Analysis of MOLA data for the Mars Exploration Rover landing sites

Authors


Abstract

[1] We have used Mars Orbiter Laser Altimeter (MOLA) data to demonstrate that selected landing sites meet the Mars Exploration Rover (MER) landing system topography and slope requirements at hectometer and kilometer scales. To provide a comprehensive analysis, we constrained slopes within each landing ellipse using four approaches: (1) measurements of local slopes at 1.2 km length scales using both an adirectional maximum gradient method and a higher-resolution bidirectional, along-track method, (2) predictions of 100 m slopes using self-affine statistics in conjunction with (3) calculations of both pulse width and slope corrected pulse width to constrain slopes at scales smaller than the MOLA spot size (<180 m), and (4) comparisons of simultaneously acquired MOLA data with Mars Orbiter Camera data to identify the geomorphologic features associated with variations in observed slopes, pulse width, and, for this analysis only, reflectivity. The results of the analysis indicate that the selected landing sites are consistent with the MER topography 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.

1. Introduction

[2] Accurate topographic information is critically important for landing spacecraft on Mars because (1) elevation controls the atmospheric column available for slowing the spacecraft during ballistic entry and parachute descent, (2) slopes at a variety of scales affect radar acquisition of the surface, (3) slopes affect the ability of the spacecraft to land safely, and (4) local slopes and relief can impact rover mobility. For the first time in Mars exploration history, definitive elevation data at kilometer and hectometer scale are 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 of MOLA data to address engineering safety criteria established for the Mars Exploration Rover (MER) that were used during landing site selection [Golombek et al., 2003], as well as demonstrating how MOLA-derived slope, pulse width, 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 parachute to bring the spacecraft to an acceptable terminal velocity for parachute deployment and to provide enough time to jettison the heat shield, lower the lander on the bridle, measure the descent rate with the radar altimeter, inflate the airbags, and fire the solid rockets (see Crisp et al. [2003] for a description of the MER landing). Calculated density columns indicate that the MER spacecraft are capable of landing below −1.3 km with respect to the MOLA defined datum [Golombek et al., 2003].

[4] Surface slopes represent a three-fold hazard for the landing system. First, relatively small, but regular slopes over km-scale distances can add horizontal velocity and prolong bouncing or rolling by the lander within the inflated airbags. Large slopes over hundred-meter length-scales can spoof the radar altimeter, causing premature or late firing of the solid rockets and airbag inflation. Third, meter- to decameter-scale slopes can increase airbag spinup and bounce which can, in turn, induce failure on subsequent bounces by exceeding the stroke of the airbags or increasing the chance of slicing the airbags on sharp rocks. Slopes at this scale also affect the stability of the lander, rover deployment and trafficability, and power generation. Engineering safety criteria developed for these potential failure modes are that surface slopes should generally be less than 15° at 3 m scales, <5° at 100 m scales, and <2° at kilometer scales [Golombek et al., 2003]. Sophisticated landing simulations and sensitivity studies indicate that of these three slope criteria, 3 m slopes have the highest potential impact on landing survivability followed by 100 m slopes and 1 km slopes [Golombek et al., 2003]. In this paper we address only hectometer-scale and kilometer-scale slopes, as they can be assessed with MOLA data. We also discuss MOLA pulse width and derived relief within a MOLA shot, as these are a proxy for 100 m and smaller scale slopes. Three-meter slopes 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 reflectivity of features within MOC images of the landing sites. We present details of the coregistration of MOLA data to MOC imagery, and thereby review and confirm our understanding of how the topographic data relate to morphology in the images. Golombek et al. [2003] and references therein report on detailed geomorphologic analyses of MOC images. Finally, for completeness in our examination of MOLA data, we briefly examine MOLA reflectivity correlations at the MER landing sites.

[6] In summary, this paper describes in detail the topographic data and derived slope information, abstracted and summarized by Golombek et al. [2003], for the selection of landing sites for the Mars Exploration Rovers. We present the analyses carried out for seven high-priority MER landing ellipses, listed in Table 1, which are the 4 prime sites and 2 backup sites retained after the October 2001 MER Second Landing Site Workshop, plus the wind-safe site in Elysium. We also include analyses of the Viking Lander 1 (VL1), Viking Lander 2 (VL2) and Mars Pathfinder (MPF) landing sites as ground truth locations for comparative purposes (Table 1).

Table 1. MER Landing Site Ellipses Coordinate Frame Locations and Sizesa
SiteMDIM 2.0IAU/IAG 1991IAU/IAG 2000Ellipse
Lat, °Long, °Lat, °Long, °Lat, °Long, °NameMajor axis, kmMinor axis, kmAzimuth, °
  • a

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

Meridiani2.07S6.08W2.06S353.77E2.06S354.008ETM20B21191784
Gusev14.82S184.85W14.64S175.06E14.64S175.298EEP55A2961976
Elysium11.91N236.10W11.73N123.72E11.73N123.958EEP78B21551694
Isidis4.31N271.96W4.22N87.91E4.22N88.15EIP84A2 IP96B2132 14016 1688 91
Athabasca8.92N205.21W8.83N154.67E8.83N154.91EEP49B21521695
Melas8.88S77.48W8.75S282.36E8.75S282.60EVM53A2 VM53B2103 10518 2080 82
Eos13.34S41.39W13.20S318.46E13.20S318.70EVM41A981978
VL1  22.27N311.81E22.27N312.02E 20010084
VL2  47.67N134.04E47.67N134.27E 20010084
MPF  19.09N326.51E19.09N326.74E 20010084

2. MOLA Data and Topography

[7] The MOLA measured >600 million laser shots on Mars from which elevation, pulse width and reflectivity data were determined over the entire planet, and archived in the Planetary Data System (PDS). The MOLA data used for the studies reported here were acquired from the PDS using the “L” version of the Precision Experiment Data Record (PEDR) for elevation, pulse width, and reflectivity, and are shown using the planetocentric IAU/IAG 2000 coordinate system [Duxbury et al., 2002; Seidelmann et al., 2002]. Earlier versions of MOLA data, using the IAU/IAG 1991 coordinates for Mars, were used in the early phases of the MER landing site evaluations. All final evaluations were done with IAU2000 MOLA data, and landing site maps presented in this paper are all in that reference frame, even when the landing sites may initially have been mapped in older reference frames during the selection process [e.g., Golombek et al., 2003]. The “L” version of the MOLA PEDR data also provides a crossover correction for the geographic location of MOLA shots, and an updated estimate of the pulse width [Neumann et al., 2003]. We used MOLA data extending from the science phasing orbit (SPO) to the failure of MOLA's ranging mode at orbit 20333. The MOLA data contain the exact altitude, planetary radius, timing, engineering parameters, and areographic position of each MOLA 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 shot along an individual MOLA track, which can occur for reasons such as clouds, data dropouts, noise, etc. For this analysis, the topography, timing, pulse width, and reflectivity parameters were calculated following the MOLA Software Interface Specification [Smith et al., 1999], which describes the units for each data value. Topography is calculated as the difference between the planetary radius and the geoid.

[8] The MOLA data are edited for clouds, noise, and poor geolocation and assembled into the Mission Experiment Gridded Data Record (MEGDR) delivered to the PDS. The final data density allowed grid resolutions as fine as 128 pixels per degree of planetocentric longitude and latitude, although at that resolution less than 50% of pixels are sampled. Multiple shots within a single pixel are averaged, while missing data are interpolated. MOLA data density was limited by the polar geometry and orbital track spacing, leaving occasional gaps of up to 0.2° of longitude near the equator. MOLA vertical accuracy is 1 m over reasonably smooth terrain and position is accurate to 100 m [Neumann et al., 2001]. Gradient-shaded grids reveal subtle variations in slope invisible to imaging instruments, as laser altimetry is virtually unaffected by atmospheric and illumination conditions. Local slope information may be derived from profiles in the along-track direction, and the local topographic gradient from gridded data, recognizing that slope baselines are limited by the 300-m along-track spacing, or in the case of gridded data, by pixel resolution and variable across-track coverage. While gridded MOLA data products are now available, our analyses primarily used individual MOLA shots to maximize resolution over the landing sites. Use of gridded MOLA data, such as the 1/128° resolution topography grid, was limited to elevation data for regional mapping and checking the −1.3 km ellipse elevation constraint. The one exception was the first slope corrected pulse width (SCPW) data set, which was kindly provided in gridded form by the MOLA team [Garvin et al., 1999; Smith et al., 2001; J. Garvin, personal communication, 2000]. This data set provided coverage of the early landing sites between ±15°, but later sites were on the boundary of the provided data. For these locations, we have derived our own estimates of SCPW. The MOLA elevation information for the seven MER and the VL1, VL2 and MPF landing sites is listed in Table 2.

Table 2. MER Ellipse Topography
SiteEllipse CenterEllipse
Geoid, kmMOLA Elevation, kmMOLA Elevation Range, km
Meridiani3395.526−1.440−1.37 to −1.58
Gusev3394.227−1.920−1.80 to −1.93
Elysium3395.239−2.940−2.68 to −3.20
Isidis3396.115−3.740−3.68 to −3.74
Athabasca3395.096−2.640−2.51 to −2.66
Melas3395.758−3.700−2.35 to −4.13
Eos3394.427−3.850−3.2 to −4.03
VL13339.299−3.6 
VL23386.349−4.5 
MPF3393.482−3.7 

3. MOLA Slopes

[9] Slopes are derived from MOLA topographic profile data. Because the calculation of slope statistics over length-scales that are multiples of the 300-m MOLA shot spacing is straightforward, we addressed the km-scale slope requirement with 1.2 km MOLA inter-shot data. The 100-m scale slope requirement is addressed with MOLA pulse width data and also by extrapolating the slope behavior at hectometer-scale down from longer length-scales. An important consideration in making slope measurements from topographic profiles is whether or not the profile has been detrended. Detrending removes long wavelength slopes, i.e., at, or near the scale of the entire profile length considered. Although detrending has little effect on length-scales that are short (<10%) when compared to the entire profile length, we nevertheless chose not to detrend. Our reason for not detrending, despite its recommendation by Shepard et al. [2001], is that, for the purpose of MER landing site evaluation, we are interested in the slopes that the MER landing system will actually encounter. For example the potential radar-spoofing effect at any given location depends on the total slope (or relief) over a 100 m length scale, including any underlying regional slope.

3.1. Kilometer-Scale Slopes

[10] To generate 1.2-km scale slope statistics for the landing sites, we calculated both bidirectional slopes, the component of slope measured along the roughly north-south MOLA orbit track, and adirectional slopes, which are the slopes in maximal downhill direction, i.e., the local gradients.

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 two shot-intervals down-track from the location. A bad shot at either extremity yielded an invalid slope and no slope point was mapped. All the valid slope points were then gridded at 0.3 km resolution, for which multiple points within a grid cell were averaged, using the Generic Mapping Tools (GMT) software [Smith and Wessel, 1990; Wessel and Smith, 1991, 1995, 1998]. This has the effect of averaging the data from parallel tracks with less than 300 m lateral separation, and of averaging the data at track crossover points. The averaging to 0.3 km resolution removes biases to the ellipse statistics that might be introduced if two closely parallel tracks crossed a particularly rough part of the ellipse. For mapping the bidirectional slopes, the slope points were separately averaged at 1.2 km resolution to improve the visual appearance of the maps. Then, statistics were calculated for all 0.3 km pixels falling within the ellipse, and histograms of the resulting slopes plotted (Table 3, Figures 1122).

Table 3. MER 1.2 km Slope Statistics for Each Site
SiteBidirectional SlopesAdirectional Slopes
Mean ± s.d., °RMS, °NMean ± s.d.RMS, °N
Meridiani0.15 ± 0.180.266800.24 ± 0.470.53208
Gusev0.20 ± 0.440.496790.19 ± 0.290.34277
Elysium0.48 ± 0.550.739340.41 ± 0.290.51361
Isidis0.19 ± 0.240.307820.14 ± 0.100.17315
Athabasca0.20 ± 0.360.4113340.20 ± 0.290.35882
Melas1.22 ± 1.351.806981.10 ± 0.661.29307
Eos1.22 ± 1.872.236861.02 ± 1.081.48262
VL10.26 ± 0.96  0.33 ± 0.95  
VL20.28 ± 0.29  0.28 ± 0.21  
MPF0.25 ± 0.66  0.30 ± 0.51  

3.1.2. Adirectional Slope Mapping

[12] Adirectional slopes were calculated using the Generic Mapping Tools (GMT) [Smith and Wessel, 1990; Wessel and Smith, 1991, 1995, 1998], which we used to average all MOLA elevation samples within a 1.2 km grid, and then calculate 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 of all the valid points in the 1.2 km resolution grid within the landing ellipse are listed in Table 3, with definitions of the statistics discussed in Appendix A. The maps resulting from these adirectional slope determinations are sparse relative to the bidirectional slope maps because the spacing of MOLA tracks in the equatorial regions that the landing sites are located is typically greater than the 1.2 km grid, so that adjacent grid points may not contain data.

3.1.3. Results

[13] Adirectional slopes are shown in Figures 1a10a, bidirectional slopes are shown in 1b10b, and histograms of the adirectional and bidirectional slopes within each ellipse are shown in Figures 11a and 11b through 22a and 22b, respectively. The slope maps are generally consistent with the topographic maps from which they are derived with higher slopes indicated in areas of greater relief. Large craters and other high relief features show up as areas of enhanced 1.2 km slopes that exceed 5° in the maps of Meridiani, Gusev, Isidis, Athabasca, Elysium, VL1, VL2 and MPF. The maps of Melas and Eos have slopes on the 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 slope in ellipse placement. For example, in Gusev crater, the ellipse avoids the steeper slopes of the crater Thira at its eastern end and at Meridiani it avoids steeper slopes associated with the crater to the southeast of the ellipse.

Figure 1.

Maps of MOLA topographic and slope information for the Athabasca Valles (EP49B2) MER landing site. (a) 1.2 km scale adirectional slope, (b) 1.2 km scale bidirectional slope, (c) dimensionless Hurst exponent determined over the range 0.3 km to 1.2 km, (d) self-affine extrapolation of 100 m RMS slope, (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 1/128 degree gridded MOLA elevation data.

Figure 2.

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

Figure 3.

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

Figure 4.

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

Figure 5.

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

Figure 6.

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

Figure 7.

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

Figure 8.

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

Figure 9.

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

Figure 10.

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

Figure 11.

Histogram of Athabasca (EP49B2) (a) 1.2 km scale a-directional slope (°), (b) 1.2 km scale bi-directional slope (°), (c) slope corrected pulse width (m).

Figure 12.

Histogram of Elysium (EP78B2). Panel assignments as in Figure 11.

Figure 13.

Histogram of Eos (VM41A). Panel assignments as in Figure 11.

Figure 14.

Histogram of Gusev (EP55A2). Panel assignments as in Figure 11.

Figure 15.

Histogram of Isidis (IP84A2). Panel assignments as in Figure 11.

Figure 16.

Histogram of Isidis (IP96B2). Panel assignments as in Figure 11.

Figure 17.

Histogram of Melas (VM53A2). Panel assignments as in Figure 11.

Figure 18.

Histogram of Melas (VM53B2). Panel assignments as in Figure 11.

Figure 19.

Histogram of Mars Pathfinder (a) 1.2 km scale a-directional slope (°), (b) 1.2 km scale bi-directional slope (°).

Figure 20.

Histogram of Viking Lander 1. Panel assignments as in Figure 19.

Figure 21.

Histogram of Viking Lander 2. Panel assignments as in Figure 19.

Figure 22.

Histogram of Meridiani (TM20B2). Panel assignments as in Figure 11.

[14] The km-scale slopes for all the landing ellipses in Table 3 meet the engineering requirement of <2°, except the Chasmata sites of Melas and Eos which exceed the limit at less than one standard deviation from the means. Meridiani, Gusev, Isidis and Athabasca are smoothest at 1.2 km with mean slopes ∼0.2°, comparable or smoother than the VL1, VL2 and MPF sites. Elysium appears slightly rougher at km-scale with an average slope of ∼0.5°, which is greater than at previous Mars landing sites. The Melas and Eos landing sites are rougher at this scale with average slopes of ∼1.2°, consistent with parts of their ellipses located on the lower sloping parts of the canyon walls; these sites clearly have areas that exceed the engineering requirement of 2°.

[15] We note that both the mean and RMS adirectional slopes are in almost all cases lower than the mean bidirectional slopes, which should not be the case if the adirectional slope is the local gradient. In fact this behavior is an effect of our method of determining the adirectional slope, because by gridding at 1.2 km resolution we are effectively smoothing the elevation data, which then has the effect of reducing the adirectional slopes calculated between adjacent grid points. Adirectional slopes should therefore only be taken as lower bounds for the actual 1.2 km adirectional-scale slopes. Fortunately the km-scale slopes we find are so clearly within the required bounds that some error does not affect the results, especially for the selected Meridiani and Gusev landing sites. This is true even if the adirectional slopes are roughly equation image times [Kirk et al., 2003] the bidirectional slopes.

3.2. Hectometer-Scale Slopes

[16] Two independent approaches were used to assess the MER requirement that landing site slopes over 100 m length-scales to be less than 5°. First, MOLA pulse width data was used to constrain roughness at the MOLA footprint size of 75–150 m [Garvin et al., 1999; Neumann et al., 2003; Smith et al., 2001], which can then be used to infer upper limits for footprint-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 slope statistics. First we discuss the MOLA pulse width data, the calculation of slope corrected pulse width, and the use of the pulse width data for the landing sites. Then we discuss the extrapolation of surface slope using statistical methods and the results of the analysis for the MER landing sites.

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 the laser, which can be used to constrain the roughness or relief of the surface area illuminated by the laser pulse [Abshire et al., 2000; Afzal, 1994; Gardner, 1992; Garvin et al., 1999; Neumann et al., 2003]. The MOLA laser divergence for channel 1 of 93 μrad, determined during pre-flight calibration, indicates that 90% of the pulse energy illuminates and interacts with a region 150–180 m in diameter on the surface of Mars [Neumann et al., 2003; Smith et al., 1999; Zuber et al., 1992]. However, in-flight data reduction by Neumann et al. [2003] indicated that a change in threshold sensitivity settings caused the instrument to observe a smaller illuminated spot on the surface, resulting in a smaller effective divergence as low as 46 μrad for channel 1, implying a 1-σ surface illumination of ∼40-m [Neumann et al., 2003]. Generally, a slope in the illuminated surface area will cause the pulse to broaden, as a portion of the energy is reflected from the higher elevation part of a slope first, while the remainder is slightly delayed until it can reflect from lower elevations. This is true for both a single long wavelength slope, which can be estimated by measuring the elevation difference between MOLA shots, and for short wavelength slopes at rover scales, here referred to as the “slope corrected pulse width” (SCPW). Although the 300 m slope is subtracted out of these measurements, there is no knowledge of the actual slope over the footprint and the pulse spread measure cannot distinguish between a constant slope over 100 m and roughness composed of short wavelength sawtooth relief elements.

[18] It is possible to estimate and remove the effect of long wavelength slope by calculating the pulse broadening from shot to shot slope and subtracting it from the observed pulse width. It is also necessary to subtract the initial pulse width of the laser shot as well as the instrument response, as described by Gardner [1992] for an ergodic surface:

equation image

in which σs is the mean observed pulse delay, σh is the instrument response, σf is the length of the transmitted pulse, c is the speed of light, ϕ is the incidence angle of the laser, Var) is the variance of the surface profile (the SCPW squared), z is the orbital height, and θT is the laser divergence. The PEDR pulse width values have had the instrument response function removed. It can be shown geometrically that the incidence angle and long wavelength slope are expressed mathematically in equivalent form, so for small angles we add them to determine the net incidence angle. In some cases, received pulses saturate the detection system (received raw pulse width counts = 63 or energy counts = 255) because the surface was more reflective or the spacecraft was closer than anticipated; in these cases the pulses 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 an area with regional slopes, may result in small negative surface roughness values. This occurs because the channel design on the MOLA instrument precludes accurate measurement of pulse width below 6.67 ns; we use 6.67 ns, or about 1 m, as a minimum observable value. Second, and as mentioned above, the new estimates for the divergence of the laser should be used [Neumann et al., 2003], or overestimation of pulse broadening from long-wavelength slope may occur (see equation (1)). Our analysis of this effect supports the choice of a smaller divergence (46 μrad for channel 1, 70 μrad for channels 2–4) by Neumann et al. [2003], and is in fact consistent with a slightly smaller value of 37 μrad; the results shown here use the values from Neumann et al. [2003]. Third, because the along track slope does not constrain the local cross track slopes, the estimate of long wavelength slope can be biased; however, there currently is no better estimate possible. Lastly, significant off-nadir viewing geometry can result in excessive pulse spreading.

3.2.2. Mapping Pulse Width

[20] Pulse width estimates that have been corrected for flight divergence values [Neumann et al., 2003] are averaged over a 128 pixel/degree grid and mapped in raw form in Figures 1e10e. These pulse width maps show where the pulse width samples were measured for each ellipse, as a guide for possible biases in sampling over the ellipses. In addition, the occasional track with excessive pulse width values is apparent for some of the landing sites; we deliberately have left these in to illustrate the minimal nature 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 et al., 2001; J. Garvin, personal communication, 2000]. Note that these data, generated early in the MER site selection process, do not incorporate the new estimates of divergence. The statistics of SCPW, as well as pulse width, are presented in Table 4 (and in Table 10 of Golombek et al. [2003]). The maps of SCPW (Figures 1f10f), and those for pulse width, show that all the sites considered are very smooth at MOLA spot-size scales; we generated our own values of SCPW for landing sites beyond the ±15° gridded SCPW band provided by the MOLA team. The SCPW results from these data indicate pulse widths of <2 m, consistent with relief of <10 m [Garvin et al., 1999], which corresponds to the slope requirement of <5° over 100 m baselines. By this measure, the pulse width roughness data in 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.

Table 4. MER Landing Site Hectometer Slope Parameters
SiteSlope Corrected Pulse WidthaPulse WidthbSlope Corrected Pulse WidthbSelf-Affine Extrapolation
Mean ± s.d., mRMSNMean ± s.d.NMean ± s.d., mNHurst ExponentAllan Deviation, mRMS Slope, °
  • a

    J. G. Garvin (personal communication, 2000).

  • b

    Neumann et al. [2003].

  • c

    Self-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.

Meridiani0.75 ± 0.240.811520.8 ± 0.95310.8 ± 0.85440.533.41.9
Gusev1.42 ± 0.441.513401.5 ± 1.31011.1 ± 1.02960.565.83.3
Elysium1.10 ± 0.401.113661.9 ± 2.84781.5 ± 1.758790.644.02.3
Isidis1.10 ± 0.351.211405.1 ± 1.881.8 ± 2.870780.512.61.5
Athabasca1.18 ± 0.351.2 1.9 ± 2.63871.6 ± 2.418670.764.32.5
Melas1.21 ± 0.741.410283.1 ± 2.25543.4 ± 4.1182060.819.95.7
Eos1.06 ± 1.141.610264.7 ± 6.24223.9 ± 6.8165180.7811.56.6
VL1   2.1 ± 3.736401.7 ± 2.95350.53c1.8c1.0c
VL2   1.1 ± 0.49211.1 ± 0.4921   
MPF   2.0 ± 3.627422.0 ± 4.117550.3715.012.91

[22] Newer analyses that include improvements in the estimated laser divergence, as discussed above, and the resulting estimates of the RMS relief with and without longer slopes removed by Neumann et al. [2003], show Meridiani as having the lowest pulse spread (0.8 m) and Melas and Eos the highest (>3 m). The other sites cannot be readily distinguished from the VL1, 2 and MPF landing sites (∼1–2 m). By these data, all of the 4 final landing sites should be acceptable and should be no worse than the 3 locations on Mars (VL1, 2 and MPF) where radar altimeters have worked satisfactorily in successfully landing spacecraft.

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 site analysis, led us to consider another method for the quantitative estimation of hectometric slopes. Processes modifying the surface of Mars likely act over a range of scales, however, it is probably safe to assume that processes acting over 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 can measure relief as a function of scale over MOLA shot intervals of 0.3, 0.6, 0.9, and 1.2 km and use them to predict the relief and RMS slope at 100 m length scales. The correlation and consistency of the results with pulse width and SCPW observations is a test of the assumption that the surface is self-affine.

[24] Shepard et al. [1995, 2001], Shepard and Campbell [1999], and Campbell et al. [2003] summarize the statistical properties of the RMS deviation of topography (noting that it also goes by the name structure function, variogram or Allan deviation, υ). In this study we follow the Shepard et al. [2001] nomenclature:

equation image

where n is the number of samples, z is the altimetry, and Δx is the step size. For a self-affine surface the RMS deviation scales with Δx, the separation between samples along the profile, as

equation image

where H, the Hurst exponent, is a constant over some range of scales [Hurst et al., 1965]. Changes in H at a given scale suggest a change in surface process. To calculate the Hurst exponent, we assemble all the MOLA altimetry tracks in a region and generate a deviogram by plotting υ = υ(Δx) in log-log space, and fit a line to the points at 0.3, 0.6, 0.9, and 1.2 km to find H. An example is shown in Figure 23 for a 0.1 degree sized pixel containing the Mars Pathfinder landing site; for which we calculate and plot υ(Δx) up to Δx = 4.5 km, but we only fit H over 0.3–1.2 km. We then use 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

equation image

and

equation image

The extrapolated 100 m RMS slope at the Mars Pathfinder landing site from Figure 23, around 1.7, agrees favorably with the value of 2 reported by Kirk et al. [this issue; 2001].

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 the assumption of self-affine topography holds to much greater length scales in this region. To extrapolate relief to 100 m scales, the best-fit line to the 300–1200 m values is extended to smaller scales. Right panel: 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 than 2 degrees.

[25] Where our method differs somewhat from the standard deviogram analysis of a topographic profile [e.g., Shepard et al., 2001] is that we assemble the analyses from multiple separate profiles of differing lengths into a single deviogram to characterize the (1-dimensional or bidirectional) roughness of a surface. This approach is directly comparable to a standard analysis because equation (1) does not distinguish whether it is averaging over correlated or uncorrelated deviations; hence the preparation of the deviogram is merely an extension of the bidirectional slope evaluation to multiple length-scales using a larger appropriate area for averaging.

[26] We used this method to map the resulting 100 m slopes in and around the ellipses initially at 0.1° resolution for the landing site selection process [Haldemann and Anderson, 2002]. Shepard et al. [2001] caution that deviogram method should only be applied to length scales that are less than 0.1 times the profile length. In each 0.1° pixel we typically had a total of ∼75 MOLA inter-shot intervals, or a cumulative profile length of 22.5 km, which met the Shepard et al. [2001] criterion for the length scales of 0.3 km to 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 when H < 0.5 when the profile is not sufficiently long. They find that N = 100 is sufficient when H ∼ 0.5, while N = 1000 results is reasonable estimates when H = 0.25 or H = 0.75. Since most of the Hurst exponents we observe are in the range 0.4 to 0.8 we have chosen to remap the extrapolations using 0.2° pixels (Figures 1c10c), which typically provides for an average of some 350 MOLA inter-shot (300 m) intervals, or a total length of 105 km of profile. The uncertainty we add to the 100 m RMS slope is acceptable because we are not extrapolating very far outside our deviogram fit region (0.3 to 1.2 km), and because all the landing sites except MPF have H > 0.5, so Campbell et al. [2003] would suggest we are overestimating RMS slope at 100 m if we are in error for those sites. In any event, the statistics that we report in Table 4 (and reported by Golombek et al. [2003, Table 10]) are derived by averaging all of the MOLA tracks that fall in 0.1° pixels that are at least one quarter within the ellipses in Table 1, increasing the net profile length enough to provide unbiased values of H based on Campbell et al. [2003], resulting in robust full ellipse 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. This is quantitatively clear from the 100 m RMS slope column in Table 4, but also from the newer 0.2° resolution 100-m slope estimates (Figures 1d10d). These self-affine extrapolation results are generally consistent with the pulse spread results (Table 4) showing that of the final four sites, all of which meet engineering constraints, Gusev is the roughest, and that the two canyon sites, Melas and Eos, have particularly rough surfaces that don't meet the constraints at this scale. In fact the maps of slope corrected pulse width in Figures 1f and 3f7f indicate that the spatial mapping of fractal topography that we carried out is properly sampling the surface, as seen with an independent method. The argument holds at the other sites too, although the pictured non-interpolated pulse width data for those sites makes the map comparison less clear.

[28] The maps of hectometer slopes derived from this method are remarkably similar to the maps of MOLA pulse spread (compare d and f of Figures 110), which argues that both are accurately measuring the slope at 100 m scale and that locating landing ellipses on the basis of these data is appropriate. In Gusev crater (Figures 4d and 4f), both methods show higher 100 m slopes south and east of the ellipse where images show etched and knobby terrain. Slopes over 100 m scales are also slightly higher in the south central portion of this ellipse, where a fresh crater and etched terrain are present, which have been avoided in the final ellipse (EP55A3) [Golombek et al., 2003]. Similarly both maps for Meridiani (Figures 5d and 5f), show higher slopes associated with craters to the northeast, southeast and southwest of the ellipse, which have also been avoided with the 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 terrains that are generally smooth, as would be expected for locations chosen from photogeologic data to be safe, we do find one parameter that appears to be variable across several of the MER ellipses, and that is the 0.3 km to 1.2 km Hurst exponent. This variation may be due to sampling bias. For example the Hurst exponent map variation in Figure 1c bears some resemblance to the MOLA track coverage that can be inferred from Figures 1b and 1e. However, any such correlation is much less clear at the Melas site in Figure 7. Future self-affine hectometric roughness extrapolation from MOLA data will need to carefully address the issue of Hurst exponent 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 this paper seeks to characterize the nature of the surface at the landing sites through simple comparisons of simultaneously acquired MOC and MOLA measurements. These results are best used to locally illustrate how topography, slope, SCPW, and reflectivity are related to individual features observed in MOC data such as craters, scarps, and flow features, and strengthen our understanding of the MOLA slopes at each landing site that a rover may encounter. Due to the large number of MOC images for the landing sites, we focus our results on the selected sites, Meridiani and Gusev, though we briefly discuss the other sites as well.

4.1. Coregistering MOC to MOLA

[31] Narrow angle MOC data used for this project were downloaded from the PDS and the Malin Space Science Systems (MSSS) website, and consisted of raw IMQ images and the cumindex.tab table of image orientation, shape parameters, and timing. Images were acquired for the landing sites during the nominal mission (M01–M23) and during a special imaging campaign during the extended mission (E01–E18), however, as this analysis compares simultaneous MOC and MOLA data, only images through MOLA failure during E09 are used. The images are of variable length and width, may be summed in both x and y directions, and have variable pixel aspect ratios, all of which were corrected using the data in the cumindex.tab. Due to data dropouts (commonly occurring in blocks of 128 pixels) the images are occasionally shorter in length than commanded by the MSSS team, so the length of the image must be compared with the cumindex.tab, or the image rectification process that compensates for length, summing, and aspect ratio may incorrectly warp the image.

[32] MOLA and MOC data are, in theory, easily aligned using the latitude and longitude information contained within their respective data headers. Unfortunately, MOC and MOLA used different references for the shape of Mars, making such a comparison more difficult. We have developed software that allows the MOC and MOLA data to be aligned in latitude using spacecraft event times recorded in the cumindex.tab for the predicted start time and duration of MOC images, that can then be converted to the J2000 time recorded in the MOLA PEDR data, allowing us to collocate the data. While occasional errors from differences between the commanded and actual start times, as well as occasional MOLA time-tag errors [Neumann et al., 2001], can influence the data, the resulting comparison is relatively robust. The longitudinal position of MOLA data within a MOC image has been constrained empirically to be a vertical column near pixel 1674 by matching topographic features visible in hundreds of individual MOC images. Note that individual MOLA shots are offset from the actual MOC scan line by 400 m [Kirk et al., 2001], because the two instruments have different pitch orientations. Using these relationships, aligned images of MOC and MOLA data may be plotted side by side.

[33] Using this technique, we plotted MOC images in alignment with MOLA topography, slope, SCPW, and reflectivity, the sum of which we refer to here as MOC-MOLA images. A small circle indicates the surface illumination on the MOC image; as the exact size and shape of the illuminated 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 image discontinuities. If a dropout of unknown size occurs in the middle of a MOC image, it can lead to minor or major misalignments between the data sets, as it is impossible to constrain the position of the MOC data following the dropout. These problems can occur anywhere in the MOC image, including areas not shown in the landing ellipse MOC subsections illustrated here; thus, even if there are no visible dropouts in the image shown here, a dropout to the north or south in the image may cause misalignment. In the event of misalignment, one must judge from the observed features in the MOC image and the MOLA topography whether 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 observations of the MOLA topography, slope, SCPW, and reflectivity, and the simultaneously acquired MOC image number.

Table 5a. MOLA Statistics for Meridiani, Melas, and Athabascaa
LocationMOCBotLatTopLatMOLARelief, mSlope, °Roughness, mReflectivity, %MOC DropoutsFlipComment
MinAvg.S.D.MaxMinAvgS.D.MaxMinAvgS.D.MaxMinAvgS.D.Max
  • a

    Note: The values below the vertical bar for each site under relief, slope, roughness, and reflectivity columns are the minimum of Min, the average of Avg. and the standard deviation (S.D.), and the maximum of Max.

HematiteE0101056−2.25−2.2518695−1566−15519−1536000.20.6110.11.4yesnoFlat
E0200373−2.03−2.0318896−1430−14206−1413000.41.5010.21.11011114nonoFlat
E0200970−2.1−2.118984−1446−143410−1416000.10.4110.11.116160.617yesnoFlat
E0300329−2.25−2.2519273−1561−15485−1540000.20.8110.11.113150.816nonoFlat
E0301763−2.2−2.219474−1480−145910−1440000.63010.21.412140.916yesnoCrater on N. edge of ellipse
E0401682−2.25−2.2519851−1607−15778−1567011.14062.6118101.214yesyesFlat
E0401873−2.2−2.219876−1446−140110−1391010.94.2110.21.68100.812nonoCrater on S. edge of ellipse
E0502642−2.1−2.120278−1400−13867−1375000.20.7010.21.4911113nonoFlat
M0001660−2.01−2.0110408−1502−14991−1496000.10.3110.11.5nonoFlat (2 m depression in 600 m region)
M0301632−2.25−2.2511502−1466−14538−1436000.10.7110.21.6noyesFlat on N. end in ellipse
M0802647−1.99−1.9912659−1419−14153−1410000.30.8010.21.1450.35nonoFlat
M0808066−2.4−2.412898−1532−15168−1501000.42.2010.31.8340.45noyesSmall crater
M0901839−2.17−2.1712986−1408−13985−1387000.21010.21.1330.44nonoFlat
    −1607−14666.9−1375000.44.2010.41139.90.717   
MelasE0100027−8.9−8.918509−3368−320289−3124054.715131.95.8691.511yesnoLandslide deposit
E0200270−8.96−8.9618886−4136−405076−3838021.47.5110.52.88111.415yesyesSwale on S. end of image
E0202458−8.98−8.9819175−3887−3709115−3173045.624121.46581.712nonoClimbs Rim, can't see local detail
E0301135−8.92−8.9219376−3830−3645155−3386021.78.603321791.213yesnoDune covered hill on N. end of image, Scrambled egg on S.
E0401123−8.75−8.7519778−3146−2979135−2723031.77.1121.36.19121.916noyesDune filled valley over width of the ellipse
E0500744−8.95−8.9520067−3542−3361124−311904310132.29.22517yesnoSand sheet/hills
E0501626−8.98−8.9820180−4171−408476−3870021.66.6152.413460.97nonoSame as E0200270
E0502484−8.98−8.9820268−3749−360181−3370032.28.6132.110261.29nonoSand sheet and landslide deposit
M0202556−8.69−8.6911253−4033−402311−4007010.71.9010.51.6670.47nonoSlope with sand sheet over ellipse
M0400361−8.7−8.711907−3771−367262−3584021.44.8021.36.3780.69nonoSlope with Scrambled egg terrain without topography
M0804367−8.87−8.8712737−3285−324122−3184011.38.1121.98.6451.29noyesHills in scrambled egg
M0903513−8.96−8.9613064−4061−403131−3965010.82.6110.31.7120.32nonoscrambled egg
M1900264−8.9−8.916686−3413−336830−3317021.34.5131.96.21517118nonoscrambled egg
M2100404−8.9−8.917453−3746−3568136−3316021.89.7021.69.415201.823nonoHills in scrambled egg
M2301183−8.94−8.9418333−3973−3776149−3502021.67.6122138111.414nonoHills in scrambled egg
M2301631−8.88−8.8818421−4038−389988−3756021.56.4010.73.4791.111yesyesHill and sand sheet over 10 km
    −4171−362186−2723022.124021.62119.11.223   
AthabascaE04021198.928.9219908−2615−26121−2611000.51.1110.11.4nonoSlight step in smooth terrain
E05031248.658.6520310−2599−25887−2578000.10.4110.11.29100.612nonoStreamlined islands or knobs
M02005818.658.6511119−2641−256935−2511011.37.5120.66.3nono35 m step in S
M11003318.658.6513672−2653−261548−25250114.21217.4yesnoStreamlined island
M18010808.98.916464−2547−252513−2505010.51.6120.42.3yesnoHill
    −2653−258221−2505010.77.5110.47.49100.612   
Table 5b. MOLA Statistics for Gusev and Isidisa
LocationMOCBotLatTopLatMOLARelief, mSlope, °Roughness, mReflectivity, %MOC DropoutsFlipComment
MinAvgS.D.MaxMinAvgS.D.MaxMinAvgS.D.MaxMinAvgS.D.Max
  • a

    Note: The values below the vertical bar for each site under relief, slope, roughness, and reflectivity columns are the minimum of Min, the average of Avg. and the standard deviation (S.D.), and the maximum of Max.

GusevE0200665−14.8−14.818940−1822−180015−1776021.14.423.41.78.5yesnoFlat - some small cratering
E0201453−14.8−14.819053−1983−191069−1749012.3113113.824noyesSloping cratered surface
E0300012−15−1519229−1932−190620−1834011.46.911.90.76.1nonoHill
E0301511−14.7−14.719430−1938−189549−17300127.311.81.511noyesFlat
E0503287−15−1520322−1918−187518−1819011.68.901.415.31013115nonoHills in center of ellipse - Track not in image
M0301042−15.2−15.211458−2111−186443−1805024.42522.41.6149909nonoCrater in center of ellipse
M0302330−14.6−14.611546−1798−169668−160005311363.412nonoCrater inside larger crater rim
M0700813−14.9−14.912200−1950−19189−1898000.84.922.50.55.3nonoCrater, 2 x hills
M0801958−14.8−14.812615−1930−184579−1668022.61113.1211nonoInterior of crater
M1000855−14.8−14.813357−1891−179856−1679022.49.612.61.98.9582.211nonoInterior of crater
    −1927−185143−1756022.21023.61.8118101.112   
IsidisE02000494.084.0818855−3790−376219−3721000.4211.10.84.515170.518yesnoCratered terrain
E02006814.214.2118943−3778−37635−3757000.20.611.20.43nonoCratered terrain
E02022114.224.2219144−3806−378810−3773000.10.511.20.42.11214117nonoSloping cratered terrain
E03009584.134.1319345−3734−371515−3689000.31.511.10.32.3790.610nonoCratered terrain
E03015294.144.1419433−3770−37642−3757000.20.8110.43nonoCratered terrain
E04015624.194.1919835−3793−37796−3767000.20.9110.32.216170.417nonoHillocks and craters
E05004864.084.0820036−3782−375714−3734000.20.9110.43.514160.817nonoCratered terrain
E05021004.164.1620237−3787−37824−3766000.4211.20.64.28100.711nonoCratered terrain
M10019824.084.0813448−3790−376713−3745000.2101.20.96.5780.59yesno 
    −3781−37649.8−3745000.21.111.10.53.511.3130.614   

4.2. Shot to Shot Slope and Reflectivity

[35] For the comparison of the MOC images to MOLA data, we are interested in understanding the relationship between geomorphology and topography; hence we use the individual MOLA shots taken along the track of the MOC image to calculate topography, slope, SCPW, and reflectivity. Topography for each MOLA shot was calculated as described in section 2. Individual slopes are calculated at a 300-m scale at every MOLA shot location using a centered 3-point Lagrangian interpolation along track. SCPW was calculated 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 the surface, which is related to surface albedo and atmospheric opacity through Beers law [Ivanov and Muhleman, 2001]. In any given MOC image, atmospheric opacity is generally relatively constant, allowing us to constrain relative albedo differences, and provides an additional constraint on the observed variations in contrast shown in the MOC image data. Significant variance in albedo is caused by changes in surface material properties, some of which are correlative, including but not limited to dust coverage, grain size, and composition. Because the opacity in a given MOC image is generally constant, the MOLA reflectivity is a proxy for albedo, and can be used to estimate the variance of surface properties. A high variability within a given MOC image is desirable, because it suggests the potential for changes in material size, thermal properties, or composition that might be sampled by a rover. However, a high reflectivity with little variance is undesirable, as it likely indicates significant dust cover. It should be noted that orbit-to-orbit, MOLA reflectivity is thought to be accurate to ∼20%. Within an orbit for a monotonic MOC surface, reflectivity appears to vary by up to ∼2%, hence changes in reflectivities that are not obviously correlated with topography smaller than 2% are assumed to be noise. Furthermore, MOLA reflectivity is calculated from the received pulse energy, which is significantly more sensitive to detector saturation than pulse width, causing many of the measurements to be saturated. In our analysis, we only show unsaturated data (raw received energy <255 in the PEDR data).

4.3. Results: Comparison of MOLA and MOC

[37] Each MOC image that crossed either of the landing ellipses for each landing site was used to generate a set of MOC-MOLA images; only the part of the MOC image in the ellipse is shown. Sample MOC-MOLA images for Meridiani and Gusev are shown from west to east through the landing ellipse (Figures 24 and 25). Each MOC and MOLA pair contains a contrast enhanced MOC image with MOC coordinate frame latitude and longitude data, and a superposed MOLA track shown as a line with small circles illustrating each MOLA shot. Adjacent to the MOC image are three or four graphs showing topography, 300 m length scale slopes, SCPW, and reflectivity; if all reflectivity data are saturated, only three graphs are shown. The minimum, average, standard deviation, and maximum for each of these parameters is recorded in Tables 5a and 5b for each MOC image in the ellipse, as well as the MOC image number, the MOLA track, the minimum and maximum latitudes of the ellipse, whether there are data dropouts in the MOC image, and a comment on the general appearance of the area imaged.

Figure 24.

Subset of MOC images with MOLA data for Meridiani: E0401873, E0502642, and M0802647.

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.

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 the analysis are shown in Figure 24) indicate that these areas are extremely flat, with slopes averaging 0.3° ± 0.4°, where the largest 300 m length scale slopes of ∼2° (30 m of relief over 3–4 MOLA shots) are associated with highly eroded craters or gently rolling hills in MOC images E0401873 and E0502642, respectively. Similarly, the SCPW values are the lowest measurable by the MOLA throughout the region, except in image E0401873. The region has a wide range of reflectivity values, though they average 9.9 ± 0.7%; each MOC frame tends to have a relatively constant reflectivity value, and moderate variance (Table 5a). In general, the MOC-MOLA images show smooth plains interspersed with highly degraded and eroded craters, which have little topography or SCPW, e.g., MOC images M0808066, E0301763, and E0401873. While there is little overall correlation between reflectivity and the MOC images, as the reflectivity is mostly constant, there is a high correlation of reflectivity lows associated with dark floors of the degraded 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] for which the two terrain types (background plains and subdued crater) used in the landing simulations within the Meridiani ellipse are located [Golombek et al., 2003]. The background plains have extremely low slopes in the MOC stereo analysis (1–2°) and is also extremely flat (with low relief) at the inter-shot scale of 300 m with slopes ∼1°. Not surprisingly, 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 the bottom of this image shows greater relief (>50 m) and greater slopes (>2°), which is also consistent with the MOC stereogrammetry at 10 m scale. Our measures of RMS slope at 1.2 km and 100 m scale are also consistent with the RMS slope versus baseline curves reported for Meridiani from MOC 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 relatively large mean topographic relief (43 m) and slope (1.7°), and a mean SCPW of 3.6 m, as well significant variation in reflectivity (standard deviation 0.7%; Table 5b). The highest topography, slopes, and SCPW are associated with the walls of both small craters (M0301042; M0700813) and larger degraded craters (M0302330; E0201453; E0301511) within Gusev crater. The region is divided into two terrains, one that is knobby or etched, with an average 3-m SCPW, and one that is undifferentiated plains with numerous small craters, with 1–2 m SCPW (e.g., E0201453). Little reflectivity data are available for the MOC images in this region as most tracks are energy saturated.

[41] Inter-shot MOLA relief across the etched terrain in the center and right panel of Figure 25 is consistent with relief measured in MOC stereogrammetric digital elevation models for this terrain reported in Kirk et al. [2003]. The etched terrain has high relief (>100 m) and high slopes at all 6 m, 100 m, and 300 m length scales. Landing simulations in this terrain shows the highest percentage of “out of specification” events of any of the terrains investigated at the potential landing sites [Golombek et al., 2003]. Cratered plains at Gusev have much lower relief and slopes at the MOLA inter-shot scale, again consistent with MOC stereogrammetric results reported by Kirk et al. [2003], and are comparable to cratered plains investigated at other landing sites [Golombek et al., 2003]. Finally, our measures of RMS slope at 1.2 km and 100 m scale are also consistent with the RMS slope versus baseline curves from stereogrammetry reported 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), small slopes (average 0.3°), and low SCPW (1.1 m) associated with gently sloping cratered plains within the Isidis landing ellipse (Table 5b). These cratered surfaces are relatively constant in reflectivity, with little contrast along individual MOLA tracks. Small, fresh-looking craters are associated with some of the larger SCPW values (E0401562), but in general, the portions of the MOLA tracks within the landing ellipse for these MOC images are undistinguished in topography, slope, or SCPW. As with Gusev crater, there are few reflectivity data points as the MOLA data generally is energy saturated for these tracks; however, the limited data available exhibits low variance consistent with little diversity in material properties.

[43] The MOC-MOLA images of the Melas landing site show the largest range of topographic variation (average standard deviation is 86 m), as well as large average slopes (2.4°, with a range up to 24°), and SCPW (2.4 m, ranging up to 20 m; Table 5a). Not surprisingly, the roughest surfaces (7–10 m) are associated with the landslide deposits to the west and north of the ellipse, e.g., E0100027. In general, sand sheets are darker (by ∼3% in reflectivity) and smoother (SCPW of 2 m versus 5–6 m) than surrounding blocky deposits (e.g., M0804367) and layered units (E0202458). This landing site was ultimately eliminated due to concerns, in part generated by this analysis, regarding high slopes, SCPW, and topography, as well as the potential for large canyon wall-driven winds.

[44] The MOC-MOLA images of the Athabasca site typically are gently varying, with the largest variance in topography (standard deviation along track within the ellipse of 35–48 m) occurring near the one of the main fluvial channels, shown in MOC images M0200581 and M1100331. These effects are clearly associated with channels cut into the surrounding rocks seen in the MOC images. Overall, however, the slopes remain low, with an average slope of 0.7°, and a maximum of 7.5°, across the MOC images sampled here (Table 5a). Similarly, the SCPW values are just above our ability to discriminate them at an average value of 1.5 m, with a standard deviation of 0.4 m. Not surprisingly, the largest slopes and SCPW values are also associated with the channels observed in M0200581 and M1100331. For M0200581 peak SCPW is associated with what appear to be near-vertical walls on the sides of the channel ∼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 shown in M1100331, which may be a result of turbulent fluvial-depositional processes. Reflectivity is saturated for all images except E0503124, which demonstrates no reflectivity variance above the typical noise level for reflectivity.

5. Conclusions

[45] We have used MOLA data in order to verify that the landing sites selected for the MER met the topography and slope requirements of the landing system, and in conjunction with MOC imaging, characterized the topography, slope, slope corrected pulse width, and reflectivity of geomorphologic features observed in the landing ellipse. It was possible to use the MOLA data to address slope requirements at 100 m and 1.2 km length scales, using slope measurements, self-affine statistics, and pulse width measurements. For 1.2 km slopes, both the regional gradient, calculated using an adirectional slope method, and along-track slopes, calculated using a bidirectional slope technique, were measured. The self-affine statistical approach was used to predict the slopes for 100 m length scales, and was consistent with the observed pulse width, suggesting that the processes acting on the landing sites are indeed self-similar at these scales. The pulse width and slope-corrected pulse width clearly indicate hazards such as crater ejecta, and are useful indicators 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 safe per the engineering criteria for slope, and that they meet the topography requirement of being at an elevation less than −1.3 km. The pulse width analysis indicates that the surfaces within the ellipse are relatively flat, consistent with the requirements of the MER landing subsystem. We are confident that the slope analyses, in conjunction with the self-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 of the MER landing system.

[47] Lastly, the comparison of MOC and MOLA illustrate the magnitude of local topography, slopes, slope corrected pulse width, and reflectivity that are caused by local features such as craters and hills, and indicate that these features are do 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 have slopes of 0.3°, while the etched terrains of Gusev have average slopes of less than 1.7°.

Appendix A:: Smooth Region Slope Statistics

[48] For an elevation difference Δz between two points on a MOLA profile separated by interval Δx, the slope in radians or degrees is:

equation image

however, in the cases we consider for Δx = 1.2 km, where α < 2°, the tangent is essentially equal to the angle. The assumption holds because we are looking for smooth flat places to land the MER spacecraft. Thus we approximate:

equation image

It then follows that the mean slope is

equation image

The standard deviation from this mean is

equation image

so

equation image

What we call the root mean square (RMS) slope is slightly different, and is the sample standard deviation from the mean slope, which is the square root of the sample variance of the set of N values of αi(Δx):

equation image

so

equation image

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

Acknowledgments

[49] The work described in this paper was performed at the Jet Propulsion Laboratory, a division of the California Institute of Technology, under contract to NASA, and at the University of Hawaii. The work was supported by the NASA Mars Data Analysis Program and the MER project. The authors thank Jim Garvin for providing digital copies of his pulse spread data set as well as the entire MOLA science team and Oded Ahraronson for spirited discussions about how to use the MOLA data to address the MER elevation and slope landing site safety criteria. Finally, we thank Anton Ivanov who provided a MOLA database that eased rapid manipulation of the data, and Megan Kennedy, who worked on the initial analysis effort.

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