GLD100: The near-global lunar 100 m raster DTM from LROC WAC stereo image data

Authors


Abstract

[1] We derived near-global lunar topography from stereo image data acquired by the Wide-angle Camera (WAC) of the Lunar Reconnaissance Orbiter Camera (LROC) system. From polar orbit tracks, the LROC WAC provides image data with a mean ground resolution at nadir of 75 m/pixel with substantial cross-track stereo overlap. WAC stereo images from the one-year nominal mission and the first months of the science mission phase are combined to produce a near-global digital terrain model (DTM) with a pixel spacing of 100 m, the Global Lunar DTM 100 m, or “GLD100.” It covers 79°S to 79°N latitudes, 98.2% of the entire lunar surface. We compare the GLD100 with results from previous stereo and altimetry-based products, particularly with the Lunar Orbiter Laser Altimeter (LOLA) altimetry, which is the current topographic reference for the Moon. We describe typical characteristics of the GLD100 and, based upon the comparison to the LOLA data set, assess its vertical and lateral resolution and accuracy. We conclude that the introduced first version of the stereo-based GLD100 is a valuable topographic representation of the lunar surface, complementary to the LOLA altimetry data set. Further improvements can be expected from continuative investigations.

1. Introduction

[2] Herein we present the first near-global lunar digital terrain model (DTM) with both a lateral resolution generally ≪1 km and a vertical accuracy of ∼10 m. The model was derived via stereo-photogrammetric analysis of cross-track stereo overlap of Lunar Reconnaissance Orbiter Camera (LROC) Wide-angle Camera (WAC) images [Robinson et al., 2010].

[3] Existing topographic models of planet and satellite surfaces were derived from laser altimetric measurements as well as from photogrammetric processing of stereo-image data. In 1994, cameras onboard the Clementine spacecraft [Nozette et al., 1994] collected a global digital image data set that allowed for topographic measurements at scales of 200 to 1,000 m [Cook et al., 2000], whereas the Laser Image Detection and Ranging (LIDAR) instrument provided semi-global altimetry for northern and southern latitudes up to 60–70°, partly with a spacing of several tens of kilometers at the equator [Zuber et al., 1994]. Subsequently, a global model representing the Unified Lunar Control Network 2005 (ULCN 2005) was produced from Clementine data and former control point networks [Archinal et al., 2006], which, however, does not represent a dense global raster DTM. The Laser Altimeter (LALT) onboard the Japanese Selene mission (2007–2009, [Araki et al., 2009]) provided the first global lunar topography model for all latitudes with longitudinal gaps of up to 10 km at low latitudes. The lunar science community also looks forward to more or less global DTM results from the Selene LISM TC (Lunar Imager/Spectrometer Terrain Camera) and respective literature about that. At the time of our analysis and writing, such data were not available. First stereo-photogrammetric evaluations of imagery of the Chinese Chang'E-1 mission (2007–2009) indicate the potential for the derivation of DTMs with ∼500 m horizontal resolution and a vertical accuracy of 100–400 m [Wu et al., 2011], but detailed publications about such data sets are currently pending. Chang'E-1 laser altimetry yielded ∼30 m vertical accuracy, but with >7 km lateral spacing [Ping et al., 2009]. The most recent products from Lunar Reconnaissance Orbiter (LRO) LOLA altimetry data [Smith et al., 2010], comprising laser altimeter measurement every 10–20 m along track, are considered the current topographic reference for the Moon. It consists of more than three billion single shots (status of March 2011 Planetary Data System (PDS) release, http://pds-geosciences.wustl.edu/missions/lola.htm, the latest available LOLA data set at the time of writing) and an additional gridded data set, with high absolute accuracy (∼1 m vertical and ∼30 m lateral [Smith et al., 2011]). Nevertheless, low latitude longitudinal gaps of over 4 km exist.

[4] Each month of the LRO mission, the Lunar Reconnaissance Orbiter Camera (LROC) Wide-angle Camera (WAC) [Robinson et al., 2010] provides overlapping image data with 75 m/pixel mean ground resolution at nadir and substantial across-track stereo coverage (>50% from subsequent orbits) of almost the entire lunar surface. Variations of the illumination between two data sets from subsequent orbits (∼2 h/orbit) are as small as only 1°. With respect to coverage, almost global image acquisition under different illumination conditions within each month promises a high degree of completeness and redundancy. Altogether, WAC stereo data serve as an ideal data source for the derivation of high-resolution topographic information through systematic stereo image processing. Complementary to data sets from laser altimetry that provide precise elevations along profile-like tracks, a more contiguous topographic data set can be expected from stereo-photogrammetric processing of LROC WAC image data.

2. Image Characterization and Stereo Conditions

[5] After the commissioning phase (30 June through 15 September 2009) and the primary mission phase (through 15 September 2010), LRO entered its science mission phase. While commissioning was characterized by an elliptical orbit (45–190 km altitude), the primary mission and the first months of the science mission are characterized by a quasi-circular polar orbit. The orbit altitude varies between 35 and 65 km, with a mean of 50 km [Tooley et al., 2010].

[6] The LROC WAC [Robinson et al., 2010] consists of a 1024 × 1024 CCD detector, which is divided into sub-frames for seven different spectral bands: two ultraviolet bands and five bands in the visible spectrum. Visible wavelength sub-frames consist of 14 lines, while hundreds of sub-frames form a WAC image (“push-frame” principle). The topological continuity within WAC image strips depends on the actual spacecraft orientation. If the spacecraft is moving in the “forward” direction (+x), the raw images are topologically consistent, whereas in case of a “backward” moving spacecraft (−x, periodically necessary for thermal considerations), the sub-frames do not form a contiguous and topologically correct data set. Image rectification corrects for these effects (Figure 1). In either case, based upon experience from commissioning phase observations, sub-frame delays were optimized toward continuous WAC ground coverage without gaps between sub-frames. Topological consistency is a pre-requisite for an area-based image matching procedure, the core of stereo-photogrammetric image processing toward a DTM as described in section 4.

Figure 1.

Subsets (∼20 × 20 km) of LROC WAC images (subsets of ∼21 sub-frames, sub-frame boundaries are indicated by tics at left sides of Figures 1a and 1c): (a) raw data in case of spacecraft moving “forward,” WAC image M128467900C, (b) rectified data, (c) raw data in case of spacecraft moving “backward,” M110777928C, and (d) rectified data.

[7] The instantaneous field of view (IFOV) of the WAC is 5.15 arcmin. Thus, from an altitude of 50 km the LROC WAC provides a resolution on ground of 75 m/pixel at nadir. The entire cross-track field of view is 90.3° in the monochrome mode with 1008 pixels per line, and 61.5° in the color mode with 704 pixels per line. Within the polar orbit, single WAC images cover ≥10° of latitudes (i.e., ∼300 km image length, depending on orbital beta angle).

[8] For WAC stereo processing we chose image data from the 604 nm band from images collected in the color mode over a 17 month period [Robinson et al., 2010]. CCD-lines of this band are located near the center of the boresight of the visible optics (∼1.6° off-nadir). Thus, they provide near-nadir viewing with a minimum influence of residual geometric calibration errors, compared to more off-nadir bands. The respective swath width is about 59.5 km (image width). At the equator, WAC color mode images from subsequent orbits overlap to about 52% and provide a stereo angle of about 33°. The stereo angle decreases toward the poles (at 80° latitude it is only 5°) from adjacent orbits while the cross-track stereo overlap increases to more than 90%.

3. Camera/Spacecraft Alignment, Camera Calibration, and Orientation Data

[9] Before LRO's arrival at the Moon, accurate WAC spacecraft alignment data in SPICE format (Spacecraft Planet Instrument C-matrix Events, [Acton, 1996]) were not available. With a subset of the entire WAC stereo data set we investigated the alignment parameters (rotation matrix from the spacecraft to the camera coordinate system) by using Monte Carlo techniques. Best fit alignment angles for roll (cross-track rotation) and yaw (rotation around the vertical axis) components were selected from the minimum of the apparent stereo model distortions (we use the phrase “stereo model” for the 3D surface model that is derived from stereo-processing of two overlapping images). The best fit pitch (along-track rotation) component was detected from a comparison of stereo models that were derived from the same pair of WAC stereo image strips, but from different spectral bands. Different bands provide different along-track offsets in the flight direction within the focal plane. Thus, the different stereo models will differ with respect to the vertical level, if the along-track alignment is not correct.

[10] Although camera distortion parameters were calibrated prior to launch, analysis of stereo models and other LROC WAC investigations, indicate that there is still some potential for improvement in the sub-pixel range in the outer portions of the field-of-view. A description of the pre-flight calibration and recent results from in-flight calibrations are given by Speyerer et al. [2012]. Stereo-analysis, particularly in case of small stereo angles, is rather sensitive to residual distortions. Therefore we were able to improve the geometric calibration information (focal length and distortion parameters) to some extent. Similar to the previous detection of best fit alignment parameters, we achieved the improvement by minimizing the stereo model distortions and using the mean forward ray intersection accuracy as the decisive parameter. Note, that due to the significant WAC distortion, at the nominal orbit altitude of 50 km the ground pixel resolution for the WAC visible bands increases from 75 m/pixel at nadir to up to ∼115 m/pixel toward the edges of image lines. Figure 2 illustrates the effect of the current improvement of the alignment and geometric parameters for a single stereo model. With improved calibration and alignment data, accuracy was improved from a priori 38 m to 18 m. The standard deviation (1σ) of vertical deviations relative to the LOLA data set decreased from 149 m to 34 m. For this stereo model we applied the stereo-processing pipeline that was systematically applied within the final derivation of the GLD100 global raster DTM, which is described in detail in section 4. Results of a quantitative comparison of the entire GLD100 with the LOLA data set (Figure 2e) are described in section 7.

Figure 2.

(a) Raw WAC stereo images (M136491313C and M136484548C), 88 m/pixel scale at nadir, (b) rectified images, (c) derived DTM, (d) stereo model distortions (forward ray intersection accuracy) before and after improvement of calibration and alignment information, and (e) vertical deviations to LOLA data before and after improvement of calibration and alignment information.

[11] SPICE kernels provide information about spacecraft clock, nominal orbit position, target position, and pointing data. The orbit information was substituted by improved orbit kernels provided by the LOLA team. They are a result of a combined analysis of radio tracking, orbit crossovers, and Earth-based laser ranging [Mazarico et al., 2011]. The version of the improved orbit kernels, which was used for our DTM generation, is based upon the LP150Q gravity model [Konopliv et al., 2001], while most recent orbit analyses of the LOLA team refer to a refinement of the GLGM-3 (Goddard Lunar Gravity Model 3) gravity model [Mazarico et al., 2010]. The use of identical orbit position information allows for a direct comparison of topography information derived from the LROC WAC and LOLA (see section 7). The lunar coordinate reference system used for all investigations within this work is the mean Earth/polar axis system and the DE421 ephemeris model. All heights are defined radially, relative to a sphere with a radius of 1,737.4 km.

4. Stereo Processing

[12] In preparation for the following stereo-photogrammetric processing steps, we converted the PDS-formatted LROC WAC raw image data to the VICAR (Video Image Communication and Retrieval) file format (NASA, The VICAR Image Processing System, 1995, available at http://www-mipl.jpl.nasa.gov/external/vicar.html) and calibrated the image data considering the respective radiometric calibration files that are provided by the camera team [Robinson et al. 2010]. The VICAR-based software system at the German Aerospace Center (DLR) is used for the following stereo-photogrammetric processing pipeline (Figure 3).

Figure 3.

Stereo-photogrammetric processing line for LROC WAC stereo images.

[13] With modifications to account for specific mission and sensor characteristics, the stereo-photogrammetric processing pipeline was developed and successfully applied to a series of planetary stereo-image data sets [e.g., Giese et al., 2006; Gwinner et al., 2009; Preusker et al., 2011, 2012]. DLR's stereo-processing pipeline is now applied to each WAC stereo model. Because of illumination conditions (shadows cast at low sun angles) and poor stereo conditions, stereo models taken at latitudes higher than 80°N/S are excluded from stereo image processing.

[14] An important pre-requisite for the applied area-based image processing steps is to provide topologically consistent imagery. Therefore, the first step of the stereo-processing line is to rectify the raw WAC images based upon the given information on orbit position, pointing, alignment, and calibration. Geometric rectification of a single WAC image uses subsequent direct (geo)referencing of all sub-frames of the WAC image, from image to ground, combined with indirect resampling within the raw image. A priori DTM data (gridded LOLA data) were used as initial topography information for this orthorectification. Additional lookup tables are stored during the rectification in order to relate rectified image coordinates to raw image geometry. The rectification step reduces the search area for the image matching process and, thus, reduces the number of mismatches of similar image patterns in a larger vicinity. Nevertheless, due to interpolation within the LOLA data set at longitudinal gaps, incorrect heights cause displacements (cross-track parallaxes) of up to hundreds of meters, requiring adaptations to search areas for the subsequent image matching. The stereo-image matching step is the core of the stereo-processing line. We apply area-based image matching to all pixels of the full-resolution rectified stereo images using image patches of 17 × 17 pixels. With the help of the previously stored lookup tables, the derived tie point coordinates were transformed back from the rectification geometry to the raw image geometry. We then combined the derived raw image coordinate pairs with the respective orientation, alignment, and calibration data and derived three-dimensional ground points by forward ray intersection [Scholten et al., 2005]. Mismatches are found and eliminated by an upper limit of the 3D forward ray intersection accuracy to a given threshold. We selected 50 m intersection accuracy as an appropriate upper limit for the definition of gross errors and the respective elimination of outliers.

[15] The 3D surface points from all stereo models are combined to one common data set, which is the input for the derivation of the DTM raster. An intermediate 100 m raster LROC WAC DTM is finally derived by a Gaussian distance weighted averaging over a maximum distance of 400 m. The result of this first iteration is then used as the topographic reference for a second and final loop. With this preliminary WAC DTM, remaining parallaxes within the newly rectified images are reduced to a minimum (<100 m) and the subsequent image matching is redone within a significant reduction of search areas (now only 75–150 m). The WAC DTM produced in the first iteration yields better topologic consistency and significantly reduces the number of blunders and outliers. The result of this second processing loop is the final 100 m raster DTM, the GLD100.

5. GLD100 Stereo Processing Statistics

[16] WAC stereo data of the entire primary mission phase (12 months) and the first 5 months (until January 2011) of the following science mission phase were used to produce the 100 m raster DTM, GLD100. Stereo models with image data that were acquired during low sun phases (beta angle of the LRO orbit plane >87°) were excluded from the final GLD100. Due to multiple coverage (global coverage under different illumination within each month), local gaps in temporary shadow areas were reduced significantly. A total number of ∼69,000 stereo models provided about 100 billion points, i.e., ∼2,640 points/km2, an average of 26 points per 100 m cell of the GLD100.

[17] The final GLD100 data set extends from 79°S to 79°N with DTM data covering as much as 99.96% of this latitudinal range. Thus, only 0.04% required interpolation, mostly at latitudinal gaps on the nearside (caused by systematic WAC image sequencing) and in areas of shadow at latitudes beyond latitudes of 70° North and South. The total elevation range of the GLD100 extends to almost 20 km. The lowest elevation (−9094 m) within the GLD100 is found within a small crater in the Antoniadi basin at 70.35°S, 187.55°E. The highest elevation (up to 10,761 m) is near Engelhardt crater at 5.43°N, 201.38°E. For comparison, the lowest and highest elevations reported by Smith et al. [2010] are −9117 m and 10,783 m.

[18] The mean relative accuracy is indicated by the mean 3D forward ray intersection accuracy of the final set of points, i.e., 18 m (1σ), which corresponds to 0.24 WAC pixel. This is a cumulative measure for the influence of all relevant geometric parameters and demonstrates the high accuracy of the geometric calibration model, the WAC alignment, the relative accuracy of the orbit and pointing information, and the accuracy of the image correlation that has been performed by the applied area-based image matching algorithm. The high redundancy within the entire data set allows the elimination of single stereo models with a mean relative 3D accuracy >50 m from the final global model. Figure 4 shows the distribution of the mean 3D forward ray intersection accuracy over time. The periodical increases and decreases reflect the variation of the LRO orbit altitude and the respective monthly maneuvers that are routinely performed in order to stabilize the LRO spacecraft within its nominal orbit.

Figure 4.

Mean 3D forward ray intersection accuracy over time (gaps: no WAC data).

6. GLD100: The Entire Data Set and Full-Resolution Subsets

[19] Near-global representations in Equidistant map projection of the entire GLD100, maximum bi-directional slopes at 500 m baselines derived after binning of the original 100 m pixels of the GLD100 and calculated from four neighbor 500 m pixels, and histograms of heights and slopes are shown in Figure 5.

Figure 5.

Equidistant maps (79°N to 79°S, 180°W to 180°E) and histograms of GLD100 heights and bi-directional slopes.

[20] A global 100 m/pixel LROC WAC orthoimage mosaic was released to the Planetary Data System (PDS) in March 2011 [Speyerer et al., 2011]. This mosaic was derived with a preliminary version of the GLD100 and LOLA data of the polar regions as the topographic references. The mosaic was released as ten regional tiles, two polar views in Stereographic (conformal) projection from 60 to 90°N and S latitudes, and eight tiles in Equidistant (center latitude = 0°) projection, covering 0–60°N and S latitudes and 0–90°, 90–180°, 180–270°, 270–360°E longitudes. The final GLD100 DTM has been PDS-released with the identical tiling scheme and map projections (available e.g., from http://wms.lroc.asu.edu/lroc/rdr_product_select and http://europlanet.dlr.de/LROC). Color-coded hill-shaded representations of the respective tiles are shown in Figure 6.

Figure 6.

GLD100 tiling scheme: two polar views in Stereographic (conformal) projection from 60 to 90°N and S latitudes, and eight tiles in Equidistant (center latitude = 0°) projection, covering 0–60°N and S latitudes and 0–90°, 90–180°, 180–270°, 270–360°E longitudes.

[21] Figure 7 shows local height and slope variations for a subset (Crisium basin) of the upper left Equidistant tile in Figure 6. In order to emphasize mare structures, the height range of the color representation is stretched to 1,000 m, while slope variations are stretched to 0–3°.

Figure 7.

Crisium basin (17°N, 60°E). (left) Color-coded hill-shaded GLD100. (right) Bi-directional GLD100 slopes (500 m baseline). 650 × 450 km. Bottom: Bi-directional slope histogram (for slopes <3°).

[22] The GLD100 offers the opportunity for a variety of detailed morphologic studies, without limitations in terms of the longitudinal gaps within the available topography information. Preliminary versions have already been used within a variety of investigations, e.g., for the analysis of non-basaltic volcanism [Jolliff et al., 2011a], for mapping of thermal inertia [Bauch et al., 2011], for investigation of mare, cryptomare, and nonmare plains [Jolliff et al., 2011b], for the global search for previously undetected basins [Oberst et al., 2011], and as topographic reference information for orthorectification of lunar image data [Speyerer et al., 2011]. Figure 8 provides topography and slope visualizations for different morphological structures at full resolution, such as central peak craters, linear faults, graben structures, and volcanic domes. For investigations on the morphology of craters, the contiguous character of a DTM from stereo processing allows to derive profiles in any azimuth. Linear features like rills, grabens, and faults can be investigated over its entire length. Finally, investigations on the distribution and characteristics of mall spot-like features like domes do not suffer from typical gaps between tracks from altimetry measurements that may fail to hit them at all, particularly in low or mid latitudes. Figure 8 subsets of the GLD100 are in local Lambert azimuthal (equal-area) projection and cover areas of 150 × 150 km. Bi-directional slopes at an effective baseline of 500 m are shown in addition.

Figure 8.

(left) Color-coded hill-shaded subsets of GLD100. (right) Bi-directional GLD100 slopes (500 m baseline), 150 × 150 km: (a) Tycho crater (43°S, 349°E). (b) Linear fault, Rupes Recta (22°S, 352°E). (c) Mare filled Vallis Alpes, note the sinuous rill on the floor (50°N, 3°E). (d) Volcanic domes, western part of Marius Hills (12°N, 306°E).

7. Qualitative and Quantitative Comparison: GLD100 Versus Other Lunar Topography Data Sets

[23] Figure 9 shows subsets of shaded relief maps of the same region (at the Aristarchus Plateau, 25°N, 312°E) from gridded DTMs, derived from other instruments, as well as the GLD100 model. Compared with the topography, as it is visible in the LROC WAC images (Figures 9a and 9b), the topography represented in the DTM from Selene-LALT altimetry data (Figure 9d), is coarse. Longitudinal gaps between LALT laser tracks are typically 2–5 km wide at this location. Tracks of LROC LOLA altimetry data are much denser (Figure 9e), with an average track spacing of about 1 km that allows for a gridded representation (Figure 9f), but gaps of up to 4 km are still visible within this subset at latitude of 25°N. The LOLA data set has also been used for short-baseline slope and roughness analysis [Rosenburg et al., 2011], but cross-track (East-west) analysis is limited by the longitudinal gaps. Finally, the LROC WAC GLD100 DTM (Figure 9c) is completely filled with topographic information. Compared to the full image resolution, smoothing effects within the GLD100 are apparent due to the area-based stereo-image matching and DTM filtering. Features with less than 1.5 km in width (e.g., rills) are partly visible, but depths and heights are affected to some extent by smoothing, while structures with a lateral expansion of more than 1.5 km are typically well represented with a reliable depth or height information within the GLD100. Features of less than ∼300–500 m in width typically comprise depths/heights of only few tens of meters, which is, as described following paragraphs, close to the vertical resolution of the GLD100. Such small feature are typically not represented in the GLD100.

Figure 9.

Hill-shaded relief subsets (40 × 70 km) from Aristarchus Plateau, 25°N, 312°E and LROC WAC images for comparison: (a) LROC WAC image M102471795C with illumination from the West.and ∼15° solar elevation, (b) mosaic of LROC WAC images M1119111212C /M111918011C with illumination from the South-East and ∼55° solar elevation, (c) LROC WAC GLD100 raster DTM, (d) Selene-LALT raster DTM, (e) LRO LOLA (tracks only, without raster interpolation), and (f) LRO LOLA raster DTM.

[24] We compared the GLD100 with altimetry data from the LRO LOLA instrument [Smith et al., 2010] as the current reference. In order to match both data sets, we computed a LOLA DTM from the LOLA shots, laterally identical to the GLD100 100 m raster in Sinusoidal (equal-area) projection for latitudes equatorward of 79°N and S. We transformed the body-fixed Cartesian coordinates of all LOLA shots (3.17 billion shots within latitudes ≤79°) to geographic coordinates and then to the Sinusoidal map projection of this 100 m raster and stored the mean heights of the LOLA shots within each pixel. The total area of latitudes ≤79° covers 3.72 billion pixels (100 m/pixel scale) and ∼834 million (22.4%) contain LOLA measurements. For those pixels that contain at least one LOLA shot, the average is 3.8 measurements per pixel. We then compared this gridded LOLA data set with the GLD100 and found the median of the vertical deviations is +3.0 m, while the mean is +1.7 m, with a standard deviation (1σ) of 24.0 m. The mean absolute value of the deviations is 17.8 m, i.e., less than one third of the image resolution of a WAC pixel. Figure 10a shows the distribution of the vertical deviations and the absolute values of these deviations, both calculated for 500 m grid cells.

Figure 10.

LOLA versus GLD100 vertical deviations: (left) Standard deviation (1σ) and (right) mean absolute deviation. (top) Using GLD100 data of the nominal and science mission phase, (middle) GLD100 data of the nominal mission phase, and (bottom) GLD100 data of the science mission phase.

[25] As described before, the deviations are small relative to the WAC ground pixel resolution. Nevertheless, small systematic effects are apparent. First, the deviations increase with larger slopes (compare right parts of Figure 10). Second, deviations are typically lower on the nearside than on the farside, particularly at the South Pole-Aitken basin (high southern latitudes on the farside). In order to further investigate these effects, we derived refined figures for the deviations to LOLA, separating GLD100 data of the nominal and science mission phases (Figures 10b and 10c).

[26] The deviations are almost equally distributed for the nominal mission case and are only slightly higher on the farside. With science mission data, the increase toward the South Pole-Aitken basin at the farside and at high northern latitudes is much more obvious, although the deviations are still small if compared to the WAC pixel resolution. For both mission phases an obvious correlation between the vertical deviations and local slopes can be determined. Table 1 provides detailed statistics for the deviations to the LOLA altimetry data set for different parts of the lunar surface, for the different mission phases, and for different slopes.

Table 1. Mean Vertical Deviations LOLA Versus WAC GLD100a
 NearsideFarsideGlobal
  • a

    The a / b / c values are as follows: a, slopes ≤1° (only nearside maria considered); b, slopes >1°; c, all slopes.

Standard Deviations () (m)
Nominal mission GLD100 subset10 / 21 / 18− / 24 / 23− / 23 / 21
Science mission GLD100 subset11 / 26 / 22− / 32 / 30− / 30 / 27
Nominal and science mission GLD1009 / 21 /18− / 25 / 24− / 24 / 21
 
Mean Absolute Value of Deviations (m)
Nominal mission GLD100 subset8 / 16 / 13− / 19 / 17− / 18 / 15
Science mission GLD100 subset9 / 19 / 15− / 25 / 23− / 23 / 20
Nominal and science mission GLD1007 / 16 / 13− / 19 / 18− / 18 / 16

[27] Compared with the LOLA data set, GLD100 farside deviations are slightly larger than for nearside data, as well as vertical deviations of GLD100 data are slightly larger in the science mission than in the nominal mission phase. Possible reasons for this effect are hardware degradation within one of the two sensors, and/or a change of one or both sensor alignments, and/or reduced quality of the crossover corrections for the science mission LOLA orbit kernels. Nevertheless, these vertical effects are small (only 0.1 to 0.2 times the WAC resolution of 75 m/pixel) and are further reduced within the combined (nominal and science mission) data set.

[28] It also must be considered, to what extent the vertical deviations listed in Table 1 were caused by lateral sampling effects of LOLA spots to the GLD100 grid. Therefore, we calculated the mean deviation of LOLA spot heights to the mean height value of each 100 m pixel. With a mean distance (D) of ∼39.9 m of a single LOLA shot from the center of a 100 m pixel and a mean surface slope (S) of the entire data set of 6.4°, we derived the vertical component (V) of the sampling effect for a single LOLA shot by V = D ⋅ tan(S) = 4.5 m. For the mean (Vmean) of the average of n = 3.8 LOLA shots/pixel we get Vmean = V/sqrt(n) = 2.3 m. For slopes <2.8° this vertical effect is <1 m, while it increases up to 14 m for slopes of 30–35°. Thus, for the estimation of the vertical accuracy of the GLD100, this average vertical effect of 2.3 m (max. Fourteen m) of the lateral sampling of LOLA spots to the 100 m pixels has to be considered. Finally, a slight lateral residual misalignment between the LOLA and the LROC WAC, even if only a few tens of meters, may cause an additional contribution to the listed vertical LOLA/GLD100 deviations, on the same order of the previously described sampling effects. From these estimates and the statistics of the previous comparison with the LOLA data set, we report that the mean vertical accuracy of the GLD100 is better than 20 m globally, and better than 10 m for flat maria.

[29] We estimated the absolute vertical accuracy of the GLD100 using reference coordinates from Davies and Colvin [2000] of seven landing sites (Lunokhod-2 and Apollo). The accuracy of the reference coordinates sites without lunar laser ranging reflectors (LRRR, Apollo 12, 16, and 17) was stated as ∼30 m. We measured vertical deviations to the reference coordinates at these sites of −37 m, 40 m, and 42 m. The vertical differences for those sites with LRRRs (Lunokhod-2, Apollo 11, 14, and 15) were only 11 m, 3 m, −15 m, and −3 m. Davies and Colvin [2000] stated that the errors of LRRR coordinates are less than 5 m.

8. Summary and Outlook

[30] The GLD100 was derived from ∼69,000 stereo models and represents the first contiguous lunar topography model for latitudes equatorward of 79°N and S at a 100 m grid spacing. Since it is based upon contiguous imagery and is thus free of gaps, the DTM allows for a variety of geoscientific analyses, precise volume estimations, regional slopes and roughness, and profiles in latitudinal as well as in longitudinal direction. It also provides an ideal 3D reference for orthorectification of image data sets from various lunar missions. A comparison with LRO LOLA altimetry measurements shows a good match without significant offsets. The mean vertical accuracy over the entire GLD100 data set is better than 20 m and better than 10 m for nearside maria. This has been confirmed by a comparison with reference coordinates of lunar landing sites.

[31] Apart from detailed investigations of GLD100 slope and roughness parameters, we expect further improvements of this initial version of the GLD100. Local outliers may exist at or near small local depressions or isolated topographic highs where current image matching parameter settings are too restrictive. We intend to detect and to eliminate such blunders and to further minimize the amount of local artifacts as well as noise by adaptations of the entire set of stereo processing parameters. Furthermore, the GLD100 is expected to benefit from results of investigations toward a refined WAC camera model and improved alignment data, based upon in-flight measurement. Finally, stereo models with large stereo-angles, not from subsequent orbits but from orbits further apart in time, will help to improve the quality of the GLD100, particularly at high latitudes. We will also investigate procedures to merge the GLD100 model with the LOLA data set, at high latitudes as well as globally, and with other high-resolution DTMs, e.g., with local DTMs from LROC NAC stereo processing. Finally, Selene mission LISM TC DTMs that yet have not been considered will also be of great interest and subject to future comparisons and analyses.

Acknowledgments

[32] The dedicated work of the LRO and LROC mission operations teams made the acquisition of the WAC global stereo data set possible. We appreciate the supply of improved LRO orbit kernels by the LOLA team. This work is dedicated to Jörg Albertz (1936–2010), the spiritus rector of planetary photogrammetry and cartography at the Technical University Berlin.

Ancillary

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