Map Projections and Georeferencing

1. Map Projections and Georeferencing

2. What is a georeference?
A numerical description of a place that
can be mapped.

3. What is an acceptable
georeference?
A numerical description of a place that
can be mapped
and that describes the spatial extent of
a locality
and its associated uncertainties.

4. What is a coordinate system?
• A coordinate system is a reference system used to represent the locations
of geographic features, imagery, and observations, such as Global
Positioning System (GPS) locations, within a common geographic
framework.
Each coordinate system is defined by the following:
• Its measurement framework, which is either geographic (in which spherical
coordinates are measured from the earth's center) or planimetric (in which
the earth's coordinates are projected onto a two-dimensional planar surface)
• Units of measurement (typically feet or meters for projected coordinate
systems or decimal degrees for latitude-longitude)
• Several hundred geographic coordinate systems and a few thousand
projected coordinate systems are available for use. In addition, you can
define a custom coordinate system.

5. Types of coordinate systems
• A global or spherical coordinate system such as latitude-longitude.
These are often referred to as geographic coordinate systems.
• A projected coordinate system such as universal transverse
Mercator (UTM), Albers Equal Area, or Robinson, all of which (along
with numerous other map projection models) provide various
mechanisms to project maps of the earth's spherical surface onto a
two-dimensional Cartesian coordinate plane. Projected coordinate
systems are referred to as map projections.
Coordinate systems (both geographic and projected) provide a
framework for defining real-world locations.

6. What is a spatial reference?
• A spatial reference includes the following:
• The coordinate system
• The coordinate precision with which coordinates are
stored (often referred to as the coordinate resolution)
• Processing tolerances (such as the cluster tolerance)
• The spatial extent covered by the dataset (often referred
to as the spatial domain)

7. Coordinate Systems
A geographical coordinate system uses a three-dimensional spherical
surface to define locations on the earth.
Divides space into orderly structure of locations.
Two types: cartesian and angular (spherical)

8. Parallels and Meridians
Meridians are great circles of constant
longitude
Example is the prime meridian
latitude (φ): angular distance from
equator
longitude (λ): angular distance from
standard meridian
St. Louis 38° 39' N 90° 38' W
New York 40° 47' N 73° 58' W
Los Angeles 34° 3' N 118° 14' W
Rome 41° 48' N 12° 36' E
Sydney 33° 52' S 151° 12' E
Parallels are circles of constant latitude
Example is the equator

9. Earth’s Shape
The shape of earth can be approximated as a sphere or spheroid. Most
often it is modeled as a spheriod.
a
ba
flattening
)( −
=
ab
WGS 84 (World Geodetic System of 1984)
a = 6378.137 km
b = 6356.752 km
flattening = 1/ 298.257 = 0.00335

10. Datum
While a spheroid approximates the shape of the earth, a datum defines the
position of the ellipsoid relative to the center of the Earth
The datum provides a frame of reference for measuring locations on the
surface of the Earth
A datum is chosen to align a spheroid to closely fit the Earth’s surface in a
particular area

11. Datums
It is important to ensure that the datum of a dataset matches with the datum
setting of your GIS and with other data sets being used.

12. Map Projections: Flattening the Earth
A map projection
is the orderly transfer of positions of places on the surface of the
earth to corresponding points on a flat map.
is the systematic arrangement of the earth’s parallels and
meridians onto a plane surface.
uses mathematical formulas to relate spherical coordinates on the
globe to flat, planar coordinates.
[ ]






=






ϕ
λ
T
y
x

13. Distortion
All projections introduce distortions in the map.
Some projections minimize distortions in some of these properties at the
expense of maximizing errors in others.
Some projections are attempts to only moderately distort all of these
properties.
The map properties that are distorted during projection are:
On Earth On Map
Distance (length)
Angle
Area
Scale
Shape

14. Universal Transverse Mercator (UTM)
• Implemented as an internationally standard coordinate system
– Initially devised as a military standard
• Uses a system of 60 zones
– Maximum distortion is 0.04%
• Transverse Mercator because the cylinder is wrapped around the Poles, not the
Equator
Zones are each six degrees of longitude numbered from west to east

15. Georeferences as Measurements
• Some georeferences are metric
– They define location using measures of distance from fixed places
• E.g., distance from the Equator or from the Greenwich Meridian
• Others are based on ordering
– For example street addresses in most parts of the world order houses along
streets
• Others are only nominal
– Placenames do not involve ordering or measuring

16. Converting Georeferences
• GIS applications often require conversion of projections and ellipsoids
– These are standard functions in popular GIS packages
• Street addresses must be converted to coordinates for mapping and
analysis
– Using geocoding functions
• Placenames can be converted to coordinates using gazetteers
Gazetteers provide information about geographical areas or
locations using place names and can be linked to
coordinate systems .

17. Summary
Projections are needed to represent 3-D surface on a flat plane
There are hundreds of projections – choose the one that fits your mapping
purpose best
- preserve distance
- preserve shape
- preserve direction
Choosing a coordinate system is also important (if you have are mapping a
dataset, you should know it’s projection and coordinate system)
Different coordinate systems use different datums in order to approximate
the shape of the earth.