Our present knowledge of the topography of Mars is completely inadequate for addressing a wide range of geophysical, geological, and atmospheric problems. The data acquired to date by several techniques has not provided us with reliable and consistent values for even the equatorial and polar radii, and large uncertainties exist in the altitudes of many of the major volcanic constructs. While much of this can be blamed on a lack of reliable data, we feel that much more could be done to improve the analysis of the present data in a consistent global system that would necessarily involve the re-analysis of early spacecraft and Earth-based data in conjunction with more recent models of Mars' gravity field

Smith, D. E.

Zuber, M. T.

English

NASA Technical Reports Server

THE TOPOGRAPHY OF MARS: A RE-EVALUATION OF CURRENT DATA; D.E. Smith 1,
and M.T. Zubet 2,1 , 1Laboratory for Terrestrial Physics, NASA/Goddard Space Flight Cente ,_Greenbett,
MD 20771,2Dept. of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218.
Our present knowledge of the topography of Mars is completely inadequate for addressing a wide
range of geophysical, geological, and atmospheric problems. The data acquired to date by several
techniques has not provided us with reliable and consistent values for even the equatorial and polar radii
and large uncertainties exist in the altitudes of many of the major volcanic constructs. While much of this
can be blamed on a lack of reliable data, we feel that much more could be done to improve the analysis of
the present data in a consistent global system that would necessarily involve the re-analysis of early
spacecraft and Earth-based data in conjunction with more recent models of Mars' gravity field.
Current topographic knowledge of Mars is based entirely on measurements obtained by the early
Mariner and Viking spacecraft and on Earth-based radar measurements [1-4]. Radio occultation
measurements of the Mariner 9 spacecraft and the Viking 1 and 2 Orbiters are the primary near-global data
sets. The principle behind these observations is that knowledge of the time when the signal from a
spacecraft is "lost" behind the planet can be used (in conjunction with knowledge of the position of the
spacecraft and the planet) to estimate the radius of the planet at the time of occultation. These data have
formed the basis of several determinations of global Mars topography [3,5,6] but only about 400
measurements from the primary and extended phases of these missions are available. The principal
sources of error in these data are the spacecraft position [4] at the km level, the timing of the actual loss of
signal at the hundreds of msecs of time (-1 km) and the actual location of the grazing ray at the time of
occultation due to local topography [1]. Depending on the orbital radius of the spacecraft at the time of
occultation, the geometry of the spacecraft and planet, and the topography of the limb, these errors can
amount to several kilometers in the planetary radius, although this is often not the case. The effect of
refraction through the 6 mbar atmosphere contributes up to a maximum of a few tens of meters to the error
in radius, even if neglected completely. Figure 1 shows how 300 Mariner 9 and Viking orbiter occultation
measurements [1,4] are distributed across the planet, ranging in latitude between approx. 75N and S and
spread across all longitudes. If these data were uniformly distributed across the planet they would have a
mean separation of approximately 800 kin, equivalent to a spherical harmonic representation of degree
and order 17. Even if each value only had an accuracy of only 1 km, the basic shape of the planet at the
sub-kilometer level would not be in doubt and the mean equatorial planetary radius known to a few
hundred meters even in the absence of other data.
The Earth-based radar data [7,8] provide a direct measure of the distance to the surface of the
planet from Earth and by inference of the planetary surface from its center. The measurement is the
distance to the point on the surface normal to the incoming wave and has a resolution of 10 to 30 km in
longitude and 80 to 120 km in latitude, depending the distance of Mars from Earth and on transmitter
power [8]. Because of the limitations in the variation in geometry of the orbit of Mars and its spin axis
direction from Earth, radar observations are generally limited to 25 degrees of the Mars equator. A typical
observation period will produce radar returns from a strip of almost constant latitude [7] with a range
precision of better than 100 meters. The primary source of error appears to be the planetary ephemeris
which was thought to be at the kilometer level in the late seventies and early eighties when most of the
calculations of Mars topography were performed. This error is of particular significance for estimating the
global scale topography and must be accounted for when combining radar data with occultation data by
the estimation of biases or adjustments to the ephemeris directly. At a lesser level are errors introduced
by the solar plasma, which depend on the radar frequency, and are typically at the tens of meters level.
The radar data are an orthogonal data set to the occultation data and together provide the strongest
measurements of the global shape of Mars.
The third data set that has been used in deriving the global topography is from the infrared and
ultraviolet sensors on the Mariner 6, 7 and 9 spacecraft [9-12]. These sensors provided data about the
total atmospheric column content of carbon dioxide thus enabling the topography of the planet's surface
to be inferred with respect to an equipotential surface (usually the 6.1 mbar surface) based upon a model
of the atmosphere. The instrumental precision of the measurements for a clear atmosphere is probably
equivalent to a few hundred meters in altitude above the reference surface [9] with a spatial resolution of a
10x30 kilometers for the UV measurements and 125x125 kilometers for the IR. Over thirty thousand
measurements were obtained globally by Mariner 9 [11,12]. Systematic effects arising from assumptions
about the atmosphere and its constancy over space and time introduce much larger errors on a global
scale thus making the measurements of greater value in some local region but limited in their ability to
provide geodetic control on a planetary scale. Further, these measurements only provide altitude
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1290 MARS TOPOGRAPHY: Smith, D.E. and Zuber, M.T.
deviations from the reference surface and are unable to independently describe the planet in terms of
areocentric radii. In contrast to these data providing strong information about the shape of Mars, it is clear
[B. Jakosky, pers. comm.] that an improved topographic model would make the atmospheric data from
these instruments even more valuable. More recently the infrared spectrometer on board the Phobos
spacecraft obtained nine spectral images of Mars [13]. From the measurement of carbon dioxide
absorption, topographic data of 150 meter quality has been derived for certain local regions. These results
show some systematic differences with both radar and the occultation data at the few hundred meter level
and suggest more major discrepancies for the altitudes of some of the major volcanoes which are not
easily observed at their peaks by either the occultation or Earth based radar. The most significant limitation
of all these instrumental observations is that they are all referenced to the 6.1 mbar surface and therefore
are not providing any topographic information on planetary scales of a 1000 km or larger.
On regional and local scales photogrammetric techniques have been used extensively to derive
the topography [6,14-18]. Photogrammetry provides precise detailed information on a local level that
requires little or no long wavelength control. However, its obvious strength at local scales is its inherent
weakness on the planetary scale and, indeed, in nearly all global models the photogrammetric results have
been treated as detail that is added to the long wavelength geodetic control provided by other data,
usually occultation and radar. Thus, issues of compensation and isostasy are difficult or impossible to
address with the photo data and little progress has been made in this respect for over a decade. A further
limitation is the lack of validity of the reference areoid on all medium and shorter length scales. Even the
most recent models of the gravity field of Mars [19] contain only minimal information at wavelengths less
than 500 km. Thus, even regional problems requiring slope information with respect to the areoid cannot
be reliably addressed. Further discussion of Mars topography and its limitations can be found in [20-23].
It is our opinion that all the data that contribute to our knowledge of Mars topography should be re-
analyzed. This would include the occultation data, which would benefit from significantly improved orbits
for the spacecraft now available, the Earth-based radar data, the incorporation of improved global gravity
models [19] and planetary ephemerides, the application of a priori information based on the present
topographic models, the use of consistent and improved reference models and parameters of the
planetary coordinate system, incorporation of lander atmospheric data and position, and the application of
computing techniques and facilities not available a decade ago. We might then be reasonably sure of the
extent to which our ignorance of Mars topography is limited by the data.
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References: [1]Kliore, A.J. et al. (1972) Icarus, 17, 484. [2]Kliore, A.J. et al (1973). [3]Christensen, E.
(1975) JGR.,78, 4411. [4]Lindal, G.F. et al. (1979) JGR, 8443. [5]Wu, S.S.C. (1977) XV Internationa/
Congr Surveyors, Comm.. V Stockholm, Sweden. [6]Bills, B.G. and A.J. Ferrari, (1978) JGR,83, 3
497.[7]Roth et al., (1980) Icarus, 42, 287. [8]Downs et al, (1982) JGR, 87, 9747.[9]Herr, et al., (1970)
Astron. J., 75, 883. [10]Barth, and Herd, (1971) Science, 173, 197. [11]Herd, et al, (1972) Icarus, 17,
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The topography of Mars: A re-evaluation of current data

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