MAPPING THE TOPOGRAPHY OF MARS 
David E. Smith 
Laboratory for Terrestrial Physics 
NASA/Goddard Space Flight Center 
Greenbelt, MD 20771 
USA 
Maria T. Zuber 
Department of Earth, Atmospheric and Planetary Sciences 
Massachusetts Institute of Technology 
Cambridge, MA 02139-4307 
USA 
Commision IV, Working Group 5 
KEY WORDS: Cartography, Geology, Mapping, Extraterrestrial 
ABSTRACT 
Data from the Mariner and Viking missions of the seventies have been re-analyzed to derive a new model for the fundamental 
shape of the planet Mars in preparation for the arrival of several spacecraft and landers over the next several years. This model 
is believed to be a significant improvement at the longer wavelengths over earlier models and is being used to gain new insight 
into large scale processes in the planets history. Later this year, the US will send the Mars Global Surveyor mission to Mars 
followed by the Mars Pathfinder lander, that will arrive in the late summer of 1997. The MGS will carry a laser altimeter as 
part of its complement of instruments which will map the entire planet on horizontal scales of a kilometer and provide a new 
framework for future high resolution mapping of the planet. 
1 INTRODUCTION 
The fundamental shape of the planet Mars upon which all 
maps of the planet have been referenced is based on the 
analysis of radio occultation measurements of the Mariner 
9 and Viking 1 and 2 spacecraft of the nineteen seventies. 
These observations are a record of the times when the radio 
signal from the spacecraft was either lost behind the planet or 
emerged from behind the planet and when the ray path was 
tangential to the surface on the limb (Kliore et al, 1973; Lin- 
dall et al, 1979). The location of the planet and spacecraft 
at the time of the occultation provide a measure of the radius 
of the planet at the occultation point. Nearly 400 of these 
measurements were acquired from these missions and subse- 
quently used to construct a model for the long wavelength 
shape of Mars (Smith and Zuber, 1966). 
Earth-based radar observations have also played a major role 
in our understanding of the shape of Mars but to a large 
extent were not included in the early analyses that defined 
the shape of the planet. The radar data (Downs et al, 1982), 
along with photographic images (Wu, 1989, 1991), have been 
the basis of the high resolution models of Mars topography, 
which were superimposed upon the shape defined largely by 
occultations. Thus, for many years the size of Mars was in 
error by several kilometers although relative locations were 
better known. Atmospheric instrumentation has also been 
used to infer shape and topography of Mars but these mea- 
surements were based on assumptions about the location and 
shape of the 6.1 mbar surface which was derived from an early 
low degree model for the gravity field of Mars (Lorel et al, 
1973) that we now know to be in error and could not, be- 
cause of its limitation in resolution, represent even some of 
the largest geological features of Mars. 
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2 RESULTS 
Recently, these observations have been re-analyzed employing 
improved ephemerides of the spacecraft and planet and a new 
model of the long wavelength shape of Mars has been devel- 
oped. A covariance analysis suggests that the new model has 
an rms error of ~ 500 meters with a range of 300 meters to 
1.2 km. The largest sources of error are the orbital errors of 
the three spacecraft. The topography is defined as the dif- 
ference between the shape of the planet and an equipotential 
surface. Using the most recent models for the gravity field of 
Mars (Smith et al, 1993; Konopliv et al 1995), which have 
geoid errors of the order of 100 meters at long wavelengths, 
a comparison with the DTM suggests errors in the latter of 
1 km (rms), with some locations at the 3 km level. A similar 
comparison with the Consortium topography model indicates 
errors of many kilometers and a systematic error from the 
south pole to north pole of about 5 km. 
We find no discrete topographic offset between the shapes of 
the northern and southern hemispheres although prominent 
impact basins, such as Hellas and Isidis, are clearly seen. On 
the other hand, the geopotential topography, which corre- 
sponds to the planetary radius minus the radius of the Mar- 
tian geoid or gravitational equipotential, shows the topog- 
raphy has an offset in elevation between the northern and 
southern hemispheres. A histogram of the geopotential to- 
pography exhibits a bimodal distribution of elevations that 
corresponds to systematic elevation differences between the 
northern and southern hemispheres. 
This re-analysis of the topography has led to a re-examining 
of the hypotheses for the existence and formation of the hemi- 
spheric dichotomy of Mars with the recognition that the to- 
pographic low associated with the northern hemisphere is a 
result of the center of mass/center of figure offset for the 
planet and not necessarily an impact (s). We also note that 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996