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Introduction to Geodetic Datums
Geodetic
datums define the size and shape of the earth and the origin and orientation
of the coordinate systems used to map the earth. Hundreds of different datums
have been used to frame position descriptions since the first estimates
of the earth's size were made by Aristotle. Datums have evolved from those
describing a spherical earth to ellipsoidal models derived from years of
satellite measurements.
Modern
geodetic datums range from flat-earth models used for plane surveying to
complex models used for international applications which completely describe
the size, shape, orientation, gravity field, and angular velocity of the
earth. While cartography, surveying, navigation, and astronomy all make
use of geodetic datums, the science of geodesy is the central discipline
for the topic.
Referencing
geodetic coordinates to the wrong datum can result in position errors of
hundreds of meters. Different nations and agencies use different datums
as the basis for coordinate systems used to identify positions in geographic
information systems, precise positioning systems, and navigation systems.
The diversity of datums in use today and the technological advancements
that have made possible global positioning measurements with sub-meter accuracies
requires careful datum selection and careful conversion between coordinates
in different datums.
The Figure of the Earth
Geodetic
datums and the coordinate reference systems based on them were developed
to describe geographic positions for surveying, mapping, and navigation.
Through a long history, the "figure of the earth" was refined
from flat-earth models to spherical models of sufficient accuracy to allow
global exploration, navigation and mapping. True geodetic datums were employed
only after the late 1700s when measurements showed that the earth was ellipsoidal
in shape.
Geometric Earth Models
Early
ideas of the figure of the earth resulted in descriptions of the earth as
an oyster (The Babylonians before 3000 B.C.), a rectangular box, a circular
disk, a cylindrical column, a spherical ball, and a very round pear (Columbus
in the last years of his life).
Flat
earth models are still used for plane surveying, over distances short enough
so that earth curvature is insignificant (less than 10 kms).
Spherical
earth models represent the shape of the earth with a sphere of a specified
radius. Spherical earth models are often used for short range navigation
(VOR-DME) and for global distance approximations. Spherical models fail
to model the actual shape of the earth. The slight flattening of the earth
at the poles results in about a twenty kilometer difference at the poles
between an average spherical radius and the measured polar radius of the
earth.
Ellipsoidal
earth models are required for accurate range and bearing calculations over
long distances. Loran-C, and GPS navigation receivers use ellipsoidal earth
models to compute position and waypoint information. Ellipsoidal models
define an ellipsoid with an equatorial radius and a polar radius. The best
of these models can represent the shape of the earth over the smoothed,
averaged sea-surface to within about one-hundred meters.
Earth Surfaces
The
earth has a highly irregular and constantly changing surface. Models of
the surface of the earth are used in navigation, surveying, and mapping.
Topographic and sea-level models attempt to model the physical variations
of the surface, while gravity models and geoids are used to represent local
variations in gravity that change the local definition of a level surface.
The
topographical surface of the earth is the actual surface of the land and
sea at some moment in time. Aircraft navigators have a special interest
in maintaining a positive height vector above this surface.
Sea
level is the average (methods and temporal spans vary) surface of the oceans.
Tidal forces and gravity differences from location to location cause even
this smoothed surface to vary over the globe by hundreds of meters.
Gravity
models attempt to describe in detail the variations in the gravity field.
The importance of this effort is related to the idea of leveling. Plane
and geodetic surveying uses the idea of a plane perpendicular to the gravity
surface of the earth, the direction perpendicular to a plumb bob pointing
toward the center of mass of the earth. Local variations in gravity, caused
by variations in the earth's core and surface materials, cause this gravity
surface to be irregular.
Sample US image:g96us[1].jpg
Geoid
models attempt to represent the surface of the entire earth over both land
and ocean as though the surface resulted from gravity alone. Bomford described
this surface as the surface that would exist if the sea was admitted under
the land portion of the earth by small frictionless channels.
The
WGS-84 Geoid defines geoid heights for the entire earth.
The
U. S. National Imagery and Mapping Agency (formerly the Defense Mapping
Agency) publishes a ten by ten degree grid of geoid heights for the WGS-84
geoid.
By
using a four point linear interpolation algorithm at the four closest grid
points, the geoid height for any location can be determined.
The
same grid can be used to produce a contour map of geoid heights for the
globe
Sample Image: geoid2.gif
The National Imagery and Mapping Agency publishes a 0.25 degree model of
the WGS-84 Geoid (1441 by 721 grid points).
Sample Images NIMA 0.25Deg WGS84 Height Model : geopt25.gif; geopt25(1).gif
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