SOFTWARE INTERFACE SPECIFICATION
 
 
SPHERICAL HARMONICS ASCII DATA RECORD (SHADR)
 
 
 
 
prepared by
Frank G. Lemoine
Code 698, Planetary Geodynamics Laboratory
NASA Goddard Space Flight Center
Greenbelt, Maryland, 20771 USA
 
Peggy L. Jester
SGT, Inc. / Code 614.1
NASA GSFC/ Wallops Flight Facility
Wallops Island VA, 23337 USA
 
Version 2.1
22 May 2013
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
|====================================================================|
|                                                                    |
| DOCUMENT CHANGE LOG                                                |
|                                                                    |
|====================================================================|
|REVISION|REVISION| SECTION    | REMARKS                             |
| NUMBER | DATE   | AFFECTED   |                                     |
|--------+--------+------------+-------------------------------------|
| 1.0    |06/02/20| All        |Adapted MGS SHADR SIS to include     |
|        |        |            |Mars Reconnaissance Orbiter and      |
|        |        |            |MESSENGER.                           |
|--------+--------+------------+-------------------------------------|
| 1.0    |06/03/15| All        |Miscellaneous edits                  |
|        |        |            |                                     |
|====================================================================|
| 1.0    |06/06/29| All        |Integration of PDS review comments   |
|====================================================================|
| 1.1    |07/04/04| 4.2.2.1    |Integration of RS review comments    |
|        |        | 4.2.2.2    |                                     |
|        |        | Appendix C |                                     |
|====================================================================|
| 1.2    |08/07/28| 2.3        |Updated file naming convention       |
|        |        |            |for MRO                              |
|====================================================================|
| 2.0    |13/04/17| All        |Adapted to include GRAIL             |
|====================================================================|
| 2.1    |13/05/22| All        |Minor edits                          |
|====================================================================|
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Contents
Document Change Log................................................. 2
Contents...........................................................  3
Acronyms and Abbreviations...........................................5
 
1. General Description...............................................6
1.1. Overview........................................................6
1.2. Scope...........................................................6
1.3. Applicable Documents............................................6
1.4. System Siting...................................................8
1.4.1. Interface Location and Medium.................................8
1.4.2. Data Sources, Transfer Methods, and Destinations..............8
1.4.3. Generation Method and Frequency...............................8
1.5. Assumptions and Constraints.....................................8
1.5.1. Usage Constraints.............................................8
1.5.2. Priority Phasing Constraints..................................8
1.5.3. Explicit and Derived Constraints..............................8
1.5.4. Documentation Conventions.....................................8
1.5.4.1. Data Format Descriptions....................................9
1.5.4.2. Time Standards..............................................9
1.5.4.3. Coordinate Systems..........................................9
1.5.4.4. Limits of This Document.....................................9
1.5.4.5. Typographic Conventions....................................10
2. Interface Characteristics........................................11
2.1. Hardware Characteristics and Limitations.......................11
2.1.1. Special Equipment and Device Interfaces......................11
2.1.2. Special Setup Requirements...................................11
2.2. Volume and Size................................................11
2.3. Labeling and Identification....................................11
2.4. Interface Medium Characteristics...............................12
2.5. Failure Protection, Detection, and Recovery Procedures.........12
2.6. End-of-File Conventions........................................12
3. Access...........................................................13
3.1. Programs Using the Interface...................................13
3.2. Synchronization Considerations.................................13
3.2.1. Timing and Sequencing Considerations.........................13
3.2.2. Effective Duration...........................................13
3.2.3. Priority Interrupts..........................................13
3.3. Input/Output Protocols, Calling Sequences......................13
4. Detailed Interface Specifications................................14
4.1. Structure and Organization Overview............................14
4.2. Detached PDS Label.............................................14
4.2.1. Label Header.................................................14
4.2.2. TABLE Object Definitions.....................................17
4.2.2.1. SHADR Header Object Definition.............................18
4.2.2.2. SHADR Coefficients Object Definition.......................20
4.2.2.3. SHADR Covariance Object Definition.........................22
4.3. Data File......................................................24
4.3.1. SHADR Header Object/Block....................................24
4.3.2. SHADR Coefficients Block.....................................26
4.3.3. SHADR Covariances Block......................................27
 
 
 
Appendix A. Description of Spherical Harmonic Model Normalization...28
A.1 Definition of Model for the Potential...........................28
A.2 Definition of the normalization used............................29
 
Appendix B. Example Data Products...................................31
B.1. Example Label..................................................31
B.2. Example Data Object............................................37
 
Tables
4-3-1. SHADR Header Block...........................................25
4-3-2. SHADR Coefficients Block.....................................26
4-3-3. SHADR Covariance Block.......................................27
 
Figures
4-2-1. SHADR Label Header...........................................15
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ACRONYMS AND ABBREVIATIONS
ANSI      American National Standards Institute
APL       Applied Physics Laboratory
ARC       Ames Research Center
ARCDR     Altimetry and Radiometry Composite Data Record
ASCII     American Standard Code for Information Interchange
CCSDS     Consultative Committee for Space Data Systems
CD-WO     Compact-disc write-once
CNES      Centre National d'Etudes Spatiales
CR        Carriage Return
dB        Decibel
DSN       Deep Space Network
DVD       Digital Video Disc or Digital Versatile Disc
EGM96     Earth Gravitational Model 1996
FEA       Front End Assembly
GRAIL     Gravity Recovery and Interior Laboratory
GSFC      Goddard Space Flight Center
IEEE      Institute of Electrical and Electronic Engineers
IAU       International Astronomical Union
JHU       Johns Hopkins University
JPL       Jet Propulsion Laboratory
J2000     IAU Official Time Epoch
K         Degrees Kelvin
kB        Kilobytes
km        Kilometers
LAST      Laser Altimeter Science Team (MESSENGER)
LF        Line Feed
LP        Lunar Prospector (mission or spacecraft)
MB        Megabytes
MESSENGER MErcury Surface Space ENvironment, GEochemistry, and Ranging
          (acronym for mission to Mercury)
MGN       Magellan
MGS       Mars Global Surveyor
MIT       Massachusetts Institute of Technology
MLA       MESSENGER Laser Altimeter
MO        Mars Observer
MRO       Mars Reconnaissance Orbiter
NAIF      Navigation and Ancillary Information Facility
NASA      National Aeronautics and Space Administration
NAV       Navigation Subsystem/Team
ODL       Object Definition Language (PDS)
PDB       Project Data Base
PDS       Planetary Data System
RST       Radio Science Team
SCET      Space Craft Event Time
SDS       Science Data System
SFDU      Standard Formatted Data Unit
SHADR     Spherical Harmonics ASCII Data Record
SHBDR     Spherical Harmonics Binary Data Record
SHM       Spherical Harmonics Model
SIS       Software Interface Specification
SPARC     Sun Scaleable Processor Architecture
SPK       Spacecraft and Planet Kernel Format, from NAIF
TBD       To Be Determined
UTC       Universal Time Coordinated
 
 
1. GENERAL DESCRIPTION
 
1.1. Overview
 
This Software Interface Specification (SIS) describes Spherical Harmonics
ASCII Data Record (SHADR) files. The SHADR is intended to be general and may
contain coefficients for spherical harmonic expansions of gravity,
topography, magnetic, and other fields.
 
 
1.2. Scope
 
The format and content specifications in this SIS apply to all phases of the
project for which a SHADR is produced.
 
The SHADR was defined initially for gravity models derived from Magellan
(MGN) and Mars Observer (MO) radio tracking data [1], but the format is more
generally useful. The original SHADR has been adapted for the Mars Global
Surveyor (MGS), Lunar Prospector (LP), Mars Reconnaissance Orbiter (MRO),
and MESSENGER missions. This update of the SIS was made to include the
Gravity Recovery and Interior Laboratory (GRAIL) mission [16]. Some of the
original mission-specific documentation has been omitted, but the file
format descriptions should still be applicable for the GRAIL mission.
 
Specifics of the various models are included in [2], which will be updated
as data for new spherical harmonic models are incorporated within the SHADR
definition. A Spherical Harmonic Binary Data Record is also defined [3],
which may be more suitable for large models or when all error covariances
will be included in the final product.
 
The Jet Propulsion Laboratory (JPL), Pasadena, California, manages the Mars
Reconnaissance Orbiter Mission [4], the Mars Global Surveyor Mission, and the
GRAIL Mission for the National Aeronautics and Space Administration (NASA).
The Johns Hopkins  University, Laurel, Maryland, USA manages the MESSENGER
Mission [5,6] for NASA.
 
 
1.3. Applicable Documents
 
[1] Tyler, G.L., G. Balmino, D.P. Hinson, W.L. Sjogren, D.E. Smith, R. Woo,
S.W. Asmar, M.J. Connally, C.L. Hamilton, and R.A. Simpson, Radio Science
Investigations with Mars Observer, J. Geophys. Res., 97, 7759-7779, 1992.
 
[2] Simpson, R.A., Interpretation and Use of Spherical Harmonics ASCII Data
Record (SHADR) and Spherical Harmonics Binary Data Record (SHBDR), Version
1.0, 1993.
 
[3] Lemoine, F.G., Software Interface Specification: Spherical Harmonics
Binary Data Record (SHBDR), 2006.
 
[4] Mars Reconnaissance Orbiter Mission Plan, Revision C: July 2005,
prepared by Robert Lock.  Document JPL D-22239, MRO-31-201.
 
[5] McAdams, J. V. (JHU/APL), MESSENGER mission overview and trajectory
design, American Institute of Aeronautics and Astronautics, American
Astronautical Society (AIAA/AAS) Astrodynamics Specialist Conference, Paper
AAS 03-541, 20 pp., Big Sky, MT, August 3-7, 2003.
 
[6] McAdams, J. V., D. W. Dunham, R. W. Farquhar, A. H. Taylor, and
B. G. Williams, Trajectory design and maneuver strategy for the MESSENGER
mission to Mercury, 15th American Astronautical Society (AAS)/American
Institute of Aeronautics and Astronautics (AIAA) Space Flight Mechanics
Conference, Paper AAS 05-173, 21 pp., Copper Mountain, CO, Jan. 23-27, 2005.
 
[7] Seidelmann, P.K., V.K. Abalakin, M. Bursa, M. E. Davies, C. de Bergh,
J. H. Lieske, J. Oberst, J. L. Simon, E. M. Standish, P. Stooke, P. C.
Thomas, Report of the IAU/IAG Working Group on Cartographic Coordinates and
Rotational Elements of the Planets and Satellites: 2000, Celes. Mechanics
and Dyn. Astronomy, 82, 83-110, Dec 2002.
 
[8] MRO-D-22685, Rev B., Planetary Constants and Models, 05-15-2003.
 
[9] Konopliv, A.S, C.F. Yoder, E. M. Standish, D.-N. Yuan, and
W. L. Sjogren, A global solution for the Mars static and seasonal gravity,
Mars orientation, Phobos, Deimos Masses, and Mars Ephemeris, Icarus, 182(1),
23-50, 2006.
 
[10] Konopliv A.S., S.W. Asmar, E. Carranza, W.L. Sjogren, and D.N. Yuan,
Recent Gravity models as a results of the Lunar Prospector Mission, Icarus,
150, 1-18, 2001.
 
[11] Lambeck, Kurt, Geophysical Geodesy, Oxford University Press, Oxford,
UK, 1988.
 
[12] Kaula, William M., Theory of Satellite Geodesy, Applications of
satellites to geodesy, Dover Publications, Mineola, NY, 2000.
 
[13] Lemoine, FG, SC Kenyon, JK Factor, RG Trimmer, NK Pavlis, CM Cox,
SM Klosko, SB Luthcke, MH Torrence, YM Wang, RG Williamson, EC Pavlis,
RH Rapp and TR Olson, The Development of the Joint NASA GSFC and the
National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96,
NASA/TP-1998-206861, NASA Goddard Space Flight Center, Greenbelt, Maryland
20771, July 1998.
 
[14] JPL D-7116, Rev. F, Planetary Science Data Dictionary Document, Jet
Propulsion Laboratory, Pasadena, California, October 20, 2008.
(http://pds.jpl.nasa.gov/documents/psdd/psdd.pdf)
 
[15] JPL D-7669 Part 2, Planetary Data System Standards Reference, PDS
Version 3.8, Jet Propulsion Laboratory, February 27, 2009.
(http://pds.jpl.nasa.gov/documents/sr/index.html)
 
[16] Roncoli, R. B., and K. K. Fujii, Mission Design Overview for the
Gravity Recovery and Interior Laboratory (GRAIL) Mission, AIAA/AAS
Astrodynamics Specialist Conference, Toronto, Ontario, Canada, 2010.
http://arc.aiaa.org/doi/pdf/10.2514/6.2010-8383.
 
[17] Standish, E. M., Jr. (November 1982), Conversion of positions and
proper motions from B1950.0 to the IAU system at J2000.0, Astronomy and
Astrophysics 115 (1): 20-22. Bibcode 1982A&A...115...20S.
http://adsabs.harvard.edu/full/1982A%26A...115...20S
 
[18] Folkner, William M., The Planetary and Lunar Ephemeris DE 421, 2009.
IPN Progress Report 42-178.
http://ipnpr.jpl.nasa.gov/progress_report/42-178/178C.pdf
 
 
1.4. System Siting
1.4.1. Interface Location and Medium
SHADR files are created at the institution conducting the science analysis.
SHADR files can be electronic files or can be stored on compact-disc
write-once (CD-WO) or DVD type media.
 
1.4.2. Data Sources, Transfer Methods, and Destinations
SHADR files are created from radio tracking, vertical sounding, in situ,
and/or other measurements at the institution conducting the scientific data
analysis. They are transferred to and deposited in a data system (such as
the PDS) specified by the managing institution.
 
1.4.3. Generation Method and Frequency
Spherical Harmonic Models are developed separately at each institution
conducting scientific analyses on raw data; each model meets criteria
specified by the investigators conducting the analysis. Each model requires
data with complete sampling (in terms of longitude and latitude coverage on
the planet), so that SHADR files will be issued infrequently and on
schedules which cannot be predicted at this time.
 
 
1.5. Assumptions and Constraints
1.5.1. Usage Constraints
None.
 
1.5.2. Priority Phasing Constraints
None.
 
1.5.3. Explicit and Derived Constraints
None.
 
1.5.4. Documentation Conventions
1.5.4.1. Data Format Descriptions
The reference data unit is the byte. Data may be stored in fields with
various sizes and formats, viz. one-, two-, and four-byte binary integers,
four- and eight-byte binary floating-point numbers, and character strings.
Data are identified throughout this document as:
 
char 8 bits character
uchar 8 bits integer
short 16 bits integer
long 32 bits integer
float 32 bits floating point (sign, exponent, and mantissa)
double 64 bits floating point (sign, exponent, and mantissa)
u (prefix) unsigned (as with ulong for unsigned 32-bit integer)
other special data structures such as time, date, etc. which are described
within this document
 
If a field is described as containing n bytes of ASCII character string
data, this implies that the leftmost (lowest numbered) byte contains the
first character, the next lowest byte contains the second character, and so
forth.
 
An array of n elements is written as array[n]; the first element is
array[0], and the last is array[n-1]. Array[n][m] describes an n x m element
array, with first element array[0][0], second element array[0][1], and so
forth.
 
Floating point (real) numbers are represented as double precision character
strings in the FORTRAN 1P1E23.16 format. Fixed point (integer) numbers are
represented using the FORTRAN I5 format.
 
1.5.4.2. Time Standards
SHADR files use the January 1.5, 2000 epoch as the standard time. Within the
data files, all times are reported in Universal Coordinated Time (UTC) as
strings of 23 ASCII characters. The time format is
"YYYY-MM-DDThh:mm:ss.fff", where "-", "T", ":", and "." are fixed
delimiters; "YYYY" is the year "19nn" or "20nn"; "MM" is a two-digit month
of year; "DD" is a two-digit day of month; "T" separates the date and time
segments of the string; "hh" is hour of day; "mm" is the minutes of hour
(00-59); "ss" is the seconds of minute (00-59); and "fff" is fractional
seconds in milliseconds.
 
The date format is "YYYY-MM-DD", where the components are defined
as above.
 
1.5.4.3. Coordinate Systems
The SHADR uses the appropriate planetocentric fixed body coordinate system
[7,8]. This may be an IAU system (e.g. IAU2000 [7]) or the new
body-fixed Mars reference frame defined by Konopliv et al. [9]. At present,
the MESSENGER mission has adopted the IAU2000 model for Mercury [7].
The coordinate system for lunar geopotential models will be a body figure
axis system defined by the lunar librations which are resolved by lunar
laser ranging [10], or a more coarse frame defined by the IAU [7].
 
GRAIL uses the DE 421 Lunar Body-Fixed Frame [17] as defined in the DE 421
planetary ephemeris [18].
 
1.5.4.4. Limits of This Document
This document applies only to SHADR data files.
 
1.5.4.5. Typographic Conventions
This document has been formatted for simple electronic file transfer and
display. Line lengths are limited to approximately 80 ASCII characters,
including line delimiters. No special fonts or structures are included
within the file. Constant width characters are assumed for display.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
2. INTERFACE CHARACTERISTICS
 
2.1. Hardware Characteristics and Limitations
2.1.1. Special Equipment and Device Interfaces
 
Users of the SHADR product must have access to the data system (or media)
on which the SHADR files are stored.
 
2.1.2. Special Setup Requirements
None.
 
 
2.2. Volume and Size
SHADR products have variable length, depending on the degree and order of
the model and the number of tables included. A model of degree and order N
will require approximately (N*(N+1)/2)*137 bytes for storage of spherical
harmonic coefficients and associated uncertainties. A SHADR file for the
geopotential that contains coefficients and coefficient standard deviations
through degree 90 will be 510 kB in size. Vector quantities (e.g., magnetic
field) may be described by a single SHADR (in which all components are
represented) or by a separate SHADR for each field component. If the single
SHADR includes covariances, the file size will be approximately 27 times
larger than the combined volumes of the three component files because of the
inter-component covariance terms. In general, the SHBDR [3] is recommended
when the data include error covariances because of the smaller data volume
associated with binary formats.
 
 
2.3. Labeling and Identification
The length of file names is limited to 27 or fewer characters before the
period delimiter and 3 characters after the period delimiter. Each file has
a name which describes its contents. The name includes the following
structure which uniquely identifies it among SHADR products. Beginning with
the MRO gravity products the following naming convention is used:
GTsss_nnnnvv_SHA.TAB
where
 
"G" denotes the generating institution
    "J" for the Jet Propulsion Laboratory
    "G" for Goddard Space Flight Center
    "M" for Massachusetts Institute of Technology
"T" indicates the type of data represented
    "G" for gravity field
"sss" is a 3-character modifier specified by the data producer.
This modifier is used to indicate the source spacecraft or project, such as
GRX for the pair of GRAIL spacecraft.
"_" the underscore character is used to delimit modifiers in the file name
for clarity.
"nnnnvv" is a 4- to 6-character modifier specified by the data producer.
Among other things, this modifier may be used to indicate the target body,
whether the SHADR contains primary data values as specified by "T" or
uncertainties/errors, and/or the version number. For GRAIL, this modifier
indicates the degree and order of the solution for the gravity field,
topography or magnetic field.
"SHA" denotes that this is an ASCII file of Spherical Harmonic coefficients
".TAB" indicates the data is stored in tabular form.
 
Each SHADR file is accompanied by a detached PDS label; that label is a file
in its own right, having the name GTsss_nnnnvv_SHA.LBL.
 
 
2.4. Interface Medium Characteristics
SHADR products are electronic files.
 
 
2.5. Failure Protection, Detection, and Recovery Procedures
None.
 
 
2.6. End-of-File Conventions
End of file labeling complies with standards for the medium on which the
files are stored.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
3. ACCESS
 
3.1. Programs Using the Interface
Data contained in SHADR files will be accessed by programs at the home
institutions of science investigators. Those programs cannot be identified
here.
 
3.2. Synchronization Considerations
3.2.1. Timing and Sequencing Considerations
N/A
3.2.2. Effective Duration
N/A
3.2.3. Priority Interrupts
None.
3.3. Input/Output Protocols, Calling Sequences
None.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4. DETAILED INTERFACE SPECIFICATIONS
 
4.1. Structure and Organization Overview
The SHADR is a file generated by software at the institution conducting
scientific data analysis. Each SHADR file is accompanied by a detached PDS
label.
 
 
4.2. Detached PDS Label
The detached PDS label is a file with two parts -- a header, and a set of
one, two, or three PDS TABLE object definitions. The header contains
information about the origin of the file and its general characteristics
such as record type and size. The TABLE object definitions describe the
format and content of the tables that make up the SHADR data file. The SHADR
Header Table Object definition is required. The SHADR Coefficients Table
Object definition is required if there is a SHADR Coefficients Table in the
file; the SHADR Covariance Table Object definition is required if there is a
SHADR Covariance Table. Each detached PDS label is constructed of ASCII
records; each record in the label contains exactly 80 characters. The last
two characters in each record are the carriage-return (ASCII 13) and
line-feed (ASCII 10) characters. An example of a complete label and data
object is given in APPENDIX C.
 
4.2.1 Label Header
The structure of the label header is illustrated in Figure 4-2-1.
Keyword definitions are given below.
PDS_VERSION_ID =
The version of the Planetary Data System for which these data have been
prepared; set to PDS3 by agreement between the mission and PDS.
 
RECORD_TYPE =
The type of record. Set to "FIXED_LENGTH" to indicate that all logical
records have the same length.
 
RECORD_BYTES =
The number of bytes per (fixed-length) record. It is usually most convenient
if this has been set equal to the length of records in the
SHADR_COVARIANCE_TABLE.
 
FILE_RECORDS =
The number of records in the SHADR file: instance dependent.
 
^SHADR_HEADER_TABLE =
File name and record number at which SHADR_HEADER_TABLE begins. Set to
("GTsss_nnnnvv_SHA.TAB ",1) where " GTsss_nnnnvv_SHA.TAB " is the file name
as described in Section 2.3, and 1 is the record number since this is the
first record in the SHADR file.
 
 
 
 
 
 
 
|====================================================================|
|                                                                    |
| Figure 4-2-1 SHADR Label Header                                    |
|====================================================================|
|                                                                    |
| PDS_VERSION_ID = PDS3                                              |
| RECORD_TYPE = FIXED_LENGTH                                         |
| RECORD_BYTES = nnn                                                 |
| FILE_RECORDS = nnn                                                 |
| ^SHADR_HEADER_TABLE = ("GTsss_nnnnvv_SHA.TAB",1)                   |
| ^SHADR_COEFFICIENTS_TABLE = ("GTsss_nnnnvv_SHA.TAB ",nn)           |
| ^SHADR_COVARIANCE_TABLE = ("GTsss_nnnnvv_SHA.TAB ",nnn)            |
| INSTRUMENT_HOST_NAME = "cccccccccccccccccccc"                      |
| TARGET_NAME = "cccc"                                               |
| INSTRUMENT_NAME = "ccccccccccccccccccccccc"                        |
| DATA_SET_ID = "ccccccccccccccccccccccc"                            |
| OBSERVATION_TYPE = "ccccccccccccc"                                 |
| ORIGINAL_PRODUCT_ID = "ccccccccccccc"                              |
| PRODUCT_ID = " GTsss_nnnnvv_SHA.TAB "                              |
| PRODUCT_RELEASE_DATE = YYYY-MM-DD                                  |
| DESCRIPTION = "cccccccccccccccccc"                                 |
| START_ORBIT_NUMBER = nnnn                                          |
| STOP_ORBIT_NUMBER = nnnn                                           |
| START_TIME = YYYY-MM-DDThh:mm:ss                                   |
| STOP_TIME = YYYY-MM-DDThh:mm:ss                                    |
| PRODUCT_CREATION_TIME = YYYY-MM-DDThh:mm:ss.fff                    |
| PRODUCER_FULL_NAME = "cccccccccccc"                                |
| PRODUCER_INSTITUTION_NAME = "ccccccccccc"                          |
| PRODUCT_VERSION_TYPE = "cccccccccccc"                              |
| PRODUCER_ID = "ccccccc"                                            |
| SOFTWARE_NAME = "ccccccc;Vn.m"                                     |
|====================================================================|
 
^SHADR_COEFFICIENTS_TABLE =
File name and record number at which the SHADR_COEFFICIENTS_TABLE begins.
The Coefficients Table is optional; this pointer will not appear in the
SHADR label if there is no Coefficients Table. Set to
("GTsss_nnnnvv_SHA.TAB",nn) where "GTsss_nnnnvv_SHA.TAB" is the file
name as described in Section 2.3, and "nn" is the record number in the
file where the Coefficients Table begins.
 
^SHADR_COVARIANCE_TABLE=
File name and record number at which SHADR_COVARIANCE_TABLE begins.
The Covariance Table is optional; this pointer will not appear in the SHADR
label if there is no Covariance Table. Set to ("GTsss_nnnnvv_SHA.TAB",nn)
where "GTsss_nnnnvv_SHA.TAB" is the file name as described in Section 2.3,
and "nn" is the record number in the file where the Covariance Table begins.
 
INSTRUMENT_HOST_NAME =
Name of the spacecraft; acceptable names include "MARS GLOBAL SURVEYOR"
"LUNAR PROSPECTOR", "MARS RECONNAISSANCE ORBITER", "MERCURY SURFACE, SPACE,
ENVIRONMENT, GEOCHEMISTRY, AND RANGING", "MAGELLAN", and "GRAVITY RECOVERY
AND INTERIOR LABORATORY".
TARGET_NAME =
A character string which identifies the target body.
For MRO or MGS SHADR files, the character string "MARS".
For MESSENGER SHADR files the character string will be "MERCURY".
For LP and GRAIL SHADR files, the character string will be "MOON".
For Magellan SHADR files, the character string will be "VENUS".
 
INSTRUMENT_NAME =
Name of the instrument; set to "RADIO SCIENCE SUBSYSTEM" for products
generated from radio science data, or set to other instrument names as
appropriate. Set to "LUNAR GRAVITY RANGING SYSTEM" for GRAIL.
 
DATA_SET_ID =
Identifier for the data set of which this SHADR product is a member.
-Set to "MRO-M-RSS-5-SDP-Vn.m" for Mars Reconnaissance Orbiter;
-Set to "MESS-H-RSS-5-SDP-Vn.m" for MESSENGER;
-Set to "MGS-M-RSS-5-SDP-Vn.m" for MGS; and "
-Set to "LP-L-RSS-5-SHGBDR-L2-Vn.m" for Lunar Prospector;
-Set to "GRAIL-L-LGRS-5-RDR-Vn.m" for GRAIL.
The suffix Vn.m indicates the version number of the data set.
 
OBSERVATION_TYPE=
A character string which identifies the data in the product. For the
spherical harmonic model of a gravity field, the character string
"GRAVITY FIELD". For a model of planet topography, the character string
"TOPOGRAPHY".
 
ORIGINAL_PRODUCT_ID =
Optional. An identifier for the product provided by the producer.
Generally a file name, different from PRODUCT_ID, which would be recognized
at the producer's home institution.
 
PRODUCT_ID =
A unique identifier for the product within the collection identified by
DATA_SET_ID. Generally, the file name used in pointers ^SHADR_HEADER_TABLE,
^SHADR_COEFFICIENTS_ TABLE, and/or ^SHADR_COVARIANCE_TABLE. The naming
convention is defined in Section 2.3.
 
PRODUCT_RELEASE_DATE =
The date on which the product was released to the Planetary Data System;
entered in the format "YYYY-MM-DD", where components are defined in
Section 1.5.4.2.
 
DESCRIPTION =
A short description of the SHADR product.
 
START_ORBIT_NUMBER =
Optional. The first orbit represented in the SHADR product. An integer.
 
STOP_ORBIT_NUMBER =
Optional. The last orbit represented in the SHADR product. An integer.
 
START_TIME =
Optional. The date/time of the first data included in the model, expressed
in the format "YYYY-MM-DDThh:mm:ss" where the components are defined in
section 1.5.4.2.
 
STOP_TIME =
Optional. The date/time of the last data included in the model, expressed
in the format "YYYY-MM-DDThh:mm:ss" where the components are defined
in section 1.5.4.2.
 
PRODUCT_CREATION_TIME =
The time at which this SHADR was created; expressed in the format "YYYY-MM-
DDThh:mm:ss.fff" where the components are defined in Section 1.5.4.2.
 
PRODUCER_FULL_NAME =
The name of the person primarily responsible for production of this SHADR
file. Expressed as a character string, for example "JAMES T. KIRK".
 
PRODUCER_INSTITUTION_NAME =
The name of the institution primarily responsible for production of this
SHADR. Standard values include:
 
"STANFORD UNIVERSITY"
"GODDARD SPACE FLIGHT CENTER"
"JET PROPULSION LABORATORY"
"CENTRE NATIONAL D'ETUDES SPATIALES"
"MASSACHUSETTS INSTITUTE OF TECHNOLOGY"
 
PRODUCT_VERSION_TYPE =
The version of this SHADR. Standard values include "PREDICT", "PRELIMINARY",
and "FINAL".
 
PRODUCER_ID =
The entity responsible for creation of the SHADR product. For products
generated by the Mars Reconnaissance Orbiter Gravity Science Team set to
"MRO GST". For products generated by the MESSENGER Laser Altimeter Science
Team set to "MESS LAST". For products generated by the Mars Global Surveyor
Radio Science Team, set to "MGS RST". For products generated by the GRAIL
Science Data System, set to "SDS".
 
SOFTWARE_NAME =
The name and version number of the program creating this SHADR file;
expressed as a character string in the format "PROGRAM_NAME;n.mm"
where "PROGRAM_NAME" is the name of the software and "n.mm" is the version
number. (e.g. "SOLVE;200201.02")
 
4.2.2 TABLE Object Definitions
TABLE object definitions completely define the TABLE objects for each SHADR
file. Minor tailoring of the definitions for different OBSERVATION_TYPES
precludes specification of exact definitions here. DESCRIPTION values, for
example, will likely be tailored for each product type. In no case should
there be a need to change the structure of the file, however. Entries "*"
are provided by the label generating program based on information supplied
elsewhere.
 
4.2.2.1 SHADR Header Object Definition
Each SHADR Header Object is completely defined by the Header Object
Definition in its Label. The Definition which follows gives the structure of
the Header Object; some of the DESCRIPTION values may vary from product to
product. The SHADR Header Object Definition is a required part of the SHADR
label file. It immediately follows the label header.
 
OBJECT = SHADR_HEADER_TABLE
ROWS = 1
COLUMNS = 8
ROW_BYTES = 137
ROW_SUFFIX_BYTES = 107
INTERCHANGE_FORMAT = ASCII
DESCRIPTION = "The SHADR header includes descriptive
information about the spherical harmonic coefficients which follow
in SHADR_COEFFICIENTS_TABLE. The header consists of a single record
of eight (delimited) data columns requiring 137 bytes, a pad of
105 ASCII blank characters, an ASCII carriage-return, and an ASCII
line-feed."
 
OBJECT = COLUMN
NAME = "REFERENCE RADIUS"
DATA_TYPE = "ASCII REAL"
START_BYTE = 1
BYTES = 23
FORMAT = "E23.16"
UNIT = "KILOMETER"
DESCRIPTION = "The assumed reference radius of the
spherical body."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "CONSTANT"
DATA_TYPE = "ASCII REAL"
START_BYTE = 25
BYTES = 23
FORMAT = "E23.16"
UNIT = "KM^3/SEC^2"
DESCRIPTION = "For a gravity field model the assumed
gravitational constant GM in kilometers cubed per seconds squared
for the body. For a topography model, set to 1."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "UNCERTAINTY IN CONSTANT"
DATA_TYPE = "ASCII REAL"
START_BYTE = 49
BYTES = 23
FORMAT = "E23.16"
UNIT = "KM^3/SEC^2"
DESCRIPTION = "For a gravity field model the
uncertainty in the gravitational constant GM in kilometers cubed per
seconds squared for the planet. For a topography, set to 0."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "DEGREE OF FIELD"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 73
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "The degree of model field."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "ORDER OF FIELD"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 79
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "The order of the model field."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "NORMALIZATION STATE"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 85
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "The normalization indicator.
For gravity fields:
0 coefficients are unnormalized
1 coefficients are normalized
2 other."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "REFERENCE LONGITUDE"
POSITIVE_LONGITUDE_DIRECTION = "EAST"
DATA_TYPE = "ASCII REAL"
START_BYTE = 91
BYTES = 23
FORMAT = "E23.16"
UNIT = "DEGREE"
DESCRIPTION = "The reference longitude for
the spherical harmonic expansion; normally 0."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "REFERENCE LATITUDE"
DATA_TYPE = "ASCII REAL"
START_BYTE = 115
BYTES = 23
FORMAT = "E23.16"
UNIT = "DEGREE"
DESCRIPTION = "The reference latitude for
the spherical harmonic expansion; normally 0."
END_OBJECT = COLUMN
 
END_OBJECT = SHADR_HEADER_TABLE
 
4.2.2.2 SHADR Coefficients Object Definition
 
The SHADR Coefficients Object is completely defined by the Coefficients
Object Definition in the label. Small differences in DESCRIPTION values
should be expected from product to product. The structure outlined in the
Definition below should not vary, however.
 
The SHADR Coefficients Object is an optional part of the SHADR data file.
This allows the SHADR to be used for targets which are too small or too
remote to have easily discerned coefficients, but for which estimates of
mass have been obtained (e.g., satellites Phobos and Deimos). If the
Coefficients Object is not included in the SHADR file, either the SHADR
Coefficients Object Definition will be omitted or the number of rows will be
set to zero (ROWS = 0). If the SHADR Coefficients Object is not included,
the pointer ^SHADR_COEFFICIENTS_TABLE will not appear in the label header.
If the SHADR Coefficients Object Definition is included in the label, it
immediately follows the SHADR Header Object Definition.
 
No requirements are placed on the order in which coefficient values appear
in the table or that all possible combinations of the pairs {m,n} be
included. The coefficients are defined by their COEFFICIENT DEGREE and
COEFFICIENT ORDER; see [2] for interpretation.
 
OBJECT = SHADR_COEFFICIENTS_TABLE
ROWS = *
COLUMNS = 6
ROW_BYTES = 107
ROW_SUFFIX_BYTES = 15
INTERCHANGE_FORMAT = ASCII
DESCRIPTION = "The SHADR coefficients table contains the
coefficients for the spherical harmonic model. Each row in the table
contains the degree index n, the order index m, the coefficients Cnm
and Snm, and the uncertainties in Cnm and Snm. The (comma delimited)
data require 107 ASCII characters; these are followed by a pad of 13
ASCII blank characters, an ASCII carriage-return, and an ASCII
line-feed."
 
OBJECT = COLUMN
NAME = "COEFFICIENT DEGREE"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 1
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = " The degree index n of the C and S
coefficients in this record."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "COEFFICIENT ORDER"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 7
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "The order index m of the C and S
coefficients in this record."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "C"
DATA_TYPE = "ASCII REAL"
START_BYTE = 13
BYTES = 23
FORMAT = "E23.17"
UNIT = "N/A"
DESCRIPTION = "The coefficient Cnm for this
spherical harmonic model."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "S"
DATA_TYPE = "ASCII REAL"
START_BYTE = 37
BYTES = 23
FORMAT = "E23.17"
UNIT = "N/A"
DESCRIPTION = "The coefficient Snm for this spherical
harmonic model."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "C UNCERTAINTY"
DATA_TYPE = "ASCII REAL"
START_BYTE = 61
BYTES = 23
FORMAT = "E23.17"
UNIT = "N/A"
DESCRIPTION = "The uncertainty in the coefficient Cnm
for this spherical harmonic model."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "S UNCERTAINTY"
DATA_TYPE = "ASCII REAL"
START_BYTE = 85
BYTES = 23
FORMAT = "E23.17"
UNIT = "N/A"
DESCRIPTION = "The uncertainty in the coefficient Snm
for this spherical harmonic model."
END_OBJECT = COLUMN
 
END_OBJECT = SHADR_COEFFICIENTS_TABLE
 
4.2.2.3 SHADR Covariance Object Definition
The SHADR Covariance Object is completely defined by the Covariance Object
Definition in the label. Small differences in DESCRIPTION values should be
expected from product to product. The structure established by the
Definition below should not change, however. The SHADR Covariance Object is
an optional part of the SHADR data file. If the Covariance Object is not
included, either the Covariance Object Definition will be omitted or the
number of rows will be set to zero (ROWS = 0). If the SHADR Covariance
Object is not included, the pointer ^SHADR_COVARIANCE_TABLE will not appear
in the label header. If the SHADR Covariance Object Definition is included
in the label, it immediately follows the SHADR Coefficients Object
Definition.
 
No requirements are placed on the order in which covariance values appear in
the table. Nor is there a requirement that all possible combinations of the
quadruplet values {i,j,n,m} be included. By careful editing and use of
symmetry arguments, it may be possible to define all covariances with fewer
than the maximum number of rows in the table.
 
OBJECT = SHADR_COVARIANCE_TABLE
ROWS = *
COLUMNS = 8
ROW_BYTES = 119
ROW_SUFFIX_BYTES = 3
INTERCHANGE_FORMAT = ASCII
DESCRIPTION = "The SHADR covariance table contains
the covariances for the spherical harmonic model coefficients.
For each index quadruplet {i,j,n,m} the covariances of CijCnm,
SijSnm, CijSnm, and SijCnm are given. In each row of the table the
(comma delimited) indices occupy 24 ASCII characters and the (comma
delimited) covariances occupy 95 ASCII characters. These are followed
by an ASCII blank, an ASCII carriage-return and an ASCII line-feed."
 
OBJECT = COLUMN
NAME = "COEFFICIENT DEGREE I"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 1
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "The degree index i of the C and S terms
in this record."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "COEFFICIENT ORDER J"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 7
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "The order index j of the C and S terms
in this record."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "COEFFICIENT DEGREE N"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 13
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "The degree index n of the C and S terms
in this record."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "COEFFICIENT ORDER M"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 19
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "The order index m of the C and S terms
in this record."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "COVARIANCE (C_IJ,C_NM)"
DATA_TYPE = "ASCII REAL"
START_BYTE = 25
BYTES = 23
FORMAT = "E23.16"
UNIT = "N/A"
DESCRIPTION = "Covariance (C_IJ,C_NM) the coefficients
of this spherical harmonic model."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "COVARIANCE (S_IJ,S_NM)"
DATA_TYPE = "ASCII REAL"
START_BYTE = 49
BYTES = 23
FORMAT = "E23.16"
UNIT = "N/A"
DESCRIPTION = "Covariance (S_IJ,S_NM) for the
coefficients of this spherical harmonic model."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "COVARIANCE (C_IJ,S_NM)"
DATA_TYPE = "ASCII REAL"
START_BYTE = 73
BYTES = 23
FORMAT = "E23.16"
UNIT = "N/A"
DESCRIPTION = "Covariance (C_IJ,S_NM) for the
coefficient of this spherical harmonic model."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "COVARIANCE (S_IJ,C_NM)"
DATA_TYPE = "ASCII REAL"
START_BYTE = 97
BYTES = 23
FORMAT = "E23.16"
UNIT = "N/A"
DESCRIPTION = "Covariance (S_IJ,C_NM) for the
coefficients of this spherical harmonic model."
END_OBJECT = COLUMN
 
END_OBJECT = SHADR_COVARIANCE_TABLE
 
 
4.3. Data File
 
Each SHADR data file comprises a SHADR Header TABLE Object, an (optional)
Coefficients TABLE Object, and an (optional) Covariances TABLE Object.
 
Each TABLE Object comprises one or more data blocks. The TABLE Objects were
defined in Section 4.2. The data blocks are illustrated below.
 
4.3.1. SHADR Header Object/Block
 
The SHADR Header Object contains the parameters necessary to interpret the
data in the SHADR file. The structure of the SHADR Header Object is defined
in Section 4.2.2.1. The SHADR Header Object is a one-row table; hence the
Header Object and the Header Block are logically synonymous. The structure
of the Header Block is shown in Table 4-3-1. Note that the logical content
of the Header Object is delimited by the ASCII carriage return and line feed
characters. The physical block is padded to 244 bytes (an integral multiple
of RECORD_BYTES).
 
 
 
 
 
 
 
|====================================================================|
|                                                                    |
| Table 4-3-1. SHADR Header Block                                    |
|                                                                    |
|====================================================================|
| Col No | Offset | Length | Format | Column Name                    |
|--------+--------+--------+--------+--------------------------------|
| 1 | +0 | 23     | E23.16 |Planetary Radius                         |
|--------+--------+--------+--------+--------------------------------|
| 2 | 24 | 23     | E23.16 |Constant                                 |
|--------+--------+--------+--------+--------------------------------|
| 3 | 48 | 23     | E23.16 |Uncertainty in Constant                  |
|--------+--------+--------+--------+--------------------------------|
| 4 | 72 | 5      | I5     |Degree of Field                          |
|--------+--------+--------+--------+--------------------------------|
| 5 | 78 | 5      | I5     |Order of Field                           |
|--------+--------+--------+--------+--------------------------------|
| 6 | 84 | 5      | I5     |Normalization State                      |
|--------+--------+--------+--------+--------------------------------|
| 7 | 90 | 23     | E23.16 |Reference Longitude                      |
|--------+--------+--------+--------+--------------------------------|
| 8 | 114| 23     | E23.16 |Reference Latitude                       |
|--------+--------+--------+--------+--------------------------------|
|   | 137| 105    |        | blanks                                  |
|--------+--------+--------+--------+--------------------------------|
|   | 242| 1      |        | carriage return                         |
|--------+--------+--------+--------+--------------------------------|
|   | 243| 1      |        | line feed                               |
|--------+--------+--------+--------+--------------------------------|
|   | +244                 |                                         |
|========|========|========|========|================================|
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4.3.2. SHADR Coefficients Block
 
The SHADR Coefficients Object is made up of one or more SHADR Coefficient
Blocks. Each block contains one pair of coefficients and associated
uncertainties for the overall model defined by the SHADR product. The
structure of the SHADR Coefficients Object is defined in Section 4.2.2.2.
 
The structure of an individual block is shown in Table 4-3-2.
Note that the logical content of the Coefficients Block is delimited by the
ASCII carriage return and line feed characters. The Coefficients Block is,
by definition, an integral multiple of RECORD_BYTES.
 
|====================================================================|
|                                                                    |
| Table 4-3-2. SHADR Coefficients Block                              |
|                                                                    |
|====================================================================|
| Col No | Offset | Length | Format | Column Name                    |
|--------+--------+--------+--------+--------------------------------|
| 1      | +0     | 5      | I5     |Coefficient Degree n            |
|--------+--------+--------+--------+--------------------------------|
| 2      | 6      | 5      | I5     |Coefficient Order m             |
|--------+--------+--------+--------+--------------------------------|
| 3      | 12     | 23     | E23.16 |Cnm                             |
|--------+--------+--------+--------+--------------------------------|
| 4      | 36     | 23     | E23.16 |Snm                             |
|--------+--------+--------+--------+--------------------------------|
| 5      | 60     | 23     | E23.16 |Uncertainty in Cnm              |
|--------+--------+--------+--------+--------------------------------|
| 6      | 84     | 23     | E23.16 |Uncertainty in Snm              |
|--------+--------+--------+--------+--------------------------------|
|        | 107    | 13     |        | blanks                         |
|--------+--------+--------+--------+--------------------------------|
|        | 120    | 1      |        | carriage return                |
|--------+--------+--------+--------+--------------------------------|
|        | 121    | 1      |        | line feed                      |
|--------+--------+--------+--------+--------------------------------|
|        | +122                     |                                |
|========|========|========|========|================================|
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4.3.3. SHADR Covariance Block
 
The SHADR Covariance Object is made up of one or more SHADR Covariance
Blocks. Each block contains the CijCnm, SijSnm, CijSnm, and SijCnm
covariances for the overall model defined by the SHADR product. The
structure of the SHADR Covariance Object is defined in Section 4.2.2.3. The
structure of an individual block is shown in Table 4-3-3. Note that the
logical content of the Covariance Block is delimited by the ASCII carriage
return and line feed characters. The SHADR Covariance Block is, by
definition, an integral multiple of RECORD_BYTES.
 
|====================================================================|
|                                                                    |
| Table 4-3-3. SHADR Covariance Block                                |
|                                                                    |
|====================================================================|
| Col No | Offset | Length | Format | Column Name                    |
|--------+--------+--------+--------+--------------------------------|
| 1      | +0     | 5      | I5     |Coefficient Degree i            |
|--------+--------+--------+--------+--------------------------------|
| 2      | 6      | 5      | I5     |Coefficient Order j             |
|--------+--------+--------+--------+--------------------------------|
| 3      | 12     | 5      | I5     |Coefficient Degree n            |
|--------+--------+--------+--------+--------------------------------|
| 4      | 18     | 5      | I5     |Coefficient Order m             |
|--------+--------+--------+--------+--------------------------------|
| 5      | 24     | 23     | E23.16 |Covariance {Cij,Cnm}            |
|--------+--------+--------+--------+--------------------------------|
| 6      | 48     | 23     | E23.16 |Covariance {Sij,Snm}            |
|--------+--------+--------+--------+--------------------------------|
| 7      | 72     | 23     | E23.16 |Covariance {Cij,Snm}            |
|--------+--------+--------+--------+--------------------------------|
| 8      | 96     | 23     | E23.16 |Covariance {Sij,Cnm}            |
|--------+--------+--------+--------+--------------------------------|
|        | 119    | 1      |        | blank                          |
|--------+--------+--------+--------+--------------------------------|
|        | 120    | 1      |        | carriage return                |
|--------+--------+--------+--------+--------------------------------|
|        | 121    | 1      |        | line feed                      |
|--------+--------+--------+--------+--------------------------------|
|        | +122                     |                                |
|========|========|========|========|================================|
 
 
 
 
 
 
 
 
 
 
 
APPENDIX A.
 
A.1 Definition of Spherical harmonic models for the geopotential.
 
Spherical harmonics satisfy Laplace's equation in spherical coordinates.
The gravity potential field of the planets and the mathematical
representation of magnetic fields and topographic fields are readily
expressed in terms of spherical harmonics. Useful reviews are by Lambeck
[11] (Section 2.2, Elements of Potential Theory) and Kaula [12] (Section 1.1
Potential Theory, and Section 1.2 Spherical Harmonics).
 
The expression for the geopotential takes the form
 
V = (GM/r) + (GM/r)*SUMMATION_n SUMMATION_m (Re/r)**n [Cnm" cos(mL) + Snm"
sin(mL)]* Pnm"(sin(phi))
(Equation A-1-1)
 
where GM is the gravitational constant of the planet, r is the radial
distance of the test point from the origin, and Re is the assumed reference
radius of the spherical planet for which the coefficients were calculated.
The summations take place from degree n=1 to infinity, and order m=0 to n;
Cnm" and Snm" refer to the normalized spherical harmonic coefficients (see
Section A.2 below); L is the longitude; the Pnm" are the normalized
associated Legendre functions of degree n and order m; and phi is the
latitude of the test point. If we assume the origin is at the center of mass,
the degree one terms vanish, and the summation in degree starts at degree
n=2.
 
A "solution" for a spherical harmonic model of the geopotential refers to a
solution for these spherical harmonic coefficients and the gravitational
constant, GM, of the body.
 
In practice the spherical harmonic series is truncated at a maximum degree
nmax. For MRO, the likely degree of truncation will be between n=100 and
n=120. For MESSENGER, gravity solutions for the planet Mercury will likely
be truncated at degree 20. The degree of truncation depends on the quality
of the tracking data and the orbits of the spacecraft in the geopotential
solution. For Lunar Prospector derived gravity solutions, the maximum degree
has ranged from n=100 to n=165 [10]. For GRAIL, which used a different
measurement technique, the gravity signal to noise ratio was very strong and
the truncation was at a high degree. nmax was unprecedented 660 for the
Prime Mission.  The field size is expected to exceed 1000 for the combined
Prime and Extended missions solution.
 
If the origin is placed at the center of mass, the degree 1 terms vanish
from the spherical harmonic expansion, and the first summation above is then
from (n=2) to the maximum degree, nmax.
 
Figure 1, section 1.2 from Kaula [11] gives examples of spherical harmonics.
The zonal terms, m=0, have n zeros in a distance pi along a north-south
meridian; in other words, they represent only latitudinal variations in the
potential.
 
Zonal terms may be represented in the literature as Jn = - Cn0.
 
Aside from GM, C20 is the most significant term in the gravity field (for
planets such as the Earth and Mars), and reflects the dynamical expression
of the planet's polar flattening.
 
Tesseral harmonics (coefficients where n is not equal to m, and m > 0, have
n-m zeros in a distance pi along a meridian (like the tesserae of a mosaic).
 
Sectoral harmonics are coefficients where n=m and are constant in sectors of
longitude (N-S) and have n zero crossings in a distance pi along a meridian
of latitude (E-W).
 
A.2 Definition of the normalization used for geopotential coefficients.
The normalization for spherical harmonic coefficients is given by
Lambeck[11]
 
Cnm" = Cnm/PI_nm (Equation A-2-1)
 
where Cnm" is normalized and Cnm is un-normalized, and
 
[PI_nm]**2 = (2 - delta_0m) * (2n+1) * (n-m)! / (n+m)! (Equation A-2-2)
 
delta_0m refers to the Kronecker delta function -- unity for coefficients
where m=0 (the zonal terms), zero for order m > 0.
 
For zonal coefficients (m=0) the relation reduces to
Cnm" = Cnm / sqrt(2n+1)
 
For example, for the Earth C20 = -1.08262668355E-03 (un-normalized) so
 
C20" = C20 / sqrt(5) = -4.8416537173572E-04 (normalized)
 
Working the process backwards for Earth's C22 we have
 
C22" = .24391435239839D-05
 
from the Earth Gravitational Model 1996, EGM96, [13].
 
[PI_nm]**2 = (2-0)*(2n+1) (2-2)! / (4)!
= 2*5*1/(4!) = 5/12
 
which yields
 
C22 = sqrt(5/12) * (.24391435239839E-05)
= 1.5744604E-06
closely matching Lambeck's [11] result (page 14).
 
Likewise for Earth's S22, we have the normalized value [13]
 
S22" = -.14001668365394E-05
 
Thus,
 
S22= sqrt(5/12) * (-.14001668365394E-05)
= -9.038038E-07 (un-normalized)
 
which matches closely the example given by Lambeck [11].
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
APPENDIX B EXAMPLE DATA PRODUCTS
 
APPENDIX B.1 Example Label
 
The following lists an example SHADR LBL file for a Mars Global Surveyor
derived gravity solution. For GRAIL the "INSTRUMENT_HOST_NAME" would be
listed instead of MARS GLOBAL SURVEYOR. The DESCRIPTION would be changed to
reflect the data content of the GRAIL-derived gravity solutions. Other
fields (e.g., PRODUCT_RELEASE_DATE, PRODUCT_ID, INSTRUMENT NAME, START_TIME,
STOP_TIME, PRODUCT_CREATION TIME) would also be changed as appropriate.
 
This example can be found in its original electronic form at the URL
http://pds-geosciences.wustl.edu/geodata/mgs-m-rss-5-sdp-v1/mors_1021/sha/
 
PDS_VERSION_ID = PDS3
RECORD_TYPE = FIXED_LENGTH
RECORD_BYTES = 122
FILE_RECORDS = 4185
^SHADR_HEADER_TABLE = ("GGM1041C.SHA",1)
^SHADR_COEFFICIENTS_TABLE = ("GGM1041C.SHA",3)
INSTRUMENT_HOST_NAME = "MARS RECONNAISSANCE ORBITER"
TARGET_NAME = "MARS"
INSTRUMENT_NAME = "RADIO SCIENCE SUBSYSTEM"
DATA_SET_ID = "MRO-M-RSS-5-SDP-V1.0"
OBSERVATION_TYPE = "GRAVITY FIELD"
ORIGINAL_PRODUCT_ID = "MGM1041C"
PRODUCT_ID = "GGM1041C.SHA"
PRODUCT_RELEASE_DATE = 2003-03-28
DESCRIPTION = "
This file contains coefficients and related data for a spherical
harmonic model of the Mars gravity field. Input data are from
radio tracking of the Mars Global Surveyor spacecraft; no Mariner
9 or Viking data are included. Coordinate system is IAU 2000
(Seidelmann et al., Celestial Mechanics and Dynamical Astronomy,
82(1), 83-110, January 2002).
Constants relevant for Mars in IAU 2000 are:
alpha (right ascension) = 317.68143 deg - 0.1061 deg/century
delta (declination) = 52.88650 deg - 0.0609 deg/century
Wo (prime meridian) = 176.630 deg
Wdot = 350.89198226 deg/day
Gravitational constants obtained from the solution are:
GM (Mars) = 4.282837024529127 E+13 m**3/s**2
sigma = 0.617 E+05 m**3/s**2
GM (Phobos) = 0.68012569 E+06 m**3/s**2
sigma = 0.842 E+04 m**3/s**2
 
The model was constructed from 2,568,683 observations, summarized
in the table below. MGS data are limited to tracking from the
Aerobraking Hiatus and Science Phasing Orbit (SPO) subphases of
the Orbit Insertion phase of the mission and to February 1999 to
May 2002 after the orbit was circularized.
Time Periods Total
Arcs Observations
------------------------ ---- ------------
Hiatus 2 24119
SPO-1 8 31014
SPO-2 17 144253
Feb-Mar 1999 10 86069
2 Apr 1999 - 22 May 2002 167 2186533
Doppler + Crossovers 5 96875
------------------------ ---- ------------
Total 2568863
Orbit reconstruction was improved using Mars Orbiter Laser
Altimeter (MOLA) data on 5 arcs between March and December 1999.
Inter-arc and intra-arc crossovers at 21679 points were included
in the orbit solutions. Crossovers poleward of 60 degrees north
and south were excluded to avoid possible contamination by any
time-varying signature in the polar caps. The altimeter data were
edited for large off-nadir angles as well as for the roughness and
slope of the terrain. The crossovers supplemented the normal
radiometric tracking for these arcs, which included 75196 Doppler
and range observations.
One-way Doppler data were included once these data started to
become available in March 2000 (just after the start of the first
Beta Supplement operations). Range biases were adjusted on a pass
by pass basis, and frequency biases were adjusted for the one-way
data.
The Gravity Calibration Orbit (GCO, February 1999) data were
weighted at 0.0044 Hz (0.16 mm/s). Data for 2000 and for 2001
through the start of Relay 16 operations were weighted at 0.18
mm/s. Data after the start of Relay 16 operations in 2001 were
weighted at 0.357 mm/s in light of the higher RMS fit for these
data. The one-way data were downweighted with respect to the
two-way data by a factor of 2, and are thus weighted at 0.36 mm/s
for the 2000-2001 data and at 0.71 mm/s for Relay 16.
Compared to the GMM2B model, this model contains about 2.5 times
as much data. The data were also rigorously re-edited to remove
spurious signatures which were particularly apparent in some of
the arcs with one-way Doppler data. Finally, the non-conservative
force model was refined to include the high gain antenna. This
improvement reduced the average solar radiation reflectivity
(Cr)from 1.15 to 1.05.
The gravity model was derived using a Kaula type constraint:
sqrt(2)*13*10**(-5)/L**2 (Kaula, W.M., Theory of Satellite
Geodesy, Blaisdell, Waltham, MA, 1966).
Further improvements to the model are expected as additional MGS
data are incorporated.
 
The C20 coefficient is given in the zero-tide system, meaning
that the deformation due to the (solar-induced) permanent tide
is included in the coefficient. An apriori K2 Love number of
0.10 was used in the derivation of this model.
This product is a set of two ASCII tables: a header table and a
coefficients table. Definitions of the tables follow.
This Mars gravity model was produced by F.G. Lemoine under the
direction of D.E. Smith of the MGS Radio Science Team."
START_TIME = 1997-10-13T00:00:00
STOP_TIME = 2002-05-27T23:59:59
PRODUCT_CREATION_TIME = 2003-02-05T20:34:50
PRODUCER_FULL_NAME = "FRANK G. LEMOINE"
PRODUCER_INSTITUTION_NAME = "GODDARD SPACE FLIGHT CENTER"
PRODUCT_VERSION_TYPE = "FINAL"
PRODUCER_ID = "MRO GST"
SOFTWARE_NAME = "SOLVE;200201.02"
 
OBJECT = SHADR_HEADER_TABLE
ROWS = 1
COLUMNS = 8
ROW_BYTES = 137
ROW_SUFFIX_BYTES = 107
INTERCHANGE_FORMAT = ASCII
DESCRIPTION = "The SHADR header includes
descriptive information about the spherical harmonic coefficients
which follow in SHADR_COEFFICIENTS_TABLE. The header consists of
a single record of eight (delimited) data columns requiring 137
bytes, a pad of 105 unspecified ASCII characters, an ASCII
carriage-return, and an ASCII line-feed."
 
OBJECT = COLUMN
NAME = "REFERENCE RADIUS"
DATA_TYPE = "ASCII REAL"
START_BYTE = 1
BYTES = 23
FORMAT = "E23.16"
UNIT = "KILOMETER"
DESCRIPTION = "The assumed reference radius
of the spherical body."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "CONSTANT"
DATA_TYPE = "ASCII REAL"
START_BYTE = 25
BYTES = 23
FORMAT = "E23.16"
UNIT = "KM^3/S^2"
DESCRIPTION = "For a gravity field model the
assumed gravitational constant GM in km cubed per seconds
squared for the body. For a topography model, set to 1."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "UNCERTAINTY IN CONSTANT"
DATA_TYPE = "ASCII REAL"
START_BYTE = 49
BYTES = 23
FORMAT = "E23.16"
UNIT = "KM^3/S^2"
DESCRIPTION = "For a gravity field model the
uncertainty in the gravitational constant GM in km cubed per
seconds squared for the planet (or, set to 0 if not known).
For a topography model, set to 0."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "DEGREE OF FIELD"
DATA_TYPE = "ASCII INTEGER"
 
START_BYTE = 73
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "Degree of the model field."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "ORDER OF FIELD"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 79
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "Order of the model field."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "NORMALIZATION STATE"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 85
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "The normalization indicator.
For gravity field:
0 coefficients are unnormalized
1 coefficients are normalized
2 other."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "REFERENCE LONGITUDE"
POSITIVE_LONGITUDE_DIRECTION = "EAST"
DATA_TYPE = "ASCII REAL"
START_BYTE = 91
BYTES = 23
FORMAT = "E23.16"
UNIT = "DEGREE"
DESCRIPTION = "The reference longitude for
the spherical harmonic expansion; normally 0."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "REFERENCE LATITUDE"
DATA_TYPE = "ASCII REAL"
START_BYTE = 115
BYTES = 23
FORMAT = "E23.16"
UNIT = "DEGREE"
DESCRIPTION = "The reference latitude for the
spherical harmonic expansion; normally 0."
END_OBJECT = COLUMN
 
END_OBJECT = SHADR_HEADER_TABLE
 
OBJECT = SHADR_COEFFICIENTS_TABLE
ROWS = 4183
COLUMNS = 6
ROW_BYTES = 107
ROW_SUFFIX_BYTES = 15
INTERCHANGE_FORMAT = ASCII
DESCRIPTION = "The SHADR coefficients table
contains the coefficients for the spherical harmonic model. Each
row in the table contains the degree index n, the order index m,
the coefficients Cnm and Snm, and the uncertainties in Cnm and
Snm. The (delimited) data require 107 ASCII characters; these are
followed by a pad of 13 unspecified ASCII characters, an ASCII
carriage-return, and an ASCII line-feed."
 
OBJECT = COLUMN
NAME = "COEFFICIENT DEGREE"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 1
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "The degree index n of the
C and S coefficients in this record."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "COEFFICIENT ORDER"
DATA_TYPE = "ASCII INTEGER"
START_BYTE = 7
BYTES = 5
FORMAT = "I5"
UNIT = "N/A"
DESCRIPTION = "The order index m of the C and S
coefficients in this record."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "C"
DATA_TYPE = "ASCII REAL"
START_BYTE = 13
BYTES = 23
FORMAT = "E23.17"
UNIT = "N/A"
DESCRIPTION = "The coefficient Cnm for this
spherical harmonic model."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "S"
DATA_TYPE = "ASCII REAL"
START_BYTE = 37
BYTES = 23
FORMAT = "E23.17"
UNIT = "N/A"
DESCRIPTION = "The coefficient Snm for this
spherical harmonic model."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "C UNCERTAINTY"
DATA_TYPE = "ASCII REAL"
START_BYTE = 61
BYTES = 23
FORMAT = "E23.17"
UNIT = "N/A"
DESCRIPTION = "The uncertainty in the
coefficient Cnm for this spherical harmonic model."
END_OBJECT = COLUMN
 
OBJECT = COLUMN
NAME = "S UNCERTAINTY"
DATA_TYPE = "ASCII REAL"
START_BYTE = 85
BYTES = 23
FORMAT = "E23.17"
UNIT = "N/A"
DESCRIPTION = "The uncertainty in the
coefficient Snm for this spherical harmonic model."
END_OBJECT = COLUMN
END_OBJECT = SHADR_COEFFICIENTS_TABLE
END
 
 
 
 
 
 
 
 
 
 
 
 
 
APPENDIX B.2 Example SHADR Data Object
 
The following lists the first few lines from an example SHADR file, the
MGM1041C Gravity solution.
 
Note that the lines here wrap after 70 characters whereas the header record
length is 244 and the coefficient record length is 122.
 
3.3970000000000000E+03, 4.2828370245291269E+04,
6.1699999999999995E-05, 90, 90, 1, 0.0000000000000000E+00,
0.0000000000000000E+00
2, 0,-8.7450461309664714E-04, 0.0000000000000000E+00,
8.6998585172904000E-11, 0.0000000000000000E+00
2, 1, 3.4361530466444738E-10,-2.6812730136287860E-10,
5.2026417903363999E-11, 5.1856231628722999E-11
2, 2,-8.4585864260034122E-05, 4.8905472151326622E-05,
2.4262638528121999E-11, 2.4711067535925999E-11
3, 0,-1.1889488636438340E-05, 0.0000000000000000E+00,
7.1845677542599005E-11, 0.0000000000000000E+00