Lecture 1 – The Geoid April 2009

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Lecture 21 – The Geoid

  • 2 April 2009

  • GISC-3325

Class Update

  • Read Chapter 10 of text.

  • Deadline for Reading Assignments (2) is 16 April 2009.

  • Good set of definitions are available at:

    • http://www.geod.nrcan.gc.ca/hm/gloss_e.php#qg
  • Good article on latest U.S. geoid model

    • http://www.ngs.noaa.gov/GEOID/USGG2009/tech.html


  • The equipotential surface of the Earth's gravity field which best fits, in a least squares sense, global mean sea level.

  • Dependent upon the irregular distribution of masses of the Earth.

  • It is the surface to which heights refer.

  • There are two “implementations” of geoid modeling: gravimetric and hybrid.

Geoid Model and Horizontal Datum

  • NAD 83

    • Earth-centered (geocentric) ellipsoid. GRS-80.
    • Heights determined by GPS are computed with respect to it.
  • NAD 27

    • Fitted to the reference ellipsoid.
    • NOT geocentric.
    • No geoid model associated with NAD 27.


  • Based on a minimum-constraint adjustment of Canadian-Mexican-U.S. leveling observations.

  • The height of the primary tidal benchmark at Father Point/Rimouski, Quebec, Canada, was held fixed as the constraint.

  • This constraint satisfies the requirements of shifting the datum vertically to minimize the impact of NAVD 88 on U.S. Geological Survey (USGS) mapping products

NAVD 88 datum + global geopotential

  • A “recent” study by Rapp (1996) compares ITRF93 GPS positions and a global geopotential model against the NAVD 88 vertical datum.

  • Rapp found a mean offset for the NAVD88 datum of -27 cm when computed with a set of 397 GPS points.

    • In sense that NAVD 88 is beneath global geoid model.

Marine Geoid

  • Height of the sea surface caused by both gravity and the active ocean circulation.

  • Topex/Poseidon launched 1992.

SST Equations

  • a = c*(delta_t / 2)

    • “a” distance from satellite to sea surface
    • “C” is speed of light (electromagnetic energy)
    • “delta_t” is roundtrip time of signal
  • h = N + Hbar + a

    • “h” ellipsoid height
    • “N” is geoid height
    • “Hbar” is difference between mean instantaneous sea level and geoid
    • “a” height observation from satellite

Sea Surface Topography SST

  • SST: Deviation of the mean sea surface from the geoid.

  • Differs from geoid by 1-2 meters due to

    • Salinity difference
    • Large-scale differences in atmospheric pressure
    • Strong ocean currents
  • Use of SST yields precision of ~ 2 meters.

Gravity Datums

  • Potsdam Gravity Reference System 1909

    • Standard until IGSN adopted (60 years)
    • +/- 3 milliGals
  • International Gravity Standardization Net 1971

      • Worldwide network: 24,000 gravimeter, 1,200 pendulum and 10 absolute measurements.
      • Collected over twenty years.
      • Adjusted by a small Working Group of the International Association of Geodesy.
      • Datum is determined not by an adopted value at a single station, but by the gravity values for 1854 stations obtained from a single least squares adjustment of absolute, pendulum and gravimeter data.
      • Standard error +/- 50 microGals

Surface Gravity measurements

  • Absolute

    • Formerly pendulum now falling mass
  • Relative

    • Each meter has own calibration value.
    • Observations made at a number of points with the differences the measurement.
    • Require observations be made in loops that start and end on same point to account for drift in instrument.

Gravity Measurement Reductions

  • Gravity anomaly is the difference between the actual acceleration of gravity at a point on the surface of the earth and the computed normal acceleration of gravity of the same point on the level ellipsoid.

  • Free-air - Only accounts for the elevation of the station not mass between the station and the geoid.

  • Bouguer – Accounts for the variations of gravity due to differences in the density and mass of underlying materials.

Geoid Height

  • Distance from the ellipsoid to the geoid measured along the normal to the ellipsoid.

    • Geoid height, geoid separation or geoid undulation

Stokes function

U.S. Geoid models

  • Gravimetric geocentric geoid

    • based on Earth Gravity Model, DEM data, and gravity measurements.
    • Current model USGG 03 (beta version USGG 09 is posted to NGS site)
  • Hybrid

    • based on Gravimetric Model with datum transformations plus GPS on benchmarks
    • Current model is Geoid 03 (beta version Geoid 09 is posted to NGS site)

Gravimetric geoid data used

  • 2.6 million terrestrial, ship, and altimetry-derived gravity measurements

  • 30 arc-second Digital Elevation Data

  • A1-arcsecond DEM for the Northwest USA (NGSDEM99)

  • The EGM96 global geopotential model

Geoid 03

USGG 09 Characteristics

  • One arc-minute model (2 km by 2 km nodal spacing)

  • Based on the EGM08 reference model.

    • Model is complete to spherical harmonic degree and order 2159, and contains additional coefficients extending to degree 2190 and order 2159.
  • Improved surface gravity and terrain data.

USGG 09 evaluation

  • Has significantly reduced long wavelength errors EGM 09.

  • More accurate than previous models:

    • new computation method
    • new satellite gravity model
    • improved altimetric gravity anomalies.
  • In comparison with GPSBM implied geoid undulations, the improvement goes from 9.1 cm to 7.3 cm for USGG2003 and USGG2009, respectively.

Geoid 09

  • Builds on gravimetric model.

  • Incorporates National Readjustment of 2007

    • modified most GPS-derived coordinates (including heights) at the cm- to dm-level.
    • Changes in vertical component mostly around 2 cm, with few changes exceeding 10 cm.
  • Produced by tailoring USGG2009 to fit the 12,715 points where both GPS-derived ellipsoid height and NAVD 88 differentially-determined heights were available.

GPS-derived heights

  • Differential leveling is too expensive.

  • Accurate GPS height determinations can only be achieved using differential methods.

    • GPS baselines result from the combination of data observed simultaneously at at least two sites. Common errors cancel.
  • GPS observations only yield ellipsoid heights.

  • We must apply a geoid model to approximate NAVD 88 heights.


Note on hybrid geoid modeling

  • Regional gravimetric geoids and quasi-geoid models are now commonly fitted to GPS leveling data which simultaneously absorbs leveling, GPS and quasi-geoid errors due to their inseparability.

NAVD 88 via OPUS

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