Gravity and the Geoid at NGS

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Gravity and the Geoid at NGS

• Dru A. Smith
• National Geodetic Survey
• Presented at the 2000
• Geodetic Advisor Convocation
• Silver Spring, MD
• April 11, 2000

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Topics of Discussion

• Review of height systems
• Geoid modeling
• GEOID99
• Future Directions

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Review of Height Systems

• (Helmert) Orthometric Heights
• Ellipsoid Heights
• Geoid undulations
• NAD 83 NAVD 88
• Mean Sea Level

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Geoid Modeling

• Data Sets
• Methodology

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Data Contributions

• Short Wavelength (local)
• Digital Elevation Models
• Medium Wavelength (regional)
• Surface Gravity Measurements
• Long Wavelength (global)
• Geopotential Model (EGM96)

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Need Gravity Measurements

• Terrestrial
• Ship-borne
• Altimetrically-derived

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Need Digital Elevation Models

• TOPO30 (30 arcsecond) for CONUS
• GTOPO30 (30 arc second) for Canada
• NGSDEM99 (1 arc second) for PNW

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Step 1 Grid Bouguer Anomalies

• Gravity measurements
• DEM for Bouguer plate
• DEM for Terrain Corrections

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Step 2 Compute EGM96 gravity anomalies
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Step 3 Residual Free-air anomalies

• Begin with Bouguer
• Restore Bouguer plate
• Remove EGM96

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Step 4 The Stokes Integral

• Input residual free-air anomalies
• Output residual co-geoid undulations
• 1-D FFT method

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Step 5 Compute EGM96 geoid undulations
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Step 6 G99SSS

• Begin with residual co-geoid undulations
• Add EGM96
• Add Indirect Effect
• G99SSS is
• GEOCENTRIC and
• GRAVIMETRIC

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Need GPS on Benchmarks

• NAD 83 ellipsoid heights
• NAVD 88 Helmert orthometric Heights

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Step 7 Conversion Surface

• Use Least Squares Collocation to combine
• ITRF96 / NAD 83 transformation
• NAVD 88 bias (-52 cm)
• Tilt (0.15 ppm, 327 azimuth)
• Local GPS/Leveling/Geoid misfit
• G99SSS - Conversion Surface GEOID99

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GEOID99

• Comparison to GEOID96
• GPS-derived orthometric heights
• Accuracy

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GEOID96 vs GEOID99

• 2x2
• North 54
• DEM TOPO30
• 2951 GPS/BMs
• -31 cm NAVD 88 bias
• 5.5 cm RMS wrt GPS/BMs

• 1x1
• North 58
• DEM TOPO30 NGSDEM99
• 6169 GPS/BMs
• -52 cm NAVD 88 bias
• 4.6 cm RMS wrt GPS/BMs

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GPS-derived Orthometric heights

• Local accuracy is difficult to gauge
• Few GPSBMs near each other
• Depends on
• Quality of GPS
• Simplicity of local geoid
• Method of adjustment

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Future Directions

• Gravimetric
• Improved gravimetric theory
• GRACE/CHAMP
• 1 arcsecond DEM over USA
• Hybrid Geoid
• 1 cm (1 s) GPS heights
• Leveling near CORS

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Summary

• Gravity coverage is adequate to exceptional
• 1 arc second DEM needed for all USA territories
• GEOID99 improved on the success of GEOID96
• GPS derived orthometric heights at the lt1 to 8 cm
  level

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ON-LINE NGS GEOID RESOURCES

• Official NGS Geoid Page
• http//www.ngs.noaa.gov/GEOID
• Links to all geoid models
• Links to all geoid papers from NGS
• Lots of useful geoid information
• Slideshows like this one (coming soon)