Map Projections and Coordinate Systems
Earth’s Shape and Vertical Datums
Geographic Coordinate System (latitude and
Map Projections Defined
Types of Projections.
Projection distance, area and shape
Common GIS Projections
Lambert Conformal Conic
Lambert Equal Area
State Plane Coordinates
Every State has at least one
Based on origins identified by each state
Identified on US Quadrangle maps
Universal Transverse Mercator
Transverse (uses longitude as standard line)
Selecting the proper projection
1. Map Projections
- Although for many mapping applications the earth
can be assumed to be a perfect sphere, there is a difference between the distance around the earth between the poles versus the
equator. The circumference of the earth
is about 1/300th smaller around the poles. This type of figure is termed an
oblate ellipsoid or spheroid, and is the three-dimensional shape obtained by
rotating an ellipse about its shorter axis. An estimate of the earth’s surface
based on an ellipsoid provides a determination of the elevation of every point
on the earth’s surface, including sea level, and is often called a datum. Over
time, and in different countries, many datums have
been developed and used. With more accurate means of measurement today (i.e.
satellite and GPS), recent datums are referenced from
the center of the earth rather than a theoretical surface. The resulting North American Datum of 1983
(NAD83)and the slightly refined World Geodetic System (WGS84), from the U.S.
Military in 1984, are internationally accepted as the geodetic reference system
- Geographic Coordinates simply refers to the
system of latitude and longitude. This coordinate system is formed by creating
a grid using the equator as 0 degrees and forming parallels of latitude to the
north and south (90 degrees N is the North Pole, 90 degrees S is the South
Pole), and meridians of longitude east and west (which meet at 180 degrees,
commonly called the International Date Line) of the "Prime Meridian"
which passes through Greenwich, England.
Map projections are used to transfer or
“project” geographical coordinates onto a flat surface.
The easiest way to try to transfer the information onto a flat
surface is to convert the geographic coordinates into an X and Y coordinate
system, where x is longitude and y is latitude. This is an example of
“projecting” onto a plane. Coordinates
can also be "projected" onto two other flat surfaces, a cylinder or
cone, and then unfolded into a map. The grid formed by the latitude and
longitude on a map is called the graticule. There are thousands of different map
projections all depending on how they intersect earth’s surface and how they
are oriented. For example, the line of
latitude or longitude where a projection intersects or “cuts” the earth’s
surface is called the point of contact, or standard line, where distortion is
minimized. Orientations of the three
shapes can also vary between equatorial (standard lines of latitude),
transverse (standard lines of longitude), and oblique (standard line other than
latitude or longitude). In addition,
each projection effects the distance, area, and angle
relationships of the earth surface as portrayed on the map. Ideally, these
factors would be consistent to the relationships on the real earth.
Unfortunately, some relationships are always distorted.
Types of Projections
An azimuthal or planar
projection is usually tangent to a specific point on earth’s
surface, but may also be secant. This point, or focus, may be a pole, the
equator, or other oblique point.
Normally though, the azimuthal projection is
used for polar charts due to distortion at other latitudes.
- A cylindrical projection usually places the
earth inside a cylinder with the equator tangent or secant to the inside of the
cylinder. If the cylinder is placed
perpendicular to the axis of the earth, the resulting projection is called a
In a conic projection, a cone is placed over the
earth, normally tangent to one or more lines of latitude. This tangent line is
called a standard parallel and, in general, distortion increases the further
away you get from this line. A conic projection
works best over mid latitudes for this reason.
Mathematical map projections are not based on
developable surface, but often specify a direct mathematical projection from a
spheroid onto a flat surface. These types
of map projections can change for different parts or regions of the world in
order to reduce certain distortions.
They can also be formed by merging other projections in order to get the
“best” of each.
Projection Distance, Area, and Shape
Equal area projections preserve the property of
area. On an equivalent projection all parts of the earth's surface are shown
with the correct area. However, latitudinal distances are never accurate.
Conformal projections preserve right angles
between lines of latitude and longitude and are primarily used because they
preserve direction. Area is always distorted on conformal maps. Because of
GIS’s emphasis on cartographic shapes, GIS systems often use conformal
Some projections only preserve correct distance
relationships along a few lines on the map. For example, an Equidistant
azimuthal projection has the distance to the outside
of the map portrayed correctly. These are seldom used in GIS.
A final category is compromise maps. They may be
the average of two or more projections or interrupted or broken in order to
minimize certain distortions.
Common GIS Projections
Mercator- A conformal,
cylindrical projection tangent to the equator.
Originally created to display accurate
compass bearings for sea travel. An additional feature of this projection is
that all local shapes are accurate and clearly defined.
Transverse Mercator - Similar to the Mercator
except that the cylinder is tangent along a meridian instead of the equator. The
result is a conformal projection that minimizes distortion along a north-south
line, but does not maintain true directions.
- Universal Transverse Mercator (UTM) – Based on a Transverse Mercator
projection centered in the middle of zones that are 6 degrees in longitude
wide. These zones have been created
throughout the world.
Conic – A conic, confromal projection typically
intersecting parallels of latitude, standard parallels, in the northern
hemisphere. This projection is one of
the best for middle latitudes because distortion is lowest in the band between
the standard parallels. It is similar to the Albers Conic Equal Area projection
except that the Lambert Conformal Conic projection portrays shape more
accurately than area.
State Plane – A
standard set of projections for the
- based on either the Lambert Conformal Conic or
projection, depending on the orientation of each state. Large states commonly require several state
Lambert Equal Area - An equidistant, conic
projection similar to the Lambert Conformal Conic that preserves areas.
Albers Equal Area
Conic - This conic projection uses two standard parallels to reduce some of the
distortion of a projection with one standard parallel. Shape and linear scale
distortion are minimized between standard parallels.
2. Coordinate Systems
As described under map projections, traditional coordinate
systems are based on a flat coordinate system. They are almost always a
positive quadrant coordinate system, and are easier to develop and use over a
small area. Recently, with improvements in computer processing capabilities,
GIS and GPS systems are migrating toward using the spherical coordinate system
of longitude and latitude.
State Plane Coordinate System (SPCS).
The SPCS is primarily used in engineering
applications by utility companies and local governments for doing accurate
surveys. The SPCS is based on Transverse Mercator or
Lambert Conformal conic projections with units in feet. States that elongate
north to south normally use the Lambert Conformal. Those that are elongated
east to west normally use the Transverse Mercator.
Every State has at least one SPCS zone, some as many
as five. Because they are so localized and tailored for the specific geographic
area, distortion is very small.
- Nebraskahas two zones. There are between 100 and 150 zones in the US.
Each zone is based on origins identified by each
state. Each zone will have its on origin identified by some given number west
and south of the south-western-most corner of the map. This means that
positional numbers from the origin are expressed in positive terms. Normally
locations are expressed in feet east and north of the origin. This can become
difficult when areas may need to be identified across two zones.
SPCS is identified on US Quadrangle maps by
black graticule marks.
Universal Transverse Mercator
The UTM coordinate system is commonly used in
GIS for larger scale areas within a certain UTM zone. The UTM projection is
formed by using a transverse cylindrical projection, i.e., the standard line
runs along a meridian of longitude. The effect is to minimize distortion in a
narrow strip running pole to pole.
UTM divides the earth into pole-to-pole zones 6
degrees of longitude wide. The first zone starts at the International Date Line
(180 degrees east) and the last zone, 60, starts at 174 degrees east. Northings are determined separately for the areas north and
south of the equator. Because distortion becomes extreme at northern latitudes,
UTM is not normally used above 80 degrees North or South.
United States Public Land Survey System.
The US Public Land Survey System is a grid
system based on a set of selected meridians, termed "principal
meridians," and parallels, called "baselines." Distances are
measured in the four cardinal directions from the initial point and are formed
into townships, ranges, and sections. This system is primarily used for legal
land description west of Ohio.
3. GIS Capabilities
All GIS systems must be capable of converting projections
and converting coordinates. This involves a lot of computer programming and
computational power. At a minimum, a GIS must be able to convert digitized
coordinates to latitude and longitude and reproject
them on to a flat surface.
Selecting the proper projection.
In order to select the correct projection to use, we must analyze the object
of our project. A projection should be selected which has a standard line which
is centered on the area of focus. You must also determine if correct depiction
of area, angle relationships, or distance accuracy is important. Distance may
be especially difficult if correct depiction is required over a large area.
4. Questions for Map Projections, Coordinate Systems, and GIS Capabilities
Describe the difference between a sphere and spheriod.
Describe the four basic types of projections. When is
each type normally used?
Name an example of a conformal, equal area, and
Describe the State Plane Coordinate System using Nebraska
as an example.
Why is the UTM system not used North or South of 80
Explain the key elements in selecting a projection to
use in a GIS project.
Submitted by Dave Gay on
16 February 98.
Updated by Paul Woodward on December 6, 2004