http://www.esi.utexas.edu/gk12/workshops/gis/docs/projections.ppt

Geodesy, Map Projections and Coordinate Systems

Barbara ParmenterThe 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 (, 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

Earth surface

EllipsoidSea surface

Geoid

Representations of the Earth

Earth surface

EllipsoidSea surface

Geoid

Mean Sea Level is a surface of constant gravitational potential called the 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

() (x, y)Map Projection

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

(o,o)(xo,yo)

X

Y

Origin

A planar coordinate system is defined by a pairof orthogonal (x,y) axes drawn through an origin

Universal Transverse Mercator

• Uses the Transverse Mercator projection

• Each zone has a Central Meridian (o), zones are 6° wide, and go from pole to pole

• 60 zones cover the earth from East to West

• Reference Latitude (o), is the equator

• (Xshift, Yshift) = (xo,yo) = (500000, 0) in the Northern Hemisphere, units are meters

UTM Zone 14

Equator-120° -90 ° -60 °

-102° -96°

-99°

Origin

6°

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