Vol. 84, No. 52, 30 December 2003

Online Mars Digital Elevation Model Derived from MOLA Profiles

C. Delacourt, N. Gros, and P. Allemand, Université Lyon, France; and D. Baratoux, Observatoire Midi-Pyrénées, Toulouse, France

---

Copyright 2003 American Geophysical Union

The topography of Mars is a key parameter for understanding the geological evolution of the planet [Smith et al., 1999b; Zuber et al., 1992]. Topographic data, for most applications, are presented as Digital Elevation Models (DEMs), which are characterized by their spatial resolution (the distance between neighbor points on the topographic grid) and the accuracy of elevations. The resolution and accuracy of a DEM have to be adjusted according to the expected geological applications. For lithospheric scale tectonic applications such as the crust or elastic lithospheric thickness estimation [Zuber et al., 2000], the study of the dichotomy [Smith and Zuber, 1996], or the study of large impact structure [McGill, 2001], a coarse resolution around a few kilometers is enough, and even hecto-kilometric spatial resolution with hectometer vertical accuracy can be used.

For Valles Marineris studies [Lucchitta et al., 1994], outflow channels [Williams et al., 2000], large impact craters, or volcanic structures [McEwen et al., 1999; Smith et al., 1999a], a DEM with a spatial resolution ranging from 2 to 10 km with a decametric vertical accuracy is needed. Finally, for small impact craters [Frey et al., 2001; Garvin et al., 2000], landslides [McEwen, 1989], ridges, grabens [Mangold et al., 1998; Withers and Neumann, 2001; Zuber, 1995], and eolian activities producing features a few tens of meters high, a DEM characterized by a spatial resolution better than 100 m and a vertical accuracy better than 10 m is required.

During the last three decades, three techniques have been used to produce Martian DEMs. First, the CO₂ pressure measurements realized by the Viking probes [Soffen, 1977] were used to derive a 10-km scale DEM of the entire planet with a poor kilometric precision. Then, some attempts have been achieved to produce DEMs by photogrammetric techniques on Viking images [Blasius, 1975; Dzurisin and Blasius, 1977; Thornhill et al., 1993]. These methods, which have been improved by Baratoux et al. [2001], produce DEMs with high spatial resolution close to the resolution of stereoscopic pairs of images used for the calculation. However, this technique is highly time-consuming, and the resulting DEMs are difficult to precisely register in an absolute reference frame because of the poor knowledge of the Viking orbiters position and camera orientation before photogrammetric processing. Furthermore, stereoscopic Viking images are not available on the whole surface of Mars [Kirk, 1999]. Finally, topographic data available from this method are heterogeneous and not suitable for establishing a global topographic map of Mars [Baratoux et al., 2001]. The third method of DEMs calculation uses the Mars Orbital Laser Altimeter (MOLA) launched in the frame of the Mars Global Surveyor mission in 1997, which has acquired more than 600 million topographic measurements. The precision of the altimeter was specified to be around 35 cm [Zuber et al., 1998].

The laser measures the elevation over a spot of 130 m, but the final, vertical, absolute precision is between 3 and 5 m, due to uncertainties in orbit determination. The altimeter acquired topographic data along the orbit of the satellite with one point of measure each 300 m. The topography has been measured along profiles separated by 2 km near the equator, and by some hectometers at high latitudes due to the near-polar orbit of the satellite. Locally, irregular ground track spacing produce larger spatial gaps up to 5-6 km.

However, despite this high vertical accuracy, the main limitation of this technique appears when topographic maps are needed. To create a DEM or a topographic map, an interpolation on individual MOLA measurements on regular grids is required.

The best resolutions of released DEMs produced by the MOLA team (reference available at http://www.etc.gov) are up to 1/128th degrees, equivalent to 0.5 km at the equator. Calculation of the global full-resolution Martian DEM requires very intensive computation and large disk capacities.

Only a few teams throughout the world have computed a full resolution DEM from MOLA data. To totally exploit the high potential of MOLA data, especially when local studies are conducted, we propose an Internet application that allows any user to process local DEMs of the surface of MARS with adjustable parameters of computation (area of interest and spatial resolution), and to extract all of the individual MOLA measurements over the area of interest. The final DEM can then be directly downloaded with an accompanying header file that describes the data format. Furthermore, the heterogeneity of MOLA data leads us to compute a local estimator for the quality of the DEM; this is necessary for the interpretation of small structures.

This quality estimator is computed for each point of the DEM. Its value is related to the local density of MOLA points used to compute the elevation on the regular grid. This quality map is intended to demonstrate the reliability of interpretation when small geological objects like landslides or small craters are studied from DEMs with resolutions of a few hundred meters. Furthermore, all MOLA measurements for the area of interest can be also downloaded, while such a data extraction would require the reading of the entire data set. By means of these data, all topographic profiles can also be selected for the area of interest. In addition, subroutines written in Interactive Data Language can be downloaded. These subroutines read the DEM and ancillary files and plot and select topographic profiles on the area of interest.

Forty-four CD-ROMs containing MOLA points classified by profiles across the planet are available from NASA (http://wufs.wustl.edu/missions/mgs/mola/). So for a given area, topographic data are distributed over numerous files not located on the same CD-ROM. First, the relevant topographic information for DEM processing must be extracted: geographic coordinates of each point, local radius of the planet, and elevation, which is the local difference with the geoïd given by up-to-date gravity models of Mars [Smith et al., 1999a]. Then, the extracted points are classed by area of 5°E x 5°E corresponding to 2592 files for the whole planet. This step is fundamental for improving the speed of access to data. All of the MOLA points for a given area are then grouped into a file that is saved directly to the application server. After the request of a DEM computation on a selected area with a given resolution, the points belonging to this area are extracted.

Then, from this irregularly spaced set of points, a Delaunay triangulation is performed to obtain the interpolated topographic data over a regular grid. During this step, the quality factor map (Q) is processed for each point of the final DEM. Q represents the minimum distance between each DEM's point and the three vertices of the triangles formed by the three closest MOLA points obtained after Delaunay triangulation. For visibility, Q is then arbitrarily divided into six classes. Specific applications require more precise knowledge of the accuracy. Then, ancillary files are created, including a file containing all of the MOLA points used during the interpolation process and an image file in tiff format, which is a color-coded topographic map of the area.

All of the modules have been developed with Interactive Data Language (IDL) by Research Systems, Inc. [2001a]. IDL is a complete computing environment for the interactive analysis and visualization of data [Marschallinger, 2001] that integrates an array-oriented language with mathematical analysis. A net version of IDL, ION (IDL On the Net, Research Systems, Inc. [2001b]) has been implemented on a Web server (http://image.univ-lyon1.fr).

A recognition step is first required. A form that includes information (such as identity and topic of interest) has to be filled out to obtain access to the server. The account is created within 48 hours; login and password are sent to the user by e-mail. The access is totally free of charge. The user can then connect to the server (http://image.univ-lyon1.fr/MARS), which is part of the Web site of the "Laboratoire Dynamique de la Lithosphère UMR 5570". The user clicks on the Mars section. At this step, a tutorial section shows how to use the application with an example; then the user can move onto the application section.

The parameters for DEM computation can be set in two different ways (Figure 1a): directly on a map of Mars by clicking on the area of interest or by typing the coordinates of a rectangle of interest and the desired spatial resolution. To avoid irrelevant computations that may saturate the processor, the spatial resolution is limited to 0.3 km and the coverage is limited to 10°E x 10°E, which corresponds to 600 km x 600 km on Mars at the equator.

Fig. 1. When selecting the area of interest "Map of Mars," the user can click the center of the area of interest and associated coordinates of the selected area.

Before the processing step, the user can check the localization of the selected area on a map of Mars and modify the spatial resolution of the output DEM. Then the DEM is interpolated. The computation time does not exceed a few minutes. Time can be saved by disabling computation of the quality factors. Finally, an image of the DEM is plotted (Figure 2a) and the various files can be downloaded. A directory is created on the local server disks from where the user can download, rename, and erase the created files (Figure 2b). In addition, two programs written in IDL could be downloaded on the first page of the site (MOLAREAD.pro and SELECTORBIT). Those programs read all of the downloaded files and put the data into variables that can be manipulated by the user. They also allow selection of a particular profile and a plot of this profile can be made.

Fig. 2. This figure shows (a) a calculated DEM; (b) an associated accuracy map; (c) a Viking image of the area (this image is not supplied by the application); and (d) an example of an altitude profile.

Fig. 3. This image of downloading windows lists the downloading files: Mola.lis gives the CD used for the interpolation; mola;tif is an image of the DEM; mola_dem.dat is the DEM binary file in PDS format with header mola_dem.hdr; mola_groundtrack.ps is a postscript file of the position of the mola profile; mola_pts.dat contains each value of the profile; and mola_qmp is the DEM quality map.

Baratoux, D., C. Delacourt, and P. Allemand, Digital Elevation Models derived from Viking images: Method and comparison to MOLA data, J. Geophys. Res., 106, 32,927-32,941, 2001.

Blasius, K. R., J. A. Cutts, J. E. Guest, and H. Masursky, Geology of Valles Marineris: First analysis of imaging from the Viking Orbiter primary mission., J. Geophys. Res., 82, 4067-4091, 1977.

Dzurisin, D., and K. R. Blasius, Topography of the polar layered deposits of Mars, J. Geophys. Res., 80, 3286-3306, 1975.

Frey, H. V., E. L. Frey, S. E. H. Sakimoto, K. Shockey, and J. Roark, A very large population of likely buried impact basins in the northern lowlands of Mars revealed by MOLA data, XXXII Lunar and Planetary Sci. Conf., Houston, Tex., pp. 1680-1681, 2001.

Garvin, J. B., S. E. H. Sakimoto, J. J. Frawley, and C. Schnetzler, North polar region craterforms on Mars: Geometric characteristics from the Mars Orbiter Laser Altimeter, Icarus, 144, 329-352, 2000.

Kirk, R., A database of Viking Orbiter image coverage of Mars for cartographic and scientific use, Proc. Fifth Int. Conf. on Mars, Pasadena, California, 1999.

Lucchitta, B. K., N. K. Isbell, and A. Howington-Krauss, Topography of Valles Marineris: Implications for erosional and structural history, J. Geophys. Res., 99, 3783-3798, 1994.

Mangold, N., P. Allemand, and P. Thomas, Wrinkle ridge of Mars: Structural analysis and evidence for shallow deformation controlled by ice-rich decollements, Planet. Space Sci., 46, 345-356, 1998.

Marschallinger, R., Three-dimensionnal reconstruction and visualization of geological materials with IDL-examples and source code, Comp. Geosci., 27, 419-426, 2001.

McEwen, A., Mobility of large rock avalanches: Evidence from Valles Marineris, Mars, Geology, 17, 1111-1114, 1989.

McEwen, A. S., M. C. Malin, M. H. Carr, and W. K Hartmann, Voluminous volcanism on early Mars revealed in valles marineris, Nature, 397, 584-586, 1999.

McGill, G. E., Utopia Basin revisited: Regional slope and shorelines from MOLA profiles, Geophys. Res. Lett., 28, 411-414, 2001.

Research Systems, Inc., IDL Reference Guide, Research Systems, Inc., Boulder, Colo., 1173 pp., 2001a.

Research Systems, Inc., ION Reference Guide, Research Systems, Inc., Boulder, Colo., 782 pp., 2001b.

Smith, D. E., W. L. Sjogren, G. L. Tyler, G. Balmino, F. G. Lemoine, and A. S. Konopliv, The gravity field of Mars: Results from Mars Global Surveyor, Science, 286, 94-97, 1999a.

Smith et al., The global topography of Mars and implications for surface evolution, Science, 284, 1495-1503, 1999b.

Smith, D. E., and M. T. Zuber, The shape of Mars and the topographic signature of the hemispheric dichotomy, Science, 271, 184-188, 1996.

Soffen, G. A., Scientific results of the Viking Project, Science, 194, 3959, 1977.

Thornhill, G. et al., Topography of Apollinaris Patera and Ma'adim Vallis: Automated extraction of Digital Elevation Model, J. Geophys. Res., 98, 581-587, 1993.

Williams, R. M., R. J. Phillips, M. Malin, Flow rates and duration within Kasei Valles, Mars: Implications for the formation of a martian ocean, Geophys. Res. Lett., 27, 1073-1076, 2000.

Withers, P., and G. A. Neumann, Enigmatic northern plains of Mars, Nature, 410, 651, 2001.

Zuber, M. T., Wrinkle ridges, reverse faulting, and the depth of penetration of lithospheric strain in Lunae Planum, Mars, Icarus, 114, 80-92, 1995.

Zuber, M. T. et al., The Mars Orbiter laser altimeter investigation, J. Geophys. Res., 97, 7781-7797, 1992.

Zuber, M. T., et al., Shape of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter (MOLA), Geophys. Res. Lett., 25, 4393-4396, 1998.

Zuber, M. T. et al., Internal structure and early thermal evolution of Mars from Mars Global Surveyor topography and gravity, Science, 287, 1788-1793, 2000.