashave been mapped as completelysnow-covered. The right image is the result of the SMA mapping subpixelmethod that calculatesthe fraction of snow, cloud, and vegetation in each pixel. This image is the snowfraction image, and dark pixels represent low or no snow cover, brighter pixels representincreasing snow cover.

3.4. Estimating Surface Layer Grain Size size represents the mean grain size of the distribution [Nolin et al., 1993b]. Other particle size distributions 3.4.1. Grain size mapping. Beforeproceeding could yield the same optically equivalent grain size, but with the descriptionof the grain size mapping method, giventhe nature of snowgrain metamorphism[Colbeck, it is appropriate to discusswhat is meant by the term 1983; Colbeck,1989], it is unlikely that this would oc- "grain size" for remote sensingof snow. An optically cur. For computational efficiencyin performing the Mie equivalent sphere is used to approximate the ice crys- calculations,we use a singleoptically equivalent/mean tals in the snowpack. This equivalent sphere is that grain size to represent the range of snow grain sizesfor which has the same volume-to-surface ratio as the ir- a lognormal size distribution. regularly shapedgrains in the snowpack[Dobbins and As described earlier, grain size affects albedo in the Jizmagian, 1966]. Randomly orientedspheroids have near-infrared region, and for relatively pure snow, it is been shownto be opticallyequivalent to spheres[Mug- the dominant property determining the spectrally inte- nai and Wiscombe,1980]. Radiative transfer models grated albedo. Furthermore, changesin grain size are allow us to relate the optical propertiesof snow (as directly attributable to temperature and temperature measuredby the spacebornesensor) to the snowpack gradientswithin the snowpack[Colbeck, 1983]. physical properties. In the work presentedhere, the Nolin and Dozier [1993]describe a methodfor using grain size distributionis modeledusing the optically a radiative transfer model to convert snow surface re- equivalentsphere for a monodispersionof particles Al- flectancein a near-infrared channelto snow grain size. though a "natural" distribution of snow grain size is Given its slope and aspect, the illumination geome- thoughtto resemblea lognormaldistribution [Warren, try of a snow-coveredpixel can be determined. For a 1982],the opticallyequivalent grain size is oftenused for particular illumination geometry the surfacereflectance computational simplicity. From stereologicanalysis of in a narrowband near-infrared channel uniquely corre- snow microstructuralparameters Dozier et al., 1987], spondsto surfacelayer grain size. The spectral width of it has been shown that the optically equivalentgrain the channel is inverselyproportional to the precisionof 25,858 NOLIN' MAPPING THE MARTIAN POLAR ICE CAPS

Modeled Reflectance vs. Snow Grain Size 1.0

0.8

0.6

75 degrees

0.4 60 degrees 45 degrees 0 - 30 degrees

0.2

0.0 ] , [ , I , , t , I , • , , o 500 lOOO 15oo Groin R•dius (microns) Figure 4. Snowreflectance modeled as a functionof opticallyequivalent grain sizefor several illumination angles.There is little differencebetween the curvesfor illuminationangles between 0ø and 15ø, indicatingthat, for relativelyfiat surfaces,small changes in slopewill not significantly affect the grain size retrievals.

particle size determination. This narrowbandinversion fiectance and density have a negligible effect on snow- method is most sensitive for smaller particle sizes, such pack reflectance[Dozier, 1989b;Bobten and Beschta, as those encountered in fresh snow and snow in cold 1979],leaving grain size as the snowproperty that ex- regionssuch as the Greenlandand Antarctic ice sheets. erts the greatestcontrol over near-infraredreflectance. In this method a single, narrow spectral band (10 The wavelengthof 1.04/•m was chosenbecause it is nm) is usedto relate scaledsurface refiectm•ce to grain in a spectralregion where reflectance is particularlysen- size. First, the relationship between grain size and near- sitive to grain radius (refer to Figure 1). A secondad- infrared reflectance is modeled for each illumination an- vantage in using a band centeredat that wavelength gle using a radiative transfer model. The discreteor- is that, for Earth, there is little atmosphericscattering dinate model [Stamneset al., 1988] was used to cal- or absorption, so errors due to atmosphericcorrection culate spectral directional reflectance at A = 1.04 ttm are minimized. Furthermore, the presence of typical as a function of the optically equivalent ice grain ra- quantities of Earth dust has very little effect on snow dius. Optical parameters needed for the discrete or- reflectancein that wavelengthregion [Warren and Wis- dinate model include snowpack optical thickness, sin- combe,1980]. gle scattering albedo, and asymmetry parameter (or As described earlier, the relationship between mod- a description of the scattering phase function); these eled grain size and snowpackreflectance depends on are calculated from the snowpack physical properties: both the solar and viewing geometries. For a nadir- depth, bulk density, and equivalent grain size. Diffuse viewinginstrument over a flat surface,only a knowledge irradiance, substrate reflectance, and solar and view- of the solar geometry is required to calculatethe direc- ing geometriesare also required as model inputs. For tional reflectance. However, model results show that optically semi-infinite snowpacks,both the substratere- if the illuminationangle is greaterthan 30ø(measured NOLIN: MAPPING THE MARTIAN POLAR ICE CAPS 25,859 from the normal to the slope),it necessaryto know the eled grain size and albedo were found to closely cor- angleof solar incidencebefore proceeding with the cal- respond to measured values. These data show that culation(Figure 4). in the near-infrared wavelengths, albedo values drop A model-generatedcurve of reflectanceversus grain nearly 20% during a 10-day period during which grain size was fit with an exponential model of the form sizes increaseddramatically. This work was then spa- r = aeb, where r is the calculatedgrain radius and a and tially extended using optical remote sensing data to b are coefficientsused to generate a least squaresfit to map albedo changesover the entire ice sheet. AVHRR the model-generateddata. This establisheda functional satellite data were used to map monthly changesin relationshipbetween grain size and surfacereflectance albedo over the Greenland ice sheet during the spring that could then be inverted to transform snowpack re- and summer months. Monthly albedo images show flectanceat 1.04 pm to an estimateof snowgrain size. albedo reductions of as much as 80% in the southern To convert an image from at-sensorradiance values coastal regions. Even in areas that experience little to snowgrain size involvesthe followingsteps: or no melt, albedo decreasesof 10-20% were common. 1. Perform atmosphericcorrection to create surfacere- This researchdemonstrates the utility of using albedo flectance image. and grain size information to infer snowpackdynamics. 2. Use subpixel snow-coveredarea image to mask out 3.5. Snow Albedo Determination partially snow coveredpixels. 3. Generate reflectanceversus grain size curvesfor illu- To obtain snow albedo from remote sensingdata re- mination conditions. quires that we implement a conversionscheme that in- 4. Apply inversionscheme to surfacereflectance image corporates a knowledge of the bidirectional reflectance to a grain size image. distributionfunction (BRDF) of snow. Sucha conversion scheme has been developed for use with airborne Validation of the method was done by comparing (AVIRIS) and satellite-based(AVHRR)sensors [Nolin, the grain size estimatesderived from narrowbandre- 1995, Nolin and Stroeve,1997, Stroevee! al., 1997]and flectancedata to the grain sizesin the snowpack. Snow is currently under development for the MODIS sensor. sampleswere collectedand later analyzed using a stere- In this research,modeling snow spectral reflectance is ologictechnique that expressesthe geometricallyequiv- characterizedas a multiple scatteringproblem [Bohren alent sphereas the volume-to-surfaceratio as well as the and Barkstrom, 1974, Wiscombeand Warren, 1980]. mode and standard deviation of the particle size distri- This physically based model of snow reflectance uses bution [Perla e! al., 1986;Dozier et al., 1987, Shi et al., the equationsof Mie theoryto calculatethe scattering 1993]. Size estimatesderived from the imagesclosely propertiesfor an optically equivalentsphere. Singlepar- agree with sample grain sizesover wide range of grain ticle scattering dependson the complexrefractive index sizes[Nohn, 1993]. m: n + ik (wheren is the real part and k is the imag- A known limitation of the method is that results are inary part) and the ratio of the particle cross-sectional valid only for those pixels that are known to be com- area to the wavelength. This latter value is expressed pletely snow covered. Subpixel mixtures such as snow as a dimensionlesssize parameterx: 2•rr/,X, where r + rock + vegetation will artificially increasethe esti- is the sphere radius and ,X is the wavelength. The Dis- mated grain size. Thus it is highly advantageousto use ort model, with its ability to calculate the directional the subpixel snow mapping algorithm as a preprocess- reflectance, is appropriate for modeling the BRDF in ing step with the grain size algorithm. a multiple scattering particulate medium such as snow. An additional limitation is that this method may not Recent planetary literature has emphasizeduse of the yield a uniquegrain size when large amountsof mineral [Hapke,1993] model for calculatingthe singleand mul- particulatesare present. If ice and mineral particlesare tiple particle scattering properties. As yet, no system- present in a particulate mixture as separate grains or, atic comparisonof Hapke and the approach described if the ice is present as a coating on the mineral particle, here have been performed.The basicdifferences appear Mie theory can be used to calculate their combined ef- to be Hapke's inclusionof the effectsof interparticle fective optical properties. However, even if the mineral shadowingand the oppositioneffect [Hapke, 1993]. The types and the ice-mineral geometry is known, different approachdescribed here calculatesthe single particle combinationsof ice and mineral particles may yield the scatteringproperties using Mie.theory and the multiple same effective optical properties. scatteringproperties using a discreteordinates method. 3.4.2. Inferring snowpack energy balance dy- It has been shownto be sufficientfor terrestrialappli- namics. Recent work by Nolin and $troeve [1997] cations;however, it may be the casethat Hapke theory has demonstrated the relationship between snowpack has advantages and these should be examined in the energy balance, grain growth, and albedo. A one- future. dimensionalmodel of snowpackenergy and mass bal- The spectraldirectional-hemispherical reflectance (also ance[Jordan, 1991] was usedto calculategrain growth referredto as the albedo)is the reflectedradiance inte- and that output was then used to drive a radiative grated over the upward hemisphere and ratioed to the transfer model that calculated spectral albedo at each directirradiance [Nicodemus et al., 1977]: time step. Changes in snowpackenergy balance were seento strongly affect albedo through grain growth, es- pecially during periods of snowpack warming. Mod- a,( lU o) - fø• •'fø• lu/•0E0L (lu ' c) ) d lu d c) : /•0E0FI (3) 25,860 NOLIN: MAPPING THE MARTIAN POLAR ICE CAPS

L(/•, qS)isthe upwellingradiance at anglee (/• = In the near-infrared, grain size does affect the results cos0), azimuthqS. E0 is theincident direct irradiance at of the conversion(larger grainsare more forwardscat- the top of the snowpackat an incidenceangle 0, and F 1 tering). Albedo retrievalscan be as muchas 12% in is the upward diffuseflux (integratedover all angles). error if an incorrectgrain size is used (e.g., a radius Becausethe reflected radiance of snow dependson both of 50/•m rather than 1000/•m) [Stroeveet al., 1997]. solar and viewing geometries,we also need to consider However, if the spectral albedo data are converted into the angular distribution of the reflectedflux. The shape a broadband estimate, most of these errors are elimi- of the angular reflectance distribution is describedby nated becauseof the much higher weightingof the data the anisotropic reflectance factor f, which varies with from visiblewavelengths (which are unaffectedby grain 0, 0t, qS,and &t (primed quantitiesare sensorviewing size) [Stroeveet al., 1997]. angles): The effectsof nonsphericityand internal scattering are important to considerwhen discussingsources of error in BRDF calculations.Hapke [1993]presents an a,(O) (4) overviewof the effectsof irregularly shapedparticles on R,, the BBDF, is: scattering. Geometric optics modelsusing ray tracing are computationally intensive but can, in most cases provide accurate calculations. Empirical studies have •,(O,O', •, &')-- dI(O',&') [sr_•] (5) also shown that non-sphericity decreasesthe forward where I is the solar irradiance incident at zenith 0, az- scatteringpeak and eliminates the backscatteringpeak imuth &, F is reflectedradiance, and p0 = cos(O).The becauseof redirection of energy by internal scattering. Internal scatterers such as dust and bubbles can cause above equations all represent spectral quantifies, and wavelength dependenceshould be consideredimplicit. significantdepartures from Mie theory, especiallywhen In this paper, terminology is used that is the same as the inclusionsare dark particles. For suchcases it would that suggestedby Warren [1982]. Albedorefers to the be important to recalculatethe particlescattering phase directional-hemisphericalreflectance. The bidirectional function. McGuire [1993]has offereda methodfor em- reflectanceis the fraction of collimated light that is scat- pirically fitting phase functions to particles in which tered into a particular direction; this is the reflectance internal scattering is important. quantity most often measured by satellite-based sensors. 4. Martian Applications of Terrestrial The first step is to model both the bidirectional re- Methods fiectance and albedo for a wide range of illumination and snow conditions. Snow optical properties are first The methodspresented here have been successfully calculatedusing Mie theory, and thesespectral data are usedon Earth with a variety of instruments.Multispec- then convolved with the spectral responsefunction for tral sensors have been the dominant means of terrestrial each channel. These are then used as input to the Disoft mapping. In recentyears, airborne visible/near-infrared model to generate a look-up table that relates the bidi- imaging spectrometershave demonstrated tremendous rectional reflectance of the snow surface to its albedo. utility in mapping subpixel mixtures, grain size, and This is done for a wide range of illumination conditions albedo mapping. On Mars, where the dusty atmo- and viewing geometries. Other model inputs include sphere and intimate mixtures of dust and ices make sensor viewing zenith angle, relative azimuth between mappingthese quantities problematic, an imagingspec- sun and sensor, and the relative proportions of diffuse trometer would be highly advantageous. With such and direct surface irradiance. The model assumes an an instrument, absorptionfeatures in reflectancespec- isotropic distribution of diffuse irradiance. Reflectance- tra could be analyzed to determine particulate and ice to-albedo conversionvalues in the look-up table are cre- types. Mineral-ice concentrations could be calculated ated for a wide range of snow grain sizes. The second usingthe methodof Clark and Luccy[1984]. From these step is to calculate the illumination and viewing ge- mixture reflectance spectra, classesof mineral-ice •nix- ometries for each pixel using a digital elevation model, tures could be determined and used as end-members in solar zenith, and sensor viewing angles. Diffuse and spectral mixture analysis to map distributions of these direct surface irradiance proportions are calculated us- mixtures in the polar regions. Knowledgeof mineral ing climatology-basedestimates or measurementsof at- concentrationwould also help constraingrain size cal- toosphericconditions. As before, the satellite image is culations. Grain size estimates could also be calculated atmospherically corrected to apparent surface bidirec- from imaging spectrometerdata using the band depth tional reflectance, and then nonsnowpixels are masked [Clark and McCord, 1982]or band area [Nolin, 1993] out. The final step is to use the look-up table relat- methods. ing bidirectional reflectance to albedo used to convert To date, there has been no multispectral optical map- surface reflectance to surface albedo for each spectral ping orbiting sensorat Mars. Multispectral optical re- band. mote sensingof the polar caps would have been pos- In the visible part of the spectrum, snowBRDF is un- sible with the the Omega mapping spectrometer,the affected by differencesin grain size. Only the amount SPICAM multichannel optical spectrometer, and the of dust or soot is seen to influence the results, reducing SVET spectrophotometer on the ill-fated Mars 96 mis- the forwardscattering peak [Nolin and Steffen,1995]. sion. However, with the demise of that satellite, the NOLIN: MAPPING THE MARTIAN POLAR'ICE CAPS 25,861

Mars Orbiter Camera(MOC) flownon the Mars Global SMA also assumesthat the snow is optically thick Surveyor mission is being used to produce wide-angle and that there are no photon interactions with the un- views of the planer's surface. The MOC is not a multi- derlying substrate. The optical thickness of a snow- spectral instrument so neither the binary nor the sub- pack dependson the wavelengthof observationas well pixel ice mapping methods can be used at this time. as the snow properties: depth, grain size, density, and Ice cap features will only be mappable with this instru- concentrationof light absorbingparticulates [Warren, ment using radiance thresholdsand photogrammetric 1982, Dozier, 1989]. Unfortunately,it is impossiblefor techniques. The next multispectral instrument to fly $MA to distinguishbetween dirty snow and thin snow, by Mars will be the Miniature Integrating Camera and sinceboth act as nonlinearmixtures involving dust. For Imaging Spectrometer(MICAS) on the Deep Space 1 Martian frosts the amount of dust is presumablylarge mission, scheduledfor launch in October 1998. enough that the mineral-ice mixture will be optically A recently approved payload for the European Space thick evenfor verythin frostlayers. Clark [1981] showed Agency-sponsoredMars Express Orbiter mission in- that only a small amount of dust needs to be added to cludesa visible and near-infrared mapping spectrometer a frost for it to becomeoptically thick, even over a very (OMEGA) with a spatial resolutionof 350m to 1 km. dark substrate(6% reflectance). This instrument is expected to have a spectral range from 0.35 ttm to 5.2 ttm. Its main tasks include map- 4.2. Martian Grain Size Mapping ping the extent of the polar caps, characterizingthe temporal variability of CO2 and H20 ices, and iden- The single channel inversion method describedear- tifying dust type in the icy deposits. Also on board lier should be useful for grain size mapping of CO2 the Mars Express satellite will be the planetary Fourier frost and water ice. Rather than using a passivesensor spectrometer(PFS) that will study the compositionof with the Sun as the sourceof illumination, this method the Martian atmosphere. These atmospheric data will can be usedwith a near-infraredwavelength laser. The allow improved atmosphericcorrection for better grain Mars Orbiter LaserAltimeter (MOLA) instrumentcan size and surface albedo determinations. Last, the Sub- be implementedin virtually the same way as a narrow- surfaceSounding Radar/Altimeter (SSRA), thoughnot band spectrometer. This active mapping instrument an optical instrument, will be able to map ground ice in is a Nd:YAG laser with a wavelengthat 1.064 ttm, at Martian crust. SSRA will measure the dielectric prop- which not only water but CO2 ice reflectanceis sensitive erties of surface and subsurface materials and be able to grain size. Its 160 m spot size should allow detection to detect the presence of ice in soil pores. With more of relatively uniform frost-coveredpixels. MOLA will advancedinstrumentation, many of the persistent ques- be detecting not only the transmit and receive power tions regardingMartian ice can be addressed.These in- but alsothe slopeand aspectof the pixel. Pulse energy strumentswill provide the necessarydata allowing the calibrationfor MOLA is about 5% [Smithet al., 1998], more advancedterrestrial snow/icemapping methods which would be sufficient to distinguishbetween fine, to be applied. medium and coarse sizes. The nominal resolution of the global seamlessdigital elevation model DEM from 4.1. Mapping the Residual Ice Caps and MOLA is 0.2o x 0.2o (approximately9kin), which is Surface Frosts coarseresolution for the purposesof grain size mapping. However,in the polar regionsMOLA's point-to- Assumingthat in the early part of the next millen- point spacing will be about 300m, and with its 160m nium a mapping missionis carrying an imaging spec- footprint, a 1 km DEM is conceivablefor this region. trometer, it will be feasible to perform subpixel map- The slopeof eachlaser footprint is determinedthrough ping of ice and CO2 frostextent. There may be regions analysis of the laser return pulse width. Thus all the wherefrost coverageis both dust-freeand spatially ho- necessarycomponents are availablefor retrieving grain mogeneousbut these are not anticipated. Thus use of size from this laser altimeter. MOLA will observe the a pure ice frost spectrum as an end-member will not planet from a highly inclinedorbit, so that the polar re- work. The SMA method implies a linear mixture of gionswill be the mostintensively mapped of any region componentsin each pixel. Combinationsof ice and dust on Mars overthe 2-yearmapping mission. Furthermore, are known to behave as nonlinear mixtures. These inti- unlike a spectroradiometer,a laserdoes not requiresun- mate mixtures can be of severalforms: mixtures of pure light to map the surface so grain size determinations particles("salt-and-pepper"), or dust embeddedin ice, can be made even for those times of the year when the coating of ice over dust, or coating of dust over ice. It poles are in darkness. With its high spatial resolution may, however, be possible to partially circumvent this mapping over two annual cycles,MOLA couldprovide nonlinear mixing problem by treating the ice-mineral much needed information about seasonalCO2 frost de- mixtures as end-members. One approach would be to position, grain growth and sublimation rates. model the spectral properties of an intimate mixture of Though originally designedfor mapping water ice ice and minerals as has been done by Clark and œucey grain sizes, this single channel inversionmethod could [1984].A secondmeans would be to use Mie theory to be used for CO2 frosts as well, since CO2 reflectanceis calculate the effective optical properties; this approach sensitiveto grain size at the MOLA wavelength.The would work for both the multiparticle mixtures or ice- absorption coefficientsfor water ice and for CO2 ice dust coatings. are of the sameorder of magnitude.Although CO2 re- 25,862 NOLIN: MAPPING THE MARTIAN POLAR ICE CAPS

flectance is more highly sensitive to grain size over the tion in the near-infrared region. If there are times of the 2.0 - 4.0/•m region [Calvin, 1990],there is still a grain year and/or portionsof the frost-coveredsurface where size sensitivity at 1.064/•m. Also, as Figure 4 indicates, the dustcontent is sufficientlylow (_<1%by weight),the for water ice (and presumablyfor CO2 as well), the near-infrared single channel inversion method can be method is most sensitivefor the small frost grain sizes used to estimate grain size. Even with a grossestimate that are likely to exist at cold Martian temperatures. of fine, medium, or coarsegrain size, the near-infrared Calvin [1990] derived optical constantsfor CO2 ice albedo could be computed using radiative transfer the- that showedimprovements over those of Warren[1986]. ory. If dust content can be estimated, the visible albedo In her examination of Mariner 9 data over the ice caps, couldbe computedfor differenttypes of dust/ice grain Calvin found that the reflectancespectra most closely intimatemixture arrangements(e.g., "salt-and-pepper" resemblethose of large-grainedCO2 frosts (millimeter and coatings).Ice cap albedois a criticalparameter for to centimeter scale) with some possiblecontamination atmospheric circulation and global climate models, and by water ice and dust. However, the current CO2 op- our ability to estimate it depends on the accuracy with tical constantsare not known well enough to be able which we can perform atmospheric correction, estimate to distinguish such mixtures. Without more accurate grain size, and know the optical propertiesof the dust- determinations of the CO2 optical constantsand addi- ice mixture. tional data on dust concentrations,use of this inversion method is limited to relatively cleanfrosts containing a 5. Conclusions single ice type. As with other surfacemapping efforts, Martian dust This overview has pointed to the need for multispec- is anticipated to be a sourceof error in grain size map- tral optical imagery for frost and ice mapping on Mars. ping. Although the concentrationof Martian dust in The extent and variability of the Martian ice caps and the surface frost is unknown, it may be quite high their seasonalCO2 frost coveringcan be mapped with [Clark and McCord,1982]. The compositionof the ice- only a few spectral bands distributed through the visi- particulate mixtures will influence the MOLA refiectiv- ble and near-infrared wavelengths. For instance,just a ities. It may only be possibleto derive grain size es- few well-situatedbands (e.g., those used on the Land- timates for caseswhen measured1.06/•m refiectivities sat TM) providesufficient spectral resolution for sub- are sufficientlyhigh (>_60%)that the effectsof dust can pixel mapping. Imaging spectrometerdata would pro- be largely neglectedor accountedfor. Atmosphericdust vide the ability to quantify mineral-ice mixtures and in the Martian atmosphereexperiences large variations to better characterizethe atmosphere. These are both as a functionof both seasonand latitude [Lindner,1990] neededfor albedodeterminations, while only the former and there can be extendedperiods during which there is required for subpixelfrost/ice mapping. With the are no dust storms; for example, there have been no planned 2003 launch of the Mars Expressmission car- dust storms affecting MOLA results from the first 78 rying the OMEGA spectrometer,tests of thesemethods passes(J. Garvin, personalcommunication; 1998). are only a few years away. We will be able to learn more about frost dynamicsas 4.3. Mapping Clear-Sky Surface Albedo well as polar ice cap stratigraphythrough adaptation of terrestrialmultitemporal, multispectral mapping meth- In the same way that the discreteordinates model, ods. Seasonalchanges in frost-coveredarea will allow Disort, has been used to convert surface bidirectional detectionof the transitionfrom condensingto sublimat- reflectance to surface albedo for the Greenland ice sheet ing conditionsover the ice cap, thus providingimpor- and elsewhere,a similar modelingeffort couldbe put in tant informationabout the annual heat budgetof the place to map changesin CO2 frost albedo. For both polar regions. water ice and CO2 frost, Disort is used to model the re- Perhapsthe mostsignificant terrestrial mapping ap- lationship between satellite-measured bidirectional re- plication is the potential use of the MOLA instrument flectancesand albedo. For this mapping effort a num- to map grain size on the Martian polar caps. For dust ber of additionalmeasurements are required:(1) atmo- concentrationsless than about 1% by weight,grain size sphericcharacterization to determinethe relative pro- remainsthe dominant surfaceproperty that determines portions of direct and diffuse illumination at the ice sur- ice albedo. With its exponentialresponse to tempera- face, (2)illumination and viewinggeometries, (3) grain ture, grain size is also the physical property with the size, and (4) dust content. highestsensitivity to changesin the thermodynamic The scattering and absorbingproperties of the atmo- state of the ice. Changesin the energy balance of sphereneed to be estimated for clear-skyconditions to surfacefrost shouldbe reflectedin changinggrain size determine the relative proportions of direct beam and even before the changein frost-coveredarea could be diffuseirradiance at the surface. The greater the pro- detected. portion of diffuseirradiance, the more isotropicis the Surfacetemperature, ice type, ice-mineralmixtures, surface reflectance. and atmosphericcomposition are distinctlydifferent be- Illumination and viewing geometriescan be deter- tween Mars and Earth, so a direct application of ter- mined usinga DEM from the MOLA griddedelevation restrial snow and ice mapping methodsis not possi- data. MOLA data may alsoprovide much needed grain ble. However,expertise in mappingand interpreting size estimates, allowing more accurate albedo estima- terrestrial snow and ice may contribute to the collec- NOLIN: MAPPING THE MARTIAN POLAR ICE CAPS 25,863

tion of planetary mapping techniques. Furthermore, Dozier, J., Spectral signature of alpine snow cover from the adaptation of appropriatemethods will provide a basis Landsat Thematic Mapper, Remote Sens. Environ., 28, for comparisonof terrestrial and planetary cryospheric 9-22, 1989a. Dozier, J., Remote sensingof snow in the visible and near- components. infrared wavelengths,in Theory and Applications o• Op- tical Remote Sensing, edited by G. Asrar, pp. 527-547, Acknowledgments. I would like to thank Ted Scam- John Wiley and Sons, New York, 1989b. bos, Wendy Calvin and Bill Farrand for severaluseful dis- Dozier, J., and D. Marks, Snow mapping and classification cussionson planetary remote sensing.I am also grateful to from Landsat Thematic Mapper data, Ann. Glaciol., 9, Jeff Dozier, Roger Clark and Steve Drake for their careful 1-7, 1987. reviews and helpful comments.This researchwas supported Dozier, J., R. E. Davis, and R. 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