Transcript Document

Basic Geodesy and
Geographic Coordinate Systems
Geometric Transformations from
The Earth to the Map
What if the Earth were …
A Perfect Sphere
Modern Radius and Circumference Measurements
Sphere equal in surface area to an oblate ellipsoid (spheroid)
Geographic Coordinate System: Parallels of Latitude
and Meridians of Longitude
What if the Earth were …
An Oblate Ellipsoid
Sir Isaac
Newton’s
Idea …
Law of Gravity tells us the Earth must
be oblate due to its rotation.
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
Expedition to determine if the Earth is oblate or prolate
To Lapland
in 1736
To Ecuador in 1736
Measurements showed Polar Distance per degree
Of Latitude greater than Equatorial – It’s Oblate!
Historic and Current Oblate Ellipsoids
Name
Date
Semi-major
Axis (m)
Maupertuis
Airy
Everest
Bessel
Clarke
Clarke
International
Krasovsky
Australian
S. American
Indonesian
GRS 80
WGS 84
1738
1830
1830
1841
1866
1880
1924
1940
1965
1969
1974
1980
1984
6,397,300
6,377,563.4
6,377,276.3
6,377,397.2
6,378,206.4
6,378,249.1
6,378,388
6,378,245
6,378,160
6,378,160
6,378,160
6,378,137
6,378,137
Semi-minor
Axis (m)
6,363,806.3
6,356,256.9
6,356,075.4
6,356,079
6,356,583.8
6,356,514.9
6,356,911.9
6,356,863
6,356,774.7
6,356,774.7
6,356,774.5
6,356,752.3141
6,356,752.3142
Different Ellipsoids Used as Best Fit Surfaces
for Different Places
What if the Earth were …
A Geoidal Surface !
North American
Datum of 1927
(NAD 27)
Numerous Older Local Datums Used in
Different Places across the Globe
Numerous Older Local Datums Used in
Different Places across the Globe
Afghanistan
Herat North datum
Of 1959
International Ellipsoid
Datum Origin:
34°23’09”N,
62°10’59”E
Numerous Older Local Datums Used in
Different Places across the Globe
Philippines
Philippine Reference System
Of 1992
Clarke 1866 Ellipsoid
Datum Origin:
13°33’41”N,
121°52’03”E
Numerous Older Local Datums Used in
Different Places across the Globe
Iraq
Karbala datum
Of 1979
Clarke 1880 Ellipsoid
Datum Origin:
32°34’14”N,
44°00’50”E
Being replaced by Iraqi
Geospatial Reference System
NAD
27
vs.
NAD
83
What if the Earth were …
What ifNAD
the Earth
were … Reference Frame
83 Terrestrial
Thousands of Geodetic Control Points
And more recently by Continuously
Operating (GPS) Reference Stations
What
CORS
if the
data
Earth
allow
were
tectonic
… plate velocities to be
Determined relative to the center of the continent
So NAD 83 coordinates can be updated
What
NADif27
thetoEarth were …
NAD 83
Latitude and
Longitude
Shifts
1” Latitude ≈
30 meters
1” Longitude ≈
28 m at 25°N
20 m at 50°N
What
the Earth
TheifNAD
27 towere
NAD…83 Geographic Coordinate
Shift is large enough that we show it on
Large-scale Topographic Maps
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
What if the Earth were …
The International Terrestrial Reference Frame is
The WGS 84 Terrestrial Reference Frame
What if the
wereon
…the ground between
TheEarth
difference
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
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
What if the Earth were …
A Geoid !
Global Geoid is the Average Mean Sea Level
Surface for all the Oceans
Global Geoid Heights Relative to
WGS 84 Ellipsoid Surface
Global vs. Local Geoid
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
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.
NAVD 88 Local Geoid heights relative to
the GRS 80 Ellipsoid Surface
Most places in the U.S. the Geoid is below the ellipsoid
Cartographic Uses of NAD 83 and NAVD 88
Cartographic Uses of the Ellipsoid
Ellipsoid Heights from GPS Receivers
Must Convert Ellipsoidal Height to Elevation
H=h-N