Technical Information Page for 
G99SSS, GEOID99 and DEFLEC99

Last updated July 11, 2001

(changes since last update are shown in RED) 

G99SSS

The G99SSS geoid model is a purely gravimetric, geocentric geoid model covering the Conterminous United States. Input data for G99SSS consisted of: Using EGM96 as an underlying long wavelength model, G99SSS was computed using a 1-D FFT remove/compute/restore application of the spherical Stokes integral, where Faye anomalies approximated Helmert anomalies. In computing G99SSS, the geopotential value of the geoid was chosen as W0 = 62636856.88 m2 / s2. The G99SSS geoid undulations refer to a geocentric GRS-80 ellipsoid ( click here for details about the difficulty in defining the origin of the reference ellipsoid). G99SSS was computed on a 1 x 1 arc minute grid, covering the Conterminous United States in the region 24-58 N latitude and 230-300 E longitude.

For most regions, thirty arcsecond resolution DEMs were employed for the terrain correction calculations. In the Northwest USA (39-49N, 234-256E), however, three arcsecond DEMs (decimated from the NGSDEM99 data) were used. Because the highest frequency information in the geoid comes mostly from local terrain, and the accuracy of NGSDEM99 surpassed previous models, it was theorized that geoid signal missing at the two arcminute spacing (such as for G96SSS) could be accurately modeled if the geoid were computed at one arcminute. Details on the successful validation of this theory appear in a forthcoming paper on G99SSS and GEOID99. Additionally, a one-arcminute grid retains more information in regions of higher density gravity observations. An ellipsoid correction to reduce the spherical assumption implicit in the Stokes equation was then applied to the intermediate model to create the G99SSS model (See Fei and Sideris, 1999).

GEOID99

The GEOID99 geoid model is (in the Conterminous United States) a hybrid geoid model, combining the gravimetric geoid G99SSS with datum transformations and NAD 83 GPS ellipsoid heights on NAVD 88 leveled bench marks. Unfortunately, the areas of Alaska, Hawaii and Puerto Rico and the U.S. Virgin Islands do not currently have GPS on Bench Mark data sufficient to create a hybrid model, and in those three areas, the GEOID99 model is a purely gravimetric, geocentric geoid model.

In addition to the gravimetric geoid model G99SSS, the GEOID99 model consisted of the following input:

The G99SSS geoid undulations were compared nationally these GPS/Bench Marks. After removing a 52 cm bias and a trend (0.15 ppm, 327 degrees azimuth), an 18.2 cm RMS difference remained. These remaining differences were highly correlated, locally, due to both correlated geoid error and the state-by-state nature of each GPS adjustment (i.e. HARNs). A Gaussian covariance model (variance: 18.22 cm2, correlation length: 400 km) which approximated the empirical covariance function of the residuals was used in a least squares collocation adjustment to model the long wavelength features of these differences on a grid. This grid, along with the bias, trend and ITRF96(1997.0)/NAD 83 transformation were used to compute a conversion surface which when removed from G99SSS yields GEOID99. GEOID99 undulations have a 4.6 cm RMS difference when compared to the GPS on Bench Mark data, which represents 16% improvement over the GEOID96 model.

G99BM

The G99BM model incorporates improved intermediate wavelength control derived from the 6169 GPSBM's but refers to a GRS-80 ellipsoid centered at the ITRF96(1997.0) reference center. Like GEOID99, it is only applicable inside the Conterminous United States with limited utility in near border regions (it has been reported useful up to half a degree into Canada).  Essentially the same information was used in generating a conversion surface except the ITRF96(1997.0)/NAD 83 transformation.  Be cause we excluded the transformation grid from this conversion surface, G99BM refers to the same ellipsoid surface as G99SSS. The ITRF96(1997.0) is within a few centimeters of the locations of several other commonly used ellipsoid models, such as WGS-84 (G873), and thereby provides ready comparison to many scientific data sets.

DEFLEC99

The DEFLEC99 deflection of the vertical model is based upon GEOID99. A two-step procedure was used to compute DEFLEC99: Because DEFLEC99 is based on GEOID99, it will include both gravimetric information and (in the Conterminous United States) GPS on leveled bench mark information.

REFERENCES

Fei, Z. and M. Sideris, 1999: A new method for computing the ellipsoidal correction for Stokes's formula, accepted for publication in Journal of Geodesy.

RELATIONSHIP OF HEIGHTS TO EACH OTHER AND MSL

The below image should help to help clarify the relationship between the various geoid models and the datums that they can be used to convert between. In the below figure, I refer to a "global geopotential surface" rather than a geoid, because G99SSS does not necessarily model the true geoid. G99SSS uses the EGM96 model and incorporates further gravimetric and terrain information at higher spatial resolution. However, it depends on EGM96 to establish the bias and long wavelength tilt of the geoid, because of the gravity and terrain models are not global in coverage. To the level that EGM96 has modeled these components, G99SSS can be used to generate  an approximation of the true geoid.
 

A figure that shows which datums that the G99SSS, G99BM and GEOID99 models converts between.