Working with Map Projections
GLY 560:
GIS and Remote Sensing for
Earth Scientists
Class Home Page:
http://www.geology.buffalo.edu/courses/gly560/
Map Projection
• The transformation from the
geographic grid to a plane coordinate
system is referred to as map
projection.
• Transformation from one plane
coordinate system to another is
referred to as re-projection.
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Ellipsoid (Global) Coordinate Systems
• Global coordinates based upon
“spherical” coordinates modified to
account for imperfect shape of earth.
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Latitude-Longitude System
oThe most commonly used coordinate
system today is the latitude, longitude,
and height system.
oThe Prime Meridian and the Equator
are the reference planes used to
define latitude and longitude.
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Equator and Prime Meridian
Meridian = (N-S Longitude); Parallel = (E-W Latitude)
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Latitude-Longitude Systems
• Degree-Minute-Second (DMS)
• 1 deg = 60 min
• 1 min = 60 sec
• Decimal Degrees (DD)
• 455230= 45.875 
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Plane Coordinate Systems
• René Descartes (1596-1650) introduced
systems of coordinates based on orthogonal
(right angle) coordinates.
• These two and three-dimensional systems used
in analytic geometry are often referred to as
Cartesian systems.
• Similar systems based on angles from baselines
are often referred to as polar systems.
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Plane Coordinate Systems
• 2-D Systems
(1 plane)
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• 3-D Systems
(2 orthogonal planes)
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Projection Classes
• Conformal: preserves local shape
• Equivalent: preserves area
• Equidistant: preserves length
• Azimuthal: preserves directions
Map can have more that one property, but
conformal and equivalent are mutually
exclusive
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Projections Affect Maps
The greater the map area, the greater the impact of projection
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Conic Projection
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Cylindrical Projection
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Azimuthal Projection
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Common Map Projections
• Choice of map projection depends
upon:
• Attribute to be preserved
• Scale to be represented
• Aspect of the map
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Transverse Mercator Projection
• Secant cylindrical projection
• Straight meridians and parallels intersect at right
angles. Scale is true at the equator or at two standard
parallels equidistant from the equator. Often used for
marine navigation because all straight lines on the map
are lines of constant azimuth.
• Requires:
• Standard Parallels
• Central Meridian
• Latitude of Origin
• False Easting and Northing
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Lambert Conformal Conic
• Secant conic projection
• Area, and shape are distorted away from
standard parallels. Directions true in limited
areas. Used for maps of North America.
• Requires:
• Standard Parallels
• Central Meridian
• Latitude of Projection Origin
• False Easting and Northing
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Albers Equal-Area Conic
• Secant conic projection (similar to Lambert
Conformal Conic but preserves area instead of
shape)
• Distorts scale and distance except along
standard parallels. Used in large countries with
a larger east-west than north-south extent.
• Requires:
• Standard Parallels
• Central Meridian
• Latitude of Projection Origin
• False Easting and Northing
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Unprojected Maps
• Unprojected maps
consider longitude and
latitude as a simple
rectangular coordinate
system.
• Scale, distance, area,
and shape are all
distorted with the
distortion increasing
toward the poles.
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Datum
• To project Earth to a flat plane we
must choose an ellipsoid or spheroid
to represent the Earth’s surface.
• Choosing an ellipsoid implies a
horizontal datum for the projected
map.
• Hundreds of datums have been used.
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Reference Ellipsoids
• Reference
ellipsoids are
usually defined by
semi-major
(equatorial radius)
and flattening (the
relationship
between equatorial
and polar radii).
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Selected Reference Ellipsoids
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Clarke 1866 Datum (NAD27)
• Land-based ellipsoid running through
Meades Ranch Kansas
• Basis for North American Datum of
1927 (NAD27) still used today.
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World Geodetic System 1984
• Determined from satellite orbit data.
• Identical to GRS80
• Used for North American Datum 1983
(NAD83)
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NAD27 vs NAD83
• GIS Data providers switching from
NAD27 to NAD83.
• NAD83 tied to global positioning
system measurements
• Horizontal shift between NAD27 and
NAD83 10-100 m in conterminous US
and >200 m in Alaska.
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Coordinate Systems
• Map projections used for small-scale
maps (<1:1,000,000).
• Plane coordinate systems used for
large-scale maps (>1:24,000).
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US Plane Coordinate Systems
• Universal Transverse Mercator (UTM)
• Universal Polar Stereographic (UPS)
• State Plane Coordinate (SPC)
• Public Land Survey System (PLSS)
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Universal Transverse Mercator
• The National Imagery and Mapping Agency
(NIMA) (formerly the Defense Mapping Agency)
adopted UTM grid for military use.
• UTM divides earth’s surface between 84N and
80S into 60 zones about 360 km wide.
• Each of 60 zones mapped onto transverse
mercator projection.
• False origin assigned to each UTM zone. In
Northern Hemisphere, UTM measured from
false origin at equator and 500,000 m West of
central meridian.
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UTM Zones
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UTM Zones
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UTM on USGS Maps
• On 7.5-minute
quadrangle
maps the UTM
grid lines are
indicated at
intervals of 1,000
meters, by blue
ticks in the
margins of the
map or with full
grid lines.
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State Plane System
• In United States, State Plane System developed
in the 1930s and was based on NAD27.
• While the NAD-27 State Plane System has been
superseded by the NAD-83 System, maps in
NAD-27 coordinates (in feet) are still in use.
• Most USGS 7.5 Minute Quadrangles use
several coordinate system grids including
latitude and longitude, UTM kilometer tic marks,
and State Plane coordinates.
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Public Land Survey System
• Public Land Rectangular Surveys have been
used since the 1790s to identify public lands in
the United States.
• Appears on large-scale USGS topographic
maps
• Abbreviations used for Township (T or Tps),
Ranges (R or Rs), Sections(sec or secs), and
directions (N, E, S, W, NE, etc.).
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Public Land Survey System
• Each state has a
principle meridian
running N-S, and a
baseline running E-W.
• When measuring in a
N-S direction, each
square is called a
township.
• When measuring in an
E-W direction, each of
these squares is called
a range.
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