Technical Information Page for
G99SSS, GEOID99 and DEFLEC99
Last updated July 11, 2001
(changes since last update are shown in RED)
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.
2.6 million terrestrial, ship, and altimetric gravity measurements
30 arc second Digital Elevation Data
A 1 arcsecond DEM for the Northwest USA (NGSDEM99)
global geopotential model
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).
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
6169 NAD 83 GPS heights on NAVD 88 leveled bench marks
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.
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
Compute slopes of GEOID99 using bicubic splines to yield deflections of
the vertical at the surface of the geoid.
Use simple Bouguer anomalies to compute a plumb-line curvature correction
to change the geoid-surface deflections into deflections of the vertical
at the Earth's surface.
Fei, Z. and M. Sideris, 1999: A new method for computing the ellipsoidal
correction for Stokes's formula, accepted for publication in Journal
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.