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Geographic Information Systems

Coordinate Systems

1. Map Scale

- A ratio between a distance on the map and the corresponding distance on the earth

The distance on the map is always expressed as one, e.g., 1 : 100,000

- Common map scales

1 : 24,000

1: 100,000

1 : 250,000

1 : 1,000,000

Map Scale

- Small and large scale

Which one is a larger map scale?

1 : 24,000 or 1 : 100,000

- Spatial scales
- Map scale (large vs. small)
- Resolution (fine vs. coarse)
- Extent (large vs. small)

2. Coordinate Systems

Basic elements of a coordinate system

- an origin, then the

location of every

other point can be

stated in terms of

- adefineddirection and
- a distance in the

direction

2 Coordinate Systems

- Spherical coordinate systems

Geographic coordinate system

- Rectangular coordinate systems

UTM (Universal Transverse Mercator)

State Plane

2 (1) Spherical Coordinate Systems

- Based on a perfect sphere
- Geographic coordinate system

- great circles

small circles

- meridians

parallels

- Latitude

- Longitude

courtesy: http://www.colorado.edu/geography/gcraft/

Latitude

- Measured northward or southward from the equator to poles
- Ranging 0-900 north or south
- The measuring units are degrees, minutes, and seconds, 10 = 60’ and 1’=60”
- The length of one degree latitude is similar everywhere, ≈ 111km/69miles

Longitude

- Measured eastward or westward from the Prime Meridian at Greenwich, England to the International Date Line
- Ranging 0-1800 east or west
- The measuring units
- Length of one degree longitude reduces toward poles

courtesy: Mary Ruvane, http://ils.unc.edu/

900 latitude

Lines of Latitude

(East/West - parallels)

Prime

Meridian 00

Lines of Longitude

(North/South - meridians)

Central Parallel 00

Latitude and LongitudeReading Latitude and Longitude

- 19050’ S: 19 degrees 50 minutes Latitude South
- 43050’ W: 43 degrees 50 minutes Longitude West

- 43050’ W

2 (2) Rectangular Coordinate Systems

- Also referred to as Planar, Cartesian, and Grid coordinate system
- It converts Earth’s curved surface onto a flat map surface
- The x value is given first and called easting, then the y value is given and called northing

2 (2) (i) UTM

- Universal Transverse Mercator

coordinate system

- A rectangular coordinate

system for the WORLD

Gerardus Mercator (1512-1594)

Courtesy of the Library of Congress, Rare Book Division, Lessing J. Rosenwald Collection.

UTM Zones and Rows

- Measuring unit: meter
- Map projection: Universal Transverse Mercator
- Zones: north-south columns of 60longitude wide, labeled 1 to 60 eastward beginning at the 1800 meridian
- Rows: east-west rows of 80 latitude high, labeled from C to X (without I, O) beginning at 800 S latitude
- Quadrilaterals

UTM Zones of the World

courtesy: http://www.colorado.edu/geography/gcraft/

A UTM Zone

- We always use zones

and rarely use rows

courtesy: http://www.colorado.edu/geography/gcraft/

UTM Easting and Northing

- Each of the 60 zones has its own central meridian
- The central meridian of a zone is given the easting of 500,000m and the equator is given a northing value of 0 for the northern hemisphere
- For southern hemisphere, the equator is given a northing value of 10,000,000m

Calculate Your Own Zone

44003’ Latitude N, 71058’ Longitude W = Zone ?

courtesy: http://www.colorado.edu/geography/gcraft/

2 (2) (ii) State Plane Coordinate

- A rectangular coordinate system for the UNITED STATES
- Measuring unit: foot
- Zones: The U.S. is divided into 120 zones. Zone boundaries follow state and county lines

State Plane

http://www.cnr.colostate.edu/class_info/nr502/lg3/datums_coordinates/spcs.html

2 (2) (ii) State Plane Coordinate

- Projections: Each zone has its own projection system

- Transverse Mercator for states of N-S extent

- Lambert\'s conformal conic projection for states of E-W extent

State Plane

- The central meridian of a zone is given 2,000,000ftFalse Easting
- False origin: it is established in the south and west of the zone as 0, 0
- False easting, and false northing
- Zones may overlap

Difference between Systems

UTM and many other coordinate systems are defined based on the geographic coordinate system

Difference between Systems

- Try to use the rectangular systems as much as possible, and not to use geographic system for calculation
- Remotely sensed imagery and digital elevation models routinely use UTM
- Land record system routinely use State Plane
- know how to convert between projections (will be discussed in the lab)

3. Topographic Maps

- Planimetric maps

- Graphical representation of the shape and horizontal location of physical features of land and other physical entities.

- Topographic maps

- identity elevation of the land in contour lines.

Topographic Maps

- A map series published by USGS
- It is bound by parallels on the north and south, meridians on the east and west, 7.5’ span in either direction
- The maps are created from aerial photos
- The features are topography, vegetation, railroad, streams, roads, urban, etc.
- Three coordinate systems are marked, geographical, UTM, and State Plane

4. Datum

- Geodetic datum: are established to provide positional control that supports surveying and mapping projects covering large geographic areas, such as a country, a continent or the whole world

North American Datum of 1927 (NAD27) North American Datum of 1983 (NAD83)

- Coordinates change if datum changes: a control point in CA

On NAD83: -117 12 57.75961, 34 01 43.77884

On NAD27: -117 12 54.61539, 34 01 43.72995

Datum

- Vertical datum: is the zero surface from which all elevations or heights are measured

5. Map Projections

- A means of converting coordinates on a curved surface to coordinates on a plane
- Map projections vs. coordinate systems

- Map projections define how positions on the earth’s curved surface are transformed onto a flat map surface

- Coordinate systems superimposed on the surface to provide a referencing framework on which positions are measured

Map Projections

- A classification of map projections
- By conceptual methods

Cylindrical, Azimuthal, and Conic

- By distortions

Conformal, Equal-area, Equidistant, and Azimuthal

Map Projections – by Methods

- Cylindrical

1. Mercator 2. Transverse Mercator

http://exchange.manifold.net

Map Projections - by Methods

http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html

Map Projections - by Distortions

- Conformal projections It retains shapes about a point
- Equal-area projections It retains correct relative size
- Equidistant projections It retains uniform scale in all directions but only from one or two points
- Azimuthal projections It retains correct directions from one or two points

Map Projections - by Distortions

courtesy: Mary Ruvane, http://ils.unc.edu/

Conformal –

preserves shape

Equivalent -

preserves area

Equivalent -

preserves area

Compromise -

preserves neither

Commonly Used Projections

- Transverse Mercator: cylindrical conformal
- Lambert\'s conformal conic

http://www.youtube.com/watch?v=b1xXTi1nFCo&feature=player_embedded

http://www.youtube.com/watch?v=AI36MWAH54s

Commonly Used Projections

- UTM as a coordinate system
- UTM as a means of projection

Readings

- Chapter 2

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