Coordinate Systems, Datums and Projections for GIS
Presented by
Vicki Drake
 Adapted from High Desert Technologies, Inc.
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To understand some basic concepts on projections and coordinate systems for GIS.
Geodesy--The shape of the Earth
 Coordinate Systems
 Geodetic Datums
Map projections--From a round world to a flat map.
Map based grid systems--Locating points on the map.
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The earth was initially thought to be flat.
Later thought to be a sphere.
 Babylonian thought – “an oyster”, round pear (Columbus), a cylindrical column
French geographers in the 1730’s proved that the earth is an ellipsoid.
 A slight flattening of the Earth at the poles results in 20 km difference
between equatorial radius and polar radius
 Common ellipsoids used are Clarke 1866 or 1880 and more recently the Geodetic
Reference System of 1980 (GRS80)
...And then there’s the Geoid
 A hypothetical figure of the earth that represents the surface as being at mean
sea level, but still influenced by gravitational pull, density of earth’s materials, and
hydrostatic forces.
Ellipsoid or Geoid??
This effects how elevation is measured, and also effects somewhat the location of
a point on the earth.
When working between different coordinate systems, you need to know how
elevation is being measured:
Height above ellipsoid (HAE)
Height above Geoid (HAG)
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Earth Surfaces
• The Earth’s surface is highly irregular and constantly changing
• Topographic and sea-level models attempt to show physical variations of surface
• Gravity models and geoids are used to represent local variations in gravity that change
level surface definition
• The topographical surface of Earth is the actual surface of land and sea
• Sea-level is the average surface of the oceans (tidal forces and gravity differences are
“smoothed” over)
• Gravity models describe difference in gravity field caused by variations of Earth’s core
and surface materials
• Geoid models seek to represent entire Earth surface over both land and ocean –
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Idea – the surface resulted from gravity alone
The WGS-84 Geoid defines geoid heights for the entire Earth
Basic Coordinate Systems
• Coordinate systems can represent points in two-dimensional or three-dimensional space
• Rene Descartes (1596-1650) introduced coordinate systems based on right angle
coordinates
• Similar systems based on angles from baselines are often referred to as polar systems
• Plane Coordinate Systems
– Two-dimensional coordinate systems defined with respect to a single plane
– Three-dimensional coordinate systems defined with respect to two orthogonal (right
angle) planes
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Cartesian Coordinates in a Plane
Geodetic Datums
• Geodetic datums define the reference systems that describe the size and shape of the
Earth
• Datums have evolved from describing a spherical Earth to ellipsoidal models derived from
years of satellite measurements.
• Types of Modern Geodetic Datums
– Flat-Earth models for plane surveying
– Complex models that describe size, shape, orientation, gravity field and angular
velocity of Earth
– GPS is based on the World Geodetic System 1984 (WGS-84)
Geodetic Datums
• Troubles with Datums
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Different nations and agencies use different datums as basis for coordinate systems
used to identify positions in GIS, and other precise positional and navigational
systems.
Diversity of datum available today due to technological advancements require careful
datum selection and careful conversion between coordinates in different datums.
Coordinate values resulting from interpreting latitude, longitude and height values
based on one datum as though they were based in another datum can cause position
errors of up to one kilometer
Global Coordinate Systems
• Global coordinate systems specify locations on the Earth’s surface
• The western geodesy, the equator, the Tropics of Cancer and Capricorn, and lines of
latitude and longitude are used to locate positions on the Earth
• Various units of length and angular distance have been used
• The meter is related to both length and angular distance – having been defined in the
18th century as “one-millionth of the distance from the pole to the equator”.
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• The most commonly used coordinate system today is latitude, longitude and height
system.
• The Prime Meridian and Equator are the reference planes used to define latitude and
longitude.
Latitude and Longitude based on Prime Meridian and Equator
Latitude
The Geodetic Latitude and Longitude
• The Geodetic Latitude 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 reference plane and a plane
passing through the point, both planes being perpendicular to the equatorial plane.
• The Geodetic Height at a point is the distance from the reference ellipsoid to the point
in a direction normal to the ellpisoid.
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Geodetic Latitude, Longitude & Height
Earth Centered (X,Y,and Z)
• Earth Centered, Earth Fixed Cartesian coordinates are also used to define threedimensional positions.
• Earth centered, earth-fixed, X,Y,and Z Cartesian Coordinates (XYZ) define the threedimensional position with respect to the center of the mass of the reference ellipsoid
• The Z-axis points toward the North Pole
• The X-axis is defined by the intersection of the plane of the Prime Meridian, and the
equatorial plane
• The Y-axis completes the right-handed orthogonal system by a plane 900 east of the Xaxis and its intersection with the equator
Understanding Projections for GIS
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Distortion--It is impossible to flatten a round object without distortion.
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Projections try to preserve one or more of the following properties:
 Area--sometimes
 Shape--usually
 Direction--or
referred to as equal area (for small areas)
referred to as “conformality”, again for small sections
“azimuthality” - cardinal directions (N,S,E,W)
 Distance
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Projections are created by transferring points on the earth onto a flat surface. You
can think of this as having a light in the middle of the earth, shining through the
earth’s surface, onto the projection surface. There are three basic methods for
doing this:
 Planar--projection
surface laid flat against the Earth
 Cylindrical--projection
 Conic--cone
 Where
surface wrapped around the Earth
is placed on or through the surface of the Earth
the projection surface touches the Earth is the “Standard Line.”
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Developing a cylindrical Projection
Universal Mercator Projection
Conic Projection
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Once points have been projected from the earth’s surface to a map, a coordinate
system is established that provides a common reference on the ground. There are two
basic types in use in the United States:
 State Plane Coordinate System
 One or more zones for each state.
 Units are usually in feet.
 Usually based on Lambert Conic Conformal projection for East-West trending
states and UTM projection for states running North-South.
 Usually has a “False Easting” or “False Northing” so that all units are positive.
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 UTM
Coordinate System
 Used primarily by federal agencies.
 Units are usually in meters.
 Usually based on UTM projection.
 Usually has a “False Northing” and “False Easting” so that all units are positive.
State Plane Coordinates –NAD 27
• In the U.S., the State Plane System was developed in the 1930s, and was based on the
North American Datum 1927 (NAD27)
• NAD27 coordinates are based on the “foot” unit of measure
• Maps in NAD 27 coordinates (in feet) are still in use, even though the system has been
superseded by NAD-83
• Most USGS 7.5 minute Quadrangles use several coordinate system grids, including
latitude and longitude, UTM km tic marks, and applicable State Plane coordinates.
State Plane Coordinates NAD 83
• The State Plane System 1983 is based on the North American Datum 1983
• NAD 83 coordinates are based on the meter
• State plane systems were developed in order to provide local reference systems that
were tied to a national datum
• Some smaller states use a single state plane zone
• Larger states are divided into several zones
• States plane zone boundaries often follow county boundaries
State Plane Coordinates
Oregon North NAD 83
State Plane Coordinates –
Oregon South NAD 83
Universal Transverse Mercator (UTMs)
UTM coordinates define two dimensional, horizontal, positions
• UTM zone numbers designate 6 degrees longitudinal strips extending from 80 degrees
South latitude to 84 degrees North latitude
• UTM zone characters designate 8 degree zones extending north and south from the
equator
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• There are special UTM zones between 0 degrees and 36 degrees longitude above 72
degrees latitude and a special zone 32 between 56 degrees and 64 degrees north
latitude
Coordinate Zones - UTM
UTM Coordinate Example
• Eastings are measured from the central meridian (with a 500km false easting to insure
positive coordinates)
• Northings are measured from the equator (with a 10,000km false northing for positions
south of the equator)
• Each zone has a central meridian. Zone 14, for example, has a central meridian of 99
degrees west longitude. The zone extends from 96 to 102 degrees west longitude
Coordinate systems and Datums
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Coordinate systems are tied to Datums--which are a collection of established
reference points sometimes referred to as a “Geodetic Contrl Network” used for
control. The two datums widely used are:
 North
American Datum 1927 (NAD 27)
on Clarke Ellipsoid of 1866
 North American Datum 1983 (NAD 83)
 Based on the GRS80 Ellipsoid
* High-Accuracy Reference Networks (HARNS), also called High Precision Geodetic
Networks (HPGNS) are starting to be used by some states.
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Coordinate System – NAD Datum Points, 1927
Coordinate Points NAD Datum Points for 1983
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Understanding Projections for GIS
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Hopefully you now know enough about ellipsoids, projections, datums and coordinate
systems to understand why some systems have been used and to determine the
parameters needed to project data from one system to another.
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Key parameters to look for in the metadata:
 Projection
or coordinate system
degrees, lat/long, State Plane, or Universal Transverse Mercator
 Decimal
(UTM)
 Standard
parallel(s) and or meridians
 False Easting/Northing
 Type of Spheroid/Ellipsoid – or geoid
 Type of Datum: NAD 27 – NAD 83 or ???
 Units – meters or feet
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