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Geodesy, Map Projections and
Coordinate Systems
Barbara Parmenter
The University of Texas at Austin
Additional slides andgraphics provided with permission
from Professor David Maidment, The University of Texas at
Austin
Geodesy, Map Projections and
Coordinate Systems
• Geodesy - the shape of the earth and
definition of earth datums
• Map Projection - the transformation of a
curved earth to a flat map
• Coordinate systems - (x,y) coordinate
systems for map data
Types of Coordinate Systems
• Geographic coordinates (f, l, z)
• Projected coordinates (x, y, z) on a local
area of the earth’s surface
Shape of the Earth
We think of the
earth as a sphere
It is actually a spheroid,
slightly larger in radius at
the equator than at the poles
The shape of the earth
• the spheroid is still an approximation to the
earth’s actual shape
• the earth is larger in the southern
hemisphere, and has other smaller bulges
Sea surface
Ellipsoid
Earth surface
Geoid
Representations of the Earth
Mean Sea Level is a surface of constant
gravitational potential called the Geoid
Sea surface
Ellipsoid
Earth surface
Geoid
For accurate mapping:
• Different spheroids are used in different regions,
each chosen to fit the observed datum of each
region
• Accurate conversion between latitude and
longitude and projected coordinates requires
knowledge of the specific figures of the earth that
have been used
• The actual shape of the earth can now be
determined quite accurately by observing satellite
orbits
Geodetic datums
• Define the reference systems that describe
the size and shape of the earth
• Hundreds of different datums have been
used to frame position descriptions
• Datums have evolved from those describing
a spherical earth to ellipsoidal models
derived from years of satellite
measurements.
Geodetic datums
• 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
• The diversity of datums in use today requires
careful datum selection and careful conversion
between coordinates in different datums.
Geodetic datums
• Some geodetic datums are based on ellipsoids that touch
the surface of the earth at a defined point.
• North American Datum 1927 (NAD27) - tangent point in
Kansas. NAD27- NOT a global datum.
• Karbala datum for Iraq
• Other datums are "topocentric" datums with a reference
ellipsoid that has its center at the center of mass of the
earth.
• Word Geodetic System 1984 (WGS-84) is an example of a
global datum. These global datums can be better fits to the
gravity surface for the entire earth but can be less accurate
in specific areas.
Geodesy and Map Projections
• Geodesy - the shape of the earth and
definition of earth datums
• Map Projection - the transformation of a
curved earth to a flat map
• Coordinate systems - (x,y) coordinate
systems for map data
Earth to Globe to Map
=
Geographic and Projected Coordinates
(f, l)
Map Projection
(x, y)
All projections have distortions
•
•
•
•
•
Shape
Area
Distance
Direction
Angle
Projections Preserve Some
Earth Properties
• Area - correct earth surface area (Albers
Equal Area) important for mass balances
• Shape - local angles are shown correctly
(Lambert Conformal Conic)
• Direction - all directions are shown correctly
relative to the center (Lambert Azimuthal
Equal Area)
• Distance - preserved along particular lines
• Some projections preserve two properties
Types of Projections
• Conic (Albers Equal Area, Lambert
Conformal Conic) - good for East-West
land areas
• Cylindrical (Transverse Mercator) - good
for North-South land areas
• Azimuthal (Lambert Azimuthal Equal Area)
- good for global views
Conic Projections
(Albers, Lambert)
Cylindrical Projections
(Mercator)
Transverse
Oblique
Azimuthal
(Lambert)
Geodesy and Map Projections
• Geodesy - the shape of the earth and
definition of earth datums
• Map Projection - the transformation of a
curved earth to a flat map
• Coordinate systems - (x,y) coordinate
systems for map data
Coordinate System
A planar coordinate system is defined by a pair
of orthogonal (x,y) axes drawn through an origin
Y
X
Origin
(xo,yo)
(fo,lo)
Universal Transverse
Mercator
• Uses the Transverse Mercator projection
• Each zone has a Central Meridian (lo),
zones are 6° wide, and go from pole to pole
• 60 zones cover the earth from East to West
• Reference Latitude (fo), is the equator
• (Xshift, Yshift) = (xo,yo) = (500000, 0) in
the Northern Hemisphere, units are meters
UTM Zone 14
-99°
-102°
-96°
6°
Origin
-120°
-90 °
Equator
-60 °
Summary Concepts
• To prepare a map, the earth is first reduced
to a globe and then projected onto a flat
surface
• Three basic types of map projections: conic,
cylindrical and azimuthal
• A particular projection is defined by a
datum, a projection type and a set of
projection parameters
Summary Concepts (Cont.)
• Standard coordinate systems use particular
projections over zones of the earth’s surface
• Types of standard coordinate systems in
US: UTM, State Plane