L 5 Map
Projections
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Map projections are used to transfer or
“project” geographical coordinates onto a
flat surface. .
There are many projections:
Maine example:
• NAD 27 Universal Transverse Mercator – Zone 19N
• NAD 27 Maine State Plane
– East Zone
– West Zone
• NAD 83 Universal Transverse Mercator– Zone 19N
• NAD 83 Maine State Plane
– East Zone
– Central Zone
– West Zone
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Many Projections: Minnesota example
http://rocky.dot.state.mn.us/geod/projections.htm
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Projections may be categorized by:
1.The location of projection source
2.The projection surface
3.Surface orientation
4.Distortion properties
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Categorized by the Location of Projection
Source
Gnomonic center of globe
Stereographic at the antipode
Orthographic at infinity
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Source:http://www.fes.uwaterloo.ca/crs/geog165/mapproj.htm
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The projection
surface:
Cone – Conic
Cylinder Cylindrical
Plane Azimuthul
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Projection Surfaces – “developable”
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The Tangent Case vs. The Secant
Case
In the tangent case the cone, cylinder or
plane just touches the Earth along a
single line or at a point.
• In the secant case, the cone, or
cylinder intersects or cuts through the
Earth as two circles.
• Whether tangent or secant, the location
of this contact is important because it
defines the line or point of least
distortion on the map projection.
• This line of true scale is called the
standard parallel or standard
line.
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Standard Parallel
• The line of latitude in a conic or cylindrical
projection where the cone or cylinder
touches the globe.
• A tangent conic or cylindrical projection
has one standard parallel.
• A secant conic or cylindrical projection has
two standard parallels.
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The Orientation of the Surface
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Projections Categorized by
Orientation:
Equatorial - intersecting equator
Transverse - at right angle to
equator
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Specifying Projections
1. The type of developable surface (e.g., cone)
2. The size/shape of the Earth (ellipsoid,
datum), and size of the surface
3. Where the surface intersects the ellipsoid
4. The location of the map projection origin on
the surface, and the coordinate system
units
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Defining a Projection – LCC
(Lambert Conformal Conic)
• The LCC requires
we specify an
upper and lower
parallel
• An ellipsoid
• A central meridian
• A projection origin
origin
central
meridian
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Conformal Projections
• Locally preserves angles/shape.
• Any two lines on the map follow the same
angles as the corresponding original lines
on the Earth.
• Projected graticule lines always cross at
right angles.
• Area, distance and azimuths change.
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Equidistant Projections
• A map is equidistant when the distances
between points differs from the distances
on Earth by the same scale factor.
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Equivalent/Equal Area
Projection
• Equivalent/equal area projections maintain
map areas proportional to the same areas
of the Earth.
• Shape and scale distortions increase near
points 90o from the central line.
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“Standard” Projections
• Governments (and other organizations)
define “standard” projections to use
• Projections preserve specific geometric
properties, over a limited area
•Imposes uniformity, facilitates data exchange,
provides quality control, establishes limits on
geometric distortion.
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National Projections
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Map Projections vs. Datum
Transformations
• A map projections is a systematic
rendering from 3-D to 2-D
• Datum transformations are from one
datum to another, 3-D to 3-D or 2-D to 2-D
• Changing from one projection to another
may require both.
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From one Projection to Another
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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.
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• Lambert Conformal 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.
• 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.
• State Plane – A standard set of projections for the United
States
– based on either the Lambert Conformal Conic or transverse mercator
projection, depending on the orientation of each state. Large states
commonly require several state plane zones.
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Map Projections Summary
• Projections specify a two-dimensional
coordinate system from a 3-D globe
• All projections cause some distortion
• Errors are controlled by choosing the proper
projection type, limiting the area applied
• There are standard projections
• Projections differ by datum – know your
parameters
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Coordinate Systems
• Once map data are projected onto a planar surface,
features must be referenced by a planar coordinate
system.
• Coordinates in the GIS are measured from the origin
point. However, false eastings and false northings
are frequently used, which effectively offset the
origin to a different place on the coordinate plane.
• The three most common systems you will encounter
in the USA are:
Coordinate
– State Plane
systems
– Universal Transverse Mercator (UTM)
– Public Land Survey System
– non-coordinate systems
Lecture(PLSS)
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State Plane Coordinate Systems
• Uses Lambert conformal conic (LCC) and
Transverse Mercator (TM, cylindrical)
• LCC when long dimension East-West
• TM when long dimension N-S
• May be mixed, as many zones used as
needed
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State Plane Coordinate System
California
State Plane
Zones
• Each state partitioned
into zones
• Each zone has a
different projection
specified
• Distortion in surface
measurement less than
1 part in 10,000 within a
zone
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State Plane Coordinate System Zones
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Maine State Plane
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State Plane Coordinate System
e.g., Maine East State Plane Zone
Projection: Transverse_Mercator
False_Easting: 700000.000000
False_Northing: 0.000000
Central_Meridian: -67.875000
Scale_Factor: 0.999980
Latitude_Of_Origin: 43.833333
Linear Unit: Meter (1.000000)
Geographic Coordinate System: GCS_North_American_1983
Angular Unit: Degree (0.017453292519943295)
Prime Meridian: Greenwich (0.000000000000000000)
Datum: D_North_American_1983
Spheroid: GRS_1980
Semimajor Axis: 6378137.000000000000000000
Semiminor Axis: 6356752.314140356100000000
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Inverse Flattening: 298.257222101000020000
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UTM – Universal Transverse
Mercator
• UTM define horizontal positions worldwide by dividing the surface of the Earth
into 6o zones.
• Zone numbers designate the 6o
longitudinal strips extending from 80o
south to 84o north.
• Each zone has a central meridian in the
center of the zone.
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Universal Transverse Mercator –
UTM System
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UTM Zone
Details
Each Zone is 6 degrees wide
Zone location defined by a
central meridian
Origin at the Equator, 500,000m
west of the zone central Meridian
Coordinates are always positive
(offset for south Zones)
Coordinates discontinuous across
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zone boundaries
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Universal Transverse Mercator
Projection – UTM Zones for the U.S.
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UTM Zone 19N
•
•
•
•
•
•
•
Projection: Transverse_Mercator
False_Easting: 500000.000000
False_Northing: 0.000000
Central_Meridian: -69.000000
Scale_Factor: 0.999600
Latitude_Of_Origin: 0.000000
Linear Unit: Meter (1.000000)
•
•
•
•
•
•
•
•
Geographic Coordinate System: GCS_North_American_1983
Angular Unit: Degree (0.017453292519943295)
Prime Meridian: Greenwich (0.000000000000000000)
Datum: D_North_American_1983
Spheroid: GRS_1980
Semimajor Axis: 6378137.000000000000000000
Semiminor Axis: 6356752.314140356100000000
Inverse Flattening: 298.257222101000020000
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False Easting/Northing
• False easting – the value added to the x
coordinates of a map projection so that
none of the values being mapped are
negative.
• False northing are values added to the y
coordinates.
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Central Meridian
• Every projection has a central meridian.
• The line of longitude that defines the center
and often the x origin of the projected
coordinate system.
• In most projections, it runs down the middle
of the map and the map is symmetrical on
either side of it.
• It may or may not be a line of true scale.
(True scale means no distance distortion.)
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Central Meridian
http://www.geography.hunter.cuny.edu/~jochen/GTECH361/lectures/lecture04
/concepts/Map%20coordinate%20systems/Projection%20parameters.htm
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Scale Factor
• 0 > scale factor < =1
• The ratio of the actual scale at a particular
place on the map to the stated scale on
the map.
• Usually the tangent line or secant lines.
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Coordinate Systems Notation
Latitude/Longitude
Degrees Minutes Seconds
Degrees Minutes (decimal)
Degrees (decimal)
45° 3' 38" N
45° 3.6363' N
45.0606° N
State Plane (feet)
2,951,384.24 N
UTM (meters)
4,996,473.72 N
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ArcGIS
Datums and Projections
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Datum Transformations
Moving your data between coordinate systems sometimes includes
transforming between the geographic coordinate systems.
Because geographic coordinate systems contain datums that are
based on spheroids, a geographic transformation also changes the
underlying spheroid
ArcGIS Help
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Datum Transformations
A geographic transformation is always defined in a particular direction.
When working with geographic transformations, if no mention is made of the
direction, an application or tool like ArcMap will handle the directionality
automatically.
For example, if converting data from WGS 1984 to NAD 1927, you can pick a
transformation called NAD_1927_to_WGS_1984_3 and the software will apply it
correctly.
(ArcMap automatically loads one geographic transformation. It's designed for the
lower 48 states of the United States and converts between NAD 1927 and NAD
1983.)
ArcGIS Help
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Graph the Following
Distance
Distance
Time
Time
50
1
55000
60
100
2
110000
120
150
3
165000
180
200
4
220000
240
250
5
275000
300
300
6
330000
360
350
7
385000
420
400
8
440000
480
450
9
495000
540
500
10
550000
600
550
11
605000
660
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Graph the Following
Distance
Km
Distance
M
Time
Hr
Time
Min.
50
1
55000
60
100
2
110000
120
150
3
165000
180
200
4
220000
240
250
5
275000
300
300
6
330000
360
350
7
385000
420
400
8
440000
480
450
9
495000
540
500
10
550000
600
550
11
605000
660
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Define The Projection
• Predefined
• Custom
• Import
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Predefined
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Custom & Import
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Custom & Import
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Reproject “On the Fly”
• Two or more layers with different
DEFINED projections.
• First layer in the data frame defines the
projection for the data frame.
• Next layer added, ArcGIS will
automatically reproject it to the data frame.
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Defining The Projection for A
Data Frame
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Project
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Project
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