map projections and coordinate systems · 2020. 6. 28. · specifying projections • the type of...
TRANSCRIPT
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NASA
Map Projections and Coordinate Systems
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Map Projections
A systematic
rendering
3-D spherical
to
2-D Cartesian
system.
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Many Projections: Minnesota examplehttp://rocky.dot.state.mn.us/geod/projections.htm
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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:
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Projection Surfaces – “developable”
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Developable Surface- Cone
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Developable Surface - Cylinder
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Projections are like political parties, they distort everything
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Distortion properties:
preserve local shape - conformal (orthomorphic)
preserve scale – equidistant
preserve direction – azimuthal
preserve great circles – gnomic
preserve circular shapes - stereographic
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Distortion Varies Across Map
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Distortion varies by developable
surface
CylindricalConic
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Projections Categorized by
Orientation:
Equatorial - intersecting equator
Transverse - at right angle to
equator
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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
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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
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Defining a Projection – LCC(Lambert Conformal Conic)
• The LCC requires
we specify an
upper and lower
parallel
• A spheroid
• A central meridian
• A projection origin
centralmeridian
origin
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Many LCC Projections: Minnesota examplehttp://rocky.dot.state.mn.us/geod/projections.htm
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Lecture Question:
Ellipsoid, Projection
Are the related? How
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Lecture Question:
What is a developable surface?
What are the common shapes?
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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.
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State Plane Coordinate System Zones
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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
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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
e.g., Minnesota Central State Plane Zone
Projection type: Lambert Conformal Conic
Spheroid: GRS80
Central Meridian: -94.25
Reference Latitude: 45.00
1st Stand. Parallel: 45.6166666
2nd Stand. Parallel: 47.05
False Easting: 800000
False Northing: 100000
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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
zone boundaries
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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
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Coordinate Systems Notation
Latitude/Longitude
Degrees Minutes Seconds 45° 3' 38" N
Degrees Minutes (decimal) 45° 3.6363' N
Degrees (decimal) 45.0606° N
State Plane (feet) 2,951,384.24 N
UTM (meters) 4,996,473.72 N
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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
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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
• Changing from one projection to
another may require both
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Simple Projection: Example
f = 30, l = 45
Example:
X = R (30*p/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
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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
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Non-Coordinate Systems
Public Land Survey System
(PLSS)
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Have you ever looked out the windows while flying
on an airplane over central and western US?
![Page 41: Map Projections and Coordinate Systems · 2020. 6. 28. · Specifying Projections • The type of developable surface (e.g., cone) • The size/shape of the Earth (ellipsoid, datum),](https://reader036.vdocuments.net/reader036/viewer/2022062607/60347b3ad7f3d14c415777fe/html5/thumbnails/41.jpg)
Have you ever looked out the windows while flying
on an airplane over central and western US?
![Page 42: Map Projections and Coordinate Systems · 2020. 6. 28. · Specifying Projections • The type of developable surface (e.g., cone) • The size/shape of the Earth (ellipsoid, datum),](https://reader036.vdocuments.net/reader036/viewer/2022062607/60347b3ad7f3d14c415777fe/html5/thumbnails/42.jpg)
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
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Historical Surveying
Metes and Bounds
from Mercer County, Kentucky Deed Book 7, p.417
13 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 stump
thence up the creek S 20 poles to 2 beach
thence east 41 poles to a small walnut in Arnett's line
thence north 50 east 80 poles to a linn hickory dogwood in said line
thence north 38 poles to an ash
thence west 296 poles with Potts's line till it intersects with Tolly's line
thence 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
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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 System
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Public Land Survey System PLSS(digitized Section, township and Range information
Begun by Thomas Jefferson(To pay war debts to Revolutionary War Soldiers
Land allotments rather than hard currency)
Used in much of the Central and Western US
Established for inventory and transfer of property
Grid system
6 square mile Sections within
East West oriented Ranges
North South oriented Townships
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Source:http://www.ca.blm.gov/cadastral/meridian.html
PLSS – a method of defining parcels by successive subdivision
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Measurement Systems
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How much a man behind an ox
could plow in one day
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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
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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?
![Page 54: Map Projections and Coordinate Systems · 2020. 6. 28. · Specifying Projections • The type of developable surface (e.g., cone) • The size/shape of the Earth (ellipsoid, datum),](https://reader036.vdocuments.net/reader036/viewer/2022062607/60347b3ad7f3d14c415777fe/html5/thumbnails/54.jpg)
Have you ever looked out the windows while flying
on an airplane over central and western US?
![Page 55: Map Projections and Coordinate Systems · 2020. 6. 28. · Specifying Projections • The type of developable surface (e.g., cone) • The size/shape of the Earth (ellipsoid, datum),](https://reader036.vdocuments.net/reader036/viewer/2022062607/60347b3ad7f3d14c415777fe/html5/thumbnails/55.jpg)
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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 acres
1 mile by 1 mile
160 acres3
20
acre
s
40 acres
“Aliquot division”
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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
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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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REVIEW
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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
REVIEW
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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
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Next Slides are examples of:
Public Land Survey System PLSS(digitized Section, township and Range information
Grid system
6 square mile Sections within
East West oriented Ranges
North South oriented Townships
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