Geoid Computations At NGS: Where Are We And Where Are We Going?

Yan Ming WangGeodesist

NGS/NOAA Brown-BagJanuary 19, 2010

• Geoid computation fundamentals and NGS geoid computation history

• The latest geoid models: USGG09 and GEOID09

• Challenges to cm-geoid computations

Overview

• 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

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

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

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

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

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

GRACE(Gravity Recovery and Climate Experiment)

Long wavelength geoid from GRACE

• 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

Long wavelength diff (5°) NAVD88-GRACE

• 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

Geoid Difference: EGM08-EGM96

Gravity data coverage

3” SRTM elevation used for CONUS

FA-EGM08 FA-EGM08-

RTM

Mean -1.9 0.6

STD 10.6 5.4

RTM effect on gravity (mGal)

RTM Geoid (5’ -3”)

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

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

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

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?

• 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

Objective: a geoid of accuracy in 1-2cm in a spatial resolution of 100 km

GOCE(Gravity field and steady-state Ocean Circulation Explorer)

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

• 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

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

• 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

NGS geoid web sitehttp://www.ngs.noaa.gov/GEOID/

Acknowledgment: Figures and tables provided by Jarir Saleh and Xiaopeng Li

Q&A