1

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

2

Cone – Conic

Cylinder -Cylindrical

Plane -Azimuthul

The projection surface: Projection Surfaces – “developable”

Developable Surface- Cone Developable Surface - Cylinder

3

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

4

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

5

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?

6

“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

7

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.

8

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

9

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

10

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?

11

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

12

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

13

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

14

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

15

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

16

Lake City

7.5 minute

USGS

Topographical

Map

1:24,000 scale

17

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)

18

19

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

20

21