Apparent thermal inertia and the surface heterogeneity of Mars · Apparent thermal inertia and the...

Icarus 191 (2007) 68–94www.elsevier.com/locate/icarus

Apparent thermal inertia and the surface heterogeneity of Mars

Nathaniel E. Putzig a,b,∗,1, Michael T. Mellon a

a Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80309, USAb Department of Geological Sciences, University of Colorado, Boulder, CO 80309, USA

Received 15 August 2006; revised 14 April 2007

Available online 27 June 2007

Abstract

Thermal inertia derivation techniques generally assume that surface properties are uniform at horizontal scales below the footprint of theobserving instrument and to depths of several decimeters. Consequently, surfaces with horizontal or vertical heterogeneity may yield apparentthermal inertia which varies with time of day and season. To investigate these temporal variations, we processed three Mars years of MarsGlobal Surveyor Thermal Emission Spectrometer observations and produced global nightside and dayside seasonal maps of apparent thermalinertia. These maps show broad regions with diurnal and seasonal differences up to 200 J m−2 K−1s−1/2 at mid-latitudes (60◦ S to 60◦ N) and600 J m−2 K−1s−1/2 or greater in the polar regions. We compared the seasonal mapping results with modeled apparent thermal inertia and creatednew maps of surface heterogeneity at 5◦ resolution, delineating regions that have thermal characteristics consistent with horizontal mixtures orlayers of two materials. The thermal behavior of most regions on Mars appears to be dominated by layering, with upper layers of higher thermalinertia (e.g., duricrusts or desert pavements over fines) prevailing in mid-latitudes and upper layers of lower thermal inertia (e.g., dust-coveredrock, soils with an ice table at shallow depths) prevailing in polar regions. Less common are regions dominated by horizontal mixtures, suchas those containing differing proportions of rocks, sand, dust, and duricrust or surfaces with divergent local slopes. Other regions show thermalbehavior that is more complex and not well-represented by two-component surface models. These results have important implications for Marssurface geology, climate modeling, landing-site selection, and other endeavors that employ thermal inertia as a tool for characterizing surfaceproperties.© 2007 Elsevier Inc. All rights reserved.

Keywords: Mars; Mars, surface; Infrared observations

1. Introduction

Understanding the physical properties of the near-surfacelayer is critical to many elements of the Mars exploration effort.Apart from a few sites where spacecraft have landed, nearly allour information regarding the nature of the surface is the prod-uct of remote-sensing instruments. While visible images havebeen an important piece of the puzzle by providing the geolog-ical context of morphologic features, certain aspects of the sur-

* Corresponding author. Address for correspondence: Southwest ResearchInstitute, Department of Space Studies, 1050 Walnut Street, Suite 300, Boul-der, CO 80302, USA. Fax: +1 303 546 9687.

E-mail address: [email protected] (N.E. Putzig).1 Now at Department of Earth and Planetary Sciences, Washington Univer-

sity, Saint Louis, MO 63130, USA and Southwest Research Institute, Boulder,CO 80302, USA.

0019-1035/$ – see front matter © 2007 Elsevier Inc. All rights reserved.doi:10.1016/j.icarus.2007.05.013

face materials, such as composition, grain size, and the presenceof volatiles in the subsurface, are not readily understood fromvisible image data alone. Spectral imaging and multi-spectralmapping provide some insight into these characteristics, andtemperature derived from spectral radiance measurements is thebasis for investigating many of the physical attributes of mar-tian surface materials. Through numerical modeling, one mayrelate the surface temperature, which is greatly influenced bytime-varying factors such as diurnal and seasonal variations ofthe local insolation and atmospheric constituents, to the physi-cal properties of near-surface materials.

Such numerical models generally treat the thermal behaviorof the martian surface as an upper boundary condition on theheat equation, where upward radiative loss is balanced by heatflux due to insolation, downwelling atmospheric radiation, andseasonal CO2 condensation, together with subsurface heat con-duction:

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Mars thermal inertia and surface heterogeneity 69

(1)

εσT 4S = SM(1 − A) cos i + FIR + L

∂m

∂t+ I

√π

P

∂T

∂Z′

∣∣∣∣Z′=0

.

Here, ε is the emissivity of the surface or CO2 frost if present,σ is the Stefan–Boltzmann constant, TS is surface temperature,SM is the insolation at Mars, A is albedo, i is the solar incidenceangle, FIR is downwelling atmospheric radiation, L is the latentheat of CO2 sublimation with m the mass of CO2 frost and t

time, I is thermal inertia, P is the diurnal or seasonal period,T is subsurface temperature, and Z′ is depth normalized to thethermal skin depth δ. The thermal skin depth is the e-foldingdepth of the subsurface diurnal or seasonal thermal wave givenby

(2)δ ≡ I

ρc

√P

π,

where the density ρ and heat capacity c are bulk material prop-erties of the near-surface layer. Thermal inertia is defined as acombination of bulk thermal conductivity k, density, and heatcapacity such that

(3)I ≡ √kρc.

Hereinafter, we use the proposed SI derived unit of thermal in-ertia, tiu, defined by Putzig (2006, pp. 10–11):

(4)tiu ≡ J m−2 K−1 s−1/2.

To convert to the historical units of 10−3 cal cm−2 K−1 s−1/2,divide by a factor of 41.84 (Kieffer et al., 1977).

One may infer from the subsurface conduction term [the lastterm in Eq. (1)] that thermal inertia is the key material prop-erty controlling the diurnal and seasonal surface temperaturevariations. For granular materials under Mars surface temper-atures and pressures, conductivity tends to dominate the ther-mal inertia (Wechsler et al., 1972; Jakosky, 1986) and is con-trolled primarily by physical characteristics, such as particlesize and porosity, within a thermal skin depth of the subsurface.In general, surfaces of unconsolidated, fine-grained materialswill have low values of thermal inertia, cemented surfaces andsurfaces composed of sand-sized grains will have intermediatevalues, and rocky surfaces and bedrock outcrops will have highvalues.

If surface materials are horizontal and either homogeneousor mixed only on horizontal and vertical scales much smallerthan a diurnal thermal skin depth, they will exhibit uniformlychanging temperature and a constant value of thermal inertia(Jakosky, 1986). If they contain divergent slopes or are mixedat larger scales, different surface components may have dif-ferent temperatures at any given time. The surface tempera-ture as observed from an orbiting spacecraft will be a com-posite mixture of the component temperatures on the scaleof the observing-instrument resolution (∼3 km for the MarsGlobal Surveyor Thermal Emission Spectrometer, MGS-TES;Christensen et al., 2001) and on depth scales on the order of aseasonal thermal skin depth (a few decimeters to a few meters,depending on the properties of the surface materials). Where

horizontal mixtures or near-surface layers of differing mate-rials are present in the instrument’s field of view, the appar-ent thermal inertia derived from surface temperature observa-tions will vary with time of day and season (or season only,if the surface layer is homogeneous and thicker than a diurnalskin depth but thinner than a seasonal skin depth), due to thenonlinear relationship between temperature and thermal inertia[see Eq. (1)] and any differential heat storage in the subsur-face. Similar effects will occur for surfaces where portions ofthe field of view have non-zero slopes (Putzig and Mellon,2007).

Since the earliest radiometric observations of Mars (Sintonand Strong, 1960), diurnal temperature has exhibited anom-alous behavior which appears to be incompatible with homo-geneous models of surface materials. Some consideration wasgiven to surface heterogeneity as a possible cause, calling onanalogous studies of lunar temperature observations (Jaegerand Harper, 1950) which invoked a layered regolith. Differ-ences between surface albedo as determined from visible-bandobservations and as derived from temperature data in tandemwith thermal inertia (Kieffer et al., 1977; Palluconi and Kief-fer, 1981; Fergason et al., 2006a, 2006b) are also suggestiveof surface heterogeneity, but have never been fully explained(Hayashi et al., 1995). The presence of an atmosphere at Marscomplicates the thermal behavior. While early thermal mod-els neglected most atmospheric effects (e.g., Morrison et al.,1969; Kieffer et al., 1973, 1977), subsequent efforts to com-pensate for airborne dust and other atmospheric phenomena(Jakosky, 1979; Palluconi and Kieffer, 1981; Ditteon, 1982)reduced but did not eliminate the anomalies. Modeling of het-erogeneous surfaces (Jakosky, 1979; Ditteon, 1982) providedqualitative explanations, but no detailed assessment of the re-lationship to the diurnal, seasonal, and geographic variationsobserved on Mars was pursued. Christensen (1982) developeda technique to estimate rock abundance at the surface by com-paring different spectral bands in individual observations. Hefound that rocks alone were insufficient to explain observedgeographic variations in thermal inertia (Christensen, 1986),and other types of heterogeneity, such as regional variationsin the degree of induration (Jakosky and Christensen, 1986),remained the most likely explanation for the temperature anom-alies.

Studies of ground-ice stability in the polar regions as wellas at lower latitudes (Paige, 1992; Mellon and Jakosky, 1993,1995; Vasavada et al., 2000; Mellon et al., 2004) and the recentdetection of near-surface hydrogen attributed to the presence ofground ice (Boynton et al., 2002; Feldman et al., 2004) haveimplications for near-surface heterogeneity. To the extent thatground ice forms within a seasonal skin depth of the surface,seasonal variation in apparent thermal inertia is expected. Pre-vious global mapping of thermal inertia by Putzig et al. (2005)showed high nighttime values in the north polar region. Whilethey suggested that these results may have been due to either at-mospheric effects or modeling artifacts associated with the po-lar dawn, modeling of the thermal behavior of ground ice in thisregion by Chamberlain and Boynton (2005) demonstrated thatsimilar effects may occur if near-surface ground ice is present.

70 N.E. Putzig, M.T. Mellon / Icarus 191 (2007) 68–94

In an effort to estimate depth to ground ice for Phoenix Lan-der site characterization, Titus et al. (2006) fit TES brightnesstemperature observations to two-layer thermal-model results,yielding estimates of ground-ice depth well within a seasonalskin depth in all three of their study regions.

Current modeling of the effects that horizontal mixtures ofmaterials and partially sloped surfaces have on apparent thermalinertia is presented by Putzig and Mellon (2007). In that effort,we used the numerical thermal model presented here to obtaintemperatures for idealized surfaces of constant properties andthen found effective temperatures for multi-component surfacesby performing a linear mix of the Stefan–Boltzmann function[left-hand side of Eq. (1)]. Modeled values of apparent thermalinertia were determined from the effective temperatures usingthe same derivation algorithm as is used here for obtaining ap-parent thermal inertia from TES observations. To investigate theeffects of layering, Mellon and Putzig (2007) employed a mod-ified numerical model of a layered subsurface (see Mellon etal., 2004). They used this layered thermal model to compute ef-fective temperatures for idealized layered surfaces and derivedapparent thermal inertia to examine its variations. In this work,we use these heterogeneity-modeling techniques to compare theeffects of simple two-component, horizontally mixed and lay-ered surfaces to the apparent thermal inertia derived from TESdata, with the goal of globally mapping the different types ofheterogeneity that may explain the variations observed in thedata.

In the following section, we describe our modifications ofthe thermal model and algorithm developed by Mellon et al.(2000) and the derivation of thermal inertia from TES data, dis-cuss our methods of mapping seasonal apparent thermal iner-tia, summarize the heterogeneity-modeling methods employedherein, and explain our technique for mapping the surface het-erogeneity of Mars. In Section 3, we present our TES mappingresults, local comparisons between TES and model results forlanded-spacecraft sites and other regions of interest, and globalmaps of heterogeneity. We conclude with a summary of our re-sults and a discussion of their implications for the greater Marsexploration effort.

2. Methodology

Prior to the MGS-TES mission, the thermal inertia of themartian surface was generally derived by fitting multiple, co-located spacecraft observations of brightness temperature fromvarious times of day to modeled temperature curves. The tech-nique treated both albedo and thermal inertia as free parame-ters in matching the observed diurnal temperature oscillations(e.g., Kieffer et al., 1973, 1977; Palluconi and Kieffer, 1981;Hayashi et al., 1995). Because the TES instrument observedthe surface from a fixed-local-time orbit, there are generallyonly two times of day available (02:00 and 14:00 local time,given in Mars hours and minutes, with 24:00 per sol, or Marsday), and overlapping groundtracks are relatively rare. Thus,the multi-point curve-fitting technique is not appropriate for theTES dataset.

2.1. Thermal inertia derivation

For deriving thermal inertia from TES brightness tempera-ture observations, Mellon et al. (2000) developed a single-pointmethod (cf. Zimbelman and Kieffer, 1979; Christensen and Ma-lin, 1988) which was employed to produce global maps ofnighttime thermal inertia by Jakosky et al. (2000), Mellon etal. (2000), and Putzig et al. (2005) with increasingly higherspatial resolution and coverage. In this method, a numericalthermal model is used to generate a lookup table of tempera-tures for intervals of season, time of day, latitude, surface pres-sure, dust opacity, albedo, and thermal inertia (Jakosky, 1979;Haberle and Jakosky, 1991; Mellon et al., 2000). Each ob-served brightness temperature is correlated with other dataand interpolated through the lookup table to find the best-fitting thermal inertia. Because measurements of geographicand temporal opacity variations were not then available, theinterpolation algorithm assumed a constant infrared dust opac-ity of 0.1 at 6.1 mbar, scaled to the local elevation. This wasfound to be consistent with average TES spectral observationsduring much of the mapping mission (Mellon et al., 2000;Smith et al., 2001b; Smith, 2004; Putzig et al., 2005) but did notaccount for any local or seasonal opacity variations. Water-ice-cloud opacity was not expected to be available and is not takeninto account by the thermal model. Instead, individual observa-tions from locations and times of high dust- or water-ice-cloudopacity were removed prior to mapping (Mellon et al., 2000;Putzig et al., 2005).

Derivation of thermal inertia by Mellon et al. (2000) andPutzig et al. (2005) produced values at the limits of the lookup-table bounds (24 and 800 tiu) and their mapping results con-tained large gaps at the highest elevations. For this work, wemodified the thermal model and derivation algorithm of Mellonet al. (2000) to accommodate a wider range of thermal inertiaand atmospheric pressure, and we added a more realistic transi-tion of properties for times when CO2 frost is accumulating. Foremissivity and albedo, we use a cosine-weighted transition frombare-ground values when no CO2 frost is present to CO2-icevalues when the CO2-frost mass reaches 6 kg/m2. This func-tional dependence agrees well with albedo and emissivity mod-els for CO2 frost (Warren et al., 1990). All other thermal modelparameters remain the same as those described by Mellon etal. (2000), including iteration intervals of 144 times each Marsday for surface and subsurface temperatures and 24 times eachMars day for atmospheric temperatures. The modified numeri-cal thermal model, which was run for three Mars years to elimi-nate initial conditions, produced surface temperatures which aregenerally accurate to better than 0.1 K for the full range of para-meters considered. We generated a new lookup table, expandingthe range of thermal inertia to 5–5000 tiu and the range of pres-sure to 0.8–15.0 mbar. We also decreased the node spacing forinfrared dust opacity from 0.5 to 0.4 to reduce interpolation er-rors, and we modified the interpolation algorithm to incorporatemeasured dust opacity, account for inter-annual albedo varia-tions, and employ 1

20◦-resolution Mars Orbiter Laser Altimeter

(MOLA) maps of elevation (used for surface pressure determi-nations) and planetary radii (used for an approximate regional


Table 1Lookup-table and algorithm enhancements

Dimension Lookup-table range [nodes] Data source and map resolution

Mellon et al. (2000) This work Mellon et al. (2000) This work

Mars day 0–668 [84] Same TES ephemeris SameMars hour 1–24 [24] Same TES ephemeris Adjusted by 1

20◦ slope map

Latitude (◦N) −90 to 90 [37] Same TES ephemeris Adjusted by 120

◦ slope mapDust opacity 0.0–1.0 [3] 0.0–0.8 [3] Assumed constant at 0.1 2-day 5◦ maps of TES dataa

Pressure (mb) 3.0–10.0 [3] 0.8–15.0 [5] Scaled 1◦ elevation map Scaled 120

◦ elevation mapAlbedo 0.15–0.35 [3] Same 1

4◦ TES map 3 annual 1

20◦ TES maps

Thermal inertia (tiu) 24–800 [10] 5–5000 [21] 14

◦ nighttime map 120

◦ nightside and dayside maps

a Dust opacity data from Smith et al. (2001b), Smith (2004).

Fig. 1. Model diurnal surface temperature computed for node values from the lookup table that was created for the derivation of thermal inertia. Nodes of thermalinertia are 5, 7, 10, 14, 20, 28, 40, 56, 79, 112, 158, 223, 316, 446, 630, 889, 1256, 1774, 2506, 3540, and 5000 tiu. Albedo nodes are 0.15, 0.25, and 0.35. Surfacepressure nodes are 0.8, 2, 5, 10, and 15 mbar. Dust opacity nodes are 0.0, 0.4, and 0.8. In each panel, dashed curves are identical and represent values held constantwhen varying parameters in the other panels (I = 223 tiu, A = 0.25, P = 5 mbar, τD = 0.0). At the fixed season and latitude used here (LS = 0 at the equator),CO2 frost forms at night on surfaces with thermal inertia below ∼56 tiu, reducing the temperature to 148 K (upper left panel). Compare Mellon et al.’s (2000) Fig. 1.

slope correction). Each of these elements is discussed in detailbelow and a summary of lookup-table and algorithm enhance-ments is presented in Table 1. In Fig. 1, model diurnal curvesfor each node in thermal inertia, albedo, atmospheric pressure,and dust opacity show the relative influence of each parameteron surface temperature.

The MGS spacecraft completed 12 orbits each Mars day,with orbit tracks spaced at approximately 30◦ in longitude.Atmospheric dust and water-ice-cloud opacity (Smith et al.,2001b; Smith, 2004) were derived from daytime observations

and can vary significantly over the course of a few days. Fig. 2shows the seasonal variation of the globally averaged TESdust opacity for all orbits included in our processing, span-ning two complete Mars years and portions of two others (MarsYears 24–27, following the convention of Clancy et al., 2000,p. 9563). Globally, the dust opacity shows a regular cycle,with dust-storm activity commencing near LS = 135, intensi-fying after the equinox at LS = 180, and continuing throughthe southern spring and early summer to about LS = 310.Apart from a late-summer storm during Mars Year 26, a trend


Fig. 2. TES atmospheric infrared dust opacity, globally averaged each Mars dayfor orbits 1583–24,346, color-coded by Mars Year following the convention ofClancy et al. (2000). Dotted line at 0.2 opacity shows local threshold valueused to select thermal inertia for mapping. Trends are remarkably consistentfrom year to year outside of the peak dust-storm seasons (LS ∼ 180–310).

of declining opacity generally follows as dust settles out ofthe atmosphere. Dust opacity affects surface temperatures inmuch the same way as thermal inertia (Fig. 1; Jakosky, 1979;Haberle and Jakosky, 1991; Mellon et al., 2000) and an analy-sis aimed at understanding seasonal variations in thermal inertiamust consider seasonal dust-opacity variations as well. Whiledust opacity has its greatest influence on surface temperaturesnearest the time of observation, spatial coverage by TES islimited to 12 orbits per day spaced at about 30◦ in longitude.To optimize spatial and temporal coverage, we mapped day-time opacity of dust and water-ice clouds (Smith et al., 2001b;Smith, 2004) for two Mars days (24 orbits, including the currentand previous days) at 5◦ resolution in longitude and latitude,when processing observations for each sol. We interpolatedeach map to provide complete coverage for use in the derivationand mapping of thermal inertia for both nighttime and daytimeobservations.

The surface albedo of Mars has been observed to changesignificantly from year to year, which is attributable to the redis-tribution of dust that occurs predominantly during global duststorms (Pleskot and Miner, 1981; Christensen, 1988). Since wewere processing observations spanning three Mars years duringwhich global storms had been observed (Geissler, 2005), wecreated separate annual maps of TES visible-bolometer albedo(Christensen et al., 2001) for each Mars year at 1

20◦ resolution,

filtering out seasons and locations with high dust and water-ice-cloud opacity (using thresholds in the infrared of 0.2 and 0.1,respectively). Maps of TES albedo for the latest year included,Mars Year 26, and the change since the first year included, MarsYear 24, are presented in Fig. 3. Albedo changes of ∼0.05are common in many broad regions, with more-isolated areashaving brightened or darkened by 0.10 or greater. An accuratemeasure of albedo is important to the derivation of thermal in-ertia, particularly in the daytime when albedo has larger effectson surface temperature (Mellon et al., 2000).

Regional and local surface slopes also can have large ef-fects on diurnal and seasonal surface temperature variations(Spencer, 1990; Colwell and Jakosky, 2002; Putzig and Mel-lon, 2007). In this context, slope refers to deviations of thesurface from a sphere and not from a gravitational potentialsurface, since the thermal effects are driven by the solar in-cidence angle. Prior work has not accounted for slope in thederivation of thermal inertia from orbital observations becausethe incorporation of full slope corrections is computationallyimpractical for a global study and regional slopes are gener-ally limited to a few degrees (e.g., 99.4% of the surface has anaverage slope of less than 10◦ at TES 1

20◦ resolution). How-

ever, slope based on planetary radii includes polar flatteningdue to Mars’ spin, which when combined with the N–S hemi-spheric topographic dichotomy (Smith et al., 2001a), results inpoleward median slopes of 0.15◦ and 0.23◦ in the southern andnorthern hemispheres, respectively, as determined from MOLAradii binned at TES resolution. Small hemispherical and otherregional slopes will introduce a slight bias in apparent thermalinertia if they are not taken into account. We therefore incor-porated an approximate correction for slope, wherein the truetime of day and latitude of each observation are adjusted to ef-fective time of day and latitude based on the average slope overeach observational footprint. Our approximate correction in-cludes the effect of changes in insolation due to slope at ∼3-kmresolution, but not the effect of differences in atmospheric pathlength.

To quantify the atmospheric-path-length effect and deter-mine maximum slope values for applying our approximate cor-rections, we modified the thermal model to include full correc-tions for slope angle and azimuth. For 02:00 and 14:00 localtimes, the approximate corrections begin to deviate from fullcorrections within a few degrees of slope, but they improve theaccuracy of derived thermal inertia up to high angles in three ofthe four cardinal directions (50◦ or more for N–S slopes and 20◦or more for eastward slopes). The approximate correction dete-riorates for westward slopes greater than 10◦ due to the delay ofheating toward late afternoon which causes a pronounced skewin the diurnal temperature curve (Putzig and Mellon, 2007).Consequently, we do not apply the effective-time-of-day ad-justment for observations where the westward component ofslope exceeds 10◦. Slopes greater than about 15◦ in any direc-tion will produce highly inaccurate results with or without theapproximate corrections, so we chose to apply the correctionsfor all slope components in the other cardinal directions. Over99.95% of map pixels have average slopes less than 20◦, so ourapproximate corrections improve the accuracy of apparent ther-mal inertia nearly everywhere.

The slope corrections discussed here refer to the averageslope within each map pixel. Sub-pixel slope effects on appar-ent thermal inertia are a separate concern and were investigatedby Putzig and Mellon (2007) using the modifications to thethermal model discussed above. We present a comparison ofmodeled apparent thermal inertia for partially sloped surfacemodels with TES results in Section 3.2.


Fig. 3. TES global albedo for Mars Year 26 (top) and the change of albedo between Mars Years 24 and 26 (bottom). Albedo maps were binned at 120

◦ per pixel andinfilled between 87◦ S and 87◦ N latitude. Large interannual changes occur after major dust storms.

2.2. Thermal inertia mapping

Using our modified interpolation algorithm, we processedthree Mars years of brightness temperature observations fromTES orbits 1583–24,346 to derive apparent thermal inertia. Werestricted our mapping and analysis to bolometer-derived values

because of their lower uncertainty and lack of dependence onpotentially nonunit emissivity, relative to spectrometer-derivedvalues (Mellon et al., 2000; Putzig et al., 2005). As discussedabove, the effect of dust opacity on surface temperature is sim-ilar to that of thermal inertia, and therefore any inaccuracy inthe mapped dust opacity may lead to inaccurate thermal in-


ertia. Also, each result may be affected by physics that is notincluded in the thermal model, such as the effects of water-iceclouds. Therefore, thermal inertia values were excluded for ob-servations with infrared dust opacity greater than 0.2 or infraredwater-ice-cloud opacity greater than 0.1 as mapped for the twodays prior to the temperature observations, and for brightnesstemperatures below 160 K (to avoid CO2 frost). We also ex-plicitly rejected TES orbits 2135–2146 which correspond tothe particularly severe global dust storm during Mars Year 26(2001). The remaining results were used to produce 36 night-side and 36 dayside seasonal maps, each encompassing 10◦of LS at 1

20◦ per pixel resolution (∼3 × 3 km at the equator),

which is approximately equivalent to the intrinsic resolution ofthe TES instrument.

Throughout this work, the terms ‘nightside’ and ‘dayside’refer respectively to the southbound and northbound legs ofthe MGS orbit. Local times for these orbit legs were nominally02:00 and 14:00, but they varied rapidly between these times asthe spacecraft crossed the polar regions near 87◦ latitude. Con-sequently, the polar regions of some seasonal nightside mapscontain observations from periods when the Sun was continu-ously above the horizon. Previous global mapping of TES ther-mal inertia (Mellon et al., 2000; Putzig et al., 2005) employedonly nighttime data—with selection criteria that restricted cov-erage to polar night—and the maps were therefore limited tolate summer when CO2 frost was absent in these regions. Ad-ditionally, both the northbound and southbound orbit legs wereincluded, thereby mixing different local times. Due to the sea-sonal and diurnal variability which will be discussed below(Section 3.1), the resulting thermal inertia values were not rep-resentative of the average surface properties, especially in thenorth. By mapping our results on the basis of local time ratherthan solar zenith angle, adjacent regions within each seasonalmap contain observations from similar portions of the diurnalthermal cycle. In the polar regions, seasonal changes in ther-mal forcing occur gradually over broad geographical areas, andthus the inclusion of observations near the terminator will notadversely affect the mapping results.

As with previous TES mapping efforts (Mellon et al., 2000;Putzig et al., 2005), we compensated for the shrinking of themap-pixel scale with latitude due to converging lines of lon-gitude by binning each value of thermal inertia into all thelongitudinal bins covered by its nominal observational foot-print at each latitude. The TES instrument’s downtrack smearof 5.4 km (see Putzig et al., 2005) and longitudinal variationswithin each observation ensure that any given observation doesnot fall entirely within a single map pixel, even at low latitudes.Additionally, overlapping observations of any particular loca-tion are only partially coincident with each other and the valuesof thermal inertia calculated from them are not linearly relatedto the fluxes measured. For practical reasons, we performedonly a simple linear averaging of thermal inertia within eachbin and thus the values within any given pixel throughout eachmap are actually representative of a somewhat larger area.

To provide a complete global representation of nightside anddayside thermal inertia, as well as a basis for comparison to pre-vious global nighttime mapping results of Mellon et al. (2000)

Table 2Model surface materials

Typematerial

Inertiaa Albedo Densitya Heatcap.a

Skin depth (m)

Diurnal(δD)

Seasonal(δS)

Dust 56 0.26 1375 837 0.008 0.212Sandb 223 0.16 1650 837 0.027 0.702Duricrust 889 0.23 1875 854 0.093 2.413Rock 2506 0.16 2500 837 0.201 5.206

a Thermal inertia in tiu, density in kg m−3, heat capacity in J kg−1 K−1.b Material used for slope mixtures.

and Putzig et al. (2005), we latitudinally cropped each of the36 seasonal maps and produced nightside and dayside medianmaps. The median operator should be more representative ofthe surface properties than the mean, due to the fact that sea-sonal variations in apparent thermal inertia can be quite largeand nonlinear (see Section 3.1).

2.3. Heterogeneity modeling

In order to understand the diurnal and seasonal variationsin apparent thermal inertia observed in TES results (see Sec-tion 3.1), we employed the numerical techniques of Putzigand Mellon (2007) and Mellon and Putzig (2007) to producea suite of two-component diurnal and seasonal temperaturecurves for idealized surface materials (dust, sand, duricrust, androck), where each component has fixed values of thermal iner-tia, albedo, density, and heat capacity (see Table 2). Values ofthermal inertia for each material were selected on lookup-tablenodes to minimize interpolation errors and values of albedowere chosen at TES global modes (Putzig et al., 2005). Repre-sentative values for basaltic materials were adopted for densityand heat capacity, modified in the case of duricrust to approxi-mate the effects of sulfate cements in pore spaces. The duricrustthermal inertia of 889 tiu is representative of a basaltic regolithwith 45% porosity in which 5% of the pore space is filled bysulfate salts. Depending on the degree of cementation, thermalinertia can vary by an order of magnitude for a given base gran-ular material. For horizontal mixtures of materials, the thermalmodel described in Section 2.1 was used to generate surfacetemperatures TSi

for each component. For partially sloped sur-faces, we generated component temperatures for a limited set ofslopes (1◦, 5◦, 10◦, 45◦, and 90◦) and azimuths (0◦, 45◦, 90◦,180◦, and 270◦) and a single material (sand). Effective tempera-tures TSe for horizontal mixtures of materials or slopes were de-termined by performing a linear mix of the Stefan–Boltzmannfunction, assuming unit emissivity (see Section 2.4):

(5)σT 4Se

= σ∑

i

AiT4

Si,

where Ai is the fractional area of the ith model component(Putzig and Mellon, 2007). For layered materials, we used alayered version of the thermal model (Mellon et al., 2004;Mellon and Putzig, 2007) to generate effective temperatures forvarious two-layer configurations of the same idealized compo-nents. The layered model allows a single upper layer over a


Table 3Modeling parameters

Parameter Values [count]

Mix percentage 0, 10, 30, 50, 70, 90, 100Layer thicknessa δS/512–2δS by ×2 [11]Time of day 02:00 and 14:00Season (Mars day) 0–668, every 8 [84]Latitude (◦N) −90 to 90, every 10◦ [19]Slope angle (◦) 0,b 1, 5, 10, 45, 90Slope azimuth (◦) 0,b 45, 90, 180, 270

a See Table 2 for δS values.b Fixed slope value for material mixtures.

substrate, where each layer may have distinct, fixed materialproperties. The thickness of the upper layer may be set to val-ues greater than about δS/512, where δS is the seasonal skindepth. For thicknesses greater than about a seasonal skin depth,the upper layer becomes thermally “opaque” and the model re-sults are indistinguishable from the constant-properties case.

For each class of heterogeneity (mixed and layered), appar-ent thermal inertia is derived from the modeled temperaturesusing the same algorithm employed for TES data derivations(see Section 2.1). To avoid introducing numerical uncertaintyin the apparent thermal inertia of layered surfaces, a separatelookup table was generated from the layered thermal modelassuming only one layer (Mellon and Putzig, 2007). Thermalinertia was derived for local times 02:00 and 14:00 every 10◦ ofLS at 10◦ intervals of latitude, assuming constant values of zerofor elevation and dust opacity. Models were run with compo-nent horizontal-mixing ratios of 0:100, 10:90, 30:70, and 50:50and upper-layer thicknesses of δS/512 to 2δS spaced at powersof 2. See Table 3 for a summary of modeling parameters.

Modeled seasonal variations in apparent thermal inertia fordifferent material mixtures or layers can be qualitatively simi-lar for any given local time (Putzig and Mellon, 2007; Mellonand Putzig, 2007). Thus, our initial efforts to compare TES dataand model variations separately for nightside and dayside ob-servations yielded matches to different model types for manylocations at these two times of day. When modeling resultsfor different local times (e.g., 02:00 and 14:00) are consideredtogether, the behavior of the different model types are morereadily distinguishable. We therefore developed a simultane-ous (nightside and dayside) curve-matching technique for thepurpose of finding the best-fit between TES-data and model re-sults for apparent thermal inertia (see Section 3.2). For a givenlocation and model type (e.g., mixed dust and rock, layeredduricrust over dust, etc.), we first extract nightside and daysideTES data from the seasonal maps, calculating the median valuein the specified region for each season. Next, we linearly inter-polate the modeled seasonal curves of apparent thermal inertiabetween modeled latitudes to the specified latitude. We thenfind the sum of the annual median of dayside and nightsideresults for the TES data and for the set of bounding modeledseasonal curves. Using the ratio of the differences between thedata and model summed medians, we linearly interpolate thebounding modeled seasonal curves to find an estimated closest-fitting set of curves for the current model type. A null-match

results where the sum of data medians does not fall betweenthe sum of medians for any set of model curves. Where we dofind a match, we then calculate the RMS of differences betweenthe TES data and the interpolated model curves for dayside andnightside and sum them together. Within each class of models(mixed and layered), we select the model type with the mini-mum sum of RMS differences between data and model as thebest-fit for that class. Given the actual nonlinear nature of thebase model results, any intermediate estimates of mixing ra-tio or layer thickness derived from this fitting technique maycontain substantial errors and should be interpreted accordingly(see Section 3.2).

To facilitate the production of global heterogeneity maps,we automated the matching of TES data to modeled seasonalcurves as described above by applying a selection threshold(chosen empirically at 40 tiu) to the RMS of the differencesbetween the data and estimated best-fit model curves. Matchesare further restricted to those having an RMS of differences thatis less than 5% of the difference in thermal inertia of the model-component materials. The latter restriction eliminates spuriousmatches between highly variable TES results and relativelyinvariable low-thermal-contrast model results (predominantlythose with dust and sand components). Matches with nightsideor dayside RMS values exceeding these thresholds are not con-sidered for heterogeneity mapping. We applied our matchingalgorithm at a resolution of 5◦ per pixel to capture variationsin regional surface characteristics without introducing higher-order seasonal variations seen in higher-resolution TES resultswhich tend to derail the matching algorithm.

2.4. Uncertainty

Mellon et al. (2000) estimated a computational uncertaintyof 6% for nighttime bolometric thermal inertia for a 180 Ksurface, and this value remains essentially unchanged for ourmodified algorithm. Small reductions in the interpolation un-certainty for thermal inertia, atmospheric pressure, and dustopacity due to finer node spacing do not significantly alterthe total computational uncertainty. A similar analysis of day-time bolometric thermal inertia for a 270 K surface yielded acomputational uncertainty of 15%, predominantly due to thehigher daytime surface temperatures causing a large increasein the thermal model uncertainty (from 1.4 to about 11%),which is partially offset by an attendant reduction in the in-strument uncertainty (from 2.7 to about 1%). The atmosphericmodel includes some simplifying assumptions that may lead totemperature-dependent errors of 10–20% in the infrared flux(Haberle and Jakosky, 1991).

As discussed by Mellon et al. (2000), other, less-tractablesources of uncertainty not included in the above reported val-ues are of greater concern. These sources comprise physics nottaken into account by the thermal model and inaccuracies in theancillary data used to obtain values for the other dimensions ofthe lookup table, especially the albedo, dust opacity, and surfacepressure (scaled from elevation). We investigated the sensitivityof thermal inertia to errors in these ancillary data throughout therelevant ranges for Mars and found them to vary substantially


Fig. 4. Sensitivity of nightside and dayside thermal inertia to errors in albedo,dust opacity, and surface pressure. (a) Deviation in thermal inertia scaled to de-viation in each of the other parameters as a function of thermal inertia. (b) Errorin thermal inertia resulting from a 1% error in each of the other parameters. Dis-played sensitivities are for LS = 0 at the equator and are based on differencesfound between lookup-table nodes (see Fig. 1) adjacent to those of the ther-mal inertia values where symbols are posted. Behavior is representative of thatfound for other seasons and latitudes. See text for discussion.

with the mean thermal inertia value, as shown in Fig. 4. Albedoerrors generally have a larger effect than errors in dust opacityor atmospheric pressure (see also Fig. 1). On a percentage ba-sis, the influence of albedo errors on thermal inertia is largestduring the daytime, when it typically decreases with increas-ing thermal inertia up to about 700 tiu, above which it increasesslightly. The influence of albedo errors on nighttime thermalinertia typically increases with thermal inertia, becoming largerthan that during the daytime at extremely high thermal iner-tia (>1800 tiu). The effects of dust opacity errors are generallylarger during the daytime, and the nighttime effects show a pro-nounced minimum near 1200 tiu. This minimum represents thepoint where surfaces of increasingly high thermal inertia donot warm up sufficiently during the day to allow the additionalnighttime downwelling radiation from the dusty atmosphere towarm the surface back up to the temperature it would have hadwere there no dust. At these high thermal inertia values, the in-fluence of dust opacity on surface temperature becomes moreakin to that of albedo than to that of thermal inertia (cf. Fig. 1).In contrast, pressure effects are generally smaller during the

daytime than at night and show a smoothly varying behaviorwith increasing thermal inertia.

Actual errors in the values of these parameters as determinedfrom TES and MOLA data are thought to be relatively small.Uncertainty in the visible bolometer measurement (Christensenet al., 2001) results in an albedo uncertainty of approximately0.001 (0.5% for an albedo of 0.2). Smith (2004) estimated theaccuracy of individual opacity retrievals at 0.05 or 10%. Pres-sure is determined by scaling Viking Lander pressures (Tillmanet al., 1993) to surface elevation, which we obtain from a map ofMOLA data binned at 20 pixels per degree. Smith et al. (2001a)report an accuracy of about 1 m for individual MOLA obser-vations, so the effects of elevation errors on those in pressureare negligible. Deviations of local and regional surface pressurefrom the Viking-determined values due to atmospheric dynam-ics (e.g., Zurek et al., 1992) may occur, but the surface pressureaccuracy should typically be better than 1%.

Significantly larger errors may result from inaccurate valuesdue to erroneous assumptions in the thermal model, the needto interpolate where observations are absent, or—in the caseof albedo or dust opacity—undetected inter-annual or seasonalchanges resulting from the redistribution of dust on the surfaceor in the atmosphere. A re-evaluation of atmospheric dust prop-erties by Clancy et al. (1995) suggests that the visible-to-9-µmextinction opacity ratio may increase with dust opacity and beas high as ∼2.5 for visible opacities less than 1.0 (we assume aconstant ratio of 2.0), potentially yielding an effective overesti-mate in opacity of ∼20%. On the other hand, Wolff and Clancy(2003) and Smith (2004) point out that the TES-derived at-mospheric dust opacities are likely to underestimate extinctionby 20–30%, and are actually more consistent with absorptionopacities. In either case, such errors of ∼25% in opacity wouldresult in thermal inertia errors of ∼7.5% at 223 tiu (Fig. 4b).

Relative to previous TES thermal inertia results (Jakosky etal., 2000; Mellon et al., 2000; Putzig et al., 2005) we achievedsome reduction in the uncertainties related to interpolation andtemporal variations by including two-day dust opacity mapsand higher-resolution maps of elevation and annual albedo.Restriction to nighttime-only in these earlier mapping effortswas predicated on concerns about greater daytime sensitivityto inaccuracies in albedo, which has been shown to vary sig-nificantly between global dust storms (e.g., Pleskot and Miner,1981; Christensen, 1988; see also Fig. 3). By using separateannual maps of higher-resolution albedo, we have sufficientlyreduced this source of uncertainty to provide greater confidencein daytime results and allow the first global dayside mappingof apparent thermal inertia. Our inclusion of an approximateregional-slope correction reduces uncertainty due to regionalslopes of less than ∼15◦ (see also Putzig and Mellon, 2007) andcorrects an error in the solar incidence angle which was intro-duced by the use of areocentric latitudes (i.e., polar flattening).Other uncertainty sources that are difficult to quantify includeuncorrected atmospheric effects (e.g., water-ice clouds, hori-zontal transport), non-Lambertian albedo (Pleskot and Miner,1981; Putzig et al., 2005), and sub-pixel surface frosts. Sinceboth the calculation of TES bolometric brightness temperaturesand the thermal model assume unit emissivity, spatial variabil-


ity in emissivity should not be a significant source of error inthe derived thermal inertia (Mellon et al., 2000).

The heterogeneous-surface modeling results are subject tothe same numerical uncertainty as are those derived from TESobservations. As discussed above, linear interpolation of themodeled thermal inertia in latitude and in mixing percentageor layer thickness was performed to produce best-fit curves andtheir associated RMS differences with respect to the TES data.Departures from linearity may result in substantial errors inthese interpolated results and RMS values, which we estimatemay be as high as 10% for horizontal-mixture models and 20%or more for layered models. The latter models exhibit increas-ingly nonlinear behavior for extremely thin upper layers withhigher thermal inertia and also for layer thicknesses greater thana diurnal skin depth (δD ≈ δS/26) for upper layers with lowerthermal inertia.

3. Results and analysis

In this section, we present our results for global seasonalmapping of TES-derived apparent thermal inertia, comparisonsbetween results from TES data and idealized two-componentsurface modeling at selected locations, and global heterogeneitymaps showing the best-fitting results for two-component hori-zontally mixed and layered materials.

3.1. TES apparent thermal inertia maps

The 36 seasonal maps of apparent thermal inertia derivedfrom TES brightness temperatures as described in the previoussection showed latitudinally dependent bands of high thermalinertia immediately equatorward of zones where data were re-jected due to low temperature (<160 K) that is a likely indicatorof complete CO2-frost coverage at the surface. We attributedthese zones of high thermal inertia to partial CO2-frost cover-age in the affected regions, and we cropped these maps at fixedlatitudes to remove the frosted regions. Figs. 5 and 6 show asampling of seasons throughout the year. Each seasonal mapcontains data from three Mars years and shows a high degree ofregional consistency, which reflects a lack of large inter-annualvariations in apparent thermal inertia. A systematic variation ofregional apparent thermal inertia over the course of the martianyear is evident in the maps. At mid-latitudes (60◦ S to 60◦ N),the seasonal maps show a general sinusoidal trend of ther-mal inertia in time, with a nightside maximum near LS = 110and minimum near LS = 260, and a dayside maximum nearLS = 220 and minimum near LS = 0. The polar regions aremore limited in seasonal coverage and show a greater magni-tude of change between each map for the available seasons,with nightside apparent thermal inertia generally increasing anddayside generally decreasing with season, converging towardsimilar values.

Maps of the amplitude of the seasonal variations in appar-ent thermal inertia for nightside and dayside observations arepresented in Fig. 7. Nearly all locations show amplitudes ofvariation greater than 50 tiu, with dayside amplitudes higherthan nightside by ∼50 tiu on average. Areas of high thermal

inertia generally show greater amplitudes of variation than ar-eas of low thermal inertia (compare Fig. 8), but the geographicpattern of amplitudes differs between nightside and dayside.The largest amplitudes occur over the permanent polar ice caps,more broadly in the polar regions on the dayside, over the Thar-sis and Olympus Mons volcanoes on the dayside, and in Hellas(290◦ W, 40◦ S) and Argyre (45◦ W, 50◦ S) basins. These latteroccurrences are the result of very high apparent thermal inertianear the edge of the cropped regions from isolated seasons dur-ing the southern fall and winter (LS = 0–180; see Figs. 5 and 6),and may be associated with partial CO2-frost coverage. Apartfrom a band near 80◦ N on the nightside where only one or twoseasons were available, the lowest amplitudes of variation occuron the nightside for a region surrounding Alba Patera (110◦ W,40◦ N) and extending eastward to about 55◦ W. Nightside lowamplitudes also occur on the flanks of the Tharsis and OlympusMons volcanoes to the south. On the dayside, these same loca-tions show moderate to very large (several 100 tiu) variations.Homogeneous surfaces should not exhibit large amplitudes ofseasonal variation in apparent thermal inertia—such behavior isindicative of surface heterogeneity (Putzig and Mellon, 2007;Mellon and Putzig, 2007). The ubiquitous nature of the vari-ability suggests that the surface of Mars is heterogeneous nearlyeverywhere at TES scale (∼3 km).

Nightside and dayside global maps of apparent thermal in-ertia created by selecting the median of the seasonal maps foreach 1

20◦ pixel are presented in Fig. 8. While grossly similar

at mid-latitude—exhibiting similar patterns of high and lowthermal inertia—the nightside and dayside median maps havesubstantial regional differences. The dayside median map gen-erally shows lower thermal inertia at mid-latitudes and higherthermal inertia in the polar regions. Both maps show orbit-track-aligned streaks, which are due to the combination of largeseasonal variations and incomplete geographic coverage dur-ing any given season. These effects are more pronounced athigher latitudes, where seasonal coverage is limited and season-to-season variations are larger (see also Figs. 5 and 6). Thegreatest differences between nightside and dayside occur in thepolar regions (60◦–90◦; see Fig. 9). Interestingly, the increasein mapping resolution and the expansion in range of thermal in-ertia to include values for surface ice allows us to distinguishindividual canyons and troughs in the north polar cap as well assome details of outlying permanent ice features. In the south,a dramatic difference between nightside and dayside results isevident, with a large region of low nightside apparent thermalinertia mostly absent on the dayside. A region over the southpolar residual cap of elevated nightside apparent thermal iner-tia poleward of 80◦ S expands greatly on the dayside.

The nightside and dayside mapping results are largely con-sistent with those derived earlier from Viking and TES obser-vations (Kieffer et al., 1977; Palluconi and Kieffer, 1981; Paigeet al., 1994; Paige and Keegan, 1994; Vasavada et al., 2000;Jakosky et al., 2000; Mellon et al., 2000; Putzig et al., 2005).Fig. 10 shows normalized histograms comparing our TES re-sults with those of Putzig et al. (2005) and with Viking resultsfrom Palluconi and Kieffer (1981) and Jakosky et al. (2000).Jakosky et al. (2000) reprocessed Viking data using the same


Fig. 5. TES global nightside bolometric apparent thermal inertia for 10◦-LS seasons every 20◦ of LS. Maps include 3 Mars years of observations and were rebinnedfrom 1

20◦ to 1

2◦ per pixel, cropped to remove seasonal CO2-frost effects, and infilled at uncropped latitudes. Maps show systematic seasonal variations (see text).

algorithm as that used by Putzig et al. (2005), which includedatmospheric effects not considered by Palluconi and Kieffer(1981) that are largely responsible for the shift between the twoViking curves in Fig. 10. Many artifacts of high thermal iner-tia seen in previous TES maps have been reduced or eliminatedusing our revised algorithm. The inclusion of measured dustopacity in the derivation algorithm, the choice of compositingseasons with a median rather than mean operator, and the choiceof selecting data by local time (i.e., nightside) rather than by in-solation angle (i.e., nighttime) are collectively responsible forgreatly reducing the presence of orbital-track-aligned streaksattributable to seasonal variations. Streaks which remain aremore likely to represent heterogeneity in surface characteristics

(discussed below) rather than atmospheric effects or transientvolatiles on the surface. These improvements are reflected inthe shift between the Putzig et al. (2005) nighttime curve andour nightside curve in Fig. 10.

The dayside mapping results represent a new product thatis critical to the analysis of seasonal variability of apparentthermal inertia and its relationship to surface heterogeneity.While dayside seasonal variations are qualitatively similar tothose of the nightside, the magnitude of the dayside variationsis greater, and there is a large seasonal delay between the twotrends. When compared to modeled heterogeneous-surface ap-parent thermal inertia, these distinct features of nightside anddayside trends allow us to distinguish more readily between


Fig. 6. TES global dayside bolometric apparent thermal inertia for 10◦-LS seasons every 20◦ of LS. Maps include three Mars years of observations and wererebinned from 1

20◦ to 1

2◦ per pixel, cropped to remove seasonal CO2-frost effects, and infilled at uncropped latitudes. Like nightside, maps show systematic

seasonal variations, but extrema occur at different seasons (see text).

potentially corresponding classes and types of heterogeneitymodels.

3.2. Local heterogeneity analysis

Figs. 11–14 present local comparisons of TES-derived andheterogeneous-model apparent thermal inertia for various sitesof interest. The surface models considered are horizontal mix-tures and layers of two components composed of materials withproperties representative of dust, sand, duricrust, and rock (Ta-ble 2). Tables 4–7 summarize for each site the model class andtype, and where applicable, the estimated best-fit horizontal-mixing percentages or upper-layer thicknesses and the RMS of

differences between the TES data and modeled apparent ther-mal inertia.

The locations in Figs. 11a–11e are 5◦ × 5◦ boxes cen-tered at each past landing site—Viking Landers 1 and 2, MarsPathfinder Lander, and the Mars Exploration Rover sites at Gu-sev and Meridiani, MER-A and MER-B. The site for Fig. 11fis a 9◦ × 2.5◦ box centered at the specified location whichrepresents “Box 1” wherein the 2007 Phoenix landing site ispresently being considered (Smith et al., 2007). The best-fittwo-component models are all layered cases, with duricrust-over-dust model types at the Viking, Pathfinder, and Meridi-ani sites. The fit between the TES data and the interpolatedmodel results (dash-dotted lines) for the Viking and Pathfinder


Fig. 7. Amplitude of seasonal variation in TES apparent thermal inertia for nightside (top) and dayside (bottom), using unfilled seasonal maps binned at 12

◦ perpixel. Black pixels represent no-data locations. Nightside or dayside amplitudes greater than 50 tiu are ubiquitous, suggestive of widespread surface heterogeneity.

sites is relatively good, with broadly similar seasonal variationsin apparent thermal inertia and a similar relationship betweenthe nightside and dayside behaviors. The presence of duricrustat the Viking and Pathfinder sites is well-documented (Mooreet al., 1987, 1999; Moore and Jakosky, 1989). Estimates ofareal coverage by cemented and crusted soils range as highas 86% (Moore and Jakosky, 1989). Thus, it is not surprisingthat the thermal behavior in the regions surrounding these sitesappears to be dominated by layering with duricrust-like prop-erties. Duricrust-like materials do not appear to dominate at

the Meridiani MER-B site, but similar thermal behavior mayoccur for the rover-observed layered surface, which containsfine sand (50–150 µm) interspersed with mm-sized hematitespherules that become concentrated at the surface (Soderblomet al., 2004). However, the best-fit match between data andmodel shown in Fig. 11c is not particularly close, deviatingsubstantially for seasons after LS = 200. If the thermal behav-ior seen in the data reflects surface properties, either none ofthe component material properties used in the modeling are ap-propriate, or it may be that this region is not well represented


Fig. 8. Median of 36 seasonal maps of TES global nightside (top) and dayside (bottom) bolometric apparent thermal inertia, at 120

◦ per pixel. Maps were infilledbetween 87◦ S and 87◦ N latitude for display purposes. Nightside values are generally higher at mid-latitudes and lower in the polar regions than dayside values.

by simple two-component material models. Similarly, nightsideTES results for the Viking Lander 2 region (Fig. 11d) deviatesignificantly from the model curves and may require a morecomplex surface model to explain (see later discussion of slopeeffects). For the region surrounding the Gusev MER-A site,a layered model with dust over rock provides the best fit to theTES data (Fig. 11e). This result is consistent with orbiter androver image data, such as dark-toned dust-devil tracks, drift de-posits, and dust-coated surfaces, which suggest a widespreadbut thin surface dust layer (Golombek et al., 2006). However,there are substantial deviations between the data and model re-

sults, particularly for LS = 70–270, and it seems unlikely thata simple two-component model will fully characterize the ther-mal behavior in the Gusev region.

The best-fit heterogeneous model for Phoenix Box 1 is nom-inally a sand layer over rock (Fig. 11f). However, ground icewould be thermally indistinguishable from rock. Such an inter-pretation is consistent with the analysis of Mars Odyssey Neu-tron Spectrometer data by Feldman et al. (2004), which sug-gests that near-surface ground ice is likely to be abundant in thisregion. Numerical modeling of ground ice stability (Mellon andJakosky, 1993; Mellon et al., 2004) suggests that such ground


Fig. 9. Polar-region thermal inertia. Nightside (left) and dayside (right) TES apparent thermal inertia in an orthographic projection for the north (top) and south(bottom) polar regions, 60◦ to 90◦ latitude in each hemisphere. 0◦ longitude is at the bottom for the north and at the top for the south. Maps show large differencesbetween nightside and dayside values, and seasonal variability is manifested as orbital-track-aligned streaks.

ice should be buried beneath a thin (∼few cm) veneer of ice-free soil, consistent with our estimate of sand thickness abovethe putative ground ice of δS/18 (39 mm; see Table 4) as wellas that of Titus et al. (2006), who found a best-fit model witha 58-mm-thick layer of sand-like material (I = 216 tiu) over asubstrate with high thermal inertia (700 tiu).

Note in Fig. 11f how the modeled seasonal curves for δS/8cross those for thinner layers. In this case, a minimum night-side seasonal apparent thermal inertia occurs for δS/16, with

values that are below the layer’s true thermal inertia (223 tiu).With increasing upper-layer thickness beyond this minimum,the nightside and dayside modeled seasonal curves flatten, con-verging much more toward the component value in earlier thanin later seasons, with the dayside curves actually divergingslightly at later seasons. This behavior, which is typical for layerthicknesses between a diurnal and a seasonal skin depth, hasthe potential to yield non-unique solutions when estimating theupper layer thickness based on apparent thermal inertia. The


Fig. 10. Normalized histograms of global thermal inertia as derived from TESfor our median nightside (blue) and dayside (red) results; from TES for previ-ous nighttime results (dotted purple; Putzig et al., 2005); from Viking using themulti-point method and no atmospheric corrections (dashed green; Palluconiand Kieffer, 1981); and from Viking using the single-point method with at-mospheric corrections (dashed light-blue; Jakosky et al., 2000). All show asimilar bimodal distribution. See text for further discussion.

match shown here is broadly representative of the north polarregions and shows a qualitatively good fit that is readily dis-tinguishable from other model types. However, values of theRMS of differences for extensive portions of the polar regionsare large enough to exceed the empirically chosen threshold forheterogeneity mapping (see Section 3.3).

We now consider six additional sites which have relativelyclose matches in apparent thermal inertia between TES dataand the best-fitting two-component modeled values. The Aci-dalia region, near 45◦ W, 55◦ N, exhibits high apparent thermalinertia that varies greatly over the available seasons, resultingin the streakiness of the region as seen on the median mapsin Fig. 8. This seasonal variation in the TES data is also ev-ident in Fig. 12a and well-matched by a layered model withduricrust over dust, especially for the dayside data. At a similarlatitude, the Utopia Rupes region (Fig. 12b) shows much lessseasonal variation, with a best-fit layered model of duricrustover sand. Locations in the southern mid-latitudes at DaedaliaPlanum (Fig. 12c) and Tyrrhena Terra (Fig. 12d) are well-modeled by layered two-component models with dust over rockand sand over rock, respectively. For Tyrrhena Terra, the vari-ations are much smaller, and both the data and the modeledseasonal curves oscillate around the sand thermal inertia. Thelatter behavior is indicative of a relatively thick sand layer, withthickness between a diurnal and seasonal skin depth. Similarlyto the seasonally limited case discussed above for the Phoenixlanding site, there is a potential for non-unique solutions whenestimating the upper layer thickness, with the modeled appar-ent thermal inertia reaching a minimum near a thickness ofδS/16. At a higher latitude in the southern hemisphere, Hel-las Planitia (Fig. 12e) shows a large (∼150 tiu) diurnal differ-ence in apparent thermal inertia, with a good fit using a layeredduricrust-over-dust model. Slightly further south, the Icaria re-gion (Fig. 12f) shows a lesser diurnal difference and is bettermatched with a layered duricrust-over-sand model.

In many cases, the matching algorithm may find either sim-ilar quality fits to different classes or types of model, or fail tofind any match to the available two-component model results.Most of the ambiguous multiple matches are to horizontallymixed surface models and two-layer models with upper lay-ers of lower thermal inertia. The seasonal curves for these twomodel classes often show similar variations and the same signof the diurnal difference. Two-layer models with upper layers ofhigher thermal inertia tend to have the opposite sense of varia-tion and difference relative to these other two model classes andare thus more readily distinguishable. Examples of this ambigu-ity are shown for regions in Scandia Colles (Figs. 13a and 13b)and Solis Planum (Figs. 13c and 13d). Neither model fits partic-ularly well in either case, with the dayside generally providinga better fit to one model and the nightside to the other.

The remaining sites in this set, Arabia and Malea Planum(Figs. 13e and 13f), did not yield a match for any of the two-component models considered by our matching algorithm. Nev-ertheless, some insight into the nature of the surface materialsmay be obtained by examining such results. Arabia Terra isa continent-sized region of low thermal inertia centered near330◦ W, 15◦ N (see Fig. 8). The seasonal TES apparent thermalinertia shown in Fig. 13e is representative of many portions ofthis and other regions of low thermal inertia that span the equa-tor. While the layered model results shown in the figure for aduricrust-over-dust model do not provide a good quantitative fitto the data, they do demonstrate some similarities. In particular,the extremely low dayside values of apparent thermal inertiafor the thinnest model cases and their relationship to their cor-responding nightside values is qualitatively similar to that of theTES data. A different choice of model component thermal in-ertia, such as a lower dust value, clearly would improve the fit.Note that a model with an upper layer of lower thermal inertia—such as dust over duricrust as suggested by Ditteon (1982)—isnot consistent with the TES results for these regions. For sucha model, nightside is lower than dayside apparent thermal iner-tia for the majority of seasons, whereas the TES data shows theopposite behavior. The fact that greater higher-order variabilityis generally present in the data and that the duricrust-over-dustlayered model only provides a qualitative fit lends support to theargument of Jakosky and Christensen (1986) who proposed thata combination of factors are responsible for the thermal anom-alies observed in these regions. In any event, the high albedoof these areas (see Fig. 3) will likely require a thin coating ofbright dust atop the duricrust if such is present.

At high latitudes in both hemispheres, appropriate condi-tions for determining the apparent thermal inertia of the surfacebecome very seasonally limited. At the same time, the valuesthat can be derived show large seasonal changes. These ef-fects can make it difficult to obtain good model fits in theseregions. Despite these limitations, examination of model anddata seasonal trends shows remarkably consistent behavior anda qualitatively good correspondence between the data and two-component models with upper layers of lower thermal inertia.The behavior seen for the Phoenix landing site (Fig. 11f) is rep-resentative of the north polar region. An example at a slightlyhigher latitude in the south from Malea Planum (Fig. 13f) shows


Fig. 11. Comparison of apparent thermal inertia for nightside (blue) and dayside (red), showing results extracted from TES seasonal maps (×, + symbols) andbest-fitting results from two-component models (02:00 dashed, 14:00 solid) in regions surrounding five previous and one proposed (Phoenix) landing sites on Mars.Previous landing site regions are 5◦ × 5◦ boxes centered on each site. All sites match best with the layered models shown. Colored dash-dotted curves are linearlyinterpolated between the bounding modeled seasonal curves to the median of the seasonal TES results. Black horizontal dashed and dash-dotted lines denote thermalinertia of model upper-layer and substrate, respectively. Model thicknesses were varied by powers of 2 relative to the seasonal skin depth, δS, of the upper layer.See Table 2 for δS values. The seasonal ranges for the Viking Lander 2 and Phoenix sites are restricted due to the occurrence of seasonal CO2 frost. See text fordiscussion.

similar characteristics in the TES data. However, the modelpredicts nightside CO2-frost temperature for upper-layer thick-

nesses greater than about δS/32, especially in the earlier sea-sons when extremely low nightside values occur in the TES


Fig. 12. Comparison of apparent thermal inertia extracted from TES seasonal maps and best-fitting results from two-component models in six 5◦ × 5◦ study regionscentered on the specified locations. The seasonal ranges for Acidalia, Utopia Rupes, Hellas, and Icaria are restricted due to the occurrence of seasonal CO2 frost.Colors and symbols as in Fig. 11. See text for discussion.

data, and no modeled values of apparent thermal inertia are ob-tained. This site is within the region of low thermal inertia andlow albedo defined as Unit D by Putzig et al. (2005), whichwas interpreted as a region with a low-density mantle, prob-ably overlying ice-cemented materials at depth. Although the

model presented in Fig. 13f is for a dust-over-duricrust model,a low-density residue overlying ground ice might be expectedto exhibit similar variation in apparent thermal inertia. Anotherpotential explanation for seasonal variations in the polar regionsis seasonal variation in the depth of the ice table. However, the


Fig. 13. Comparison of apparent thermal inertia extracted from TES seasonal maps with ambiguous fits to two-component model results in four 5◦ × 5◦ studyregions centered on the specified locations. The seasonal ranges for Scandia Colles and Malea Planum are restricted due to the occurrence of seasonal CO2 frost.Colors and symbols as in Fig. 11. See text for discussion.

time scale for diffusion in the dry soil layer is expected to belonger than a Mars year unless the ice table is shallower thanabout 7 mm (δS/30 for dust or δS/100 for sand) (Mellon et al.,2004), whereas most of the variations seen in the polar regionsare consistent with layer depths of a few centimeters.

As discussed in the previous section, sub-pixel slope varia-tions can have substantial effects on apparent thermal inertia.Our slope modeling was limited to a single surface material(I = 223 tiu), five angles and five azimuths, and one uniformlysloping component and one level component per model. Thus,


Fig. 14. Comparison of apparent thermal inertia extracted from TES seasonal maps and results from models of partially sloped surfaces in four 5◦ ×5◦ study regionscentered on the specified locations. Modeled seasonal curves are labeled with sloped-area percentages. The seasonal range for Viking Lander 2 is restricted due tothe occurrence of seasonal CO2 frost. Colors and symbols as in Fig. 11. Horizontal dashed line denotes the thermal inertia (233 tiu) of the model material. See textfor discussion.

Table 4Landing site best-fit layered models

Site Location Model Thickness RMS diff.a

◦W ◦N # Fig. Class Type δS mm AM PM

Viking 1 48.2 22.5 1 11a Layered Duricrust/dust δS/105 23 33 41Pathfinder 33.5 19.1 3 11b Layered Duricrust/dust δS/91 27 30 34Meridiani 5.5 −2.0 5 11c Layered Duricrust/dust δS/133 18 36 41Viking 2 226.0 47.7 2 11d Layered Duricrust/dust δS/126 19 42 30Gusev 184.5 −14.6 4 11e Layered Dust/rock δS/64 3 44 39Phoenix 126.5 68.25 6 11f Layered Sand/rock(ice) δS/18 39 34 31

Note. #—label for location on maps in Figs. 15 and 16.a 02:00 and 14:00 RMS difference between data and model seasonal thermal inertia in tiu.

the quantitative methods used for matching models of heteroge-neous materials to the data are not particularly useful here andwe restrict our analysis of partially sloped surfaces to qualita-tive comparisons. Four examples are presented in Fig. 14. Theone for Noachis Terra (Fig. 14a) shows a good match betweenthe TES data and a model with 30–50% of the terrain sloped at10◦ to the north. A better fit could be achieved with a lower

surface-material thermal inertia of about 160 tiu. The SolisPlanum location, which shows an ambiguous match to multiple-material models as discussed above (see Figs. 13c and 13d),also shows a correlation with a model of a partially sloped sur-face, with 10◦ slopes in a northeasterly direction (Fig. 14b). Inthis case, an increase of the surface material thermal inertia toabout 350 tiu would improve the fit. Where some individual


Table 5Local best-fit layered models

Site Location Model Thickness RMS diff.a


Acidalia 45.0 55.0 A 12a Layered Duricrust/dust δS/81 30 65 37Utopia 272.5 42.5 U 12b Layered Duricrust/sand δS/329 7 12 14Daedalia 137.5 −22.5 D 12c Layered Dust/rock δS/60 4 36 25Tyrrhena 272.5 −12.5 T 12d Layered Sand/rock δS/9 78 16 16Hellas 290.0 −45.0 H 12e Layered Duricrust/dust δS/123 20 29 36Icaria 122.5 −52.5 I 12f Layered Duricrust/sand δS/333 7 20 12


Table 6Local ambiguously fit heterogeneity models

Site Location Model Mix % or RMS diff.a


Scandia 142.5 62.5 C 13a Layered Dust/duricrust δS/103 2 17 33Scandia 142.5 62.5 C 13b Mixed Dust/duricrust 64:36 – 21 26Solis 95.0 −25.0 S 13c Layered Dust/duricrust δS/194 1 52 32Solis 95.0 −25.0 S 13d Mixed Dust/rock 64:36 – 53 35Arabia 330.0 15.0 B 13e Layered Duricrust/dust ∼δS/512 5 – –Malea 320.0 −75.0 M 13f Layered Dust/duricrust ∼δS/56 4 – –


Table 7Local slope heterogeneity models

Site Location Model◦W ◦N # Fig. Class Type

Noachis 5.0 −30.0 N 14a Sloped 10◦ NSolis 95.0 −25.0 S 14b Sloped 10◦ NEMeridiani 5.5 −2.0 5 14c Sloped 10◦ NEViking 2 226.0 47.7 2 14d Sloped 10◦ N

Note. #—label for location on maps in Figs. 15 and 16.

models provide only partial fits to the data, a combination ofmodels might serve to more fully explain the observed behavior.

As shown in Fig. 11c, the MER-B Meridiani site is not wellmatched by a simple duricrust-over-dust layered model. In par-ticular, the model mismatches are greatest near the equinoxes(LS = 90 and 270). A model in which 50% of the region has10◦ slopes to the northeast (Fig. 14c) produces diurnal dif-ference extrema at these same seasons. If these slope effectswere combined with the layered model effects, a better fitto the observed seasonal behavior at Meridiani might be ex-pected. While the average slope in the Meridiani region makesit one of the flattest locations on the planet, widespread dune-forms have been observed and traversed by the rover—thus,regional sub-pixel slopes on the order of 10◦ are not unrea-sonable. At the Viking Lander 2 site, a fairly good daysidefit was found using a duricrust-over-dust model, but large de-viations in the nightside data at early and late seasons wereobserved (see Fig. 11d). A model for this location using par-tial northward slopes of 10◦ (Fig. 14d) shows similar early-and late-season deviations but does not itself characterize therelationship between the nightside and dayside mean apparentthermal inertia. Here again, a combination of the layered and

sloped models might result in a better overall fit to the data.However, interpretations such any these should be made cau-tiously, since the effects on apparent thermal inertia of differenttwo-component models do not mix linearly (Putzig and Mellon,2007).

3.3. Global heterogeneity maps

We applied our simultaneous curve-matching algorithmglobally at 5◦ intervals of longitude and latitude to producemaps of surface heterogeneity. Given the potential for ambigu-ous results between horizontal mixtures and surfaces with lowthermal inertia upper layers as described above, we appliedthe matching algorithm separately for horizontally mixed andlayered models. No sloped-surface models were considered.The restriction of matches to those with RMS differences lessthan 40 tiu and 5% of the model thermal contrast was cho-sen by trial and error to remove spurious matches. Maps ofmatches for models of horizontally mixed materials, showingmodel type and areal percentage of the component with higherthermal inertia, are shown in Fig. 15. Similar maps in Fig. 16portray matches for layered models, showing model type and


Fig. 15. Global maps at 5◦ per pixel for two-component mixed materials showing model type (top) and the areal percentage of the component with higher thermalinertia (bottom) for models which correspond best to the TES seasonal and diurnal mapping results. Model components are D: dust; S: sand; C: duricrust; and R:rock. Matches are found for the model with the minimum sum of the nightside and dayside RMS of differences between data and model results. For matchingpurposes, a linear interpolation of the modeled seasonal curves bounding the TES data results is performed. Matches are restricted to models where the RMSdifferences are simultaneously less than 40 tiu and less than 5% of the difference between the component values of thermal inertia. White areas denote locationswhere no model meets the match criteria. Locations for landers and study sites in Figs. 11–14 are shown as 1: Viking Lander 1; 2: Viking Lander 2; 3: MarsPathfinder Lander; 4: MER-A (Gusev); 5: MER-B (Meridiani); 6: Phoenix Lander Box 1; A: Acidalia; B: Arabia Terra; C: Scandia Colles; D: Daedalia Planum; H:Hellas Planitia; I: Icaria; M: Melas Planum; N: Noachis Terra; S: Solis Planum; T: Tyrrhena Terra; and U: Utopia Rupes. See text for discussion.

upper-layer thickness relative to the seasonal skin depth. Thelayered models tend to dominate, with duricrust-over-dust andduricrust-over-sand layering predominately at mid-northern lat-itudes (20◦ N–60◦ N), and layering with finer materials (dust orsand) overlying coarser materials (duricrust or rock) predom-inately poleward of 60◦ and near the equator (30◦ S–20◦ N).Where they occur, horizontally mixed dust-and-duricrust and

dust-and-rock model results generally show good matches tothe data. While the matches for the present landing sites (lo-cations 1–5) generally correspond well to the local analysispresented in the previous section, the proposed Phoenix site(location 6) shows correspondence to a dust-over-ice modelin Fig. 16 whereas our site-specific analysis suggests a sand-over-ice model. Here, the use of 5◦ of latitude in the automated


Fig. 16. Global maps at 5◦ per pixel for two-component layered materials showing model type (top) and thickness of the upper layer in units of seasonal skin depth(bottom) for the models which correspond best to the TES seasonal and diurnal mapping results. Model components are D: dust; S: sand; C: duricrust; and R: rock.Matching criteria and locations are the same as in Fig. 15. See Table 2 for material δS values and text for discussion.

mapping causes the RMS difference to exceed the threshold forthe sand-over-ice model.

In some cases, there is ambiguity between the horizon-tally mixed models and the layered models of dust over duri-crust, dust over rocks, or sand over rocks. Matches for hor-izontally mixed sand-and-duricrust and sand-and-rocks mod-els, whether isolated or co-located with layered duricrust-over-dust or duricrust-over-sand matches, are typically consistentwith either sand-dominated surfaces or thin duricrust layers(<∼δS/200), showing relatively little seasonal or diurnal vari-ation. Where ambiguities occur, the layered model results usu-

ally provide a slightly better fit to the data (see Fig. 13 andTable 6). Large, contiguous swaths of mixed sand-and-duricrustand sand-and-rock matches between 40◦ S and 65◦ S shownearly 100% sand. Actual data variations there are better fit bylayered models with a relatively thin duricrust over sand (e.g.,Fig. 12f) or relatively thick sand over rock. In the white areasof the heterogeneity maps, no match was found that met the se-lection criteria. However, these locations exhibit thermal inertiabehavior that is indicative of a heterogeneous surface of onetype or another. As shown earlier in Fig. 7, all locations showvariable apparent thermal inertia at 1 ◦ resolution, and thus un-
2


matched locations on the heterogeneity maps (Figs. 15 and 16)should not generally be construed as representing homogeneoussurfaces. Some locations in these areas may still provide rea-sonable matches to two-component models either quantitatively(e.g., Acidalia and Malea Planum) or qualitatively (e.g., Ara-bia Terra), or they may not be well represented by the singletwo-component models considered here (e.g., Meridiani). Somesurfaces may require models with three or more components,potentially including divergent slopes, to characterize their ther-mal behavior. Each additional component adds another layer ofcomplexity and increases the likelihood of ambiguous multiplesolutions (Putzig and Mellon, 2007). For particular locations,other sources of data, such as observations from landed space-craft, may constrain modeling parameters and help to discrimi-nate between the possible solutions.

Christensen (1986) produced a map of rock abundance for40◦ S–60◦ N using a spectral differencing technique appliedto Viking IRTM observations. A general correspondence is ob-served when comparing his map to our maps of horizontallymixed model matches (Fig. 15). Regions showing good agree-ment between the TES data thermal inertia behavior and thatof horizontally mixed models typically exhibit high rock abun-dance on the Christensen (1986) map (e.g., mixed dust-and-duricrust regions near Scandia Colles and mixed sand-and-rockregions near Solis Planum in Fig. 15), but there are some lo-cations showing agreement that exhibit lower rock abundance(e.g., mixed dust-and-rock regions between 30◦ S and 30◦ N inFig. 15) and there are many locations of high rock abundancethat do not display matches (e.g., regions surrounding Acidaliaand the Viking and Pathfinder lander sites). Our mixed-surfaceheterogeneity maps show regions with thermal behavior whichmay be dominated by horizontally mixed materials, regardlessof the component grain sizes. In contrast, locations with highrock abundance on the Christensen (1986) map do not neces-sarily have thermal characteristics which are dominated by hor-izontal mixtures. In fact, Christensen (1986) himself concludedthat the surface bulk thermal inertia is generally driven by thefiner components and not by the rock abundance. His conclu-sion is consistent with our assertion that subsurface layering—rather than horizontal mixing—is the primary cause of the vari-ations in apparent thermal inertia seen in the TES data.

In another analysis of Viking IRTM observations, Ditteon(1982) mapped differences between temperatures computedfrom a thermal model with homogeneous material proper-ties and those observed in the Viking 20-µm band. He foundlarge, anomalous differences over broad regions that corre-spond closely to the equatorial low-thermal-inertia, high-albedoregions (i.e., Unit A of Putzig et al., 2005). Ditteon (1982)used a two-layer thermal model to fit the observed diurnal tem-peratures, assuming a constant thermal inertia of 1250 tiu forthe lower layer and allowing the upper layer thermal inertiaand albedo to vary. He concluded that the anomalous tem-peratures in these regions could generally be explained by alayered surface with about one diurnal skin depth (∼1 cm) ofdust overlying a duricrust. His conclusion is somewhat in con-flict with our interpretation of a layer of duricrust overlyingdust in Arabia Terra (see previous discussion in Section 3.2

and the area around location B in Fig. 16). However, there areother regions in Fig. 16 that correspond to different portionsof the anomalous regions mapped by Ditteon (1982), whereTES data is matched by models with dust overlying duricrustor rocks. It appears that layering with high-over-low thermalinertia was not considered in Ditteon’s analysis, and it is un-clear how the diurnal temperature effects of such layers mightdiffer from those of layering with low-over-high thermal in-ertia that he did consider. While his attributing of the scatterin residual diurnal temperatures to spatial variations of ther-mal inertia and albedo within his study regions is plausible,it is possible that seasonal variations due to other forms ofsurface heterogeneity may be a significant contributing factor.Ditteon (1982) did not include a separate analysis of seasonalvariability, which can provide a means of distinguishing be-tween potentially ambiguous models (Putzig and Mellon, 2007;Mellon and Putzig, 2007). In general, our results indicate awider range of layering types in these regions of low thermalinertia than that suggested by Ditteon (1982). As noted ear-lier, these regions do pervasively exhibit high albedo, which isa likely indicator of a widespread coating of bright dust. Never-theless, our results suggest that any such dust coating is proba-bly much thinner than a diurnal skin depth where high-over-lowthermal inertia layering appears to dominate the thermal behav-ior.

4. Summary and implications

We enhanced the thermal model and thermal inertia deriva-tion algorithm originally developed by Mellon et al. (2000) forprocessing TES observations of bolometric brightness tempera-tures on Mars. Our enhancements included an expansion of themodeled ranges of thermal inertia and surface pressure, incor-poration of measured dust opacity, an approximate correctionfor slope, and improvements in temporal and spatial resolutionfor albedo and other ancillary data. Using this new algorithm,we reprocessed three Mars years of TES observations and thenmapped the results to produce seasonal nightside and daysidemaps of apparent thermal inertia at 1

20◦ per pixel. These maps

show systematic diurnal and seasonal variations in apparentthermal inertia that we attribute to surface heterogeneity at hor-izontal scales less than the TES instrument resolution (∼3 km)and at vertical scales less than a seasonal skin depth below thesurface.

To evaluate the potential for surface material and slope het-erogeneity as an explanation for the diurnal and seasonal vari-ability seen in the TES results, we used modified versions of thethermal model (Putzig and Mellon, 2007; Mellon and Putzig,2007) to generate apparent thermal inertia for idealized two-component surfaces with horizontally mixed materials, partiallysloped surfaces, and layered materials. The amplitude and fre-quency of diurnal and seasonal variability in the heterogeneous-surface model results corresponds quite closely with similarvariations observed in TES-derived thermal inertia. In many lo-cations, close matches can be found between individual modelsand the TES data, which suggests that, while the surface it-self is likely to be more complex than a simple two-component


model, in many cases the thermal behavior of the surface maybe dominated by the spatial relationships of one or two typesof material. The horizontally mixed and layered model classesmay be divided into four distinct subclasses, namely materialmixtures, slope mixtures, two-layer models with upper layers oflower thermal inertia, and two-layer models with upper layersof higher thermal inertia. The material mixtures and two-layermodels with upper layers of lower thermal inertia tend to exhibitsimilar behavior which can lead to ambiguous matches withthe TES data. In comparison, the two-layer models with up-per layers of higher thermal inertia generally show the oppositebehavior, lending a higher level of confidence to any correlationfound with these models. Slope mixtures exhibit a third style ofbehavior that is highly variable with azimuth (Putzig and Mel-lon, 2007), making them something of a wild card. In regionswhere a single two-component model does not fully charac-terize the thermal behavior, inclusion of a second model mayimprove the fit. However, such multiple-model fits are highlyspeculative and likely to be non-unique, given the potential forambiguity between different types and classes of models. Thepartially sloped model behavior is of particular concern, givenits high degree of variability. More realistic slope modeling, in-cluding a range of thermal inertia values, more azimuths, andcomparison to slope derived from higher-resolution elevationdata, perhaps including observations from landed spacecraft,would help address this concern.

An automated matching scheme was developed to produce5◦ maps of material heterogeneity for horizontal mixtures andlayers (Figs. 15 and 16). Given the aforementioned limita-tions and the poorly constrained uncertainties discussed in Sec-tion 2.4, the heterogeneity mapping results should be inter-preted in the broadest sense. Rather than focusing on individualresults, one might consider, for example, dark (purple to green)areas in Fig. 16 as likely representing surfaces dominated bylayering with an upper layer of lower thermal inertia, and light(yellow to red) areas as surfaces dominated by layering with anupper layer of higher thermal inertia.

As mentioned earlier, the multi-point derivation techniqueused previously to process Viking observations derives val-ues of both thermal inertia and a “thermally derived” albedo(Palluconi and Kieffer, 1981). Separate albedo determinationswere also made from broadband visible-spectrum observationsand large differences between the derived and observed albedowere found. This discrepancy has never been fully explained(Hayashi et al., 1995). Because the multi-point method forces asingle thermal inertia and a single albedo value from multipleobservations, any deviation from constant material properties,such as would occur for heterogeneous surfaces, will result inerrors in both thermal inertia and albedo. An analysis of ther-mally derived albedo from MER mini-TES observations byFergason et al. (2006a) suggests that causes other than het-erogeneity may dominate. Nevertheless, a re-examination ofViking results to determine the extent to which surface hetero-geneity may play a role in the Viking albedo discrepancy maybe warranted.

The variations in apparent thermal inertia derived fromTES observations and their correspondence to heterogeneous-

surface modeling results have important implications for abroad range of Mars exploration activities. Nearly all studiesto-date which have employed thermal inertia use fixed valuesfor any given location obtained from annually averaged map-ping results. Use of these fixed values to infer surface geologi-cal characteristics, such as grain size, rock abundance, and thepresence of duricrusts or bedrock may yield erroneous results.Studies which focus on temporally variable phenomena—suchas the exchange of volatiles with the subsurface, condensationof volatiles on the surface, past and present climate modeling,and atmospheric circulation and dust storms—may be greatlyaffected by seasonal and diurnal variations in apparent ther-mal inertia. For these purposes, it is unlikely that fixed annuallyaveraged values are sufficient to fully characterize the surfacelayer, whether or not they represent the annual mean behavior.The process of landing-site selection draws on these and otherstudies for the purposes of evaluating the scientific potential ofa site and assessing hazards to landing safety and trafficability,such as rocks, dust cover, and slopes. Climate conditions suchas winds and temperature extremes may also affect both land-ing safety and the life of the power supply. Accurate thermalinertia is particularly important to evaluating local temperaturevariations. The skew in fixed values of thermal inertia due toaveraging may be somewhat alleviated by the use of a medianoperator, but the seasonal and diurnal variations in the apparentthermal inertia are of greater importance to a better understand-ing of the surface properties. While relating these variations tothe physical characteristics which cause them is not straight-forward, the results presented here show great promise for theuse of relatively simple models in constraining the nature ofsurface heterogeneity at particular locations on the martian sur-face.

Acknowledgments

We thank Robin Fergason, James Zimbelman, and BenjaminBrown for critical reviews which greatly improved this manu-script. Funding for this research was provided through NASA’sMars Data Analysis Program (MDAP).

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Apparent thermal inertia and the surface heterogeneity of Mars · Apparent thermal inertia and the...

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