from the reference surface to the point, measured along

the line perpendicular to every equipotential surface in

between. A series of equipotential surfaces can be used

to represent the gravity field. One of these surfaces, the

geoid, is specified as the referenced system from which

orthometric heights are measured. The geoid itself is

defined as a potential surface and natural variations in

gravity induce a smooth, continuous, curvature to 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

(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

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

the GRS80 ellipsoid. These heights are referred to as

NAD83 GPS ellipsoidal heights. Unlike the WGS84

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

geodetic (ellipsoid based) or the orthometric height

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