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 The distance on the map is always expressed as one, e.g., 1 : 100,000 ► Common map scales 1 : 24,000 1 : 24,000 1: 100,000 1: 100,000 1 : 250,000 1 : 250,000 1 : 1,000,000 1 : 1,000,000

Map Scale ► Small and large scale Which one is a larger map scale? 1 : 24,000 or 1 : 100,000 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 Basic elements of a coordinate system ► an origin, then the location of every location of every other point can be other point can be stated in terms of stated in terms of ► a defined direction and ► a distance in the direction direction

2 Coordinate Systems ► Spherical coordinate systems Geographic coordinate system Geographic coordinate system ► Rectangular coordinate systems UTM (Universal Transverse Mercator) UTM (Universal Transverse Mercator) State Plane State Plane

2 (1) Spherical Coordinate Systems ► Based on a perfect sphere ► Geographic coordinate system - great circles - great circles small circles small circles - meridians - meridians parallels parallels - Latitude - Latitude - Longitude - Longitude courtesy: courtesy:

Latitude ► Measured northward or southward from the equator to poles ► Ranging north or south ► The measuring units are degrees, minutes, and seconds, 1 0 = 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 east or west ► The measuring units ► Length of one degree longitude reduces toward poles

Latitude and Longitude courtesy: Mary Ruvane, courtesy: Mary Ruvane, Lines of Longitude (North/South - meridians) 90 0 latitude Lines of Latitude (East/West - parallels) Central Parallel 0 0 Prime Meridian 0 0

Reading Latitude and Longitude ► ’ S: 19 degrees 50 minutes Latitude South ► ’ W: 43 degrees 50 minutes Longitude West ’ W ’ 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 coordinate system ► A rectangular coordinate system for the WORLD system for the WORLD Gerardus Mercator ( ) 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 6 0 longitude wide, labeled 1 to 60 eastward beginning at the meridian ► Rows: east-west rows of 8 0 latitude high, labeled from C to X (without I, O) beginning at 80 0 S latitude ► ► Quadrilaterals

UTM Zones of the World courtesy: courtesy:

A UTM Zone ► We always use zones and rarely use rows and rarely use rows courtesy: courtesy:

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 courtesy: courtesy: ’ Latitude N, ’ Longitude W = Zone ?

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

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 2,000,000ft False 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: , On NAD27: ,

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 Cylindrical, Azimuthal, and Conic ► By distortions Conformal, Equal-area, Equidistant, and Azimuthal Conformal, Equal-area, Equidistant, and Azimuthal

Map Projections – by Methods ► Cylindrical 1. Mercator 2. Transverse Mercator

Map Projections - by Methods ► Azimuthal ► Conic

Map Projections - by Methods

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, courtesy: Mary Ruvane, Conformal – preserves shape Equivalent - preserves area Compromise - preserves neither Equivalent - preserves area

Commonly Used Projections ► Transverse Mercator: cylindrical conformal ► Lambert's conformal conic player_embedded player_embedded player_embedded player_embedded

Commonly Used Projections ► UTM as a coordinate system ► UTM as a means of projection

Readings ► Chapter 2