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
5
(No Transcript)
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
(No Transcript)
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
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
AFRICAN ABSOLUTE GRAVITY POINTS
30 JUN 2006
18
(No Transcript)
19
(No Transcript)
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
(No Transcript)