Geodetic Datum Overview
Peter H. Dana
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Introduction to Geodetic Datums
Geodetic datums define the size and shape of the earth and the
orientation of the coordinate systems used to map the earth.
different datums have been used to frame position descriptions
first estimates of the earth's size were made by Aristotle.
evolved from those describing a spherical earth to ellipsoidal
from years of satellite measurements.
Modern geodetic datums range from flat-earth models used for
to complex models used for international applications which
describe the size, shape, orientation, gravity field, and
of the earth. While cartography, surveying, navigation, and
make use of geodetic datums, the science of geodesy is the
for the topic.
Referencing geodetic coordinates to the wrong datum can result
errors of hundreds of meters. Different nations and agencies use
datums as the basis for coordinate systems used to identify
geographic information systems, precise positioning systems, and
systems. The diversity of datums in use today and the
that have made possible global positioning measurements with
accuracies requires careful datum selection and careful
coordinates in different datums.
The Figure of the Earth
Geodetic datums and the coordinate reference systems based on
developed to describe geographic positions for surveying,
navigation. Through a long history, the "figure of the earth"
from flat-earth models to spherical models of sufficient
accuracy to allow
global exploration, navigation and mapping. True geodetic datums
only after the late 1700s when measurements showed that the
earth was ellipsoidal
Geometric Earth Models
Early ideas of the figure of the earth resulted in descriptions
earth as an oyster (The Babylonians before 3000 B.C.), a
a circular disk, a cylindrical column, a spherical ball, and a
pear (Columbus in the last years of his life).
Flat earth models are still used for plane surveying, over
enough so that earth curvature is insignificant (less than 10
Spherical earth models represent the shape of the earth with a
a specified radius. Spherical earth models are often used for
navigation (VOR-DME) and for global distance approximations.
models fail to model the actual shape of the earth. The slight
of the earth at the poles results in about a twenty kilometer
at the poles between an average spherical radius and the
radius of the earth.
Ellipsoidal earth models are required for accurate range and
over long distances. Loran-C, and GPS navigation receivers use
earth models to compute position and waypoint information.
models define an ellipsoid with an equatorial radius and a polar
The best of these models can represent the shape of the earth
smoothed, averaged sea-surface to within about one-hundred
Reference ellipsoids are usually defined by semi-major
and flattening (the relationship between equatorial and polar
Other reference ellipsoid parameters such as semi-minor axis
and eccentricity can computed from these terms.
Many reference ellipsoids are in use by different nations and
The earth has a highly irregular and constantly changing
of the surface of the earth are used in navigation, surveying,
Topographic and sea-level models attempt to model the physical
of the surface, while gravity models and geoids are used to
variations in gravity that change the local definition of a
The topographical surface of the earth is the actual surface
of the land
and sea at some moment in time. Aircraft navigators have a
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
cause even this smoothed surface to vary over the globe by
Gravity models attempt to describe in detail the variations in
field. The importance of this effort is related to the idea of
Plane and geodetic surveying uses the idea of a plane
the gravity surface of the earth, the direction perpendicular
to a plumb
bob pointing toward the center of mass of the earth. Local
gravity, caused by variations in the earth's core and surface
cause this gravity surface to be irregular.
Geoid models attempt to represent the surface of the entire
both land and ocean as though the surface resulted from
Bomford described this surface as the surface that would exist
if the sea
was admitted under the land portion of the earth by small
The WGS-84 Geoid defines geoid heights for the entire earth.
The U. S. National Imagery and Mapping Agency (formerly the
Agency) publishes a ten by ten degree grid of geoid heights
for the WGS-84
Coordinate systems to specify locations on the surface of the
been used for centuries. In western geodesy the equator, the
Cancer and Capricorn, and then lines of latitude and longitude
to locate positions on the earth. Eastern cartographers like
used other rectangular grid systems as early as 270 A. D.
Various units of length and angular distance have been used
The meter is related to both linear and angular distance,
having been defined
in the late 18th century as one ten-millionth of the distance
pole to the equator.
The most commonly used coordinate system today is the
and height system.
The Prime Meridian and the Equator are the reference planes
used to define
latitude and longitude.
The geodetic latitude (there are many other defined latitudes)
of a point
is the angle from the equatorial plane to the vertical
direction of a line
normal to the reference ellipsoid.
The geodetic longitude of a point is the angle between a
and a plane passing through the point, both planes being
to the equatorial plane.
The geodetic height at a point is the distance from the
to the point in a direction normal to the ellipsoid.
Earth Centered, Earth
Fixed X, Y,
Earth Centered, Earth Fixed Cartesian coordinates are also
used to define
three dimensional positions.
Earth centered, earth-fixed, X, Y, and Z, Cartesian
coordinates (XYZ) define
three dimensional positions with respect to the center of
mass of the reference
The Z-axis points toward the North Pole.
The X-axis is defined by the intersection of the plane
define by the prime
meridian and the equatorial plane.
The Y-axis completes a right handed orthogonal system by a
east of the X-axis and its intersection with the equator.
X, Y, and Z
Datum types include horizontal, vertical and complete datums.
Datums in Use
Hundreds of geodetic datums are in use around the world.
The Global Positioning system is based on the World Geodetic
Parameters for simple XYZ conversion between many datums and
published by the Defense mapping Agency.
Coordinate values resulting from interpreting latitude,
height values based on one datum as though they were based in
can cause position errors in three dimensions of up to one
Datum conversions are accomplished by various methods.
Complete datum conversion is based on seven parameter
include three translation parameters, three rotation parameters
and a scale
Simple three parameter conversion between latitude, longitude,
in different datums can be accomplished by conversion through
Earth Fixed XYZ Cartesian coordinates in one reference datum and
origin offsets that approximate differences in rotation,
The Standard Molodensky formulas can be used to convert
and ellipsoid height in one datum to another datum if the Delta
for that conversion are available and ECEF XYZ coordinates are
Bomford, G. 1980. Geodesy. Oxford: Clarendon
Burkard, Richard K. 1983. Geodesy for the Layman.
Washington, DC: NOAA.
National Imagery and Mapping Agency. 1997.
Department of Defense World Geodetic System 1984: Its Definition
with Local Geodetic Systems. NIMA TR8350.2 Third Edition 4 July
MD: National Imagery and Mapping Agency.
National Oceanic and Atmospheric Administration.
1986. Geodetic Glossary. Rockville, MD: National Geodetic
Schwarz, Charles R. 1989. North American Datum
of 1983. Rockville, MD: National Geodetic Survey.
Torge, Wolfgang. 1991 Geodesy, 2nd Edition,
New York: deGruyter.