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

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.

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

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  1. Geoid Computations At NGS: Where Are We And Where Are We Going? Yan Ming Wang Geodesist NGS/NOAA Brown-Bag January 19, 2010

  2. Overview • Geoid computation fundamentals and NGS geoid computation history • The latest geoid models: USGG09 and GEOID09 • Challenges to cm-geoid computations

  3. Where the geoid is used • Vertical datum definition H(Orth)=h(Ellip)-N(grav) • Ocean circulation MODT=MSSH(Altim)-N(Grav) • Crustal motion (future?): subsidence and uplift H=h(Ellip)-N(grav)+[hdot(ellip)-Ndot]*DT

  4. Fundamentals of geoid computation 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 ……

  5. History of NGS geoid computations • GEOID90(Milbert, D. G., 1991; EOS) • GEOID96(Smith, D.A. and D.G. Milbert, 1999, JG) • GEOID99 (Roman, D.R. and D.A. Smith, 2000, GGGG2000) • GEOID03 (Roman, D. R., Y. M. Wang, W. Henning, J. Hamilton, 2004, SLI) • GEOID09 (Roman, D.R, Y.M. Wang, J. Saleh, and X.P. Li, 2010)

  6. NGS geoid computation methods Before USGG09: 1. Simplified Helmert 2nd condensation Terrain correction (30”+3” DEMs) Bouguer anomaly for gravity gridding Stokes 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

  7. 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 anomaly Harmonic continuation effects on mm level 3” 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

  8. USGG09 and GEOID09 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

  9. GRACE(Gravity Recovery and Climate Experiment)

  10. Long wavelength geoid from GRACE

  11. Difference between NAVD88 and GRACE • Geoid height difference: dN=N(NAVD88)-N(GRACE) where N(NAVD88)=H(BM)-h(BM) N(GRACE) is computed to degree and order 120

  12. Long wavelength diff (5°) NAVD88-GRACE

  13. EGM08 • 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

  14. Geoid Difference: EGM08-EGM96

  15. Gravity data coverage

  16. 3” SRTM elevation used for CONUS

  17. RTM effect on gravity (mGal)

  18. RTM Geoid (5’ -3”)

  19. STD of GPS/Leveling Comparisons

  20. Deflections of Vertical Comparisons

  21. Conclusions • USGG09 fits GPS/tide gage-derived geoid heights to better than 5 cm • 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 • 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

  22. What Next? Goal: a gravimetric geoid with absolute accuracy of 1-2 cm We need: • Accurate theory/computation method (why N America geoid is different when computed by Canada and US?) • Accurate and evenly distributed gravity data • Very accurate topographic effects to gravity and geoid, accurate mass density of topography • Data fusion • Gravimetric geoid validation methods and data sets

  23. Accurate theory/computation method • 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

  24. Objective: a geoid of accuracy in 1-2cm in a spatial resolution of 100 km GOCE(Gravity field and steady-state Ocean Circulation Explorer)

  25. 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

  26. Accurate topographic effects to gravity and geoid • 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?

  27. Data Fusion 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?)

  28. Gravimetric geoid validation methods and data sets • Short wavelength: DOV, potential number differences • Few long unconstraint GPS/leveling lines • Tide gauge data sets (mean sea level + mean ODT + GPS ) • Astrogeodetic geoid?

  29. Q&A NGS geoid web site http://www.ngs.noaa.gov/GEOID/ Acknowledgment: Figures and tables provided by Jarir Saleh and Xiaopeng Li

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