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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

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1 map scale
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
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
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


2 coordinate systems1
2 Coordinate Systems
  • Spherical coordinate systems

Geographic coordinate system

  • Rectangular coordinate systems

UTM (Universal Transverse Mercator)

State Plane

2 1 spherical coordinate systems
2 (1) Spherical Coordinate Systems
  • Based on a perfect sphere
  • Geographic coordinate system

- great circles

small circles

- meridians


- Latitude

- Longitude


  • 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
  • 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
latitude and longitude
courtesy: Mary Ruvane,

900 latitude

Lines of Latitude

(East/West - parallels)


Meridian 00

Lines of Longitude

(North/South - meridians)

Central Parallel 00

Latitude and Longitude
reading latitude and longitude
Reading 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
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
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
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
UTM Zones of the World


a utm zone
A UTM Zone
  • We always use zones

and rarely use rows


utm easting and northing
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
Calculate Your Own Zone

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


2 2 ii state plane coordinate
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
State Plane

2 2 ii state plane coordinate1
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 plane1
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
Difference between Systems

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

difference between systems1
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
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
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
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

  • Vertical datum: is the zero surface from which all elevations or heights are measured
5 map projections
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
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
Map Projections – by Methods
  • Cylindrical

1. Mercator 2. Transverse Mercator

map projections by methods1
Map Projections - by Methods
  • Azimuthal
  • Conic

map projections by methods2
Map Projections - by Methods

map projections by distortions
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 distortions1
Map Projections - by Distortions

courtesy: Mary Ruvane,

Conformal –

preserves shape

Equivalent -

preserves area

Equivalent -

preserves area

Compromise -

preserves neither

commonly used projections
Commonly Used Projections
  • Transverse Mercator: cylindrical conformal
  •  Lambert\'s conformal conic

commonly used projections1
Commonly Used Projections
  • UTM as a coordinate system
  • UTM as a means of projection
  • Chapter 2