SPHERICAL HARMONICS BINARY DATA RECORD (SHBDR)

prepared by

Frank G. Lemoine

Code 698, Planetary Geodynamics Laboratory

NASA Goddard Space Flight Center

Greenbelt, Maryland, 20771 USA

Daniel S. Kahan

Section 332

Jet Propulsion Laboratory

4800 Oak Grove Dr.

Pasadena, California, 91109 USA

Version 2.3

11 September 2013

|======================================================================|

| |

| DOCUMENT CHANGE LOG |

| |

|======================================================================|

|--------+---------+------------+--------------------------------------|

| 1.0 |06/02/20 | All |Adapted MGS SHBDR SIS to include |

|--------+--------+-------------+--------------------------------------|

| 1.0 |06/03/15 | All |Miscellaneous edits |

| | | | |

|======================================================================|

| 1.0 |06/06/29 | All |Integrate PDS review comments |

|======================================================================|

| 1.1 |05/04/29 | All |Fix minor formatting issues |

|======================================================================|

| 1.2 |08/07/28 | 2.3 |Updated file naming convention |

|======================================================================|

| 2.0 |13/04/17 | All |Adapted to include GRAIL |

|======================================================================|

| 2.1 |13/05/22 | All |Minor edits |

|======================================================================|

| 2.2 |13/06/18 | All |Revised SHBDR naming convention |

|======================================================================|

| 2.3 |13/09/11 | Appendices |Revised Appendices B & C for GRAIL |

|======================================================================|

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..................................8

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...................................18

4.2.2.1. SHBDR Header Object Definition...........................18

4.2.2.2. SHBDR Names Object Definition............................20

4.2.2.3. SHBDR Coefficient Object Definition......................21

4.2.2.4 SHBDR Covariance Object Definition........................22

4.3. Data File....................................................23

4.3.1. SHBDR Header Object/Block..................................23

4.3.2. SHBDR Name Block...........................................23

4.3.3. SHBDR Coefficients Block...................................24

4.3.4. SHBDR Covariances Block....................................24

Appendix A. Description of Spherical Harmonic Model Normalization.26

A.1 Definition of Model for the Potential.........................26

A.2 Definition of the normalization used..........................27

Appendix B. Binary Data Format....................................28

Appendix C. Example Data Products.................................29

C.1. Example Label................................................29

C.2. Example Data Object..........................................35

Tables

4-3-1. SHBDR Header Block.........................................23

4-3-2. SHBDR Names Block..........................................24

4-3-3. SHBDR Coefficients Block...................................24

4-3-4. SHBDR Covariance Block.....................................25

Figures

4-2-1. SHBDR 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

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

Binary Data Record (SHBDR) files. The SHBDR 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 SHBDR is produced.

The SHBDR 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 SHBDR 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 ASCII Data Record is also defined [3],

which may be more suitable when error covariances are not 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

ASCII Data Record (SHADR), 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, F.G., S.C. Kenyon, J.K. Factor, R.G. Trimmer, N.K. Pavlis, C.M.

Cox, S.M. Klosko, S.B. Luthcke, M.H. Torrence, Y.M. Wang, R.G. Williamson,

E.C. Pavlis, R.H. Rapp and T.R. 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

SHBDR files are created at the institution conducting the science analysis.

SHBDR 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

SHBDR 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 SHBDR 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

SHBDR 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 SHBDR 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 coarser 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 SHBDR 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 SHBDR product must have access to the data system (or to media)

on which SHBDR files are stored.

2.1.2. Special Setup Requirements

None.

2.2. Volume and Size

SHBDR 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 include approximately N**2 terms and therefore the number of terms in

the covariance matrix will be of order N**4. For 8-byte storage and N=50,

the total SHBDR volume will be about 30 MB. For N=100, the total SHBDR

volume will be approximately 416 MB. Vector quantities (e.g., magnetic

field) may be described by a single SHBDR (in which all components are

represented) or by a separate SHBDR for each field component. If the single

SHBDR 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 is recommended over the SHADR [3] 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 SHBDR products. Beginning with

the GRAIL gravity products the following file naming convention is used:

GTsss_nnnnvv_SHB_Lccc.DAT

where

"G" denotes the generating institution

"J" for the Jet Propulsion Laboratory

"G" or 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 SHBDR 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.

"SHB" denotes that this is a Binary file of Spherical Harmonic coefficients

and error covariance information

"Lccc" is a 2- to 4-character modifier specified by the data producer to

indicate the degree and order to which degree (L) the gravity covariance has

been truncated, if applicable.

".DAT" indicates the data is stored in binary format.

Each SHBDR file is accompanied by a detached PDS label; that label is a file

in its own right, having the name GTsss_nnnnvv_SHB_Lccc.LBL.

2.4. Interface Medium Characteristics

SHBDR 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 SHBDR 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 SHBDR is a file generated by software at the institution conducting

scientific data analysis. Each SHBDR 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 to four 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 SHBDR data file. The SHBDR Header Table Object definition

is required. The SHBDR Names Object Definition is required if there is an

SHBDR Names Object in the file. The SHBDR Coefficients Table Object

definition is required if there is a SHBDR Coefficients Table in the file;

the SHBDR Covariance Table Object definition is required if there is a SHBDR

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.

The EXTRAS directory contains ASCII files to be used as a reference for the

user to confirm proper reading of the SHBDR binary file format.

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.

FILE_RECORDS =

The number of records in the SHBDR file: instance dependent.

^SHBDR_HEADER_TABLE=

File name and record number at which SHBDR_HEADER_TABLE begins. Set to

("GTsss_nnnnvv_SHB_Lccc.DAT",1) where "GTsss_nnnnvv_SHB_Lccc.DAT" is the

file name as described in Section 2.3, and 1 is the record number since this

is the first record in the SHBDR file.

|====================================================================|

| |

| Figure 4-2-1 SHBDR Label Header |

| |

|====================================================================|

| |

| PDS_VERSION_ID = PDS3 |

| RECORD_TYPE = FIXED_LENGTH |

| RECORD_BYTES = nnn |

| FILE_RECORDS = nnn |

| ^SHBDR_HEADER_TABLE = ("GTsss_nnnnvv_SHB_Lccc.DAT",1) |

| ^SHBDR_NAMES_TABLE = ("GTsss_nnnnvv_SHB_Lccc.DAT ",1) |

| ^SHBDR_COEFFICIENTS_TABLE = ("GTsss_nnnnvv_SHB_Lccc.DAT ",nn) |

| ^SHBDR_COVARIANCE_TABLE = ("GTsss_nnnnvv_SHB_Lccc.DAT ",nnn) |

| INSTRUMENT_HOST_NAME = "cccccccccccccccccccc" |

| TARGET_NAME = "cccc" |

| INSTRUMENT_NAME = "ccccccccccccccccccccccc" |

| DATA_SET_ID = "ccccccccccccccccccccccc" |

| OBSERVATION_TYPE = "ccccccccccccc" |

| ORIGINAL_PRODUCT_ID = "ccccccccccccc" |

| PRODUCT_ID = "GTnnnnvv.SHB" |

| 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" |

|====================================================================|

^SHBDR_NAMES_TABLE =

File name and record number at which the SHBDR_NAMES_TABLE begins. The Names

Table is required if the Coefficients Table is included in the file. This

pointer will not appear in the SHBDR label if there is no Coefficients

Table. Set to ("GTsss_nnnnvv_SHB_Lccc.DAT",nn) where

"GTsss_nnnnvv_SHB_Lccc.DAT" is the file name as described in Section 2.3,

and "nn" is the record number in the file where the Names Table begins.

^SHBDR_COEFFICIENTS_TABLE=

File name and record number at which SHBDR_COEFFICIENTS_TABLE begins. The

Coefficients Table is optional; this pointer will not appear in the SHBDR

label if there is no Coefficients Table. Set to

("GTsss_nnnnvv_SHB_Lccc.DAT",nn) where "GTsss_nnnnvv_SHB_Lccc.DAT" is the

file name as described in Section 2.3, and "nn" is the record number in the

file where the Coefficients Table begins.

^SHBDR_COVARIANCE_TABLE=

File name and record number at which SHBDR_COVARIANCE_TABLE begins. The

Covariance Table is optional; this pointer will not appear in the SHBDR

label if there is no Covariance Table. Set to

("GTsss_nnnnvv_SHB_Lccc.DAT",nn) where "GTsss_nnnnvv_SHB_Lccc.DAT" 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", and "MERCURY SURFACE,

SPACE, ENVIRONMENT, GEOCHEMISTRY, AND RANGING", and "GRAVITY RECOVERY AND

INTERIOR LABORATORY".

TARGET_NAME =

A character string that identifies the target body. For MRO- and MGS-

derived SHBDR files, the character string will be "MARS". For MESSENGER

SHBDR files the character string will be "MERCURY". For Lunar Prospector

and GRAIL SHBDR files, the character string will be "MOON".

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 SHBDR 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 that 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 ^SHBDR_HEADER_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 SHBDR product.

START_ORBIT_NUMBER =

Optional. The first orbit represented in the SHBDR product. An integer.

STOP_ORBIT_NUMBER =

Optional. The last orbit represented in the SHBDR 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 SHBDR 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 SHBDR

file. Expressed as a character string, for example "JOHANNES KEPLER".

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 SHBDR.

Standard values include "PREDICT", "PRELIMINARY", and "FINAL".

PRODUCER_ID =

The entity responsible for creation of the SHBDR 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 SHBDR 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

4.2.2.1 SHBDR Header Object Definition

Each SHBDR 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 SHBDR Header Object Definition is a required part of the SHBDR

label file. It immediately follows

OBJECT = SHBDR_HEADER_TABLE

ROWS = 1

COLUMNS = 9

ROW_BYTES = 56

INTERCHANGE_FORMAT = BINARY

DESCRIPTION = "The SHBDR header includes descriptive

information about the spherical harmonic coefficients that follow in

SHBDR_COEFFICIENTS_TABLE. The header consists of a single record of

nine data columns requiring 56 bytes. The Header is followed by a

pad of binary integer zeroes to ensure alignment with RECORD_BYTES."

OBJECT = COLUMN

NAME = "REFERENCE RADIUS"

DATA_TYPE = IEEE_REAL

START_BYTE = 1

BYTES = 8

UNIT = "KILOMETER"

DESCRIPTION = "The assumed reference radius

of the spherical body."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "CONSTANT"

DATA_TYPE = IEEE_REAL

START_BYTE = 9

BYTES = 8

UNIT = "KM^3/S^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 = IEEE_REAL

START_BYTE = 17

BYTES = 8

UNIT = "KM^3/S^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 = MSB_INTEGER

START_BYTE = 25

BYTES = 4

UNIT = "N/A"

DESCRIPTION = "The degree of model field."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "ORDER OF FIELD"

DATA_TYPE = MSB_INTEGER

START_BYTE = 29

BYTES = 4

UNIT = "N/A"

DESCRIPTION = "The order of the model field."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "NORMALIZATION STATE"

DATA_TYPE = MSB_INTEGER

START_BYTE = 33

BYTES = 4

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 = "NUMBER OF NAMES"

DATA_TYPE = MSB_INTEGER

START_BYTE = 37

BYTES = 4

UNIT = "N/A"

DESCRIPTION = "Number of valid names in the SHBDR Names

Table. Also, the number of valid coefficients in the SHBDR

Coefficients Table."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "REFERENCE LONGITUDE"

POSITIVE_LONGITUDE_DIRECTION = "EAST"

DATA_TYPE = IEEE_REAL

START_BYTE = 41

BYTES = 8

UNIT = "DEGREE"

DESCRIPTION = "The reference longitude

for the spherical harmonic expansion; normally 0."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "REFERENCE LATITUDE"

DATA_TYPE = IEEE_REAL

START_BYTE = 49

BYTES = 23

FORMAT = "E23.16"

UNIT = "DEGREE"

DESCRIPTION = "The reference latitude

for the spherical harmonic expansion; normally 0."

END_OBJECT = COLUMN

END_OBJECT = SHBDR_HEADER_TABLE

4.2.2.2 SHBDR Names Object Definition

The SHBDR Names Object is completely defined by the Names Object Definition

in the label. The definition below illustrates general structural form. The

SHBDR Names Object is an optional part of the SHBDR file. If the Names

Object is not included, either the Names Object Definition will be omitted

or the number of rows will be set to zero (ROWS = 0). If the Names Object is

not included, the pointer ^SHBDR_NAMES_TABLE will not appear in the Standard

Keywords and Values. If the Coefficients Object is included in the SHBDR

file, the Names Object is required.

OBJECT = SHBDR_NAMES_TABLE

ROWS = *

COLUMNS = 1

ROW_BYTES = 8

INTERCHANGE_FORMAT = BINARY

DESCRIPTION = "The SHBDR Names Table contains names

for the solution parameters (including gravity field coefficients) which

will follow in the SHBDR_COEFFICIENTS_TABLE. The order of the names

in the SHBDR_NAMES_TABLE corresponds identically to the order

of the parameters in the SHBDR_COEFFICIENTS_TABLE. Each coefficient

name is of the form Cnm or Snm where n is the degree of the

coefficient and m is the order of the coefficient.

Both indices are three-digit zero-filled right-justified ASCII

character strings (for example, C010005 for the 10th degree 5th order

C coefficient, or S002001 for the 2nd degree 1st order S coefficient).

The eighth byte in the table is an ASCII blank used to ensure

that the row length is equal to RECORD_BYTES. Names of other solution

parameters are limited to 8 ASCII characters; if less than 8, they

will be left-justified and padded with ASCII blanks. The Names Table

itself will be padded with ASCII blanks, if necessary, so that

its length is an integral multiple of RECORD_BYTES."

OBJECT = COLUMN

NAME = "PARAMETER NAME"

DATA_TYPE = CHARACTER

START_BYTE = 1

BYTES = 8

UNIT = "N/A"

DESCRIPTION = "The name of the coefficient or other

solution parameter, left-justified and padded with ASCII blanks

(if needed) to 8 characters."

END_OBJECT = COLUMN

END_OBJECT = SHBDR_NAMES_TABLE

4.2.2.3 SHBDR Coefficients Object Definition

The SHBDR 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 SHBDR Coefficients Object is

an optional part of the SHBDR data file. This allows the SHBDR 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 Covariance Object is included in the

SHBDR, the Coefficients Object is required.

If the Coefficients Object is not included in the SHBDR file, either the

SHBDR Coefficients Object Definition will be omitted or the number of rows

will be set to zero (ROWS = 0). If the SHBDR Coefficients Object is not

included, the pointer ^SHBDR_COEFFICIENTS_TABLE will not appear in the

label header. If the SHBDR Coefficients Object Definition is included in the

label, it immediately follows the SHBDR Names Object Definition. The order

in which coefficients appear in the Coefficients Object is defined by the

Names Object [2].

OBJECT = SHBDR_COEFFICIENTS_TABLE

ROWS = *

COLUMNS = 1

ROW_BYTES = 8

INTERCHANGE_FORMAT = BINARY

DESCRIPTION = "The SHBDR Coefficients Table

contains the coefficients and other solution parameters

for the spherical harmonic model. The order of the

coefficients in this table corresponds exactly to the

order of the coefficient and parameter names in

SHBDR_NAMES_TABLE. The SHBDR Coefficients Table will be

padded with double precision DATA_TYPE zeroes so that

its total length is an integral multiple of RECORD_BYTES."

OBJECT = COLUMN

NAME = "COEFFICIENT VALUE"

DATA_TYPE = *

START_BYTE = 1

BYTES = 8

UNIT = "N/A"

DESCRIPTION = "A coefficient Cnm or

Snm or other solution parameter as specified in the

SHBDR Names Table."

END_OBJECT = COLUMN

END_OBJECT = SHBDR_COEFFICIENTS_TABLE

4.2.2.4 SHBDR Covariance Object Definition

The SHBDR 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 SHBDR Covariance Object is an optional part of the SHBDR 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 SHBDR Covariance Object is not included, the pointer

^SHBDR_COVARIANCE_TABLE will not appear in the label header. If the SHBDR

Covariance Object Definition is included in the label, it immediately

follows the SHBDR Coefficients Object Definition. The order in which

covariance terms appear in the Covariance Object is defined by the Names

Object [2].

OBJECT = SHBDR_COVARIANCE_TABLE

ROWS = *

COLUMNS = 1

ROW_BYTES = 8

INTERCHANGE_FORMAT = BINARY

DESCRIPTION = "The SHBDR Covariance Table

contains the covariances for the spherical harmonic model

coefficients and other solution parameters. The order of

the covariances in this table is defined by the product

of the SHBDR Names Table with its transpose, except that

redundant terms are omitted on their second occurrence.

The SHBDR Covariance Table will be padded with double

precision DATA_TYPE zeroes so that its total length is

an integral multiple of RECORD_BYTES."

OBJECT = COLUMN

NAME = "COVARIANCE VALUE"

DATA_TYPE = *

START_BYTE = 1

BYTES = 8

UNIT = "N/A"

DESCRIPTION = "The covariance value

for the coefficients and other solution parameters

specified by the product of SHBDR_NAMES_TABLE with

its transpose, after omitting redundant terms."

END_OBJECT = COLUMN

END_OBJECT = SHBDR_COVARIANCE_TABLE

4.3. Data File

Each SHBDR data file comprises one or more data blocks. The data objects

were defined in Section 4.2. The data blocks are illustrated below.

The Header Object is required in each SHBDR file; the Names Object, the

Coefficients Object, and the Covariance Object are optional. If the

Covariance Object is included, both the Coefficients Object and the Names

Object are required; if the Coefficients Object is included, the Names

Object is required.

4.3.1. SHBDR Header Object/Block

The SHBDR Header Object contains the parameters necessary to interpret the

data in the SHBDR file. The structure and content of the SHBDR Header Object

are defined in Section 4.2.2.1. The SHBDR 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.

|====================================================================|

| |

| Table 4-3-1. SHBDR Header Block |

| |

|====================================================================|

|--------|--------|--------|--------|--------------------------------|

| 1 | +0 | 8 | double |Planetary Radius |

|--------|--------|--------|--------|--------------------------------|

| 2 | 8 | 8 | double |Constant |

|--------|--------|--------|--------|--------------------------------|

| 3 | 16 | 8 | double |Uncertainty in Constant |

|--------|--------|--------|--------|--------------------------------|

| 4 | 24 | 4 | long |Degree of Field |

|--------|--------|--------|--------|--------------------------------|

| 5 | 28 | 4 | long |Order of Field |

|--------|--------|--------|--------|--------------------------------|

| 6 | 32 | 4 | long |Normalization State |

|--------|--------|--------|--------|--------------------------------|

| 7 | 36 | 4 | long |Number of Names |

|--------|--------|--------|--------|--------------------------------|

| 8 | 40 | 8 | double |Reference Longitude |

|--------|--------|--------|--------|--------------------------------|

| 9 | 48 | 8 | double |Reference Latitude |

|--------|--------|--------|--------|--------------------------------|

| | +56 | |

|========|========|========|========|================================|

4.3.2. SHBDR Names Block

The SHBDR Names Object comprises one or more SHBDR Names Blocks. Each block

contains the name of one coefficient or solution parameter in the Spherical

Harmonic Model. The structure and content of the SHBDR Names Object are

defined in Section 4.2.2.2. The structure of an individual block is shown in

Table 4-3-2.

|====================================================================|

| |

| Table 4-3-2. SHBDR Names Block |

| |

|====================================================================|

|--------|--------|--------|--------|--------------------------------|

| 1 | +0 | 8 | A8 |Coefficient or Solution |

|--------|--------|--------|--------|--------------------------------|

| | +8 | |

|========|========|========|========|================================|

4.3.3. SHBDR Coefficients Block

The SHBDR Coefficients Object comprises one or more SHBDR Coefficients

Blocks. Each block contains the value of one coefficient or other solution

parameter for the overall model defined by the SHBDR product. The structure

and content of the SHBDR Coefficients Object are defined in Section 4.2.2.3.

The structure of an individual block is shown in Table 4-3-3.

|====================================================================|

| |

| Table 4-3-3. SHBDR Coefficients Block |

| |

|====================================================================|

|--------|--------|--------|--------|--------------------------------|

| 1 | +0 | 8 | double |Coefficient Cnm or Snm or |

|--------|--------|--------|--------|--------------------------------|

| | +8 | |

|========|========|========|========|================================|

4.3.4. SHBDR Covariance Block

The SHBDR Covariance Object comprises one or more SHBDR Covariance Blocks.

Each SHBDR Covariance Block contains one covariance for the overall model

defined by the SHBDR product. The structure and content of the SHBDR

Covariance Object are defined in Section 4.2.2.4. The structure of an

individual block is shown in Table 4-3-4. The SHBDR Covariance Object is an

optional component of the SHBDR file.

|====================================================================|

| |

| Table 4-3-4. SHBDR Covariance Block |

| |

|====================================================================|

|--------|--------|--------|--------|--------------------------------|

| 1 | +0 | 8 | double |Covariance Value |

|--------|--------|--------|--------|--------------------------------|

| | +8 | |

|========|========|========|========|================================|

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).

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 of the planet Mercury, solutions 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 meridian N-S in

other words they represent only latitudinal varations 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 S22" = -.14001668365394E-05

(normalized from the Earth Gravitational Model 1996, EGM96, [13])

Thus,

S22= sqrt(5/12) * (-.14001668365394E-05) = -9.038038E-07 (un-normalized)

which matches closely the example given by Lambeck [11].

APPENDIX B. BINARY DATA FORMAT

See PDS 3.8 Standards Reference, Appendix C.7, for the PC binary format.

APPENDIX C EXAMPLE DATA PRODUCTS

Appendix C.1 Example Label

The following lists an example SHBDR LBL file for a GRAIL-derived lunar

gravity solution, "GGGRX_0660PM" (GRGM660PRIM), prepared by the GRAIL

gravity team at NASA GSFC.

GRGRM660PRIM is a 660x660 gravity model based on primary mission data,

and in this example only the covariance of that solution to 50x50 is provided.

The full reference for this solution is:

Lemoine, F.G., S. Goossens, T.J. Sabaka et al., "High-degree gravity models

from GRAIL primary mission data", J. Geophys. Res., 118(8), 1676-1698,

doi: 10.1002/jgre.20118.

PDS_VERSION_ID = "PDS3"

FILE_NAME = "GGGRX_0660PM_SHB_L50.DAT"

RECORD_TYPE = FIXED_LENGTH

RECORD_BYTES = 512

FILE_RECORDS = 52998

^SHBDR_HEADER_TABLE = ("GGGRX_0660PM_SHB_L50.DAT",1)

^SHBDR_NAMES_TABLE = ("GGGRX_0660PM_SHB_L50.DAT",2)

^SHBDR_COEFFICIENTS_TABLE = ("GGGRX_0660PM_SHB_L50.DAT",43)

^SHBDR_COVARIANCE_TABLE = ("GGGRX_0660PM_SHB_L50.DAT",84)

INSTRUMENT_HOST_NAME = {"GRAVITY RECOVERY AND INTERIOR LABORATORY A",

"GRAVITY RECOVERY AND INTERIOR LABORATORY B"}

TARGET_NAME = "MOON"

INSTRUMENT_NAME = {"LUNAR GRAVITY RANGING SYSTEM A",

"LUNAR GRAVITY RANGING SYSTEM B"}

DATA_SET_ID = "GRAIL-L-LGRS-5-RDR-V1.0"

OBSERVATION_TYPE = "GRAVITY FIELD"

PRODUCT_ID = "GRGM660PRIM"

PRODUCT_RELEASE_DATE = 2012-07-31

DESCRIPTION = "

This file contains coefficients and related data for the GSFC Lunar gravity

field GRGM660PRIM, a degree and order 660 spherical harmonic model. It is

a preliminary GSFC gravity field that includes the entire nominal mission of

GRAIL tracking data (March 1, 16:30 to May 29, 16:36, 2012).

Some details describing this model are:

The spherical harmonic coefficients are fully normalized.

The reference radius = 1738.0 km

The planetary ephemeris is de421 and defines the lunar body-fixed

coordinate system.

A Kaula type power law constraint is applied to the spherical harmonics

coefficients for degrees >330 (2.5e-4/n^2).

The weighting of the data is 0.05 microns/sec for the 5-s KBRR data and

0.12mm/s for the 10-s 2-way S-band DSN tracking data.

The estimated tidal Love numbers are:

k20 = 0.024165 +/- 0.000091

k21 = 0.023915 +/- 0.000013

k22 = 0.024852 +/- 0.000017

for an aggregate k2 = 0.02427 +/- 0.000054

k30 = 0.007342+/-0.001534

This product contains the truncated n=50 covariance of the GRGM660PRIM

gravity model or GGGRX_0660PM_SHA.

The reference for the GRGM660PRIM gravity field is LEMOINEETAL2013,

published in the Journal of Geophysical Research with the DOI number

10.1002/jgre.20118 .

This product is a set of binary tables:

a header table, a names table, a coefficients table, and a covariance

table. Definitions of the tables follow. This GRAIL moon gravity model

is in the form of a Spherical Harmonics Binary Data Record (SHBDR)."

START_TIME = 2012-03-01T16:28:00.000

STOP_TIME = 2012-05-29T16:36:00.000

PRODUCT_CREATION_TIME = 2013-06-06T00:00:00.000

PRODUCER_FULL_NAME = "GSFC LEVEL-2 TEAM"

PRODUCER_INSTITUTION_NAME = "GODDARD SPACE FLIGHT CENTER"

PRODUCT_VERSION_TYPE = "PRELIMINARY"

PRODUCER_ID = "GRAIL"

/* Structure Objects */

OBJECT = SHBDR_HEADER_TABLE

ROWS = 1

COLUMNS = 9

ROW_BYTES = 56

INTERCHANGE_FORMAT = BINARY

DESCRIPTION = "The SHBDR Header includes

descriptive information about the spherical harmonic

coefficients which follow in SHBDR_COEFFICIENTS_TABLE.

The header consists of a single record of nine data

columns requiring 56 bytes. The Header is followed by

a pad of binary integer zeroes to ensure alignment

with RECORD_BYTES."

OBJECT = COLUMN

NAME = "REFERENCE RADIUS"

DATA_TYPE = PC_REAL

START_BYTE = 1

BYTES = 8

UNIT = "KILOMETER"

DESCRIPTION = "The assumed reference

radius of the spherical planet."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "CONSTANT"

DATA_TYPE = PC_REAL

START_BYTE = 9

BYTES = 8

UNIT = "N/A"

DESCRIPTION = "For a gravity field model

the gravitational constant GM in kilometers cubed per seconds

squared for the planet. For a topography model, set to 1."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "UNCERTAINTY IN CONSTANT"

DATA_TYPE = PC_REAL

START_BYTE = 17

BYTES = 8

UNIT = "N/A"

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

model, set to 0."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "DEGREE OF FIELD"

DATA_TYPE = LSB_INTEGER

START_BYTE = 25

BYTES = 4

UNIT = "N/A"

DESCRIPTION = "Degree of the model field."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "ORDER OF FIELD"

DATA_TYPE = LSB_INTEGER

START_BYTE = 29

BYTES = 4

UNIT = "N/A"

DESCRIPTION = "Order of the model field."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "NORMALIZATION STATE"

DATA_TYPE = LSB_INTEGER

START_BYTE = 33

BYTES = 4

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 = "NUMBER OF NAMES"

DATA_TYPE = LSB_INTEGER

START_BYTE = 37

BYTES = 4

UNIT = "N/A"

DESCRIPTION = "Number of valid names in

the SHBDR Names Table. Also, the number of valid

coefficients in the SHBDR Coefficients Table."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "REFERENCE LONGITUDE"

POSITIVE_LONGITUDE_DIRECTION = "EAST"

DATA_TYPE = PC_REAL

START_BYTE = 41

BYTES = 8

UNIT = "DEGREE"

DESCRIPTION = "The reference longitude for

the spherical harmonic expansion; normally 0."

END_OBJECT = COLUMN

OBJECT = COLUMN

NAME = "REFERENCE LATITUDE"

DATA_TYPE = PC_REAL

START_BYTE = 49

BYTES = 8

UNIT = "DEGREE"

DESCRIPTION = "The reference latitude for

the spherical harmonic expansion; normally 0."

END_OBJECT = COLUMN

END_OBJECT = SHBDR_HEADER_TABLE

OBJECT = SHBDR_NAMES_TABLE

ROWS = 2602

COLUMNS = 1

ROW_BYTES = 8

INTERCHANGE_FORMAT = BINARY

DESCRIPTION = "The SHBDR Names Table

contains names for the solution parameters (including

gravity field coefficients) which will follow in

SHBDR_COEFFICIENTS_TABLE. The order of the names

in SHBDR_NAMES_TABLE corresponds identically to the

order of the parameters in SHBDR_COEFFICIENTS_TABLE.

Each coefficient name is of the form Cij or Sij

where i is the degree of the coefficient and j is

the order of the coefficient. Both indices are three-

digit zero-filled right-justified ASCII character strings

(for example, C010005 for the 10th degree 5th order C

coefficient, or S002001 for the 2nd degree 1st order

S coefficient). The eighth byte in the table is an

ASCII blank used to ensure that the row length

is equal to RECORD_BYTES. Names of other solution

parameters are limited to 8 ASCII characters; if less

than 8, they will be left-justified and padded with

ASCII blanks. The Names Table itself will be padded

with ASCII blanks, if necessary, so that its length is

an integral multiple of RECORD_BYTES."

OBJECT = COLUMN

NAME = "PARAMETER NAME"

DATA_TYPE = CHARACTER

START_BYTE = 1

BYTES = 8

UNIT = "N/A"

DESCRIPTION = "The name of the

coefficient or other solution parameter, left-

justified and padded with ASCII blanks (if needed)

to 8 characters."

END_OBJECT = COLUMN

END_OBJECT = SHBDR_NAMES_TABLE

OBJECT = SHBDR_COEFFICIENTS_TABLE

ROWS = 2602

COLUMNS = 1

ROW_BYTES = 8

INTERCHANGE_FORMAT = BINARY

DESCRIPTION = "The SHBDR Coefficients Table

contains the coefficients and other solution parameters

for the spherical harmonic model. The order of the

coefficients in this table corresponds exactly to the

order of the coefficient and parameter names in

SHBDR_NAMES_TABLE. The SHBDR Coefficients Table will be

padded with double precision DATA_TYPE zeroes so that

its total length is an integral multiple of RECORD_BYTES."

OBJECT = COLUMN

NAME = "COEFFICIENT VALUE"

DATA_TYPE = PC_REAL

START_BYTE = 1

BYTES = 8

UNIT = "N/A"

DESCRIPTION = "A coefficient Cij or

Sij or other solution parameter as specified in the

SHBDR Names Table."

END_OBJECT = COLUMN

END_OBJECT = SHBDR_COEFFICIENTS_TABLE

OBJECT = SHBDR_COVARIANCE_TABLE

ROWS = 3386503

COLUMNS = 1

ROW_BYTES = 8

INTERCHANGE_FORMAT = BINARY

DESCRIPTION = "The SHBDR Covariance Table

contains the covariances for the spherical harmonic model

coefficients and other solution parameters. The order of

the covariances in this table is defined as rowwise

vector storage of the upper triangular matrix formed by

the product of the SHBDR Names Table with its transpose.

For example, if the Names Table has four entries A, B,

C, and D, then the covariances are given by the row

vectors in the upper triangular matrix of

| A | [ A B C D ] = | AA AB AC AD |

| B | | BA BB BC BD |

| C | | CA CB CC CD |

| D | | DA DB DC DD |

That is, the covariance table will list (in this order)

AA, AB, AC, AD, BB, BC, BD, CC, CD, and DD.

The SHBDR Covariance Table will be padded with double

precision DATA_TYPE zeroes so that its total length is

an integral multiple of RECORD_BYTES."

OBJECT = COLUMN

NAME = "COVARIANCE VALUE"

DATA_TYPE = PC_REAL

START_BYTE = 1

BYTES = 8

UNIT = "N/A"

DESCRIPTION = "The covariance value

for the coefficients and other solution parameters

specified by the product of SHBDR_NAMES_TABLE with

its transpose, after omitting redundant terms."

END_OBJECT = COLUMN

END_OBJECT = SHBDR_COVARIANCE_TABLE

END

Appendix C.2 Example SHBDR Data Object Output

The following lists the first few lines from an example SHBDR file, the

gggrx_0660pm_shb_l50.dat gravity field solution covariance.

We describe below the extracts from a FORTRAN program to read the above

gggrx_0660pm_shb_l50.dat covariance file, the error covariance of the

gravity solution GRGM660PRIM.

The SHB file is opened with the following FORTRAN open statement. The key is

that the SHB file is a direct access binary file with a record length (in

this example) of 512 bytes.

i.e.

open (10, file='gggrx_0660pm_shb_l50.dat', status ='old', access='DIRECT',

RECL=512)

The first record reads the general solution information, where the variables

have been carefully predefined at the top of the program.

...................................

real*8 ae, gm, gmsig, reflon, reflat

integer*4 lmax,mmax,inorm, nvar

read(10,rec=1) ae, gm, gmsig, lmax, mmax, inorm, nvar, reflon, reflat

...................................

On output these records are:

ae = 1738.0

gm = 4902.799807 | GM in km**3/sec**2

gmsig = 7.74E-06 | GM sigma in km**3/sec**2

lmax = 50

mmax = 50

inorm = 1

nvar = 2602 | total number of parameters in the solution.

reflon = 0.0E+0

reflat = 0.0E+0

The next step is to read the coefficient name table and compute the number

of lines in the coefficient name table. In this example file there are

64 8 byte characters per record of 512 bytes.

.....................

nline = (nvar/64) + 1

.....................

c integer multiplication on the following line is intentional

c we need to know number of variables on the last line

..........................

jend = nvar - (nvar/64)*64

..........................

Record 2, or the first record of the names table contains the following:

GM K002000 K002001 K002002 K003000 C002000 C002001 S002001

C002002 S002002 C003000 C003001 S003001 C003002 S003002 C003003

S003003 C004000 C004001 S004001 C004002 S004002 C004003 S004003

C004004 S004004 C005000 C005001 S005001 C005002 S005002 C005003

S005003 C005004 S005004 C005005 S005005 C006000 C006001 S006001

C006002 S006002 C006003 S006003 C006004 S006004 C006005 S006005

C006006 S006006 C007000 C007001 S007001 C007002 S007002 C007003

S007003 C007004 S007004 C007005 S007005 C007006 S007006 C007007

Record 42 contains the last few coefficient names of the solution:

C050030 S050030 C050031 S050031 C050032 S050032 C050033 S050033

C050034 S050034 C050035 S050035 C050036 S050036 C050037 S050037

C050038 S050038 C050039 S050039 C050040 S050040 C050041 S050041

C050042 S050042 C050043 S050043 C050044 S050044 C050045 S050045

C050046 S050046 C050047 S050047 C050048 S050048 C050049 S050049

C050050 S050050

The Coefficients table begins at Record 43:

The first eight variables of that record are:

4.90280E+03 2.41948E-02 2.38352E-02 2.49544E-02 7.34222E-03

-9.08828E-05 1.19428E-10 9.47060E-10

The first coefficient value is for GM.

The Coefficients table ends at Record 83 with 42 valid records and the

remainder zero filled:

-1.07382E-07 5.81702E-08 -2.50231E-07 -1.53542E-07 1.11406E-07

1.78570E-08 -9.91932E-08 6.97906E-08

-6.72927E-08 -6.43053E-08 5.34257E-09 9.84231E-08 -1.49303E-07

4.46417E-08 2.29334E-07 7.48138E-08

1.63668E-07 1.93044E-07 -1.20901E-09 6.59939E-08 1.98945E-07

1.22273E-07 5.10204E-08 1.89710E-08

-4.17405E-08 6.61186E-08 2.04331E-07 2.61453E-07 1.96770E-07

1.85188E-07 -2.70291E-07 3.54506E-09

-3.07759E-07 1.00677E-08 -5.41954E-09 5.20505E-08 1.19688E-07

3.69751E-07 -2.46317E-08 1.62949E-07

2.85172E-07 5.79127E-08

..........

The last valid record is the value of S(50,50) for this solution, as per

the order specified in the names record.