geoid computations at ngs: where are we and where are we going?
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Geoid Computations At NGS: Where Are We And Where Are We Going?. Yan Ming Wang Geodesist NGS/NOAA Brown-Bag January 19, 2010. Overview. Geoid computation fundamentals and NGS geoid computation history The latest geoid models: USGG09 and GEOID09 Challenges to cm-geoid computations. - PowerPoint PPT PresentationTRANSCRIPT
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Geoid Computations At NGS: Where Are We And Where Are We Going?
Yan Ming WangGeodesist
NGS/NOAA Brown-BagJanuary 19, 2010
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• Geoid computation fundamentals and NGS geoid computation history
• The latest geoid models: USGG09 and GEOID09
• Challenges to cm-geoid computations
Overview
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• Vertical datum definitionH(Orth)=h(Ellip)-N(grav)
• Ocean circulationMODT=MSSH(Altim)-N(Grav)
• Crustal motion (future?): subsidence and uplift H=h(Ellip)-N(grav)+[hdot(ellip)-Ndot]*DT
Where the geoid is used
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1. Newton’ gravitation law (integration)Difficulty: the density of the Earth’s interior masses is never known accurately
2. Geodetic boundary value problems: from free
boundary to fix-boundary (differentiation) One solution: Stokes integral: requires gravity
measured on the Earth’s surface everywhere
Another solution: Spherical harmonic series as solution of GBVPs ……
Fundamentals of geoid computation
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1. GEOID90 (Milbert, D. G., 1991; EOS)
2. GEOID96 (Smith, D.A. and D.G. Milbert, 1999, JG)
3. GEOID99 (Roman, D.R. and D.A. Smith, 2000, GGGG2000)
4. GEOID03 (Roman, D. R., Y. M. Wang, W. Henning, J. Hamilton, 2004, SLI)
5. GEOID09 (Roman, D.R, Y.M. Wang, J. Saleh, and X.P. Li, 2010)
History of NGS geoid computations
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Before USGG09:1. Simplified Helmert 2nd condensation
Terrain correction (30”+3” DEMs)Bouguer anomaly for gravity griddingStokes integral of Faye anomaly
2. Remove-restore of a global gravity model (EGM96) Computations on the sea level
3. Linearalized formula of the indirect effect added , ellipsoidal effect (Li and Sideris) added
NGS geoid computation methods
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USGG09:1. Method of harmonic continuation
Residual free-air anomaly computed on the Earth’s surface
Stokes integral of residual free-air anomalyHarmonic continuation effects on mm level3” SRTM DEM used for RTM effect (gravity and
geoid)
2. Remove-restore of a global gravity model (EGM08) Stokes kernel truncated at n=120, 360
NGS geoid computation methods
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Compare to GEOID03, we have• New global gravity models: GRACE, EGM08
• New altimetric gravity near coast
• More gravity data (80,000) gravity data from NGA
• Airborne gravity of GARV-D survey (not used)
• 3” digital elevation covers from Canada to Mexico
• 2007 National Readjustment
• New computation procedure
USGG09 and GEOID09
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GRACE(Gravity Recovery and Climate Experiment)
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Long wavelength geoid from GRACE
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• Geoid height difference:
dN=N(NAVD88)-N(GRACE)
whereN(NAVD88)=H(BM)-h(BM)
N(GRACE) is computed to degree and order 120
Difference between NAVD88 and GRACE
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Long wavelength diff (5°) NAVD88-GRACE
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• GRACE satellite only at low degree and order
• Using global terrestrial/altimetry gravity data in 5’ mean, geophysical model fill-in in areas with no data
• Using SRTM elevation for topographic reduction and geoid conversion
• Model developed to degree and order 2160
EGM08
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Geoid Difference: EGM08-EGM96
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Gravity data coverage
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3” SRTM elevation used for CONUS
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FA-EGM08 FA-EGM08-
RTM
Mean -1.9 0.6
STD 10.6 5.4
RTM effect on gravity (mGal)
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RTM Geoid (5’ -3”)
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STD of GPS/Leveling Comparisons
Territory No USGG2009 EGM08
CONUS 18398 6.32 6.36
Alaska 198 27.5 27.7
Hawaii Maui
Honolulu
Kauai
5 2.8 3.9
17 6.0 6.1
6 13.8 13.4
Guam 16 4.5 6.8
North Mariana Island Saipan
Tinian
Rota
10
35
9
2.6
2.0
2.4
3.3
1.7
2.6
American Samoa 22 5.3 11.2
Puerto Rico and the US Virgin Islands 29 1.7 3.0
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Deflection component USGG2009 EGM08
Xi Mean = 0.02529
SD = 0.87338
Mean = -0.09113
SD = 0.97803
Eta Mean = 0.16115
SD = 0.94117
Mean = 0.18889
SD = 1.03344
Deflections of Vertical Comparisons
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1. USGG09 fits GPS/tide gage-derived geoid heights to better than 5 cm
2. After removal of long wavelength error in NAVD88, USGG09 fits the GPSBMs09 to better than 3-4 cm except in the Rocky Mountains, where it fits to 5-6 cm
3. LA and TX are exceptions due to the subsidence of the GPSBMs
4. Since EGM08 uses the same data sets, the results are Similar. However, USGG09 contains more high frequency that is indicated by the DOV comparison and GPS/leveling comparisons in the Rocky Mountains
Conclusions
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Goal: a gravimetric geoid with absolute accuracy of 1-2 cm
We need:1. Accurate theory/computation method (why N America
geoid is different when computed by Canada and US?)
2. Accurate and evenly distributed gravity data
3. Very accurate topographic effects to gravity and geoid, accurate mass density of topography
4. Data fusion
5. Gravimetric geoid validation methods and data sets
What Next?
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• Investigate/review the non-linear effect in GBVPs.
• Investigate the topographic effect, impact of varying mass density
• Harmonic downward continuation effect (error?)
• Investigate an optimal way in use of the potential number differences in gravimetric geoid computation
• Investigate/review data requirement for cm-geoid
• Develop a synthetic gravity model for theory/computation method validation
Accurate theory/computation method
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Objective: a geoid of accuracy in 1-2cm in a spatial resolution of 100 km
GOCE(Gravity field and steady-state Ocean Circulation Explorer)
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GRAV-D airborne gravity should fill in the medium to high frequencies of the gravity field to about 5’ resolution
Focus: 100km to 20km frequency band
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• To model topographic effect in spherical harmonic series to degree and order 2160 (5’ resolution)
• To compute topographic effect from 5’ to 3” by Newtonian integration
• How big is the impact of varying density on the geoid?
Accurate topographic effects to gravity and geoid
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An optimal way to combine the following data sets:
• Satellite models + topo spherical harmonics (to 100km resolution)
• Surface gravity data + GRAV-D (100km to 20KM?)
• Topography (30KM to 100m)
• Potential number differences from GPS/leveling (from 1 km to 100 meters?)
Data Fusion
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• Short wavelength: DOV, potential number differences
• Few long unconstraint GPS/leveling lines
• Tide gauge data sets (mean sea level + mean ODT + GPS )
• Astrogeodetic geoid?
Gravimetric geoid validation methods and data sets
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NGS geoid web sitehttp://www.ngs.noaa.gov/GEOID/
Acknowledgment: Figures and tables provided by Jarir Saleh and Xiaopeng Li
Q&A