Data Set Overview
  =================
    The Mars Global Surveyor 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.
 
    The MOLA Experiment Gridded Data Record (EGDR) is a topographic
    map of Mars based on altimetry data acquired by the MOLA
    instrument and accumulated over the course of the mission so far.
    Two types of EGDR products are to be produced: the Initial
    Experiment Gridded Data Record (IEGDR), consisting of data
    accumulated through at least the first 30 days of the mapping
    mission, and the Mission Experiment Gridded Data Record (MEGDR),
    consisting of data accumulated over the whole primary mission
    (one Mars year). Different resolutions of the IEGDR and MEGDR may
    be released, and multiple versions of each product may be
    released.
 
    The MOLA Precision Experiment Data Records (PEDRs) are the source
    for the EGDRs. See the MOLA PEDR Software Interface Specification
    [MOLAPEDRSIS1998] and the PDS Catalog entry for the PEDR data set
    (MGS-M-MOLA-3-PEDR-L1A-V1.0) for a description of the PEDRs.
 
    Users of MOLA data must be aware of two important differences
    between the MOLA coordinate system and the Viking-era
    coordinates. These differences are significant when comparing MOLA
    groundtracks to MDIMs, USGS DTMs, or maps. MOLA uses the
    areocentric coordinate frame (see below). MOLA areocentric
    latitudes should be converted to areographic latitudes using the
    equation provided below. (Note that Viking data was processed
    assuming different radii: equatorial radius = 3393.40 km and polar
    radius = 3375.73 km for a flattening of 1/192.) There appears to
    be a residual discrepancy in latitude of less than 0.1 degree
    (6 km) magnitude, and variable sign, between MGS and Viking
    coordinates. MOLA longitudes are also areocentric, with positive
    degrees East. However, there is an additional eastward offset of
    the Viking-era coordinate system relative to the present MGS
    inertial frame. The magnitude of this offset ranges from about 0.1
    to 0.3 degrees (<20 km). More than one factor may contribute to
    this discrepancy; the 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]. Subtracting the
    Viking longitude West from 360.0 converts to longitude East.
    Subtracting 0.2 degrees from the Viking East longitude is a first-
    order correction for comparison to the MOLA data.
 
 
  Data
  ====
    The IEGDR product is a global map of planetary radius, areiod,
    topography, and number of observations, derived from MOLA PEDR
    products and aggregated into latitude-longitude bins. The binned
    data include all MOLA nadir observations from the Orbit Insertion
    phase, plus Mapping Phase nadir observations, plus off-nadir
    observations of the north pole above 86 degrees latitude acquired
    during spring 1998 and of both poles taken in July 1999. Orbits
    355 and 358 of the Orbit Insertion Phase and orbits 10709 through
    10716, inclusive, of the Mapping Phase are excluded because
    solutions for these orbits are deemed to be poor.  (Note: subtract
    10000 from MOLA mapping phase orbit number to determine the
    equivalent MGS Project orbit number.) Also excluded are shots
    more than 1 degree off-nadir (except as noted above), channel 4
    returns, and any returns not classified as ground returns, e.g.,
    clouds or noise, according to the SHOT_CLASSIFICATION_CODE.  Most
    observations have been crossover-corrected. The polar observations
    have not been fully corrected and may be revised somewhat, as the
    pointing of the instrument is not known as accurately as the range
    measurement.
 
    The IEGDR may be released at various resolutions (bin sizes).
    Examples are 1 degree latitude by 1 degree longitude bins, 0.5 by
    0.5 degree bins, and 0.25 by 0.25 degree bins. Increasingly higher
    resolution products will be released throughout the course of the
    mission as more complete coverage of the planet is obtained.
 
    The IEGDR may be released in two formats. The first (data set ID
    MGS-M-MOLA-5-IEGDR-L3-V1.0) is in the form of an ASCII table with
    one row for each latitude-longitude bin, from 90 to -90 degrees
    latitude and from 0 to 360 degrees longitude. Values for planetary
    radius, areoid, topography, and number of observations per bin are
    stored as columns in the table. The file name is in the form
    IEGnnn_v.TAB, where nnn represents the bin size and v the version.
    For example, the first release of the 0.5 by 0.5 degree IEGDR is
    named IEG050_A.TAB. The file format is described by a
    detached PDS label in a separate file of the same name, extension
    .LBL, e.g. IEG050_A.LBL.
 
    The increased volume of higher resolution products makes storage
    as an ASCII file impractical; therefore higher resolution versions
    of the IEGDR may be released as a set of images instead, one image
    each for radius, areoid, topography, and number of observations
    (data set ID MGS-M-MOLA-5-IEGDR-L3-V2.0). Each image is a binary
    array of 16-bit integers with one image line per file record. The
    image file name is in the form IEGnnn[n]k.IMG, where nnn or nnnn
    is the bin size and k is replaced by A for areoid, C for counts,
    R for radius, and T for topography. For example, a one-eighth
    degree resolution topography image would be named IEG0125T.IMG.
    Its format would be described by a detached PDS label in the file
    IEG0125T.LBL.
 
 
  Parameters
  ==========
    N/A
 
 
  Processing
  ==========
    The PEDRs incorporate the best multi-arc orbital solutions derived
    from the Goddard Mars potential model GMM1.6, and the available
    tracking. The latest spacecraft SCLK timing corrections have been
    applied.  The ranges account for instrument delays and the leading
    edge timing biases, estimated by the receiver model of
    [ABSHIRE&SUN1998]. This model assumes a Gaussian shape for the
    transmitted and surface-scattered pulse waveforms, using the
    detector threshold settings and the observed pulse width and
    energy measurements between the threshold crossings to infer the
    true pulse centroid, width, and amplitude.  The eccentric orbit
    brought MOLA much closer to the surface of Mars than the design
    called for, thus the pulse width and energy measurements were
    saturated for much of each pass.  Caution must be exercised when
    interpreting these measurements.  Laser energies are calculated
    according to the transmitter model of [AFZALETAL1997].  A post-
    launch calibration to the MOLA oscillator frequency has been
    applied, based on the difference between the spacecraft high-
    resolution timer and the MOLA clock, resulting in an estimated
    frequency of f=99,996,232 +/- 5 Hz. This frequency is given in the
    PEDR and may change due to clock drift.  The interval between
    shots, as well as the shot time-of-flight, is controlled by this
    frequency. The shot interval in seconds, delta_t = 10,000,000 / f.
 
    Time tags are given in ET seconds of MOLA fire time.  Timing of
    the shots is interpolated to ~100 microseconds. This step is
    essential in the highly elliptical orbit insertion geometry
    because the spacecraft may change its radial distance by as much
    as 1600 meters per second.
 
    The spacecraft time, from which the shot time is derived, is
    subject to further timing corrections. The range observations have
    been registered with orbital position by assuming that the actual
    time of observation is 117 milliseconds later than the time tag of
    the MOLA range as derived from the spacecraft clock.
 
    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 IAU 1991
    planetary model.
 
    Due to the inverse-square-law energy return in the link equation
    [ZUBERETAL1992], the instrument detector was saturated during a
    part of the periapsis approach.  Received pulse energy and pulse
    width are resolved during the portion of the pass when the
    detector is not saturated.  The absolute accuracy of these
    quantities is about 5%.
 
    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 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.
 
    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 positive number in
    the tables.
 
  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 [DAVIESETAL1994B], 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
    [DAVIESETAL1994B].  This coordinate system is preferred for use
    in 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
    [DAVIESETAL1994B].  This system is standard for cartography of
    Mars and most existing 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 [DAVIESETAL1994B]:
 
          Equatorial radius = 3397 km
          Polar radius      = 3375 km
          Flattening        = 0.0064763
 
    Note that the flattening is computed as one minus the ratio of
    the polar radius to the equatorial radius.  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
 
    While the official MGS Project coordinate system is the IAU 1994
    convention specified in DAVIESETAL1994B, the MOLA data are located
    in the IAU 1991 system, which differs only in the prime meridian
    W0 at J2000. To convert MOLA east longitude from IAU 1991 to IAU
    1994, one must subtract 0.033 degrees; i.e.,
 
 areocentric_longitude_East_94 = areocentric_longitude_East_91 - 0.033
 
 
  Software
  =======
    N/A
 
 
  Media/Format
  ============
    The MGS MOLA EGDR dataset is available on CD-ROM and
    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 are
    based on standards established by the Planetary Data System (PDS).

Overview
  ========
    The resolution of the data is about 40 cm vertically, and about
    330 m along-track, limited by the 10 Hz firing rate of the laser.
    The absolute, long-wavelength radial orbit error is estimated to
    be about 30 m. The uncertainty in absolute ground spot location is
    limited by the attitude knowledge of the spacecraft, and is
    estimated to be about 400 m at a nominal range of 400 km.
 
  Review
  ======
    The volume containing the MOLA EGDR dataset was reviewed
    by MGS mission scientists and by PDS.
 
  Data Coverage/Quality
  =====================
    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
    will collect observations of Mars' northern hemisphere, with
    emphasis on detailed mapping of the north polar ice cap. Late June
    and early July 1998 is expected to be the period of maximum ice
    loading for the northern cap for the current Martian year and thus
    represents an especially exciting and crucial time for MOLA
    observations. We anticipate that the observations collected during
    this period will contribute significantly towards understanding
    teh present-day Martian volatile budget. We have just completed a
    two-week period where the MGS spacecraft was tilted on alternating
    orbits so that MOLA could fill in the 2 degree coverage gap at the
    north pole that occurred because the spacecraft orbital
    inclination is not exactly 90 degrees.
 
    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. The Science Phasing Orbit was a hiatus from aerobraking
    that was needed so that the spacecraft could achieve the desired
    local time for the mapping orbit. 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.
 
    SPO-1 ended April 28, 1998, 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. The second phase of the Science Phasing
    Orbit (SPO-2) began May 29, 1998, and continued through September
    23, 1998, at which time aerobraking was resumed to bring the
    spacecraft into a near-circular mapping orbit. During the
    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.
 
    MOLA's Science Phasing Orbit 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 been collected
    during that period.
 
    Aerobraking ended in early February, 1999, and was followed by a
    transition period extending up to the beginning of the Mapping
    Phase on March 9, 1999. MOLA collected data in mapping mode
    beginning February 28, 1999. From this date through May 31, 1999,
    MOLA completed 750 orbital passes in which data were collected.
 
    Previous MOLA data was collected during the capture orbit phase of
    the MGS mission shortly after orbit insertion on September 15,
    1997. 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.
 
  Limitations
  ===========
    Our current understanding of the Martian environment, the
    capabilities of MGS, and its suite of instruments is changing
    rapidly. MOLA has met or exceeded its design expectations. It has
    demonstrated a measurement precision of 30 centimeters over flat
    terrain. 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 over
    15 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 are preliminary, and will
    be revised as our knowledge of the spacecraft and the Martian
    gravity field improves. 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 has introduced uncertainties in the
    data quality. The eccentric orbits and frequent off-nadir pointing
    during ranging cause a greater sensitivity to errors in spacecraft
    timing and attitude knowledge than expected in mapping orbit.
 
    Orbital location is derived from radio observations and a host of
    dynamic variables, most important of which is the gravitational
    attraction of Mars.  Improvements in the gravity field are best
    obtained from tracking at low elevations, now being obtained from
    MGS. The gravity model used to calculate the orbits is an interim
    solution derived from Goddard Mars Model 1. This model is given in
    the software directory as GMM1.6 for the purpose of defining an
    equipotential topographic reference surface. GMM1.6 is necessarily
    constrained and lacks detailed resolution of the polar regions, so
    that unmodeled orbital perturbations accumulate. At the same time,
    the areoid reference surface may vary by tens of meters depending
    on the choice of gravity model. The current areoid is defined by
    GMM1.6 evaluated to degree and order 50.
 
    During orbit insertion, the spacecraft radial distance from Mars
    was subject to a change of up to 1.6 meters in a millisecond due
    to orbital eccentricity, and up to 8 meters between the time the
    pulse was fired and the time it was received. Altimetric
    processing therefore depends strongly on timing accuracy and
    knowledge of the direction in which the laser was fired. MOLA data
    are time-tagged once per packet with a spacecraft time code,
    calibrated to ground time. An instrument clock synchronized to the
    Payload Data System provide 1/256 second resolution timing. The
    PEDRs contain interpolated laser transmit time to a precision of a
    tenth of a millisecond.
 
    Altimetric crossovers are used to assess the accuracy of the
    data. It has been determined that the observations have a
    systematic timing bias; further, that the attitude knowledge of
    the spacecraft is offset. The range observations have been
    registered with the orbital position by assuming that the actual
    time of observation is 117 milliseconds later than the time tag of
    the MOLA range as derived from the spacecraft clock. In addition
    it is assumed that the time tag of the attitude kernel provided by
    the MGS Project is 1.15 seconds later than the time of the
    spacecraft attitude sensor readings, due to a software filter
    delay.
 
    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 a 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 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. 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 detectors were not calibrated for the
    unusually cold conditions experienced during Orbit Insertion.
    Energy values are 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
    approximately 3% 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.