Basic Geodesy and

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Basic Geodesy and Geographic Coordinate Systems
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Geometric Transformations from The Earth to the
Map
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What if the Earth were
A Perfect Sphere
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Modern Radius and Circumference Measurements
Sphere equal in surface area to an oblate
ellipsoid (spheroid)
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Geographic Coordinate System Parallels of
Latitude and Meridians of Longitude
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What if the Earth were
An Oblate Ellipsoid
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Sir Isaac Newtons Idea
Law of Gravity tells us the Earth must be oblate
due to its rotation.
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Radius of Curvature is Larger in Polar Areas than
in Equatorial Areas
So ground distance between equal increments of
Latitude is greater in polar areas
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Expedition to determine if the Earth is oblate or
prolate
To Lapland in 1736
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To Ecuador in 1736
Measurements showed Polar Distance per degree Of
Latitude greater than Equatorial Its Oblate!
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Historic and Current Oblate Ellipsoids
Semi-major Semi-minor Name Date Axis (m)
Axis (m) Maupertuis 1738 6,397,300 6,363,806.3 Ai
ry 1830 6,377,563.4 6,356,256.9 Everest 1830 6,3
77,276.3 6,356,075.4 Bessel 1841 6,377,397.2 6,35
6,079 Clarke 1866 6,378,206.4 6,356,583.8 Clarke
1880 6,378,249.1 6,356,514.9 International 1924
6,378,388 6,356,911.9 Krasovsky 1940 6,378,245 6,3
56,863 Australian 1965 6,378,160 6,356,774.7 S.
American 1969 6,378,160 6,356,774.7 Indonesian 197
4 6,378,160 6,356,774.5 GRS 80 1980 6,378,137 6,3
56,752.3141 WGS 84 1984 6,378,137 6,356,752.3142
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Different Ellipsoids Used as Best Fit Surfaces
for Different Places
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What if the Earth were
North American Datum of 1927 (NAD 27)
A Geoidal Surface !
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Numerous Older Local Datums Used in Different
Places across the Globe
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Numerous Older Local Datums Used in Different
Places across the Globe
Afghanistan
Herat North datum Of 1959
International Ellipsoid
Datum Origin 342309N, 621059E
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Numerous Older Local Datums Used in Different
Places across the Globe
Philippines
Philippine Reference System Of 1992
Clarke 1866 Ellipsoid
Datum Origin 133341N, 1215203E
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Numerous Older Local Datums Used in Different
Places across the Globe
Iraq
Karbala datum Of 1979
Clarke 1880 Ellipsoid
Datum Origin 323414N, 440050E
Being replaced by Iraqi Geospatial Reference
System
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NAD 27 vs. NAD 83
What if the Earth were
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What if the Earth were
NAD 83 Terrestrial Reference Frame Thousands of
Geodetic Control Points And more recently by
Continuously Operating (GPS) Reference Stations
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What if the Earth were
CORS data allow tectonic plate velocities to
be Determined relative to the center of the
continent So NAD 83 coordinates can be updated
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What if the Earth were
NAD 27 to NAD 83 Latitude and Longitude Shifts
1 Latitude 30 meters 1 Longitude 28 m at
25N 20 m at 50N
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What if the Earth were
The NAD 27 to NAD 83 Geographic Coordinate Shift
is large enough that we show it on Large-scale
Topographic Maps
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World Geodetic System of 1984 (WGS 84) is the
best current global ellipsoid
6378137.0 m semi-major axis 6356752.3142 m
semi-minor axis Flattening 1/298.257223
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What if the Earth were
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The International Terrestrial Reference Frame
is The WGS 84 Terrestrial Reference Frame
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What if the Earth were
The difference on the ground between NAD 83 and
WGS 84 points with identical Latitidues and
Longitudes varies from 1.3 to 1.9 meters, with
most places about 1.5 meters
1.5 m
1.3 m
1.9 m
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New Iraqi Geospatial Reference System
GRS 80 Ellipsoid
Datum Origin Earth Center of Mass

• Terrestrial Reference Frame
• Several Continuously Operating
• Reference Stations (CORS)
• High Accuracy Reference Network
• (HARN) of accurate GPS stations

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What if the Earth were
A Geoid !
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Global Geoid is the Average Mean Sea
Level Surface for all the Oceans
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Global Geoid Heights Relative to WGS 84
Ellipsoid Surface
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Global vs. Local Geoid
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For the North American Vertical Datum of
1988 (NAVD 88) the Local Geoid Mean Sea Level
Datum Is defined by the Tidal Gauge at Rimouski,
Quebec
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North American Vertical Datum of 1988 (NAVD 88)
Terrestrial Reference Frame
What is Geodetic Leveling ? Vertical surveying
is the process of determining elevations above
mean sea-level. In geodetic surveys executed
primarily for mapping, geodetic positions are
referred to an ellipsoid, and the elevations of
the positions are referred to the geoid. However,
for satellite geodesy the geoidal heights must be
considered to establish the correct height above
the geoid. Precise geodetic leveling is used to
establish a basic network of vertical control
points. From these, the height of other positions
in the survey can be determined by supplementary
methods.
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NAVD 88 Local Geoid heights relative to the GRS
80 Ellipsoid Surface
Most places in the U.S. the Geoid is below the
ellipsoid
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Cartographic Uses of NAD 83 and NAVD 88
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Cartographic Uses of the Ellipsoid
Ellipsoid Heights from GPS Receivers
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Must Convert Ellipsoidal Height to Elevation
H h - N