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Limitations of the Mars Orbiter Laser Altimeter Dataset MARS MARS INFORMATICS The International Journal of Mars Science and Exploration Open Access Journals Technology The Mars Orbiter Laser Altimeter dataset: Limitations and improvements Sanjoy M. Som1,2, Harvey M. Greenberg1 and David R. Montgomery1,2 1Dept. of Earth and Space Sciences and Quaternary Research Center, 2Astrobiology Program, University of Washington, Seattle, WA, 98195, USA, [email protected] Citation: Mars 4, 14-26, 2008; doi:10.1555/mars.2008.0002 History: Submitted: April 20, 2007; Reviewed: October 17, 2007; Revised: April 4, 2008; Accepted: April 22, 2008; Published: June 11, 2008 Editor: Oded Aharonson, California Institute of Technology Reviewers: Oded Aharonson, California Institute of Technology; Patrick McGovern, Lunar and Planetary Institute, Universities Space Research Association Open Access: Copyright © 2008 Som et al. This is an open-access paper distributed under the terms of a Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Background: The Mars Orbiter Laser Altimeter (MOLA), part of the instrument suite onboard the Mars Global Surveyor spacecraft (MGS), mapped Martian topography between 1999 and 2001. The latest sub-polar dataset, released in 2003, is a 128 pixel per degree digital elevation model (DEM) of the planet, from –87o to +87o. Due to the orbital characteristics of MGS, the resolution is latitude- dependent, being highest near the poles. Method: We analyze the longitudinal dependence in MOLA data density and find that only a third of the DEM elevation information at the equator comes from raw measurements, the rest being interpolated. Without questioning the enormous scientific value of this dataset, we investigate its limitations qualitatively and quantitatively. We also re-interpolate the dataset using a natural- neighbor with bias scheme that is shown to reduce interpolation-induced errors, particularly for small-scale, East-West trending geomorphic features. Conclusion: We find that interpolation, especially at the equator, leads to topographical artifacts and smoothing of the terrain that should be appreciated in interpreting geomorphic features that have length scales on the order of the spacing between the orbital tracks that overlap the terrain of interest. Our new interpolation scheme is biased in the East-West direction, improving the overall quality of the elevation model. Introduction 37.5 cm range resolution but due to radial-orbit error, the vertical accuracy obtained was ~1 m when ranging a flat The Mars Orbiter Laser Altimeter (MOLA) (Zuber et al. surface (slope <2°). When the instrument ranged terrain with 1992), one of five instruments onboard the Mars Global mean slopes greater than 2°, the vertical precision was Surveyor (MGS) spacecraft, began mapping the planet in comparable to 10% of the elevation change within the 168 m September 1999 (Smith et al. 2001). With a pulse repetition in diameter footprint (Smith et al. 2001), although most of rate of 10 Hz, the laser successfully ranged the planet until the energy may have come from an area as small as 75 m in the failure of a critical component in June 2001 interrupted diameter (Smith et al. 1999). The 10 Hz frequency of the the laser trigger. While operational, the instrument surpassed laser-firing limited the along-track spacing between shots to all goals set by the MOLA investigation. It fired over 670 ~300 m (Smith et al. 1999, Smith et al. 2001). million times (each laser firing is called a “shot”), and generated nearly 9500 orbital profiles, exceeding engineering MOLA doesn’t measure elevation directly. Rather, it design limits (Smith et al. 1999). Unlike current airborne calculates the range to the surface by measuring the time-of- LIDAR instruments, MOLA did not scan from side to side in flight of individual laser pulses. This range is subtracted from the latitudes between -87° and +87°, the latitudes of interest the spacecraft’s orbit location to obtain the planetary radius in this paper (though it was aimed off-nadir to capture polar RMars. Elevation h is obtained by subtracting the areoid radius topography). As such, data was only collected along the Rareoid from the planetary radius (Smith et al. 2001). The orbital track of MGS. The MOLA instrument was capable of areoid is defined as representing the surface potential 14 Som et al: Mars 4, 14-26, 2008 measured at the mean equatorial radius (3396 km) (Smith et cross-over correction. Altimetric cross-overs are the al. 1999). difference in radial distance measured at a common location from two distinct intersecting ground tracks (Neumann et al. The MOLA instrument has been used extensively by the 2001). A cross-over analysis allows for better estimates of scientific community as an aid in understanding the geology, the spacecraft’s position during ranging, since tracking from geophysics and geomorphology of the planet, and DSN is discontinuous. Indeed, following correction, position specifically permitted significant progress in topics as is known within <100 m, which is less than a shot footprint diverse as stratigraphy (Fueten et al. 2005), volcanism (168 m in diameter), and elevation is known to within <1 m (Schultz et al. 2004), atmospheric science (Neumann et al. (Neumann et al. 2001). 1999), surface roughness (Neumann et al. 2003), past transport of water (Williams and Phillips 2001), and internal With data from PEDRs, Experiment Gridded Data Records structure (Zuber 2001). For a summary of MOLA scientific (EGDRs) are created. Initial Experiment Gridded Data achievements, see Smith et al. 2001. Records (IEGDRs), which encompass at least the first 30 days of the mission, and Mission Experiment Data Records In May 2003, the latest sub-polar MOLA DEM was released (MEGDRs) consisting of data up to when the instrument (version L) with a resolution of 128 pixel per degree (ppd), stopped working, are created from the EGDRs. while polar DEMs with resolution as high as 512 ppd were released one year later. In the current work, we will restrict The MEGDRs are the DEMs, and come from the ourselves to the sub-polar 128 ppd DEM, which extends interpolation of the PEDRs. They are gridded at several from –87o to +87o latitude. The cartographic projection resolutions: 4, 16, 32, 64 and 128 ppd for the mid-latitudes frame used in the MOLA DEM is the IAU2000 sphere for (up to ±87°) (Smith et al. 2003). In addition to the Mars (Seidelmann et al. 2002). information included in PEDRs, MEGDRs also contain the number of shots per grid cell. For clarification, a grid cell is DEMs are displayed as shaded-relief maps, which are the basic unit of composition of a dataset, which may contain models of how the topography would appear under NW several types of information for that particular unit illumination ignoring albedo. A raster DEM is a regular grid (elevation, number of shots etc…), however, what is of points, each with discrete information on elevation. The displayed on the DEM is a pixel (picture element), which is MOLA DEM grid points that did not stem from a direct the grid-cell information displayed for a particular attribute, elevation measurement by MOLA were interpolated using a such as elevation. With a shot footprint of 168 m in diameter, minimum-curvature-under-tension (MCUT) scheme (Smith the number of shots per grid cell will decrease with et al. 2001; Smith and Wessel 1990). The Generic Mapping increasing resolution, since the 4 ppd DEM has a grid cell Tool (GMT) software (Wessel and Smith 1991) was used for dimension (width scales with the cosine of the latitude) of the interpolation since it contains a built-in MCUT algorithm ~14.8 km, whereas the 128 ppd has a grid cell size of ~460 with a user selectable tension parameter (T). A tension m. parameter of 0.5 was used in the creation of the currently available MOLA DEM. Analysis As in most interpolation schemes, artifacts introduced in the dataset may skew data analysis in studies involving the Latitude-dependent resolution resulting DEMs. We first evaluate the MOLA DEM The frequency of the number of shots per grid cell varies resolution to assess potential interpretive pitfalls and errors significantly for the different resolution MOLA DEMs caused by artifacts and smoothing. We then inspect different (Figure 1). Because the laser fired at regular intervals, the interpolation schemes, and introduce a new DEM for Mars, number of shots per cell scales with grid cell size. For the UWMOLA, based on a natural-neighbor-with-bias (NNB) 128 ppd DEM, most grid cells are devoid of shots (Figure scheme. 1c), which indicates that data for the majority of the cells are generated by interpolation. Figure 1d illustrates how track Nature of the 2003 MOLA DEM spacing generates peaks in the frequency diagram in, for example, Fig 1b. In addition, the percentage of grid cells MOLA datasets are available from the NASA Planetary Data System (PDS), and can be found at different stages of processing leading to the DEM. MGS’s orbital inclination of Table 1. Percent coverage and pixel length scale 93o permitted MOLA to obtain nadir measurements of the for available MOLA DEMs between –60o and +60o mid-latitudes from -87o to +87o. Data, once sent by the latitude spacecraft and received through the Deep Space Network DEM Pixel length scale Coverage (DSN) in binary packages, were assembled into Aggregated [pixel per [km] [% of cells containing Experiment Data Records (AEDRs). The AEDRs were then degree] ≥ 1 shot] processed for errors (such as non-nadir pointing, errors in 4 14.82 100 calibration and spacecraft location…) yielding Precision 16 3.71 96 32 1.85 81 Experiment Data Records (PEDRs). PEDRs incorporate the 64 0.93 55 areoid and as such, elevation information is directly available 128 0.46 31 from them (Smith et al.
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