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Gravity Field and the Geoid

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Title: Gravity Field and the Geoid


1
Gravity Field and the Geoid
  • AFREF Technical Workshop
  • University of Cape Town, South Africa
  • 9-13 July 2006

Steve Kenyon, NGA
2
Why improve the Gravity Field?
  • Develop accurate Geoid to which land elevations
    can be referenced
  • Better calculation of orbits for geodetic
    satellites (including altimetric interferometry
    missions)
  • Adjustment and datum correction of a vast array
    of regional terrestrial, marine and airborne
    gravity survey data.
  • Improve reference frame for defining position
    coordinates
  • Contribute to new Earth Gravitational Models
  • EGM06

3
Geodetic Reference Surfaces
The Geoid is a special, undulating equipotential
surface based on gravity that closely matches
Mean Sea Level.
Geoid
Ocean
Ellipsoid
The Ellipsoid is a mathematical surface that
approximates the shape of the Earth
4
Ellipsoid and Geoid Relationship
h (Ellipsoid Ht) H (MSL Ht) N (Geoid Ht)
MSL Height, measured from the geoid
(more accurately termed Orthometric Ht.)
H
h
Geoid
Geoid Height is the offset between Ellipsoid
Height MSL for a given location
N
Ellipsoid
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6
Earth Gravitational Model 2006
  • CHAMP and GRACE satellite gravity missions
  • 100x improvement in the accuracy with which large
    regional features of the gravitational field can
    be modeled
  • Need for higher-resolution model of the
    gravitational field and geoid
  • 5 x 5 resolution
  • nm2160
  • 15 cm global RMS accuracy goal for geoid

7
Progression of EGMs
  • EGM96
  • 30x30 resolution
  • 50 cm RMS accuracy
  • 70 x 70 error propagation
  • 40 satellites used for long ?s
  • GEOSAT
  • 30 M surface gravity values
  • 29 elevation codes
  • 130 K coefficients
  • EGM06
  • 5x5 resolution
  • 15 cm RMS accuracy
  • 2160 x 2160 error propagation
  • GRACE used for long ?s
  • MSS from retracked ERS-1, GEOSAT, TOPEX, etc.
  • 55 M surface gravity values
  • SRTM, ICESAT
  • 4.7 M coefficients

8
Earth Gravitational Model 1996 15x15 Geoid
Height Grid for the US
9
Earth Gravitational Model 2006 5x5 Geoid
Height Grid for the US
10
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11
EGM06 Geoid Goals
  • EGM06 Geoid Error Goal - 15 cm Global RMS
  • 5 cm commission error from GRACE out to nm100
  • 3 cm omission error beyond 2160 following Kaula's
    Rule
  • NGAs detailed gravity data are expected to meet
    an 14 cm geoid commission error requirement for
    degrees 101-2160

12
EGM06 Geographic Accuracy Breakdown
  • Ocean areas with good altimetric data from /- 5
    cm to /- 10 cm
  • Land areas with good surface gravity data from
    /- 10 cm to /- 15 cm
  • Land areas with poor surface gravity data from
    /- 15 cm to /- 50 cm
  • Land areas with no surface gravity data from /-
    50 cm to /- 120 cm

13
UNCLASSIFIED
Data Collection Methods
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17
AFRICAN ABSOLUTE GRAVITY POINTS
30 JUN 2006
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20
Statistics of 5x5 ?g (v081005)
  • Source ? Area Min. Max. RMS ?
  • ArcGP 4.0 186.0 235.6 31.3
    8.1
  • Altimetry 67.0 -360.4 377.9 29.2
    3.1
  • Terr. 15 18.0 -284.5 443.8 42.3
    6.1
  • Fill-in 3.2 -196.9 256.4 32.3
    24.6
  • Actual 5 78.8 -360.4 669.8 29.6
    3.6
  • All 100.0 -360.4 669.8 32.3
    6.0
  • (?, ?) 19.5?, 293.5? 19.5?,
    204.5?

The Fill-in anomalies for v081005 have decreased
from 16.7 to 3.2 ? of the world compared to
PGM2004A
21
Mongolian Aerogravity Project
22
JGP95E 5x 5 Global Elevation Source Codes
23
SRTM World Coverage Map
Coverage between latitudes 60? N - 54? S 80 of
the Earths landmass
24
KINEMATIC GPS GROUND CONTROL POINT COMPARISON
WITH SRTM
25
KMS 2002 2x2?g
RMS 2.9 mgal in comparison with NGAs Best
Marine 5x5 File
26
GPS/Leveling Comparisons (2 m edit threshold)
Weighted Mean Std. Deviation (cm)
27
GPS Leveling Comparisons over Some Areas with
New ?g
Statistics before bias removal. ?2 m edit
applied.
28
Comparisons With Astronomic Deflections over CONUS
3561 stations compared. Units (arc-seconds)
29
Recent EGM06 Activities
  • Worldwide g1 analytical continuation quantities
    computed using master elevation file
  • Worldwide RTM anomalies computed
  • Currently working on a new 5 x 5 global surface
    gravity anomaly dataset
  • Major focus on coastline interface
  • MSS is in development which includes the use of
    re-tracked GEOSAT

30
Upcoming EGM06 Activities
  • Efficient spherical harmonic synthesis software
    has been received from SGT and tested
  • Official EGM06 project software
  • Provides ability to efficiently compute geodetic
    quantities to nm2160
  • Test sets to be provided
  • Available thru http//earth-info.nga.mil/GandG/
  • Validation of new EGM06
  • GPS/leveling, orbits, DOVs, etc.
  • International participation is welcome
  • Fall 2006 timeframe leading to final EGM06
    selection

31
African Geoid Issues
  • Collect all available gravity data
  • Incorporate all gravity into EGM06
  • Gap areas are a big problem
  • Determine solution to filling in gaps
  • Establish new absolute gravity where needed
  • Utilize best available elevation model for
    terrain corrections and g1 terms SRTM, etc.
  • Collect available GPS/leveling data
  • Participate in the validation of new EGM06

32
Summary
  • EGM06 is planned for late 2006
  • New surface and airborne gravity collected until
    Fall 06
  • Goal of EGM06 is 15 cm
  • nm2160
  • 5x5 resolution
  • GRACE model, Surface Gravity, Satellite
    Altimetry, SRTM and ICESAT data will be utilized
  • Error Propagation to nm2160
  • 5x5 gravity data from un-surveyed areas
  • is welcome

33
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