analysis of mola data for the mars exploration …analysis of mola data for the mars exploration...

Analysis of MOLA data for the Mars Exploration Rover

landing sites

F. Scott Anderson,1 Albert F. C. Haldemann, Nathan T. Bridges, Matthew P. Golombek,

and Timothy J. ParkerJet Propulsion Laboratory, Pasadena, California, USA

Gregory NeumannDepartment of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge,Massachusetts, USA

Received 4 June 2003; revised 8 September 2003; accepted 20 October 2003; published 24 December 2003.

[1] We have used Mars Orbiter Laser Altimeter (MOLA) data to demonstrate that selectedlanding sites meet the Mars Exploration Rover (MER) landing system topography andslope requirements at hectometer and kilometer scales. To provide a comprehensiveanalysis, we constrained slopes within each landing ellipse using four approaches:(1) measurements of local slopes at 1.2 km length scales using both an adirectionalmaximum gradient method and a higher-resolution bidirectional, along-track method,(2) predictions of 100m slopes using self-affine statistics in conjunctionwith (3) calculationsof both pulse width and slope corrected pulse width to constrain slopes at scales smaller thanthe MOLA spot size (<180 m), and (4) comparisons of simultaneously acquired MOLAdata with Mars Orbiter Camera data to identify the geomorphologic features associated withvariations in observed slopes, pulse width, and, for this analysis only, reflectivity. Theresults of the analysis indicate that the selected landing sites are consistent with the MERtopography requirement of being below �1.3 km, as well as having slopes less than 5�at length scales of 100 m and <2� at length scales of 1.2 km. INDEX TERMS: 6225 Planetology:

Solar System Objects: Mars; 6297 Planetology: Solar System Objects: Instruments and techniques; 1227

Geodesy and Gravity: Planetary geodesy and gravity (5420, 5714, 6019); 5455 Planetology: Solid Surface

Planets: Origin and evolution; 5464 Planetology: Solid Surface Planets: Remote sensing; KEYWORDS: Mars

Exploration Rover, landing site, slope, roughness, Hurst, topography

Citation: Anderson, F. S., A. F. C. Haldemann, N. T. Bridges, M. P. Golombek, T. J. Parker, and G. Neumann, Analysis of MOLA

data for the Mars Exploration Rover landing sites, J. Geophys. Res., 108(E12), 8084, doi:10.1029/2003JE002125, 2003.

1. Introduction

[2] Accurate topographic information is critically impor-tant for landing spacecraft on Mars because (1) elevationcontrols the atmospheric column available for slowing thespacecraft during ballistic entry and parachute descent,(2) slopes at a variety of scales affect radar acquisition ofthe surface, (3) slopes affect the ability of the spacecraft toland safely, and (4) local slopes and relief can impact rovermobility. For the first time in Mars exploration history,definitive elevation data at kilometer and hectometer scaleare available from MOLA (Mars Orbiter Laser Altimeter)data returned from the Mars Global Surveyor (MGS)spacecraft. In this paper we describe in detail the use ofMOLA data to address engineering safety criteria estab-lished for the Mars Exploration Rover (MER) that wereused during landing site selection [Golombek et al., 2003],

as well as demonstrating how MOLA-derived slope, pulsewidth, and reflectivity data relates to Mars Orbiter Camera(MOC) images of the landing sites.[3] The MER entry, descent and landing system requires

an adequate atmospheric density column for the parachuteto bring the spacecraft to an acceptable terminal velocity forparachute deployment and to provide enough time tojettison the heat shield, lower the lander on the bridle,measure the descent rate with the radar altimeter, inflatethe airbags, and fire the solid rockets (see Crisp et al. [2003]for a description of the MER landing). Calculated densitycolumns indicate that the MER spacecraft are capable oflanding below �1.3 km with respect to the MOLA defineddatum [Golombek et al., 2003].[4] Surface slopes represent a three-fold hazard for the

landing system. First, relatively small, but regular slopesover km-scale distances can add horizontal velocity andprolong bouncing or rolling by the lander within the inflatedairbags. Large slopes over hundred-meter length-scales canspoof the radar altimeter, causing premature or late firing ofthe solid rockets and airbag inflation. Third, meter- todecameter-scale slopes can increase airbag spinup and

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. E12, 8084, doi:10.1029/2003JE002125, 2003

1Now at Hawaii Institute of Geophysics and Planetology, University ofHawaii at Manoa, Honolulu, Hawaii, USA.

Copyright 2003 by the American Geophysical Union.0148-0227/03/2003JE002125$09.00

ROV 25 - 1

bounce which can, in turn, induce failure on subsequentbounces by exceeding the stroke of the airbags or increasingthe chance of slicing the airbags on sharp rocks. Slopes atthis scale also affect the stability of the lander, roverdeployment and trafficability, and power generation. Engi-neering safety criteria developed for these potential failuremodes are that surface slopes should generally be less than15� at 3 m scales, <5� at 100 m scales, and <2� at kilometerscales [Golombek et al., 2003]. Sophisticated landing sim-ulations and sensitivity studies indicate that of these threeslope criteria, 3 m slopes have the highest potential impacton landing survivability followed by 100 m slopes and 1 kmslopes [Golombek et al., 2003]. In this paper we addressonly hectometer-scale and kilometer-scale slopes, as theycan be assessed with MOLA data. We also discuss MOLApulse width and derived relief within a MOLA shot, as theseare a proxy for 100 m and smaller scale slopes. Three-meterslopes are addressed by Kirk et al. [2003].[5] Lastly, the MOLA data can be used to assess the

magnitude of topography, slopes, pulse width, and reflec-tivity of features within MOC images of the landing sites.We present details of the coregistration of MOLA data toMOC imagery, and thereby review and confirm our under-standing of how the topographic data relate to morphologyin the images. Golombek et al. [2003] and references thereinreport on detailed geomorphologic analyses of MOCimages. Finally, for completeness in our examination ofMOLA data, we briefly examine MOLA reflectivity corre-lations at the MER landing sites.[6] In summary, this paper describes in detail the topo-

graphic data and derived slope information, abstracted andsummarized by Golombek et al. [2003], for the selection oflanding sites for the Mars Exploration Rovers. We presentthe analyses carried out for seven high-priority MERlanding ellipses, listed in Table 1, which are the 4 primesites and 2 backup sites retained after the October 2001MER Second Landing Site Workshop, plus the wind-safesite in Elysium. We also include analyses of the VikingLander 1 (VL1), Viking Lander 2 (VL2) and Mars Path-finder (MPF) landing sites as ground truth locations forcomparative purposes (Table 1).

2. MOLA Data and Topography

[7] The MOLA measured >600 million laser shots onMars from which elevation, pulse width and reflectivity data

were determined over the entire planet, and archived in thePlanetary Data System (PDS). The MOLA data used for thestudies reported here were acquired from the PDS usingthe ‘‘L’’ version of the Precision Experiment Data Record(PEDR) for elevation, pulse width, and reflectivity, and areshown using the planetocentric IAU/IAG 2000 coordinatesystem [Duxbury et al., 2002; Seidelmann et al., 2002].Earlier versions of MOLA data, using the IAU/IAG 1991coordinates for Mars, were used in the early phases of theMER landing site evaluations. All final evaluations weredone with IAU2000 MOLA data, and landing site mapspresented in this paper are all in that reference frame, evenwhen the landing sites may initially have been mapped inolder reference frames during the selection process [e.g.,Golombek et al., 2003]. The ‘‘L’’ version of the MOLAPEDR data also provides a crossover correction for thegeographic location ofMOLA shots, and an updated estimateof the pulse width [Neumann et al., 2003]. We used MOLAdata extending from the science phasing orbit (SPO) to thefailure of MOLA’s ranging mode at orbit 20333. The MOLAdata contain the exact altitude, planetary radius, timing,engineering parameters, and areographic position of eachMOLA shot, which were spaced approximately 300 meters(or 0.1 seconds) apart from each other along the orbit track[Smith et al., 2001]. Occasionally, there is a missing shotalong an individual MOLA track, which can occur forreasons such as clouds, data dropouts, noise, etc. For thisanalysis, the topography, timing, pulse width, and reflectivityparameters were calculated following the MOLA SoftwareInterface Specification [Smith et al., 1999], which describesthe units for each data value. Topography is calculated as thedifference between the planetary radius and the geoid.[8] The MOLA data are edited for clouds, noise, and poor

geolocation and assembled into the Mission ExperimentGridded Data Record (MEGDR) delivered to the PDS.The final data density allowed grid resolutions as fine as128 pixels per degree of planetocentric longitude and lati-tude, although at that resolution less than 50% of pixels aresampled. Multiple shots within a single pixel are averaged,while missing data are interpolated. MOLA data density waslimited by the polar geometry and orbital track spacing,leaving occasional gaps of up to 0.2� of longitude near theequator. MOLA vertical accuracy is 1 m over reasonablysmooth terrain and position is accurate to 100 m [Neumannet al., 2001]. Gradient-shaded grids reveal subtle variations

Table 1. MER Landing Site Ellipses Coordinate Frame Locations and Sizesa

Site

MDIM 2.0 IAU/IAG 1991 IAU/IAG 2000 Ellipse

Lat, � Long, � Lat, � Long, � Lat, � Long, � Name Major axis, km Minor axis, km Azimuth, �

Meridiani 2.07S 6.08W 2.06S 353.77E 2.06S 354.008E TM20B2 119 17 84Gusev 14.82S 184.85W 14.64S 175.06E 14.64S 175.298E EP55A2 96 19 76Elysium 11.91N 236.10W 11.73N 123.72E 11.73N 123.958E EP78B2 155 16 94Isidis 4.31N 271.96W 4.22N 87.91E 4.22N 88.15E IP84A2

IP96B2132140

1616

8891

Athabasca 8.92N 205.21W 8.83N 154.67E 8.83N 154.91E EP49B2 152 16 95Melas 8.88S 77.48W 8.75S 282.36E 8.75S 282.60E VM53A2

VM53B2103105

1820

8082

Eos 13.34S 41.39W 13.20S 318.46E 13.20S 318.70E VM41A 98 19 78VL1 22.27N 311.81E 22.27N 312.02E 200 100 84VL2 47.67N 134.04E 47.67N 134.27E 200 100 84MPF 19.09N 326.51E 19.09N 326.74E 200 100 84

aMDIM-2 has longitude positive to the west in planetographic coordinates [USGS, 2001], while IAU/IAG coordinates are positive east in planetocentriccoordinates. Ellipse parameters for VL1, VL2, and MPF are based on the MPF ellipse size [Golombek et al., 1997] applicable for VL and MPF ballisticentry and are merely for the purposes of statistical analysis.

ROV 25 - 2 ANDERSON ET AL.: MOLA DATA FOR MER LANDING SITES

in slope invisible to imaging instruments, as laser altimetry isvirtually unaffected by atmospheric and illumination con-ditions. Local slope information may be derived fromprofiles in the along-track direction, and the local topograph-ic gradient from gridded data, recognizing that slope base-lines are limited by the 300-m along-track spacing, or in thecase of gridded data, by pixel resolution and variable across-track coverage. While gridded MOLA data products are nowavailable, our analyses primarily used individual MOLAshots to maximize resolution over the landing sites. Use ofgridded MOLA data, such as the 1/128� resolution topogra-phy grid, was limited to elevation data for regional mappingand checking the �1.3 km ellipse elevation constraint. Theone exception was the first slope corrected pulse width(SCPW) data set, which was kindly provided in griddedform by the MOLA team [Garvin et al., 1999; Smith et al.,2001; J. Garvin, personal communication, 2000]. This dataset provided coverage of the early landing sites between±15�, but later sites were on the boundary of the provideddata. For these locations, we have derived our own estimatesof SCPW. The MOLA elevation information for the sevenMER and the VL1, VL2 and MPF landing sites is listed inTable 2.

3. MOLA Slopes

[9] Slopes are derived from MOLA topographic profiledata. Because the calculation of slope statistics overlength-scales that are multiples of the 300-m MOLA shotspacing is straightforward, we addressed the km-scaleslope requirement with 1.2 km MOLA inter-shot data.The 100-m scale slope requirement is addressed withMOLA pulse width data and also by extrapolating theslope behavior at hectometer-scale down from longerlength-scales. An important consideration in making slopemeasurements from topographic profiles is whether or notthe profile has been detrended. Detrending removes longwavelength slopes, i.e., at, or near the scale of the entireprofile length considered. Although detrending has littleeffect on length-scales that are short (<10%) when com-pared to the entire profile length, we nevertheless chosenot to detrend. Our reason for not detrending, despite itsrecommendation by Shepard et al. [2001], is that, for thepurpose of MER landing site evaluation, we are interestedin the slopes that the MER landing system will actuallyencounter. For example the potential radar-spoofing effectat any given location depends on the total slope (or relief)

over a 100 m length scale, including any underlyingregional slope.

3.1. Kilometer-Scale Slopes

[10] To generate 1.2-km scale slope statistics for thelanding sites, we calculated both bidirectional slopes, thecomponent of slope measured along the roughly north-south MOLA orbit track, and adirectional slopes, whichare the slopes in maximal downhill direction, i.e., the localgradients.3.1.1. Bidirectional Slope Mapping[11] At each valid laser shot location we calculated the

bidirectional slope between the laser shot located two shot-intervals up-track from the location to the shot located twoshot-intervals down-track from the location. A bad shot ateither extremity yielded an invalid slope and no slope pointwas mapped. All the valid slope points were then gridded at0.3 km resolution, for which multiple points within a gridcell were averaged, using the Generic Mapping Tools(GMT) software [Smith and Wessel, 1990; Wessel andSmith, 1991, 1995, 1998]. This has the effect of averagingthe data from parallel tracks with less than 300 m lateralseparation, and of averaging the data at track crossoverpoints. The averaging to 0.3 km resolution removes biasesto the ellipse statistics that might be introduced if twoclosely parallel tracks crossed a particularly rough part ofthe ellipse. For mapping the bidirectional slopes, the slopepoints were separately averaged at 1.2 km resolution toimprove the visual appearance of the maps. Then, statisticswere calculated for all 0.3 km pixels falling within theellipse, and histograms of the resulting slopes plotted(Table 3, Figures 11–22).3.1.2. Adirectional Slope Mapping[12] Adirectional slopes were calculated using the Generic

Mapping Tools (GMT) [Smith and Wessel, 1990;Wessel andSmith, 1991, 1995, 1998], which we used to average allMOLA elevation samples within a 1.2 km grid, and thencalculate the maximum slope between adjacent grid points;pixels for which any neighbor is missing are not recorded.Histograms of the data were produced, and the statistics ofall the valid points in the 1.2 km resolution grid within thelanding ellipse are listed in Table 3, with definitions of thestatistics discussed in Appendix A. The maps resulting fromthese adirectional slope determinations are sparse relative tothe bidirectional slope maps because the spacing of MOLAtracks in the equatorial regions that the landing sites arelocated is typically greater than the 1.2 km grid, so thatadjacent grid points may not contain data.

Table 2. MER Ellipse Topography

Site

Ellipse Center Ellipse

Geoid, kmMOLA

Elevation, kmMOLA Elevation

Range, km

Meridiani 3395.526 �1.440 �1.37 to �1.58Gusev 3394.227 �1.920 �1.80 to �1.93Elysium 3395.239 �2.940 �2.68 to �3.20Isidis 3396.115 �3.740 �3.68 to �3.74Athabasca 3395.096 �2.640 �2.51 to �2.66Melas 3395.758 �3.700 �2.35 to �4.13Eos 3394.427 �3.850 �3.2 to �4.03VL1 3339.299 �3.6VL2 3386.349 �4.5MPF 3393.482 �3.7

Table 3. MER 1.2 km Slope Statistics for Each Site

Site

Bidirectional Slopes Adirectional Slopes

Mean ± s.d., � RMS, � N Mean ± s.d. RMS, � N

Meridiani 0.15 ± 0.18 0.26 680 0.24 ± 0.47 0.53 208Gusev 0.20 ± 0.44 0.49 679 0.19 ± 0.29 0.34 277Elysium 0.48 ± 0.55 0.73 934 0.41 ± 0.29 0.51 361Isidis 0.19 ± 0.24 0.30 782 0.14 ± 0.10 0.17 315Athabasca 0.20 ± 0.36 0.41 1334 0.20 ± 0.29 0.35 882Melas 1.22 ± 1.35 1.80 698 1.10 ± 0.66 1.29 307Eos 1.22 ± 1.87 2.23 686 1.02 ± 1.08 1.48 262VL1 0.26 ± 0.96 0.33 ± 0.95VL2 0.28 ± 0.29 0.28 ± 0.21MPF 0.25 ± 0.66 0.30 ± 0.51

ANDERSON ET AL.: MOLA DATA FOR MER LANDING SITES ROV 25 - 3

Figure 1. Maps of MOLA topographic and slope information for the Athabasca Valles (EP49B2) MERlanding site. (a) 1.2 km scale adirectional slope, (b) 1.2 km scale bidirectional slope, (c) dimensionlessHurst exponent determined over the range 0.3 km to 1.2 km, (d) self-affine extrapolation of 100 m RMSslope, (e) pulse width [Neumann et al., 2003], and (f ) roughness (slope-corrected pulse width) from J. B.Garvin (personal communication, 2000). The contour lines (1 km interval) in all panels are from 1/128degree gridded MOLA elevation data.


3.1.3. Results[13] Adirectional slopes are shown in Figures 1a–10a,

bidirectional slopes are shown in 1b–10b, and histogramsof the adirectional and bidirectional slopes within eachellipse are shown in Figures 11a and 11b through 22a and22b, respectively. The slope maps are generally consistent

with the topographic maps from which they are derived withhigher slopes indicated in areas of greater relief. Largecraters and other high relief features show up as areas ofenhanced 1.2 km slopes that exceed 5� in the maps ofMeridiani, Gusev, Isidis, Athabasca, Elysium, VL1, VL2and MPF. The maps of Melas and Eos have slopes on the

Figure 2. Maps of MOLA topographic and slope information for the Elysium Planitia (EP78B2) MERlanding site. Panel assignments as in Figure 3.


wall of the canyons that exceed 10� at the 1.2 km scale.These maps were used to avoid areas of higher 1.2 km slopein ellipse placement. For example, in Gusev crater, theellipse avoids the steeper slopes of the crater Thira at itseastern end and at Meridiani it avoids steeper slopesassociated with the crater to the southeast of the ellipse.

[14] The km-scale slopes for all the landing ellipses inTable 3 meet the engineering requirement of <2�, except theChasmata sites of Melas and Eos which exceed the limit atless than one standard deviation from the means. Meridiani,Gusev, Isidis and Athabasca are smoothest at 1.2 km withmean slopes �0.2�, comparable or smoother than the VL1,

Figure 3. Maps of MOLA topographic and slope information for the EOS Chasma (VM41A) MERlanding site. Panel assignments as in Figure 3.


VL2 and MPF sites. Elysium appears slightly rougher atkm-scale with an average slope of �0.5�, which is greaterthan at previous Mars landing sites. The Melas and Eoslanding sites are rougher at this scale with average slopes of�1.2�, consistent with parts of their ellipses located on thelower sloping parts of the canyon walls; these sites clearlyhave areas that exceed the engineering requirement of 2�.

[15] We note that both the mean and RMS adirectionalslopes are in almost all cases lower than the mean bidirec-tional slopes, which should not be the case if the adirectionalslope is the local gradient. In fact this behavior is an effect ofour method of determining the adirectional slope, because bygridding at 1.2 km resolution we are effectively smoothingthe elevation data, which then has the effect of reducing the

Figure 4. Maps of MOLA topographic and slope information for the Gusev Crater (EP55A2) MERlanding site. Panel assignments as in Figure 3.


adirectional slopes calculated between adjacent grid points.Adirectional slopes should therefore only be taken as lowerbounds for the actual 1.2 km adirectional-scale slopes.Fortunately the km-scale slopes we find are so clearly withinthe required bounds that some error does not affect theresults, especially for the selected Meridiani and Gusev

landing sites. This is true even if the adirectional slopes areroughly

ffiffiffi2

ptimes [Kirk et al., 2003] the bidirectional slopes.

3.2. Hectometer-Scale Slopes

[16] Two independent approaches were used to assess theMER requirement that landing site slopes over 100 m length-

Figure 5. Maps of MOLA topographic and slope information for the Meridiani Planum (TM20B2)MER landing site. Panel assignments as in Figure 3.


scales to be less than 5�. First, MOLA pulse width data wasused to constrain roughness at the MOLA footprint size of75–150 m [Garvin et al., 1999; Neumann et al., 2003; Smithet al., 2001], which can then be used to infer upper limits forfootprint-scale slopes. Second, under the assumption of self-affine slope statistics, 100 m scale slopes can be extrapolated

from the 0.3 km to 1.2 km MOLA bidirectional slopestatistics. First we discuss the MOLA pulse width data, thecalculation of slope corrected pulse width, and the use ofthe pulse width data for the landing sites. Then we discussthe extrapolation of surface slope using statistical methodsand the results of the analysis for the MER landing sites.

Figure 6. Maps of MOLA topographic and slope information for the Isidis Planitia (IP84A2, IP96B2)MER landing site. Panel assignments as in Figure 3.


3.2.1. Pulse Width and Slope Corrected Pulse Width[17] MOLA used four timing gates, or channels, to record

the ‘‘width’’ in nanoseconds of the reflected pulse from thelaser, which can be used to constrain the roughness or reliefof the surface area illuminated by the laser pulse [Abshireet al., 2000; Afzal, 1994; Gardner, 1992; Garvin et al.,1999; Neumann et al., 2003]. The MOLA laser divergence

for channel 1 of 93 mrad, determined during pre-flightcalibration, indicates that 90% of the pulse energy illumi-nates and interacts with a region 150–180 m in diameter onthe surface of Mars [Neumann et al., 2003; Smith et al.,1999; Zuber et al., 1992]. However, in-flight data reductionby Neumann et al. [2003] indicated that a change inthreshold sensitivity settings caused the instrument to

Figure 7. Maps of MOLA topographic and slope information for the Melas Chasma (VM53A2,VM53B2) MER landing site. Panel assignments as in Figure 3.


observe a smaller illuminated spot on the surface, resulting ina smaller effective divergence as low as 46 mrad for channel 1,implying a 1-s surface illumination of �40-m [Neumann etal., 2003]. Generally, a slope in the illuminated surface areawill cause the pulse to broaden, as a portion of the energy isreflected from the higher elevation part of a slope first, whilethe remainder is slightly delayed until it can reflect from lower

elevations. This is true for both a single long wavelengthslope, which can be estimated by measuring the elevationdifference between MOLA shots, and for short wavelengthslopes at rover scales, here referred to as the ‘‘slope correctedpulse width’’ (SCPW). Although the 300 m slope is sub-tracted out of these measurements, there is no knowledge ofthe actual slope over the footprint and the pulse spread

Figure 8. Maps of MOLA topographic and slope information for the Mars Pathfinder landing site.Panel assignments as in Figure 3.


measure cannot distinguish between a constant slopeover 100 m and roughness composed of short wavelengthsawtooth relief elements.[18] It is possible to estimate and remove the effect of

long wavelength slope by calculating the pulse broadeningfrom shot to shot slope and subtracting it from the observedpulse width. It is also necessary to subtract the initial pulse

width of the laser shot as well as the instrument response, asdescribed by Gardner [1992] for an ergodic surface:

s2s ¼ s2h þ s2f þ4

c2 cos2 fVar xð Þ þ z2 tan4 qT þ tan2 qT tan2 f

� �� ð1Þ

Figure 9. Maps of MOLA topographic and slope information for the Viking Lander 1 landing site.Panel assignments as in Figure 3.


in which ss is the mean observed pulse delay, sh is theinstrument response, sf is the length of the transmittedpulse, c is the speed of light, f is the incidence angle of thelaser, Var(x) is the variance of the surface profile (the SCPWsquared), z is the orbital height, and qT is the laserdivergence. The PEDR pulse width values have had the

instrument response function removed. It can be showngeometrically that the incidence angle and long wavelengthslope are expressed mathematically in equivalent form, sofor small angles we add them to determine the net incidenceangle. In some cases, received pulses saturate the detectionsystem (received raw pulse width counts = 63 or energy

Figure 10. Maps of MOLA topographic and slope information for the Viking Lander 2 landing site.Panel assignments as in Figure 3.


counts = 255) because the surface was more reflective or thespacecraft was closer than anticipated; in these cases thepulses are discarded, and roughness is not calculated.[19] Four pulse width measurement issues can affect the

interpretation. First, low values of pulse width (below 12 ns)are commonly noisy, and when used in association with anarea with regional slopes, may result in small negativesurface roughness values. This occurs because the channeldesign on the MOLA instrument precludes accurate mea-surement of pulse width below 6.67 ns; we use 6.67 ns, orabout 1 m, as a minimum observable value. Second, and asmentioned above, the new estimates for the divergence ofthe laser should be used [Neumann et al., 2003], oroverestimation of pulse broadening from long-wavelengthslope may occur (see equation (1)). Our analysis of thiseffect supports the choice of a smaller divergence (46 mrad

for channel 1, 70 mrad for channels 2–4) by Neumann et al.[2003], and is in fact consistent with a slightly smaller valueof 37 mrad; the results shown here use the values fromNeumann et al. [2003]. Third, because the along track slopedoes not constrain the local cross track slopes, the estimateof long wavelength slope can be biased; however, therecurrently is no better estimate possible. Lastly, significantoff-nadir viewing geometry can result in excessive pulsespreading.3.2.2. Mapping Pulse Width[20] Pulse width estimates that have been corrected for

flight divergence values [Neumann et al., 2003] are aver-aged over a 128 pixel/degree grid and mapped in raw formin Figures 1e–10e. These pulse width maps show where thepulse width samples were measured for each ellipse, as aguide for possible biases in sampling over the ellipses. In

Figure 11. Histogram of Athabasca (EP49B2) (a) 1.2 kmscale a-directional slope (�), (b) 1.2 km scale bi-directionalslope (�), (c) slope corrected pulse width (m).

Figure 12. Histogram of Elysium (EP78B2). Panelassignments as in Figure 11.


addition, the occasional track with excessive pulse widthvalues is apparent for some of the landing sites; wedeliberately have left these in to illustrate the minimalnature of these issues.[21] We also made maps using SCPW data provided by

the MOLA team (Golombek et al. [2003] refer to them as‘‘slopecor’’ pulse width data) [Garvin et al., 1999; Smith etal., 2001; J. Garvin, personal communication, 2000]. Notethat these data, generated early in the MER site selectionprocess, do not incorporate the new estimates of divergence.The statistics of SCPW, as well as pulse width, are pre-sented in Table 4 (and in Table 10 of Golombek et al.[2003]). The maps of SCPW (Figures 1f–10f), and those forpulse width, show that all the sites considered are verysmooth at MOLA spot-size scales; we generated our ownvalues of SCPW for landing sites beyond the ±15� gridded

SCPW band provided by the MOLA team. The SCPWresults from these data indicate pulse widths of <2 m,consistent with relief of <10 m [Garvin et al., 1999], whichcorresponds to the slope requirement of <5� over 100 mbaselines. By this measure, the pulse width roughness datain Table 4 show Gusev has the highest pulse spread (1.5 m),Meridiani the lowest (0.8 m), with the other sites in between(�1 m), although both meet the MER engineering criterion.[22] Newer analyses that include improvements in the

estimated laser divergence, as discussed above, and theresulting estimates of the RMS relief with and withoutlonger slopes removed by Neumann et al. [2003], showMeridiani as having the lowest pulse spread (0.8 m) andMelas and Eos the highest (>3 m). The other sites cannot bereadily distinguished from the VL1, 2 and MPF landingsites (�1–2 m). By these data, all of the 4 final landing

Figure 13. Histogram of Eos (VM41A). Panel assign-ments as in Figure 11.

Figure 14. Histogram of Gusev (EP55A2). Panel assign-ments as in Figure 11.


sites should be acceptable and should be no worse thanthe 3 locations on Mars (VL1, 2 and MPF) where radaraltimeters have worked satisfactorily in successfully landingspacecraft.3.2.3. Self-Affine Roughness Extrapolation[23] The difficulties in quantifying the MOLA pulse

width data, at least in the early phases of the landing siteanalysis, led us to consider another method for the quanti-tative estimation of hectometric slopes. Processes modify-ing the surface of Mars likely act over a range of scales,however, it is probably safe to assume that processes actingover 300–1200 m scales are also acting on 100 m scales;such a surface is said to be ‘‘self-affine’’. Assuming a self-affine surface in the regions of the landing sites, we canmeasure relief as a function of scale over MOLA shotintervals of 0.3, 0.6, 0.9, and 1.2 km and use them topredict the relief and RMS slope at 100 m length scales. The

correlation and consistency of the results with pulse widthand SCPW observations is a test of the assumption that thesurface is self-affine.[24] Shepard et al. [1995, 2001], Shepard and Campbell

[1999], and Campbell et al. [2003] summarize the statisticalproperties of the RMS deviation of topography (noting thatit also goes by the name structure function, variogram orAllan deviation, u). In this study we follow the Shepard etal. [2001] nomenclature:

u �xð Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

n

Xni¼1

z xið Þ � z xi þ�xð Þ½ 2s

ð2Þ

where n is the number of samples, z is the altimetry, and �xis the step size. For a self-affine surface the RMS deviation

Figure 15. Histogram of Isidis (IP84A2). Panel assign-ments as in Figure 11.

Figure 16. Histogram of Isidis (IP96B2). Panel assign-ments as in Figure 11.


scales with �x, the separation between samples along theprofile, as

u �xð Þ ¼ u �x0ð Þ �x=�x0

� �H¼ u0 �x=�x0

� �H ð3Þ

where H, the Hurst exponent, is a constant over some rangeof scales [Hurst et al., 1965]. Changes in H at a given scalesuggest a change in surface process. To calculate the Hurstexponent, we assemble all the MOLA altimetry tracks in aregion and generate a deviogram by plotting u = u(�x) inlog-log space, and fit a line to the points at 0.3, 0.6, 0.9, and1.2 km to find H. An example is shown in Figure 23 for a0.1 degree sized pixel containing the Mars Pathfinderlanding site; for which we calculate and plot u(�x) up to�x = 4.5 km, but we only fit H over 0.3–1.2 km. We thenuse the Hurst exponent to extrapolate the best fit line to

0.3–1.2 km scales to predict the deviation at 100 m scale.Further, from the deviogram we calculate the RMS slope, s,since it is directly related to the RMS deviation by

s �xð Þ ¼ u �xð Þ =�x ð4Þ

and

s �xð Þ ¼ s �x0ð Þ �x=�x0

� �H�1¼ s0�x=�x0

� �H�1 ð5Þ

The extrapolated 100 m RMS slope at the Mars Pathfinderlanding site from Figure 23, around 1.7, agrees favorablywith the value of 2 reported by Kirk et al. [this issue; 2001].[25] Where our method differs somewhat from the stan-

dard deviogram analysis of a topographic profile [e.g.,

Figure 17. Histogram of Melas (VM53A2). Panel assign-ments as in Figure 11.

Figure 18. Histogram of Melas (VM53B2). Panel assign-ments as in Figure 11.


Shepard et al., 2001] is that we assemble the analyses frommultiple separate profiles of differing lengths into a singledeviogram to characterize the (1-dimensional or bidirec-tional) roughness of a surface. This approach is directlycomparable to a standard analysis because equation (1) doesnot distinguish whether it is averaging over correlated oruncorrelated deviations; hence the preparation of the devio-gram is merely an extension of the bidirectional slopeevaluation to multiple length-scales using a larger appropri-ate area for averaging.[26] We used this method to map the resulting 100 m

slopes in and around the ellipses initially at 0.1� resolutionfor the landing site selection process [Haldemann andAnderson, 2002]. Shepard et al. [2001] caution that devio-gram method should only be applied to length scales thatare less than 0.1 times the profile length. In each 0.1� pixelwe typically had a total of �75 MOLA inter-shot intervals,or a cumulative profile length of 22.5 km, which met theShepard et al. [2001] criterion for the length scales of 0.3 kmto 1.2 km over which we fit the Hurst exponent in order to

extrapolate down to 0.1 km. However, Campbell et al.[2003] caution that Hurst exponent measurements (or fits)underestimate H when H > 0.5 and overestimate H whenH < 0.5 when the profile is not sufficiently long. They findthat N = 100 is sufficient when H � 0.5, while N = 1000results is reasonable estimates when H = 0.25 or H = 0.75.Since most of the Hurst exponents we observe are in therange 0.4 to 0.8 we have chosen to remap the extrapolationsusing 0.2� pixels (Figures 1c–10c), which typically pro-vides for an average of some 350 MOLA inter-shot (300 m)intervals, or a total length of 105 km of profile. Theuncertainty we add to the 100 m RMS slope is acceptablebecause we are not extrapolating very far outside ourdeviogram fit region (0.3 to 1.2 km), and because all thelanding sites except MPF have H > 0.5, so Campbell et al.[2003] would suggest we are overestimating RMS slope at100 m if we are in error for those sites. In any event, thestatistics that we report in Table 4 (and reported byGolombek et al. [2003, Table 10]) are derived by averagingall of the MOLA tracks that fall in 0.1� pixels that are at

Figure 19. Histogram of Mars Pathfinder (a) 1.2 kmscale a-directional slope (�), (b) 1.2 km scale bi-directionalslope (�).

Figure 20. Histogram of Viking Lander 1. Panel assign-ments as in Figure 19.


least one quarter within the ellipses in Table 1, increasingthe net profile length enough to provide unbiased values ofH based on Campbell et al. [2003], resulting in robust fullellipse extrapolations. Furthermore, the results of the newer,more robust 0.2 pixel analysis are consistent with the 0.1�analysis.3.2.4. Hectometer Slope Results[27] The 100-m MER landing site slopes meet the MER

landing system criteria for all but the two canyon sites. Thisis quantitatively clear from the 100 m RMS slope column inTable 4, but also from the newer 0.2� resolution 100-mslope estimates (Figures 1d–10d). These self-affine extrap-olation results are generally consistent with the pulse spreadresults (Table 4) showing that of the final four sites, all ofwhich meet engineering constraints, Gusev is the roughest,and that the two canyon sites, Melas and Eos, haveparticularly rough surfaces that don’t meet the constraintsat this scale. In fact the maps of slope corrected pulse widthin Figures 1f and 3f–7f indicate that the spatial mapping offractal topography that we carried out is properly sampling

the surface, as seen with an independent method. Theargument holds at the other sites too, although the picturednon-interpolated pulse width data for those sites makes themap comparison less clear.[28] The maps of hectometer slopes derived from this

method are remarkably similar to the maps of MOLA pulsespread (compare d and f of Figures 1–10), which arguesthat both are accurately measuring the slope at 100 m scaleand that locating landing ellipses on the basis of these datais appropriate. In Gusev crater (Figures 4d and 4f), bothmethods show higher 100 m slopes south and east of theellipse where images show etched and knobby terrain.Slopes over 100 m scales are also slightly higher in thesouth central portion of this ellipse, where a fresh crater andetched terrain are present, which have been avoided in thefinal ellipse (EP55A3) [Golombek et al., 2003]. Similarly

Figure 21. Histogram of Viking Lander 2. Panel assign-ments as in Figure 19.

Figure 22. Histogram of Meridiani (TM20B2). Panelassignments as in Figure 11.


both maps for Meridiani (Figures 5d and 5f), show higherslopes associated with craters to the northeast, southeast andsouthwest of the ellipse, which have also been avoided withthe final ellipse (TM20B3) [Golombek et al., 2003].[29] While much of the topographic and slope data that

we presented for the landing site selection shows terrainsthat are generally smooth, as would be expected for loca-tions chosen from photogeologic data to be safe, we do findone parameter that appears to be variable across several ofthe MER ellipses, and that is the 0.3 km to 1.2 km Hurstexponent. This variation may be due to sampling bias. Forexample the Hurst exponent map variation in Figure 1c

bears some resemblance to the MOLA track coverage thatcan be inferred from Figures 1b and 1e. However, any suchcorrelation is much less clear at the Melas site in Figure 7.Future self-affine hectometric roughness extrapolation fromMOLA data will need to carefully address the issue of Hurstexponent fit uncertainty better than we were able to do here.

4. MOC-MOLA Images of MER Landing Sites

[30] This final analysis of MOLA data discussed in thispaper seeks to characterize the nature of the surface at thelanding sites through simple comparisons of simultaneously

Table 4. MER Landing Site Hectometer Slope Parameters

Site

Slope CorrectedPulse Widtha Pulse Widthb

Slope CorrectedPulse Widthb Self-Affine Extrapolation

Mean ± s.d., m RMS N Mean ± s.d. N Mean ± s.d., m NHurst

ExponentAllan

Deviation, mRMS

Slope, �

Meridiani 0.75 ± 0.24 0.8 1152 0.8 ± 0.9 531 0.8 ± 0.8 544 0.53 3.4 1.9Gusev 1.42 ± 0.44 1.5 1340 1.5 ± 1.3 101 1.1 ± 1.0 296 0.56 5.8 3.3Elysium 1.10 ± 0.40 1.1 1366 1.9 ± 2.8 478 1.5 ± 1.7 5879 0.64 4.0 2.3Isidis 1.10 ± 0.35 1.2 1140 5.1 ± 1.8 8 1.8 ± 2.8 7078 0.51 2.6 1.5Athabasca 1.18 ± 0.35 1.2 1.9 ± 2.6 387 1.6 ± 2.4 1867 0.76 4.3 2.5Melas 1.21 ± 0.74 1.4 1028 3.1 ± 2.2 554 3.4 ± 4.1 18206 0.81 9.9 5.7Eos 1.06 ± 1.14 1.6 1026 4.7 ± 6.2 422 3.9 ± 6.8 16518 0.78 11.5 6.6VL1 2.1 ± 3.7 3640 1.7 ± 2.9 535 0.53c 1.8c 1.0c

VL2 1.1 ± 0.4 921 1.1 ± 0.4 921MPF 2.0 ± 3.6 2742 2.0 ± 4.1 1755 0.371 5.01 2.91

aJ. G. Garvin (personal communication, 2000).bNeumann et al. [2003].cSelf-affine extrapolation statistics for VL1 and MPF were not calculated with the 200 km 100 km synthetic ellipses listed in Table 2, but with 0.4 deg

boxes centered on the landing site.

Figure 23. Left panel: deviogram for the MOLA tracks in the 0.1 degree box centered on 326.45 E,19.45 N. The Hurst exponent derived from fitting the 300–1200 m points is H = 0.4; note that theassumption of self-affine topography holds to much greater length scales in this region. To extrapolaterelief to 100 m scales, the best-fit line to the 300–1200 m values is extended to smaller scales. Rightpanel: RMS slopes calculated from the deviogram in the left panel using equation (4) in the text. The self-affine extrapolation to hectometer step size suggests an RMS slope at the 100 m of a little less than2 degrees.


Table

5a.MOLA

StatisticsforMeridiani,Melas,andAthabasca

a

Location

MOC

BotLat

TopLat

MOLA

Relief,m

Slope,

�Roughness,m

Reflectivity,

%MOC

Dropouts

Flip

Comment

Min

Avg.

S.D.

Max

Min

Avg

S.D.Max

Min

Avg

S.D.Max

Min

Avg

S.D.Max

Hem

atite

E0101056

�2.25

�2.25

18695

�1566

�1551

9�1536

00

0.2

0.6

11

0.1

1.4

––

––

yes

no

Flat

E0200373

�2.03

�2.03

18896

�1430

�1420

6�1413

00

0.4

1.5

01

0.2

1.1

10

11

114

no

no

Flat

E0200970

�2.1

�2.1

18984

�1446

�1434

10

�1416

00

0.1

0.4

11

0.1

1.1

16

16

0.6

17

yes

no

Flat

E0300329

�2.25

�2.25

19273

�1561

�1548

5�1540

00

0.2

0.8

11

0.1

1.1

13

15

0.8

16

no

no

Flat

E0301763

�2.2

�2.2

19474

�1480

�1459

10

�1440

00

0.6

30

10.2

1.4

12

14

0.9

16

yes

no

CrateronN.edgeofellipse

E0401682

�2.25

�2.25

19851

�1607

�1577

8�1567

01

1.1

40

62.6

118

10

1.2

14

yes

yes

Flat

E0401873

�2.2

�2.2

19876

�1446

�1401

10

�1391

01

0.9

4.2

11

0.2

1.6

810

0.8

12

no

no

CrateronS.edgeofellipse

E0502642

�2.1

�2.1

20278

�1400

�1386

7�1375

00

0.2

0.7

01

0.2

1.4

911

113

no

no

Flat

M0001660

�2.01

�2.01

10408

�1502

�1499

1�1496

00

0.1

0.3

11

0.1

1.5

––

––

no

no

Flat(2

mdepressionin

600m

region)

M0301632

�2.25

�2.25

11502

�1466

�1453

8�1436

00

0.1

0.7

11

0.2

1.6

––

––

no

yes

FlatonN.endin

ellipse

M0802647

�1.99

�1.99

12659

�1419

�1415

3�1410

00

0.3

0.8

01

0.2

1.1

45

0.3

5no

no

Flat

M0808066

�2.4

�2.4

12898

�1532

�1516

8�1501

00

0.4

2.2

01

0.3

1.8

34

0.4

5no

yes

Smallcrater

M0901839

�2.17

�2.17

12986

�1408

�1398

5�1387

00

0.2

10

10.2

1.1

33

0.4

4no

no

Flat

�1607

�1466

6.9

�1375

00

0.4

4.2

01

0.4

113

9.9

0.7

17

Melas

E0100027

�8.9

�8.9

18509

�3368

�3202

89

�3124

05

4.7

15

13

1.9

5.8

69

1.5

11yes

no

Landslidedeposit

E0200270

�8.96

�8.96

18886

�4136

�4050

76

�3838

02

1.4

7.5

11

0.5

2.8

811

1.4

15

yes

yes

SwaleonS.endofim

age

E0202458

�8.98

�8.98

19175

�3887

�3709

115

�3173

04

5.6

24

12

1.4

65

81.7

12

no

no

ClimbsRim

,can’tseelocaldetail

E0301135

�8.92

�8.92

19376

�3830

�3645

155

�3386

02

1.7

8.6

03

321

79

1.2

13

yes

no

Dunecovered

hillonN.endofim

age,

Scram

bledeggonS.

E0401123

�8.75

�8.75

19778

�3146

�2979

135

�2723

03

1.7

7.1

12

1.3

6.1

912

1.9

16

no

yes

Dunefilled

valleyover

width

of

theellipse

E0500744

�8.95

�8.95

20067

�3542

�3361

124

�3119

04

310

13

2.2

9.2

25

17

yes

no

Sandsheet/hills

E0501626

�8.98

�8.98

20180

�4171

�4084

76

�3870

02

1.6

6.6

15

2.4

13

46

0.9

7no

no

Sam

eas

E0200270

E0502484

�8.98

�8.98

20268

�3749

�3601

81

�3370

03

2.2

8.6

13

2.1

10

26

1.2

9no

no

Sandsheetandlandslidedeposit

M0202556

�8.69

�8.69

11253

�4033

�4023

11

�4007

01

0.7

1.9

01

0.5

1.6

67

0.4

7no

no

Slopewithsandsheetover

ellipse

M0400361

�8.7

�8.7

11907

�3771

�3672

62

�3584

02

1.4

4.8

02

1.3

6.3

78

0.6

9no

no

SlopewithScram

bledeggterrain

withouttopography

M0804367

�8.87

�8.87

12737

�3285

�3241

22

�3184

01

1.3

8.1

12

1.9

8.6

45

1.2

9no

yes

Hillsin

scrambledegg

M0903513

�8.96

�8.96

13064

�4061

�4031

31

�3965

01

0.8

2.6

11

0.3

1.7

12

0.3

2no

no

scrambledegg

M1900264

�8.9

�8.9

16686

�3413

�3368

30

�3317

02

1.3

4.5

13

1.9

6.2

15

17

118

no

no

scrambledegg

M2100404

�8.9

�8.9

17453

�3746

�3568

136

�3316

02

1.8

9.7

02

1.6

9.4

15

20

1.8

23

no

no

Hillsin

scrambledegg

M2301183

�8.94

�8.94

18333

�3973

�3776

149

�3502

02

1.6

7.6

12

213

811

1.4

14

no

no

Hillsin

scrambledegg

M2301631

�8.88

�8.88

18421

�4038

�3899

88

�3756

02

1.5

6.4

01

0.7

3.4

79

1.1

11yes

yes

Hillandsandsheetover

10km

�4171

�3621

86

�2723

02

2.1

24

02

1.6

21

19.1

1.2

23

Athabasca

E0402119

8.92

8.92

19908

�2615

�2612

1�2611

00

0.5

1.1

11

0.1

1.4

––

––

no

no

Slightstep

insm

ooth

terrain

E0503124

8.65

8.65

20310

�2599

�2588

7�2578

00

0.1

0.4

11

0.1

1.2

910

0.6

12

no

no

Streamlined

islandsorknobs

M0200581

8.65

8.65

11119

�2641

�2569

35

�2511

01

1.3

7.5

12

0.6

6.3

––

––

no

no

35m

step

inS

M1100331

8.65

8.65

13672

�2653

�2615

48

�2525

01

14.2

12

17.4

––

––

yes

no

Streamlined

island

M1801080

8.9

8.9

16464

�2547

�2525

13

�2505

01

0.5

1.6

12

0.4

2.3

––

––

yes

no

Hill

�2653

�2582

21

�2505

01

0.7

7.5

11

0.4

7.4

910

0.6

12

aNote:Thevalues

below

theverticalbar

foreach

site

under

relief,slope,roughness,andreflectivitycolumnsaretheminim

um

ofMin,theaverageofAvg.andthestandarddeviation(S.D.),andthemaxim

um

of

Max.


acquired MOC and MOLA measurements. These results arebest used to locally illustrate how topography, slope, SCPW,and reflectivity are related to individual features observed inMOC data such as craters, scarps, and flow features, andstrengthen our understanding of the MOLA slopes at eachlanding site that a rover may encounter. Due to the largenumber of MOC images for the landing sites, we focus ourresults on the selected sites, Meridiani and Gusev, thoughwe briefly discuss the other sites as well.

4.1. Coregistering MOC to MOLA

[31] Narrow angle MOC data used for this project weredownloaded from the PDS and the Malin Space ScienceSystems (MSSS) website, and consisted of raw IMQ imagesand the cumindex.tab table of image orientation, shapeparameters, and timing. Images were acquired for thelanding sites during the nominal mission (M01–M23) andduring a special imaging campaign during the extendedmission (E01–E18), however, as this analysis comparessimultaneous MOC and MOLA data, only images throughMOLA failure during E09 are used. The images are ofvariable length and width, may be summed in both x and ydirections, and have variable pixel aspect ratios, all of whichwere corrected using the data in the cumindex.tab. Due todata dropouts (commonly occurring in blocks of 128 pixels)the images are occasionally shorter in length than com-manded by the MSSS team, so the length of the image mustbe compared with the cumindex.tab, or the image rectifica-tion process that compensates for length, summing, andaspect ratio may incorrectly warp the image.[32] MOLA and MOC data are, in theory, easily aligned

using the latitude and longitude information containedwithin their respective data headers. Unfortunately, MOCand MOLA used different references for the shape of Mars,making such a comparison more difficult. We have devel-oped software that allows the MOC and MOLA data to bealigned in latitude using spacecraft event times recorded inthe cumindex.tab for the predicted start time and duration ofMOC images, that can then be converted to the J2000 timerecorded in the MOLA PEDR data, allowing us to collocatethe data. While occasional errors from differences betweenthe commanded and actual start times, as well as occasionalMOLA time-tag errors [Neumann et al., 2001], can influ-ence the data, the resulting comparison is relatively robust.The longitudinal position of MOLA data within a MOCimage has been constrained empirically to be a verticalcolumn near pixel 1674 by matching topographic featuresvisible in hundreds of individual MOC images. Note thatindividual MOLA shots are offset from the actual MOCscan line by 400 m [Kirk et al., 2001], because the twoinstruments have different pitch orientations. Using theserelationships, aligned images of MOC and MOLA data maybe plotted side by side.[33] Using this technique, we plotted MOC images in

alignment with MOLA topography, slope, SCPW, andreflectivity, the sum of which we refer to here as MOC-MOLA images. A small circle indicates the surface illumi-nation on the MOC image; as the exact size and shape of theilluminated surface is not well constrained [Neumann et al.,2003], we show the upper limit of spot size of 180 m.Dropouts in the MOC data appear as black boxes or imagediscontinuities. If a dropout of unknown size occurs in theT

able

5b.MOLA

StatisticsforGusevandIsidisa

Location

MOC

BotLat

TopLat

MOLA

Relief,m

Slope,

�Roughness,m

Reflectivity,

%MOC

Dropouts

Flip

Comment

Min

Avg

S.D.

Max

Min

Avg

S.D.Max

Min

Avg

S.D.Max

Min

Avg

S.D.Max

Gusev

E0200665

�14.8

�14.8

18940

�1822

�1800

15

�1776

02

1.1

4.4

23.4

1.7

8.5

––

––

yes

no

Flat-somesm

allcratering

E0201453

�14.8

�14.8

19053

�1983

�1910

69

�1749

01

2.3

113

11

3.8

24

––

––

no

yes

Slopingcratered

surface

E0300012

�15

�15

19229

�1932

�1906

20

�1834

01

1.4

6.9

11.9

0.7

6.1

––

––

no

no

Hill

E0301511

�14.7

�14.7

19430

�1938

�1895

49

�1730

01

27.3

11.8

1.5

11–

––

–no

yes

Flat

E0503287

�15

�15

20322

�1918

�1875

18

�1819

01

1.6

8.9

01.4

15.3

10

13

115

no

no

Hillsin

centerofellipse

-Track

notin

image

M0301042

�15.2

�15.2

11458

�2111

�1864

43

�1805

02

4.4

25

22.4

1.6

14

99

09

no

no

Craterin

centerofellipse

M0302330

�14.6

�14.6

11546

�1798

�1696

68

�1600

05

311

36

3.4

12

––

––

no

no

Craterinsidelarger

crater

rim

M0700813

�14.9

�14.9

12200

�1950

�1918

9�1898

00

0.8

4.9

22.5

0.5

5.3

––

––

no

no

Crater,2xhills

M0801958

�14.8

�14.8

12615

�1930

�1845

79

�1668

02

2.6

111

3.1

211

––

––

no

no

Interiorofcrater

M1000855

�14.8

�14.8

13357

�1891

�1798

56

�1679

02

2.4

9.6

12.6

1.9

8.9

58

2.2

11

no

no

Interiorofcrater

�1927

�1851

43

�1756

02

2.2

10

23.6

1.8

118

10

1.1

12

Isidis

E0200049

4.08

4.08

18855

�3790

�3762

19

�3721

00

0.4

21

1.1

0.8

4.5

15

17

0.5

18

yes

no

Crateredterrain

E0200681

4.21

4.21

18943

�3778

�3763

5�3757

00

0.2

0.6

11.2

0.4

3–

––

–no

no

Crateredterrain

E0202211

4.22

4.22

19144

�3806

�3788

10

�3773

00

0.1

0.5

11.2

0.4

2.1

12

14

117

no

no

Slopingcratered

terrain

E0300958

4.13

4.13

19345

�3734

�3715

15

�3689

00

0.3

1.5

11.1

0.3

2.3

79

0.6

10

no

no

Crateredterrain

E0301529

4.14

4.14

19433

�3770

�3764

2�3757

00

0.2

0.8

11

0.4

3–

––

–no

no

Crateredterrain

E0401562

4.19

4.19

19835

�3793

�3779

6�3767

00

0.2

0.9

11

0.3

2.2

16

17

0.4

17

no

no

Hillocksandcraters

E0500486

4.08

4.08

20036

�3782

�3757

14

�3734

00

0.2

0.9

11

0.4

3.5

14

16

0.8

17

no

no

Crateredterrain

E0502100

4.16

4.16

20237

�3787

�3782

4�3766

00

0.4

21

1.2

0.6

4.2

810

0.7

11

no

no

Crateredterrain

M1001982

4.08

4.08

13448

�3790

�3767

13

�3745

00

0.2

10

1.2

0.9

6.5

78

0.5

9yes

no

�3781

�3764

9.8

�3745

00

0.2

1.1

11.1

0.5

3.5

11.3

13

0.6

14

aNote:Thevalues

belowtheverticalbarforeach

siteunderrelief,slope,roughness,andreflectivitycolumnsaretheminim

um

ofMin,theaverageofAvg.andthestandarddeviation(S.D.),andthemaxim

umofMax.


middle of a MOC image, it can lead to minor or majormisalignments between the data sets, as it is impossible toconstrain the position of the MOC data following thedropout. These problems can occur anywhere in the MOCimage, including areas not shown in the landing ellipseMOC subsections illustrated here; thus, even if there are novisible dropouts in the image shown here, a dropout to thenorth or south in the image may cause misalignment. In theevent of misalignment, one must judge from the observedfeatures in the MOC image and the MOLA topographywhether the misalignment is minor or major.[34] The exact MOLA starting and ending latitudes are

shown in Tables 5a and 5b, in addition to statistical obser-vations of the MOLA topography, slope, SCPW, and reflec-tivity, and the simultaneously acquired MOC image number.

4.2. Shot to Shot Slope and Reflectivity

[35] For the comparison of the MOC images to MOLAdata, we are interested in understanding the relationshipbetween geomorphology and topography; hence we use theindividual MOLA shots taken along the track of the MOCimage to calculate topography, slope, SCPW, and reflectiv-ity. Topography for each MOLA shot was calculated asdescribed in section 2. Individual slopes are calculated at a300-m scale at every MOLA shot location using a centered3-point Lagrangian interpolation along track. SCPW wascalculated as described in Section 3.2.1.[36] The amount of laser energy reflected from the

surface can be used to determine the reflectivity of thesurface, which is related to surface albedo and atmosphericopacity through Beers law [Ivanov and Muhleman, 2001].In any given MOC image, atmospheric opacity is generallyrelatively constant, allowing us to constrain relative albedodifferences, and provides an additional constraint on theobserved variations in contrast shown in the MOC imagedata. Significant variance in albedo is caused by changes insurface material properties, some of which are correlative,including but not limited to dust coverage, grain size, andcomposition. Because the opacity in a given MOC image isgenerally constant, the MOLA reflectivity is a proxy foralbedo, and can be used to estimate the variance of surfaceproperties. A high variability within a given MOC image isdesirable, because it suggests the potential for changes inmaterial size, thermal properties, or composition that mightbe sampled by a rover. However, a high reflectivity withlittle variance is undesirable, as it likely indicates significantdust cover. It should be noted that orbit-to-orbit, MOLAreflectivity is thought to be accurate to �20%. Within anorbit for a monotonic MOC surface, reflectivity appears tovary by up to �2%, hence changes in reflectivities that arenot obviously correlated with topography smaller than 2%are assumed to be noise. Furthermore, MOLA reflectivity iscalculated from the received pulse energy, which is signif-icantly more sensitive to detector saturation than pulsewidth, causing many of the measurements to be saturated.In our analysis, we only show unsaturated data (rawreceived energy <255 in the PEDR data).

4.3. Results: Comparison of MOLA and MOC

[37] Each MOC image that crossed either of the landingellipses for each landing site was used to generate a set ofMOC-MOLA images; only the part of the MOC image in

the ellipse is shown. Sample MOC-MOLA images forMeridiani and Gusev are shown from west to east throughthe landing ellipse (Figures 24 and 25). Each MOC andMOLA pair contains a contrast enhanced MOC image withMOC coordinate frame latitude and longitude data, and asuperposed MOLA track shown as a line with small circlesillustrating each MOLA shot. Adjacent to the MOC imageare three or four graphs showing topography, 300 m lengthscale slopes, SCPW, and reflectivity; if all reflectivity dataare saturated, only three graphs are shown. The minimum,average, standard deviation, and maximum for each of theseparameters is recorded in Tables 5a and 5b for each MOCimage in the ellipse, as well as the MOC image number, theMOLA track, the minimum and maximum latitudes of theellipse, whether there are data dropouts in the MOC image,and a comment on the general appearance of the areaimaged.4.3.1. Selected Landing Sites[38] The MOC-MOLA images of the Meridiani region

(a sub-sample of all of the MOC images produced for theanalysis are shown in Figure 24) indicate that these areas areextremely flat, with slopes averaging 0.3� ± 0.4�, where thelargest 300 m length scale slopes of �2� (30 m of relief over3–4 MOLA shots) are associated with highly eroded cratersor gently rolling hills in MOC images E0401873 andE0502642, respectively. Similarly, the SCPW values arethe lowest measurable by the MOLA throughout the region,except in image E0401873. The region has a wide range ofreflectivity values, though they average 9.9 ± 0.7%; eachMOC frame tends to have a relatively constant reflectivityvalue, and moderate variance (Table 5a). In general, theMOC-MOLA images show smooth plains interspersed withhighly degraded and eroded craters, which have littletopography or SCPW, e.g., MOC images M0808066,E0301763, and E0401873. While there is little overallcorrelation between reflectivity and the MOC images, asthe reflectivity is mostly constant, there is a high correlationof reflectivity lows associated with dark floors of thedegraded crater features, e.g., MOC image E0401873.[39] MOC image E0401873 (Figure 24 left) is the same

area used in stereogrammetry by Kirk et al. [this issue] forwhich the two terrain types (background plains and subduedcrater) used in the landing simulations within the Meridianiellipse are located [Golombek et al., 2003]. The backgroundplains have extremely low slopes in the MOC stereoanalysis (1–2�) and is also extremely flat (with low relief)at the inter-shot scale of 300 m with slopes �1�. Notsurprisingly, this is the smoothest, flattest (and safest)surface investigated at any of the potential landing sites[cf. Golombek et al., 2003]. The subdued crater at thebottom of this image shows greater relief (>50 m) andgreater slopes (>2�), which is also consistent with the MOCstereogrammetry at 10 m scale. Our measures of RMS slopeat 1.2 km and 100 m scale are also consistent with the RMSslope versus baseline curves reported for Meridiani fromMOC stereogrammetry by Kirk et al. [2003].[40] The MOC-MOLA images of Gusev (a sub-sample of

the Gusev images are shown in Figure 25) indicate rela-tively large mean topographic relief (43 m) and slope (1.7�),and a mean SCPW of 3.6 m, as well significant variation inreflectivity (standard deviation 0.7%; Table 5b). The highesttopography, slopes, and SCPW are associated with the walls


Figure 24. Subset of MOC images with MOLA data for Meridiani: E0401873, E0502642, andM0802647.


of both small craters (M0301042; M0700813) and largerdegraded craters (M0302330; E0201453; E0301511) withinGusev crater. The region is divided into two terrains, onethat is knobby or etched, with an average 3-m SCPW, and

one that is undifferentiated plains with numerous smallcraters, with 1–2 m SCPW (e.g., E0201453). Little reflec-tivity data are available for the MOC images in this regionas most tracks are energy saturated.

Figure 25. Subset of MOC images with MOLA data for Gusev: M0301042, E0503287, and E0300012.Note that the MOLA track lies just outside of image for E0503287.


[41] Inter-shot MOLA relief across the etched terrain inthe center and right panel of Figure 25 is consistent withrelief measured in MOC stereogrammetric digital elevationmodels for this terrain reported in Kirk et al. [2003]. Theetched terrain has high relief (>100 m) and high slopes at all6 m, 100 m, and 300 m length scales. Landing simulationsin this terrain shows the highest percentage of ‘‘out ofspecification’’ events of any of the terrains investigated atthe potential landing sites [Golombek et al., 2003]. Crateredplains at Gusev have much lower relief and slopes at theMOLA inter-shot scale, again consistent with MOC stereo-grammetric results reported by Kirk et al. [2003], and arecomparable to cratered plains investigated at other landingsites [Golombek et al., 2003]. Finally, our measures of RMSslope at 1.2 km and 100 m scale are also consistent with theRMS slope versus baseline curves from stereogrammetryreported for the cratered terrain by Kirk et al. [2003].4.3.2. Other or Unselected Landing Sites[42] The MOC-MOLA images of the Isidis landing site

generally show moderate topography (average 10 m), smallslopes (average 0.3�), and low SCPW (1.1 m) associatedwith gently sloping cratered plains within the Isidis landingellipse (Table 5b). These cratered surfaces are relativelyconstant in reflectivity, with little contrast along individualMOLA tracks. Small, fresh-looking craters are associatedwith some of the larger SCPW values (E0401562), but ingeneral, the portions of the MOLA tracks within the landingellipse for these MOC images are undistinguished in topog-raphy, slope, or SCPW. As with Gusev crater, there are fewreflectivity data points as the MOLA data generally isenergy saturated for these tracks; however, the limited dataavailable exhibits low variance consistent with little diver-sity in material properties.[43] The MOC-MOLA images of the Melas landing site

show the largest range of topographic variation (averagestandard deviation is 86 m), as well as large average slopes(2.4�, with a range up to 24�), and SCPW (2.4 m, rangingup to 20 m; Table 5a). Not surprisingly, the roughestsurfaces (7–10 m) are associated with the landslide depositsto the west and north of the ellipse, e.g., E0100027. Ingeneral, sand sheets are darker (by �3% in reflectivity) andsmoother (SCPW of 2 m versus 5–6 m) than surroundingblocky deposits (e.g., M0804367) and layered units(E0202458). This landing site was ultimately eliminateddue to concerns, in part generated by this analysis, regardinghigh slopes, SCPW, and topography, as well as the potentialfor large canyon wall-driven winds.[44] The MOC-MOLA images of the Athabasca site

typically are gently varying, with the largest variance intopography (standard deviation along track within theellipse of 35–48 m) occurring near the one of the mainfluvial channels, shown in MOC images M0200581 andM1100331. These effects are clearly associated with chan-nels cut into the surrounding rocks seen in the MOCimages. Overall, however, the slopes remain low, with anaverage slope of 0.7�, and a maximum of 7.5�, across theMOC images sampled here (Table 5a). Similarly, the SCPWvalues are just above our ability to discriminate them at anaverage value of 1.5 m, with a standard deviation of 0.4 m.Not surprisingly, the largest slopes and SCPW values arealso associated with the channels observed in M0200581and M1100331. For M0200581 peak SCPW is associated

with what appear to be near-vertical walls on the sides of thechannel �100–150 m in height whose slope is under-resolved due to the shot spacing of MOLA. Interestingly,SCPW increases in the tail of the streamlined island shownin M1100331, which may be a result of turbulent fluvial-depositional processes. Reflectivity is saturated for allimages except E0503124, which demonstrates no reflectiv-ity variance above the typical noise level for reflectivity.

5. Conclusions

[45] We have used MOLA data in order to verify that thelanding sites selected for the MER met the topography andslope requirements of the landing system, and in conjunctionwith MOC imaging, characterized the topography, slope,slope corrected pulse width, and reflectivity of geomorpho-logic features observed in the landing ellipse. It was possibleto use the MOLA data to address slope requirements at100 m and 1.2 km length scales, using slope measurements,self-affine statistics, and pulse width measurements. For1.2 km slopes, both the regional gradient, calculated usingan adirectional slope method, and along-track slopes, calcu-lated using a bidirectional slope technique, were measured.The self-affine statistical approach was used to predict theslopes for 100 m length scales, and was consistent with theobserved pulse width, suggesting that the processes actingon the landing sites are indeed self-similar at these scales.The pulse width and slope-corrected pulse width clearlyindicate hazards such as crater ejecta, and are useful indica-tors of surface properties at 100 m scales.[46] The 1.2 km adirectional, bidirectional, and 100 m

predicted slope results indicate that the landing sites are safeper the engineering criteria for slope, and that they meet thetopography requirement of being at an elevation less than�1.3 km. The pulse width analysis indicates that thesurfaces within the ellipse are relatively flat, consistent withthe requirements of the MER landing subsystem. We areconfident that the slope analyses, in conjunction with theself-affine slope prediction and the pulse width calculation,characterize the morphology of the landing site surfaces,and interpret the results as consistent with the capabilities ofthe MER landing system.[47] Lastly, the comparison of MOC and MOLA illustrate

the magnitude of local topography, slopes, slope correctedpulse width, and reflectivity that are caused by local featuressuch as craters and hills, and indicate that these features aredo not exceed the 100 m or 1.2 km slope requirements,albeit at 300 m scales measured by MOLA. For example,the nearly ubiquitous plains in Meridiani typically haveslopes of 0.3�, while the etched terrains of Gusev haveaverage slopes of less than 1.7�.

Appendix A: Smooth Region Slope Statistics

[48] For an elevation difference �z between two pointson a MOLA profile separated by interval �x, the slope inradians or degrees is:

a �xð Þ ¼ tan�1 �z=�xð Þ ðA1Þ

however, in the cases we consider for �x = 1.2 km, wherea < 2�, the tangent is essentially equal to the angle. The


assumption holds because we are looking for smooth flatplaces to land the MER spacecraft. Thus we approximate:

a �xð Þ � �z=�x ðA2Þ

It then follows that the mean slope is

a �xð Þh i � �xh i=�x: ðA3Þ

The standard deviation from this mean is

sa ai �xð Þ2D E

� a �xð Þh i2h i1=2

; ðA4Þ

so

sa � �z2i�

� �zh i2h i1=2

=�x: ðA5Þ

What we call the root mean square (RMS) slope is slightlydifferent, and is the sample standard deviation from themean slope, which is the square root of the sample varianceof the set of N values of ai(�x):

RMSa ¼ ai �xð Þ � a �xð Þh i½ 2D Eh i1=2

ðA6Þ

so

RMSa � �zi � �zh i½ 2D Eh i1=2

=�x: ðA7Þ

Therefore our RMS slope is related to the RMS height forsmall slopes, while the standard deviation from the meanslope, while displaying similar trends is a less tractableslope statistic [see, e.g., Shepard et al., 1995; Turcotte,1997].

[49] Acknowledgments. The work described in this paper was per-formed at the Jet Propulsion Laboratory, a division of the CaliforniaInstitute of Technology, under contract to NASA, and at the Universityof Hawaii. The work was supported by the NASA Mars Data AnalysisProgram and the MER project. The authors thank Jim Garvin for providingdigital copies of his pulse spread data set as well as the entire MOLAscience team and Oded Ahraronson for spirited discussions about how touse the MOLA data to address the MER elevation and slope landing sitesafety criteria. Finally, we thank Anton Ivanov who provided a MOLAdatabase that eased rapid manipulation of the data, and Megan Kennedy,who worked on the initial analysis effort.

ReferencesAbshire, J. B., X. Sun, and R. S. Afzal, Mars Orbiter Laser Altimeter:Receiver model and performance analysis, Appl. Opt., 39, 2440–2460,2000.

Afzal, R. S., Mars Observer Laser Altimeter: Laser transmitter, Appl. Opt.,33, 3184–3188, 1994.

Campbell, B. A., R. R. Ghent, and M. Shepard, Limits on inference of Marssmall-scale topography from MOLA data, Geophys. Res. Lett., 30(3),1115, doi:10.1029/2002GL016550, 2003.

Crisp, J. A., M. Adler, J. R. Matijevic, S. W. Squyres, R. E. Arvidson,and D. M. Kass, Mars Exploration Rover mission, J. Geophys. Res.,108(E12), 8061, doi:10.1029/2002JE002038, 2003.

Duxbury, T. C., R. L. Kirk, B. A. Archinal, and G. A. Neumann, MarsGeodesy/Cartography Working Group recommendations on Mars carto-graphic constants and coordinate systems, in Geospatial Theory: Proces-sing and Applications [CD-ROM], Int. Arch. Photogramm. Remote Sens.,XXXIV(4), article 521, 2002.

Gardner, C. S., Ranging performance of satellite laser altimeters, IEEETrans. Geosci. Remote Sens., 30, 1061–1072, 1992.

Garvin, J. B., J. J. Frawley, and J. B. Abshire, Vertical roughness of Marsfrom Mars Orbiter Laser Altimeter, Geophys. Res. Lett., 26, 381–384,1999.

Golombek, M. P., R. A. Cook, H. J. Moore, and T. J. Parker, Selection of theMars Pathfinder landing site, J. Geophys. Res., 102, 3967–3988, 1997.

Golombek, M. P., et al., Selection of the Mars Exploration Rover landingsites, J. Geophys. Res., 108(E12), 8072, doi:10.1029/2003JE002074, inpress, 2003.

Haldemann, A. F., and F. S. Anderson, Mars Exploration Rover landing sitehectometer slopes, Eos Trans. AGU, 83(47), Fall Meet. Suppl., AbstractP22-A-0390, 2002.

Hurst, H. E., R. P. Black, and Y. M. Simaiki, Long-Term Storage: AnExperimental Study, Constable, London, 1965.

Ivanov, A. B., and D. O. Muhleman, Reflected signal analysis and surfacealbedo in the Mars Orbiter Laser Altimeter (MOLA) investigation, LunarPlanet. Sci., XXXII, 1917, 2001.

Kirk, R. L., E. Howington-Kraus, and B. Archinal, High resolution digitalelevation models of Mars from MOC narrow angle stereoimages, paperpresented at ISPRS-ET Working Group IV/9 Workshop ‘‘Planetary Map-ping 2001,’’Int. Soc. for Photogramm. and Remote Sens., Houston,Tex., 2001. (Available at http://astrogeology.usgs.gov/Projects/ISPRS/MEETINGS/Flagstaff2001/abstracts/isprs_etm_OCT01_kirk_mars_moc_stereo.pdf)

Kirk, R., E. Howington-Kraus, B. Redding, D. Galuszka, T. M. Hare,B. Archinal, L. A. Soderblom, and J. Barrett, High-resolution topo-mapping of candidate MER landing sites with Mars Orbiter Cameranarrow-angle images, J. Geophys. Res., 108(E12), 8088, doi:10.1029/2003JE002131, in press, 2003.

Neumann, G. A., D. D. Rowlands, F. G. Lemoine, D. E. Smith, and M. T.Zuber, The crossover analysis of MOLA altimetric data, J. Geophys. Res.,106, 23,753–23,768, 2001.

Neumann, G., J. Abshire, O. Aharonson, J. Garvin, X. Sun, and M. Zuber,Mars Orbiter Laser Altimeter pulse width measurements and footprint-scale roughness, Geophys. Res. Lett., 30(11), 1561, doi:10.1029/2003GL017048, 2003.

Seidelmann, P. K., et al., Report of the IAU/IAG Working Group on Carto-graphic Coordinates and Rotational Elements of the Planets, and Satel-lites: 2000, Celest. Mech. Dyn. Astron., 82, 83–110, 2002.

Shepard, M. K., and B. A. Campbell, Radar scattering from a self-affinefractal surface: Near-nadir regime, Icarus, 141, 156–171, 1999.

Shepard, M. K., R. A. Brackett, and R. E. Arvidson, Self-affine (fractal)topography: Surface parametrization and radar scattering, J. Geophys.Res., 100, 11,709–11,718, 1995.

Shepard, M. K., B. A. Campbell, M. H. Bulmer, T. G. Farr, L. R. Gaddis,and J. J. Plaut, The roughness of natural terrain: A planetary and remotesensing perspective, J. Geophys. Res., 106, 32,777–32,796, 2001.

Smith, D. E., G. A. Neumann, P. G. Ford, R. E. Arvidson, E. A. Guinness,and S. Slavney, Mars Global Surveyor Laser Altimeter Precision Experi-ment Data Record, NASA Planet. Data Syst., Greenbelt, Md., 1999.

Smith, D. E., et al., Mars Orbiter Laser Altimeter (MOLA): Experimentsummary after the first year of global mapping of Mars, J. Geophys. Res.,106, 23,689–23,722, 2001.

Smith, W. H. F., and P. Wessel, Gridding with continuous curvature splinesin tension, Geophysics, 55(3), 293–305, 1990.

Turcotte, D. L., Fractals and Chaos in Geology and Geophysics, Cam-bridge Univ. Press, New York, 1997.

U.S. Geological Survey (compiler), Mission to Mars: Digital Image MapsV2.0, PDS Volumes USA_NASA_PDS_ VO_2001 V2 Through VO_2006V2 [CD-ROM], 2001.

Wessel, P., and W. H. F. Smith, Free software helps map and display data,Eos Trans. AGU, 72(41), 441, 445–446, 1991.

Wessel, P., and W. H. F. Smith, New version of the Generic Mapping Toolsreleased, Eos Trans. AGU, 76(33), 329, 1995.

Wessel, P., and W. H. F. Smith, New, improved version of the GenericMapping Tools released, Eos Trans. AGU, 79(47), 579, 1998.

Zuber, M. T., D. E. Smith, S. C. Solomon, D. O. Muhleman, J. W. Head,J. B. Garvin, J. B. Abshire, and J. L. Bufton, The Mars Observer LaserAltimeter investigation, J. Geophys. Res., 97, 7781–7797, 1992.

��F. S. Anderson, Hawaii Institute of Geophysics and Planetology,

University of Hawaii at Manoa, 1680 East-West Road, Honolulu, HI96822, USA. ([email protected])N. T. Bridges, M. P. Golombek, A. F. C. Haldemann, and T. J. Parker, Jet

Propulsion Laboratory, 4800 Oak Grove Drive, Mail Stop 183-501,Pasadena, CA 91109, USA.G. Neumann, Department of Earth, Atmospheric, and Planetary Sciences,

Massachusetts Institute of Technology, Cambridge, MA 02139, USA.


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