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NASA
Map Projections and Coordinate Systems Map Projections
A systematic rendering
3-D spherical
to
2-D Cartesian system.
Many Projections: Minnesota examplehttp://rocky.dot.state.mn.us/geod/projections.htm
Projections may be categorized by:
•The projection surface
•Distortion properties
•Surface orientation
•The location of projection source
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Cone – Conic
Cylinder -Cylindrical
Plane -Azimuthul
The projection surface: Projection Surfaces – “developable”
Developable Surface- Cone Developable Surface - Cylinder
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Projections are like political parties, they distort everything
Distortion properties:
preserve local shape - conformal (orthomorphic)
preserve scale – equidistant
preserve direction – azimuthal
preserve great circles – gnomic
preserve circular shapes - stereographic
Distortion Varies Across Map Distortion varies by developable surface
CylindricalConic
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Projections Categorized by Orientation:
Equatorial - intersecting equator
Transverse - at right angle to equator
Gnomonic -center of globe
Stereographic -at the antipode
Orthographic -at infinity
Source:http://www.fes.uwaterloo.ca/crs/geog165/mapproj.htm
Categorized by the Location of Projection Source
Specifying Projections
• The type of developable surface (e.g., cone)
• The size/shape of the Earth (ellipsoid, datum), and size of the surface
• Where the surface intersects the ellipsoid
• The location of the map projection origin on the surface, and the coordinate system units
Defining a Projection – LCC(Lambert Conformal Conic)
• The LCC requires we specify an upper and lower parallel
• A spheroid
• A central meridian
• A projection origincentralmeridian
origin
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Many LCC Projections: Minnesota examplehttp://rocky.dot.state.mn.us/geod/projections.htm
Lecture Question:
Ellipsoid, Projection
Are the related? How
Lecture Question:
What is a developable surface?
What are the common shapes?
Lecture Question:
What is a datum transformation?
How does it differ from a map projection?
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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.
State Plane Coordinate System Zones
State Plane Coordinate System
• 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
CaliforniaState PlaneZones
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
e.g., Minnesota Central State Plane Zone
Projection type: Lambert Conformal ConicSpheroid: GRS80Central Meridian: -94.25 Reference Latitude: 45.001st Stand. Parallel: 45.61666662nd Stand. Parallel: 47.05False Easting: 800000False Northing: 100000
Universal Transverse Mercator –UTM System
UTM Zone Details
Each Zone is 6 degrees wide
Zone location defined by a central meridian
Origin at the Equator, 500,000mwest of the zone central Meridian
Coordinates are always positive(offset for south Zones)
Coordinates discontinuous acrosszone boundaries
Universal Transverse Mercator Projection – UTM Zones for the U.S.
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UTM
Measurements of distance, shape & area with .04% or less distortion.*
Grid allows a slight tilt from True North. “UTM grid declination”*
From USGS 1:24k map sheet
Coordinate Systems Notation
Latitude/LongitudeDegrees Minutes Seconds 45° 3' 38" NDegrees Minutes (decimal) 45° 3.6363' NDegrees (decimal) 45.0606° N
State Plane (feet) 2,951,384.24 N
UTM (meters) 4,996,473.72 N
UTM Coordinates (meters)
Common “Topo” format283000m E “Easting” (East of the zone meridian;
remember false easting concept)
3904000m N “Northing” (North of the Equator)
Standard
UTM 10S 0545980E 4185742N
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National Projections 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
• Changing from one projection to another may require both
Simple Projection: Example
= 30, = 45
Example:
X = R (30*/180- 0)= 6,378 (1.7320)= 11,047
Y = R ln(tan(45+45/2))= 6,378 ln(1.73205)= 6,378 * 0.5493= 3,503
45
From one Projection to Another
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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
Non-Coordinate Systems
Public Land Survey System(PLSS)
Have you ever looked out the windows while flying on an airplane over central and western US?
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Have you ever looked out the windows while flying on an airplane over central and western US? Historical Surveying
Metes and Bounds
Used in many of the Eastern and Southeastern States.
Also used for land titles and transactions.
Descriptions have:
A point of beginning,definite corners, lengths and directions of the property sides, names of adjoining property owners and area.*
* Source:http://feature.geography.wisc.edu/sco/geodetic/plss.html
Historical Surveying
Metes and Boundsfrom Mercer County, Kentucky Deed Book 7, p.41713 February 1810. Rice BEADLES of Lincoln Co., Ky sells 140 acres and 36 poles of land in Mercer County on Doctors Fork to John CRAIN for 200 pounds.Land bounded as follows...: [Ref. 1]Beginning at the mouth of a branch at an ash stumpthence up the creek S 20 poles to 2 beachthence east 41 poles to a small walnut in Arnett's linethence north 50 east 80 poles to a linn hickory dogwood in said linethence north 38 poles to an ashthence west 296 poles with Potts's line till it intersects with Tolly's linethence south 30 west 80 poles to a whiteoak and sugar thence east 223 poles to beginning....
Source: http://www.outfitters.com/genealogy/land/crain.html
Metes and Bounds
Source: http://www.outfitters.com/genealogy/land/crain.html
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Source:http://www.ca.blm.gov/cadastral/meridian.html
The non-Coordinate System: The Public Land Survey SystemPublic Land Survey System PLSS
(digitized Section, township and Range information
Begun by Thomas Jefferson(To pay war debts to Revolutionary War SoldiersLand allotments rather than hard currency)
Used in much of the Central and Western US
Established for inventory and transfer of property
Grid system6 square mile Sections withinEast West oriented RangesNorth South oriented Townships
Source:http://www.ca.blm.gov/cadastral/meridian.html
PLSS – a method of defining parcels by successive subdivision
Measurement Systems
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How much a man behind an ox could plow in one day
http://www.glorecords.blm.gov/images/page2_large.gif
6 miles by 6 Miles
Each Section 1 mile by 1 mile
Measured in Chains (66 feet)
Easy way to figure acres before calculators
3 chains by 7 chains = 21 sq chains
divide by 10 to get acres
2.1 acres
Example of a PLSS Section Corner Monument
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Have you ever looked out the windows while flying on an airplane over central and western US?
Have you ever looked out the windows while flying on an airplane over central and western US?
Source:http://feature.geography.wisc.edu/sco/geodetic/geodetic_graphics/Township_Big.jpg
36 sections in a Township, each section approximately a mile square.
(80 chains x 80 chains = 6400 sq chains or 640 acres)
Note:zig-zag or boustrophedon numbering scheme
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Source:http://feature.geography.wisc.edu/sco/geodetic/geodetic_graphics/Township_Big.jpg
Sections may be further subdivided
640 acres1 mile by 1 mile
160 acres
320
acre
s
40 acres
“Aliquot division”
Format:
Section,Township, Range, Meridian, County
For Example:
Northeast Quarter of the Northeast Quarter of Section 5 in Township 101, Range 35 W of the Fifth Principal Meridian, Jackson County, Minnesota
NE 1/4, NE 1/4, S5, T101, R35W, 5th PM, Jackson County, Minnesota
Source:http://www.ca.blm.gov/cadastral/meridian.html
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Lake City
7.5 minute
USGS
Topographical
Map
1:24,000 scale
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REVIEWFormat:
Section,Township, Range, Meridian, County
For Example:
Northeast Quarter of the Northeast Quarter of Section 5 in Township 101, Range 35 W of the Fifth Principal Meridian, Jackson County, Minnesota
NE 1/4, NE 1/4, S5, T101, R35W, 5th PM, Jackson County, Minnesota
REVIEW
Lake City
7.5 minute
USGS
Topographical
Map
1:24,000 scale
(detail examples of this map follow)
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Lake City
7.5 minute
USGS
Topographical
Map
1:24,000 scale
Next Slides are examples of:
Public Land Survey System PLSS(digitized Section, township and Range information
Grid system6 square mile Sections withinEast West oriented Ranges
North South oriented Townships
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