ETL 1110-1-183
1 Apr 98
a. The orthometric height of a point is the distance
Appendix A
from the reference surface to the point, measured along
the line perpendicular to every equipotential surface in
Determination of Elevations with GPS
between. A series of equipotential surfaces can be used
Surveying Techniques
to represent the gravity field. One of these surfaces, the
geoid, is specified as the referenced system from which
A-1. Global Positioning System Ellipsoid
orthometric heights are measured. The geoid itself is
Heights
defined as a potential surface and natural variations in
gravity induce a smooth, continuous, curvature to the
a. Recent advances in GPS technology and the
plumb line and therefore physical equipotential surfaces
current fully operational status for the NAVSTAR GPS
which are normal to gravity do not remain geometrically
have made it possible to accurately measure ellipsoidal
parallel over a given vertical distance (i.e. the plumb line
height differences from GPS satellites. GPS surveys
is not quite parallel to the ellipsoidal normal).
report vertical positions in geodetic coordinates defined
with respect to the World Geodetic System of 1984
b. The NAVD88 datum is the product of a vertical
(WGS84) reference ellipsoid, a geocentric, bi-axial,
adjustment of leveled height difference measurements
ellipsoid of revolution, that is symmetric about the
made across North America. NAVD88 was constrained
equatorial axis and whose shape and size are defined by
by holding fixed the orthometric height of a single
mathematical constants corresponding to the length of its
primary tidal benchmark at Father's Point / Rimouski,
equatorial and polar axes and selected to best
Quebec, Canada and performing a minimally constrained
approximate the geoid (currently within 100 meters
general adjustment of U.S.-Canadian-Mexican leveling
globally). Although many different geodetic datums exist
observations. The vertical reference surface is therefore
throughout the world, WGS84 is the reference system
defined by the surface on which the gravity values are
most frequently used with off-the-shelf GPS equipment.
equal to the control point value. NAVD88 elevations are
The ellipsoidal height value at a given point is based on
published orthometric heights that represent the
the distance measured along the normal vector from the
geometric distance from the geoid to the terrain measured
surface of the reference ellipsoid to the point. The
along the plumb line. Orthometric height corrections were
realization and practical accuracy of WGS84 as a vertical
used to enforce consistency between geopotential based
reference frame for collecting elevation data depends on
vertical coordinates and measured leveled differences.
the actual ellipsoidal height values assigned to
NAVD88 is the most compatible vertical reference frame
benchmarks or other physically defined control points.
available to relate GPS ellipsoidal heights to orthometric
heights. Further information on the NAVD88 datum can
b. In the U.S., final positions from DGPS are
be found in Zilkoski (1992) and EM 1110-1-1004,
established with respect to NAD83. Since NAD83 is
Deformation Monitoring and Control Surveying.
based on the GRS80 ellipsoid, ellipsoid heights obtained
from GPS surveying using NAD83 control are based on
A-3.
Geoidal Heights
the GRS80 ellipsoid. These heights are referred to as
NAD83 GPS ellipsoidal heights. Unlike the WGS84
a. Geoidal heights or (geoid height values) represent
ellipsoid, the GRS80 ellipsoid is not exactly geocentric
the geoid-ellipsoid separation distance measured along
which can create problems (i.e., large errors) when
the ellipsoid normal and are obtained by taking the
converting NAD83 GPS ellipsoid heights to orthometric
difference between ellipsoidal and orthometric height
heights using some geoid models.
values (see Figure 1). Knowledge of the geoid height
enables the evaluation of vertical positions in either the
A-2. Orthometric
Heights
and
NAVD88
geodetic (ellipsoid based) or the orthometric height
Elevations
A-1
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