Data Set Overview
  =================
  The Mars Global Surveyor (MGS) spacecraft included a laser altimeter
  instrument. The primary objective of the Mars Orbiter Laser
  Altimeter (MOLA) is to determine globally the topography of Mars at
  a level suitable for addressing problems in geology and geophysics.

  A Precision Experiment Data Record (PEDR) contains MOLA science mode
  telemetry data that has been converted to engineering and physical
  units. The Aggregated Experiment Data Record (AEDR) is the source for
  the science data, while ancillary information is provided by the Radio
  Science investigation. Precision orbit, geometric, and calibration data
  have been incorporated, as well as an equipotential datum (areoid), so
  that topographic profiles may be obtained directly from the PEDR.

  Each PEDR contains a 2 second span of data, called a frame, that is
  retrieved from the 14 second MOLA science mode telemetry
  packets. Therefore, seven PEDRs are generated from each MOLA AEDR
  record. In addition to the frame data, the packet's engineering and
  housekeeping data are retained and subcommutated among the seven
  PEDRs that comprise a packet. Some of the engineering data, namely
  the background noise counters, have recently been used as a
  narrow-band radiometric data type and will be archived separately.
  Additional packet information, e.g., packet header, are stored in
  the PEDR as well as data correction values which were used to
  process the telemetry data into the PEDR data.

  A complete listing of all parameters contained in a PEDR can be
  found in Table 1 of the PEDR Software Interface Specification (SIS)
  document [MOLAPEDRSIS2003]. A description of the parameters
  contained in a PEDR is found in Table 2. The
  engineering/housekeeping data are listed in Table 3; this table also
  describes the location of the engineering/housekeeping data among
  the seven PEDRs that constitute a MOLA telemetry
  packet. Additionally, the PEDR format and contents are described in
  the PEDR Data Dictionary in Appendix B of the SIS.

  Contained in a PEDR are the range value computed at the frame mid-
  point, the planetary radius at the frame mid-point, and the
  planetary radius for each shot. Range counts are converted to units
  of length following [ABSHIREETAL2000]. There are 20 possible shots
  in a 2 second frame, numbered from 1-20. Additionally, ground and
  spacecraft location, i.e., latitude, longitude, and radial distance,
  obtained from the precision orbit data for the frame mid-point, are
  stored in the PEDR.  The change in latitude and longitude per frame
  is also stored, so that the location of individual shots may be
  obtained by interpolation via the generic formula: shot_location =
  mid_pt_location + (shot_no - 10.5)/20 * delta_location. In view of
  the parallax introduced by offnadir observations, there is an added
  first-order correction for deviations in radius from the frame mid-
  point radius to the location of each individual shot in a frame.

  The range and precision orbit data are given with respect to the
  Mars Global Surveyor center of mass. The planetary radius values are
  computed with respect to the center of mass of Mars. The locations
  of the MOLA shots are in areocentric coordinates, with the longitude
  positive Eastward. Each footprint represents the centroid of a pulse
  returned within a spot approximately 168 m in diameter, although the
  majority of the energy detected from an individual shot may come
  from a smaller area 75 m in diameter [NEUMANNETAL2003]. The
  cartographic reference frame and rotational model describing ground
  locations used in this release is the IAU2000 model
  [SEIDELMANNETAL2002] based on Viking, Pathfinder, and MGS data. This
  frame differs from the IAU1991 coordinate system used in earlier
  MOLA releases [DAVIESETAL1992B].  The most significant change is the
  longitude of the prime meridian in the J2000 epoch and reference
  frame, which has decreased by 0.238 degrees from IAU1991. The effect
  of this change is to place the center of a landmark, the crater
  Airy-0, as close as possible to 0 longitude, and reduce the
  discrepancy between Viking-era maps and the MOLA locations
  introduced by a mistaken location for the Viking-1 Lander
  [ZEITLER&OBERST1999].

  On Earth, it is customary to define topography in terms of a height
  above or below 'sea level', given that the ocean is very nearly an
  equipotential.  surface. Beneath continents, an ellipsoidal datum is
  used that closely matches the mean static oceanic surface, or geoid.
  In contrast to terrestrial practice, the topography of Mars is
  referenced to an equipotential surface, or areoid, described below.
  The areoid departs by nearly 2 km from an ellipsoid of revolution
  and cannot be described as a simple function of latitude. An earlier
  such datum [WU1991] was defined by a spherical harmonic
  expansion to degree and order four, thought to represent the height
  at which the mean atmospheric pressure would equal 6.1 mbar (the
  triple point of water). The martian atmosphere exchanges nearly 30%
  of its mass with the poles annually, so that pressure is highly
  variable with season. MOLA uses an areoid defined by a gravitational
  potential model derived from satellite tracking, and an equatorial
  mean planetary radius.  MOLA topography is the difference between
  planetary radius and areoid at a given longitude and latitude. The
  average 6.1 mbar pressure surface lies about 1.6 km below the MOLA
  areoid [SMITH&ZUBER1998], but is expected to vary by 1.5 - 2.5 km
  with season.

  The areoid is defined as a surface of constant gravitational plus
  rotational potential. The inertial rotation rate of Mars is assumed
  to be 0.70882187E-4 rad/s. This potential is the mean value at the
  equator at a radius of 3396.000 km, namely 12652804.7 m^2/s^2,
  calculated from Goddard Mars Gravity Model mgm1025
  [LEMOINEETAL2001] evaluated to degree and order 50.  Coefficients
  of mgm1025 are archived by the Radio Science investigation.  At a
  given longitude and latitude, zero elevation has a potential equal
  to the mean equatorial potential at a radius of 3396 km. The choice
  of 3396 km is convenient but somewhat arbitrary, as the radius of
  Mars at the equator varies from 3390.219 to 3411.522 km, with mean
  3396.195 km, median 3396.068, and mode 3394.324 km. In practice the
  radius of the areoid is calculated iteratively using spherical
  harmonics so that the potential due to gravity and rotation at that
  radius is equal to the equatorial value.  Earlier releases used the
  Goddard Mars potential model mgm0964c20 areoid, based on preliminary
  MGS tracking and the IAU1991 coordinate system. The mgm1025 areoid
  differs by 3 m root-mean-square (RMS) from previous releases, with
  changes as large as 27 m over the Tharsis volcanoes and elsewhere.

  Users of MOLA data must be aware of two important differences
  between the planetocentric coordinate system and Viking-era
  coordinates.  These differences are significant when comparing MOLA
  groundtracks to MDIMs, USGS DTMs, or maps. MOLA uses the areocentric
  coordinate system in IAU2000. MOLA areocentric coordinates may be
  converted to areographic coordinates by means of relations given
  below that depend on the flattening of the ellipsoid assumed.  The
  IAU2000 recommended values for mean equatorial and polar radius are
  3396.2 and 3376.2 km. Earlier IAU models gave values of 3397 and
  3375 km.  (Note that Viking data assumed equatorial radius = 3393.40
  km, and polar radius = 3375.73 km). Owing to the 3-km offset between
  the Mars center of figure and its center of mass, the polar radii
  differ from north to south by 6 km. These considerations cause
  headaches when areographic latitudes, sometimes poorly specified,
  are compared with planetocentric latitudes.

  MOLA longitudes are areocentric, with positive degrees East.
  Areographic longitudes are given as positive degrees West.  However,
  the Viking-era longitudes were less precise than MOLA's and there
  are additional offsets relative to the present IAU2000 frame.  The
  magnitude of offset varies. More than one factor may contribute to
  this discrepancy; a primary reason is a change in the IAU coordinate
  system. Other possible effects are a drift of the prime meridian due
  to uncertainties in the martian rotation period or errors in the
  Viking spacecraft orbital position that propagated through the image
  processing [SMITHETAL1998].


  Data
  ====
  The primary standard products are the Precision Experiment Data
  Record (PEDR) files.  The files are in binary format with an
  attached PDS label. The SIS document describing this standard
  product is included on this volume.

  The PEDRs contain instrument science data, spacecraft and
  sub-spacecraft location, estimates of the planetary radii, and radii
  of an areoid equipotential surface. The MOLA topography is the shot
  planetary radius minus the areoid radius at a given location.


  Parameters
  ==========
  The MOLA instrument measures the round-trip time of flight of
  infrared laser pulses transmitted from the MGS spacecraft to the
  Martian surface.  The instrument normally operated in a single
  autonomous mode, in which it produced ranging measurements.  Surface
  topography estimates can be derived from these data, given
  appropriate corrections for the position and attitude of the
  spacecraft.


  Processing
  ==========
  The PEDRs incorporate the best multi-arc orbital solutions derived
  from Goddard Mars potential models and the available tracking,
  supplemented by limited altimetric crossovers. Spacecraft clock
  conversions are applied to obtain obtain Ephemeris Time in seconds
  from the J2000 epoch, whence MGS state vectors are found for each
  shot and the corresponding pointing matrices from project-supplied
  C-kernels. Instrument timing biases and boresight offsets are given
  by the MOLA instrument kernel version 2.6. MOLA ranges account for
  instrument delays and the leading edge timing biases, estimated by
  the receiver model of [ABSHIREETAL2000]. This model uses the
  detector threshold settings and the pulse width and energy
  measurements between the threshold crossings to infer the true pulse
  centroid, width, and amplitude. During the aerobraking mission
  phases, the highly eccentric orbit brought MOLA much closer to the
  surface of Mars than the design called for. Due to the
  inverse-square-law energy return in the link equation
  [ZUBERETAL1992], the instrument detector was saturated during the
  periapsis approach.  Received pulse energy and pulse width are
  resolved during the portion of these passes when the detector is not
  saturated.  The absolute accuracy of these quantities is about 5%,
  and caution must be exercised when interpreting these measurements.
  [NEUMANNETAL2003] give a more recent analysis and calibration of the
  pulse width and energy measurements.

  Laser energies are calculated according to the transmitter model of
  [AFZALETAL1997]. During operation the laser energy declined
  gradually to about half its preflight output, as discussed in
  [SMITHETAL2001A].  Even so, returning pulses over bright terrain
  remained saturated.  A bistatic measurement of albedo is possible
  from the link equation during portions of the observations that are
  not saturated, but is affected by the two-way atmospheric
  transmittance. Further details are given in [IVANOV&MUHLEMAN1998].

  The MOLA range data are clocked by the 99.996 MHz frequency F of the
  MOLA timing oscillator, stable to 1 part in 10**8 per day, which in
  turn is calibrated with respect to the spacecraft clock and thereby
  to ground station standards. A post-launch calibration of the MOLA
  oscillator resulted in an estimated frequency F=99,996,232 +/- 5 Hz.
  This frequency changed due to clock drift and was updated daily in
  the PEDR to maintain longterm absolute calibration. The firing
  interval Delta_T was controlled by this clock so that Delta_T =
  10,000,000 / F. Eventually the oscillator circuit gain degraded from
  aging and radiation so much that F began to decrease rapidly, and
  firing ceased. Despite these changes, range accuracy was limited
  only by the 37 cm precision of the timing measurement and by the
  estimate of the pulse centroid location with respect to the
  leading-edge time (range walk). Range walk is terrain- and
  link-dependent. A pulse width measurement is incorporated into the
  calibration of [ABSHIREETAL2000], but where the energy and pulse
  width measurements are saturated, a threshold-dependent leading-edge
  timing bias derived from system characteristics is used instead of
  pulse width.  The leading-edge timing correction may underestimate
  centroid range over very bright or rough terrain by a few tenths of
  a meter.

  Time tags are given in ET seconds of MOLA fire time.  Timing of the
  shots is interpolated to ~100 microseconds. Precision was essential
  in the highly elliptical orbit insertion geometry because the
  spacecraft radial distance changed by as much as 1600 meters per
  second. Further timing corrections are discussed in the MOLA
  instrument kernel version 2.6, but no adjustment to time tags has
  been applied in the PEDR. In other words, the time of MOLA
  observations used in a dynamical sense is 117 ms later than the
  stated laser fire time.

  The ground location and planetary radius is calculated in inertial
  (J2000) coordinates as the difference between the spacecraft
  position vector and the MOLA one-way range vector. The direction of
  the MOLA vector is obtained from project-supplied spacecraft
  attitude kernels and the boresight calibration of the instrument
  with respect to the spacecraft. The one-way range of the laser shot
  to the planet is obtained from the two-way range by correcting for
  the change in spacecraft position during laser shot
  time-of-flight. The ground point position vector is transformed into
  planetary body-fixed coordinates at a time midway between the MOLA
  laser fire time and the shot receive time, using the IAU2000
  planetary model.

  There is a table entry for each non-zero shot range detection for
  all in-range packets in the data stream.  Occasional corrupted range
  values occur due to transmission errors, and some packets are lost
  entirely. A packet sequence number and checksum is generated by
  MOLA.  The sequence number was initialized to 0 just before the
  planet came within range during the SPO-1 and 2 data passes via a
  restart command, while during the Hiatus subphase the restart
  occurred earlier. During mapping the sequence number increments
  continuously to its maximum of 16,383, followed by packets numbered
  0, 0, 1, 2....  Where possible, packets with invalid checksums are
  allowed, since usually only the latter frames of 7 in the packet are
  affected.

  Some MOLA ranges are either clouds or false detections due to the
  intrinsic noise characteristics of the receiver. The MOLA ranges
  that are true ground hits are flagged with a
  shot_classification_code of 1 in the PEDR. A statistical and visual
  analysis of cloud features and morphology can be performed,
  revealing polar CO2 ice, water ice, and dust clouds at altitudes up
  to 20 km above the surface.

    Revision Notes
    --------------

    The final release of the PEDRs incorporates several minor changes
    in the data format. One purpose of these changes is to expand the
    information provided by crossover analysis, so that some estimate
    of orbit and attitude quality can be made. The intent was also to
    minimize any backward incompatibility with existing software,
    keeping the record length and label structure the same. Existing
    fields with marginally useful information were modified. These
    changes apply to PRODUCT_VERSION_TYPE = 'R010-CALIBRATED REL.',
    with the PRODUCT_ID and FILENAME version letter 'L'.

    The following two bytes were previously bit fields in the
    'SHOT_QUALITY_DESCRIPTOR_FLAG' reserved for the 'transmit power
    test'. Since the MOLA laser never failed this test, these were
    identically 0. Iterating the crossover adjustments did not always
    converge, so that the final adjustment values were larger than
    expected at some times. These values may be used to edit records
    when significantly greater than 0. All values are scaled to
    integers.

     Bytes  Type      Range  Usage
     34     unsigned  0-255  radial crossover adjustment magnitude, m
     35     unsigned  0-255  in-plane crossover adjustment, unit = 30 m

    The range window test, range comparison test, and return energy
    test were not implemented. These and spare bits have been used for
    the crossover adjustment delta-latitude and delta-longitude. These
    values may be used to recover the original frame-midpoint location
    in body-fixed (areocentric) coordinates, by subtracting them from
    the frame-midpoint values in bytes 337-340 and 341-344.

        Bytes
        41-44   signed  *       crossover delta-latitude, degrees * 10^6
        45-48   signed  *       crossover delta-latitude, degrees * 10^6

    The atmospheric opacity field in bytes 549-552 was never
    implemented. These bytes were replaced with the total along-track
    and across-track crossover adjustments, in units of 3 cm. Where
    these exceed approximately one shot spacing along-track (10000
    units, 300 m) or one half shot spacing across-track, records may
    be edited. Values of 32767 or -32768 denote invalid
    adjustments. No attempt was made to adjust tracks where attitude
    knowledge was missing, or where the laser beam incidence/emission
    angle exceeded 0.025 radians or 1.4 degrees, as measured from a
    planetary radial vector at the ground point. These values were
    described in the PEDRSIS-2.8 revision.

        549-550 signed *        crossover along-track delta
        551-552 signed *        crossover across-track delta

    The received optical pulse width, corrected, scaled
    received_pulse_energy, and surface reflectivity-transmission
    product have been recalculated following methods described in
    Neumann et al., 2003, Mars Orbiter Laser Altimeter pulse width
    measurements and footprint-scale roughness, Geophysical Research
    Letters, in press. The measured pulse width at channel threshold
    setting has been recalibrated based on inflight data as described
    therein. In particular, the inversion for received optical pulse
    width has been improved, to correspond more closely to pulse
    spreading due to surface slope, non-nadir incidence, and
    footprint-scale roughness. The bytes assigned are unchanged, but
    values will differ. Each field consists of 20 16-bit values.

      145-184 unsigned 0-65535 Received energy, attojoules
      185-224 unsigned 0-65535 Reflectivity-transmission fraction * 10^5
      245-284 unsigned 0-65535 Pulse width at trigger threshold, ns * 10
      285-324 unsigned 0-65535 Sigma-optical, one S.D., ns * 10.


  Ancillary Data
  ==============
  N/A


  Coordinate System
  =================
  The diverse processing and display requirements for various
  observational quantities necessitates flexibility in the choice of
  coordinate system.  Two systems are used to describe data products
  on this volume:

     1.  The areocentric coordinate system [DAVIESETAL1996], more
  generally described as planetocentric, is body-centered, using the
  center-of-mass as the origin.  Areocentric latitude is defined by
  the angle between the equatorial plane and a vector extending from
  the origin of the coordinate system to the relevant point on the
  surface.  Latitude is measured from -90 degrees at the south pole to
  +90 degrees at the north pole.  Longitude extends from 0 to 360
  degrees, with values increasing eastward (i.e., it is a right-handed
  coordinate system) from the prime meridian. This coordinate system
  is preferred for use in navigation and geophysical studies in which,
  for example, estimates of elevation or gravitational potential are
  generated mathematically.

     2.  The areographic system (more generally, the planetographic
  system) uses the same center-of-mass origin and coordinate axes as
  the areocentric coordinate system.  Areographic latitudes are
  defined by a vector normal to a reference ellipsoid surface.
  Longitudes are measured from the prime meridian and increase toward
  the west since Mars is a prograde rotator [DAVIESETAL1996].  This
  system was standard for cartography of Mars and most pre-MGS maps
  portray locations of surface features in areographic coordinates.
  For MGS, the following data have been adopted as standard for
  defining the reference spheroid for computing the areographic
  latitudes [SEIDELMANNETAL2002]:

          Equatorial radius  = 3396.2 km
          Polar radius       = 3376.2 km
          Flattening         = 0.0058889
          Inverse flattening = 169.81

  Note that the flattening is computed as one minus the ratio of the
  polar radius to the equatorial radius. The gravitational flattening
  of the planet is somewhat less, roughly 1/191. The relationship
  between areographic and areocentric latitudes is approximated as:

          tan(lc) = (1-f) * (1-f) * tan(lg)

  where:  f = flattening
       lg = areographic latitude
       lc = areocentric latitude

  Areocentric longitudes may be converted to areographic longitudes by
  the relation

     long_areographic = 360 - long_areocentric.


  Software
  =======
  Software for accessing the PEDR data products is provided on the
  archive volumes and on the PDS Geosciences Node web site at
  http://wwwpds.wustl.edu and the MOLA Science Team web site at
  http://ltpwww.gsfc.nasa.gov/tharsis/mola.html.


  Media/Format
  ============
  The MGS MOLA PEDR dataset will be available electronically via the
  PDS Geosciences Node web site at http://wwwpds.wustl.edu and the
  MOLA Science Team web site at
  http://ltpwww.gsfc.nasa.gov/tharsis/mola.html.  Formats will be
  based on standards established by the Planetary Data System (PDS).

Overview
  ========
  The resolution of the data is about 40 cm vertically, and about 300
  m along-track, limited by the 10 Hz firing rate of the laser.  Small
  errors in the MGS ephemeris and pointing knowledge have been
  corrected by means of crossover analysis [NEUMANNETAL2001]. The
  absolute, long-wavelength radial orbit error is estimated to be 1 m
  after adjustment. The uncertainty in absolute ground spot location
  is limited by the attitude knowledge of the spacecraft, and is
  estimated to be about 100 m at a nominal range of 400 km.


  Review
  ======
  The volume containing the MOLA PEDR topography dataset was reviewed
  by MGS mission scientists and by PDS.


  Data Coverage/Quality
  =====================
  On September 15, 1997, on the 3rd orbit after insertion, MOLA ranged
  to the surface of Mars with greater than 99% success for 21 minutes.
  A further 17 passes were collected between October 14 and November
  6, 1997 during a hiatus in the aerobraking phase necessitated by a
  study of the integrity of a solar panel that was slightly damaged
  after launch.

  MOLA collected 61 topographic profiles of Mars' northern hemisphere
  during the first phase of the MGS Science Phasing Orbit (SPO-1) that
  spanned the period from March 26, 1998 until April 28, 1998. All of
  the MOLA data collected during SPO-1 were presented in thirteen
  talks and posters during the week of May 26, 1998 at the Spring
  Meeting of the American Geophysical Union in Boston.

  MOLA's SPO-1 observations were collected during orbital passes in
  which targeted imaging of surface features was not being attempted.
  Collection of images of target sites (Viking 1 & 2 and Pathfinder
  landing sites and Cydonia) resulted in a loss of about 25% of the
  data that MOLA could have collected during that period.  SPO-1 ended
  in mid-May, just before solar conjunction. During conjunction the
  sun is in the line of sight of the spacecraft, which interferes with
  communication, so commanding of the spacecraft is minimized.

  On May 26, 1998, the Mars Global Surveyor (MGS) spacecraft entered
  into Phase 2 of the Science Phasing Orbit (SPO-2). SPO is a
  near-polar (92.869 degrees) inclination orbit with a period of 11.6
  hours and a periapsis altitude of about 170 km. During SPO-2 MOLA
  collected observations of Mars' northern hemisphere, with detailed
  mapping of the north polar ice cap. Late June and early July 1998
  was expected to be the period of maximum ice loading for the
  northern cap for the current Martian year and thus represented an
  especially exciting and crucial time for MOLA observations. The
  observations collected during this period contributed significantly
  towards understanding the present-day Martian volatile budget. For
  two weeks, the MGS spacecraft was tilted on alternating orbits so
  that MOLA could fill in the coverage gap at the north pole that
  occurred because the spacecraft orbital inclination is not exactly
  90 degrees.

  The Science Phasing Orbits represented a hiatus from aerobraking
  that was needed so that the spacecraft could achieve the desired
  local time for the mapping orbit that was entered in February,
  1999. The geometry of these orbits was not optimal for MOLA science,
  and in order to limit thermal stress on the laser and risks from
  repeated power cycling, MOLA ceased ranging in SPO after 1998 JUL
  30. An opportunity to range to the moon Phobos was provided on 1998
  SEP 12, at which time MOLA collected ranges for 63 seconds before
  swinging off the satellite limb.  Aerobraking resumed a few days
  later.

  During aerobraking passes, the MOLA instrument did not collect data
  because the instrument was not pointed at the surface during the
  period of time when the spacecraft is within ranging distance.
  During the aerobraking exit phase, MOLA was again oriented toward
  Mars and commenced mapping operations on 1999 FEB 28. The first
  ground observations were obtained on orbit 1583. Mapping officially
  began a week later, at which point the MGS project reset their orbit
  numbering to 1. To avoid conflict and maintain increasing orbits,
  MOLA added 10000 to the mapping orbit numbers, starting with orbit
  12. Issues with the high-gain antenna gymbal resulted in less than
  100% mapping coverage for several weeks, following which MOLA
  operated continuously until 2000 JUN 01, at solar
  conjunction. Mapping resumed on 2000 AUG 01 and continued through
  the end of the Primary Mission and for 5 months of the Extended
  Mission. On 2001 JUN 30 at 11:10:46 UTC, MOLA's oscillator ceased
  operation, effectively ending the possibility of further laser
  ranging. MOLA had by that time fired over 670 million times, and
  generated nearly 9500 orbital profiles, as well as more than 500,000
  ranges to clouds.


  Limitations
  ===========
  MOLA met or exceeded all of its design expectations. It has
  demonstrated a measurement precision of 40 centimeters over flat
  terrain, and measured the seasonal variations of snow depth on both
  poles. While designed for nadir-looking operation in a circular,
  365- to 445-km- high orbit, MOLA has ranged successfully to Mars at
  distances from 170 to 786 km, and to surface slopes up to 60
  degrees. MOLA has ranged to the surfaces of clouds lying at
  elevations of a few hundred meters above the surface, to nearly 20
  km high, and returned measurements of atmospheric opacity greater
  than 2 during dust storms. MOLA returned 628 ranges to the moon
  Phobos in an orbital fast-flyby. The planetary range detection rate
  in clear atmosphere has exceeded 99% over smooth and rough terrain.

  The MOLA ranges and precision orbit data have been revised as our
  knowledge of instrument, the spacecraft and the Martian gravity
  field improved. Important details of the instrument design and the
  progress of the mission are found in the files INST.CAT and
  MISSION.CAT. The orbital, atmospheric and thermal environment of the
  Orbit Insertion phase introduced uncertainties in the data
  quality. Eccentric orbits and frequent off-nadir pointing during
  ranging cause a greater sensitivity to errors in spacecraft timing
  and attitude knowledge than in mapping orbit. Thus the topography of
  Mars is mainly derived from mapping observations.

  Orbital processing of radio observations depends on conservative and
  non-conservative force modeling. The most important consideration is
  the gravitational attraction of Mars. The gravity model used to
  calculate MOLA orbits through January 2000 was the mgm0989a model,
  while the mgm1004d solution was used thereafter. These interim
  models were based on MGS and historical tracking data
  [SMITHETAL1999, LEMOINEETAL2001].  In cases where tracking data were
  absent or suspect, altimetric crossovers were used to constrain the
  orbits and incorporated into the gravity solution.  The latest
  potential model, mgm1025, is based on tracking throughout the
  primary MGS Primary Mission and some of the Extended Mission. The
  formal error in the areoid to degree and order 60 is about 1.8 m
  RMS.

  Altimetric crossovers are used to assess accuracy and correct the
  data. Using more than 75 million crossovers, one may estimate
  empirical parameters to correct the radial, along-track, and
  across-track position of each profile [NEUMANNETAL2001]. This
  procedure is nonlinear and has been iterated four times, with the
  final correction entailing adjustment of 64 parameters per
  revolution. Adjustments are concentrated at the poles, where many
  passes converge. The wavelength of corrections may be as short as 36
  km, or as long as 3000 km near the equator. The effect of these
  adjustments is to improve the registration of ground tracks, while
  temporal variations in topography and orbital accuracy are averaged
  out, so that the effective radial knowledge depends mainly on the
  uncertainty in the planetary mass constant GM, equivalent to
  decimeter errors in range.  Changes in range due to consumption of
  fuel displacing the spacecraft center-of-mass are probably greater,
  although they are not considered.

  Range measurements are affected by the counting frequency standard,
  electronic delays, and spreading of the returned pulse due to ground
  slope and detector characteristics. The MOLA timing interval unit
  has an accuracy of ~2.5 nanoseconds, its precision being extended
  from the 10 ns clock rate by two interpolator bits.  However, range
  walk due to variable threshold settings, pulse amplitude and shape,
  can be many times greater than measurement precision, especially
  over rough terrain. The MOLA instrument records the pulse width and
  amplitude during the time that the signal exceeds a
  software-controlled threshold. Shot ranges are corrected in
  processing via a mathematical receiver model [ABSHIREETAL2000],
  assuming linear instrument behavior. Flat and highly reflective
  terrain, short ranges, and abnormal atmospheric conditions can drive
  the electronics into saturation, increasing detected pulse width and
  invalidating the instrument model. The range corrections for
  saturated returns are limited to their equivalents for terrain with
  a slope of one in sixteen. Meter-level changes in topography must be
  interpreted in the context of the range correction values in the
  PEDR files.

  The returned-optical-pulse-width and energy measurements must also
  be interpreted with caution, in view of the above-mentioned effects.
  Moreover, the sensors were not calibrated over the entire range of
  temperatures experienced during Orbit Insertion. Energy values
  initially appeared slightly higher than measured by test equipment
  under optimal conditions. The unsaturated return energy and
  reflectivity measurements were only designed for 5% accuracy in any
  case.

  Lastly, the presence of highly reflective clouds, and a level of
  noise returns consistent with instrument tradeoffs, has necessitated
  an empirical classification of shots as to their origin. The first
  shot of every 140 is likely to be triggered by an internal test
  source, but may be a valid ground return, while ~1% of the shots
  result from detector noise exceeding the triggering threshold. The
  probable ground returns have been flagged based on a combination of
  measurements and a stochastic model of topographic variability. An
  unambiguous classification is often impossible, given clouds that
  often follow the surface, and the dramatic variability of Martian
  terrain. The classification should be used only as a guide.