Lecture Notes



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Lecture Basic Geodesy Concepts Lecture Notes

Text Coverage: Wolf and Ghilani: Study: Ch 19: 1-18 Problems: 19: 1-13


Geodetic surfaces:


Geoid – equipotential gravity surface, undulates, rises under a continent, deflection of the vertical, Everest trying to close a triangle in north India, at all points perpendicular with the direction of gravity, geoid height measured above/below geoid, NGS Geoid 99, Geoid 03, Geoid 06.
at higher elevations equipotential surfaces are not parallel with those at sea level, they converge toward the poles. This requires an "orthometric correction" for leveling that has a large N-S component of coverage.

NGVD 1929 – a geodetic leveling datum – an early attempt to extend a geoid under the North American Continent that approximates mean sea level on all three coasts. 26 selected tide stations. take tide readings 19 years, average hourly readings for MSL at each station. level between these MSL heights with a transcontinental grid of first order leveling, "tilt" the surface to match these 26 MSL's in a least squares adjustment, Pacific Ocean 30 ft higher than Atlantic. This is our older leveling datum. Quad sheet contours and elevations are referenced to NGVD.


NAVD 1988 – a newer geodetic leveling datum that attempts to establish a true geoid under North America. A geoid through MSL in Newfoundland was extended under the continent. Does not match MSL at any shore point except by accident. 0' to 5' difference between the NGVD and NAVD88 surfaces in most of the U.S. Must specify the datum used for all elevations.
Orthometric height = elevation, symbol H, measured relative to a geoidal surface such as NGVD, NAVD88, or other surface. Ortho means "perpendicular" or "straight" -- For a point on a mountain top, the geoidal surfaces under it are not parallel. A vertical line along gravity is dropped from the point staying perpendicular with each geoidal surface until the sea level datum is reached. The length of this curving path is "elevation".
Ellipsoid – a regular surface formed by rotating an ellipse about its minor axis to approximate the shape of the earth. The earth is flattened by its rotation with a molten core. An ellipse has a major diameter and a minor diameter with "a" being the semi-major length and "b" being the semi-minor length. If a and b are more different, the ellipsoid is more "eccentric" or "flattened". There are over 100 ellipsoids used in the history of surveying. Some are "regional" -- the ellipsoidal surface matched the sea level geoid well in one continent but matches poorly other places. Others are "international" – of a shape that attempts to match all parts of the earth reasonably well.
A Geodetic Datum – a reference surface for horizontal positions – latitudes and longitudes (phi and lambda). To make a datum you must (1) choose an ellipsoid by picking a value for "a" and "b". (2) locate the ellipsoid's center relative to the earth's center of mass (3) orient the ellipsoid's minor axis (usually parallel with earth's spin axis) (4) choose the origin point, a point of measured or presumed lat and long on the ellipsoid (5) extend a survey and adjust values of a network on the ellipsoid.
North American Datum of 1927 (NAD27) – Uses the Clarke Ellipsoid of 1866, positioned relative to the earth's center, good fit to North American geoid, not international, origin point = Meade's Ranch, Kansas ( a geodetic mark) with astronomically measured Lat, Long, and ellipsoidal height on the Clarke 1866 ellipsoid, the North American triangulation network extended from Meade

s Ranch across North America, and a least squares adjustment gave the Lat and Long of each station on this datum.


North American Datum of 1983 (NAD83) – Uses the GRS80 ellipsoid, satellite geodesy observations of the primary stations in North America permitted adjusting the horizontal control network to this ellipsoid, resulting in new Lat and Longs for each station (different from the NAD27 values), Texas State Capitol building moves 151 feet??.
Ellipsoid Normal: A straight line through a survey point will by normal to the ellipsoid at only one place. That's a station's Lat and Long on the ellipsoid. Since the various datum ellipsoids are of different shape and orientated under the ground at different positions, each survey point will have a different Lat and Long on each datum.
World Geodetic System of 1984 – WGS84 – this is the datum used by the GPS network. It uses the WSG84 ellipsoid, which is nearly identical in shape and orientation with the NAD83 ellipsoid. The "vertical" reading of a GPS receiver is NOT elevation, but an ellipsoidal or geodetic height, (symbol "h").
Geoidal Undulation (N) is the ellipsoidal height of the geoid relative to an ellipsoid. This value is given for each control station in the NGS database, see the data sheets. A negative value means that the geoid is under the ellipsoid.
GPS measures "geodetic height, h" the vertical distance above the ellipsoid of a chosen datum. To convert from GPS ellipsoidal height to geoidal height (orthometric height,elevation): h = H + N. Example: If N = -25 m, the geoid is 25 m below the ellipsoid. If GPS gives h = 100 m, then the elevation of the point H = h – N = 100 – (-25) = 125m.
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