Global Positioning System Reference
In-Depth Information
hHN
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(2.2)
Note that Figure 2.8 is illustrative and that G and/or P may be below point E.
Similarly, any or all terms of (2.2) may be positive or negative. For example, in the
conterminous United States, the geoid height, N , is negative.
The geoid is a complex surface, with undulations that reflect topographic,
bathymetric (i.e., measurements derived from bodies of water), and geologic density
variations of the Earth. The magnitude of geoid height can be several tens of meters.
Geoid height ranges from a low of about
105m at the southern tip of India to a
high of about
85m at New Guinea. Thus, for many applications, the geoid is not a
negligible quantity, and one must avoid mistaking an orthometric height for an
ellipsoidal height.
In contrast to the ellipsoid, the geoid is a natural feature of the Earth. Like
topography, there is no simple equation to describe the spatial variation of geoid
height. Geoid height is modeled and tabulated by several geodetic agencies. Global
geoid height models are represented by sets of spherical harmonic coefficients and,
also, by regular grids of geoid height values. Regional geoid height models can span
large areas, such as the entire conterminous United States, and are invariably
expressed as regular grids. Recent global models typically contain harmonic coeffi-
cients complete to degree and order 360. As such, their resolution is 30 arc-minutes,
and their accuracy is limited by truncation error. Regional models, by contrast,
are computed to a much higher resolution. One arc-minute resolution is not
uncommon, and truncation error is seldom encountered.
The best-known global geoid model is the National Geospatial-Intelligence
Agency/National Aeronautical and Space Administration (NGA/NASA) WGS 84
EGM96 Geopotential Model [9], hereafter referred to as EGM96. This product is a
set of coefficients complete to degree and order 360, a companion set of correction
coefficients needed to compute geoid height over land, and a geoid height grid
posted at 15 arc-minute spacing. EGM96 replaces an earlier global model denoted
WGS 84 (180,180), which is complete only up to degree and order 180. Most of
that WGS 84 coefficient set was originally classified in 1985, and only coefficients
through degree and order 18 were released. Hence, the first public distributions of
WGS 84 geoid height only had a 10 arc-degree resolution and suffered many meters
of truncation error. Therefore, historical references to “WGS 84 geoid” values must
be used with caution.
Within the conterminous United States, the current high-resolution geoid height
grid is GEOID03, developed by the National Geodetic Survey, NOAA. This prod-
uct is a grid of geoid heights, at 1 arc-minute resolution, and has an accuracy of 1
cm, one sigma [10]. Development is underway on a future geoid model series that
will cover all U.S. states and territories.
When height accuracy requirements approach the meter level, then one must
also become aware of the datum differences between height coordinates. For exam-
ple, as discussed in Section 2.2.3.3, the origin of the NAD 83 reference frame is off-
set about 2.2m from the center of the Earth, causing about 0.5-m to 1.5-m
differences in ellipsoidal heights in the conterminous United States. Current esti-
mates place the origin of the U.S. orthometric height datum, NAVD 88, about 30
cm to 50 cm below the EGM96 reference geopotential surface. Because of these two
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