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 a defined direction a distance direction in the and

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 0-90 0 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 0-180 0 east or west ► The measuring units ► Length of one degree longitude reduces toward poles

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

Reading Latitude and Longitude ► ► 19 0 50’ S: 19 degrees 50 minutes Latitude South 43 0 50’ W: 43 degrees 50 minutes Longitude West - 43 0 50’ 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 ► U niversal T ransverse M ercator 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 6 0 longitude wide, labeled 1 to 60 eastward beginning at the 180 0 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: 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 500,000m and the equator is given a for the northern hemisphere easting northing of value of 0 ► For southern hemisphere, the equator is given a northing value of 10,000,000m ► 671,000m Easting, 4,749,000m Northing

Calculate Your Own Zone 44 0 03’ Latitude N, 71 0 58’ 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 extent projection for states of E-W

State Plane ► The central meridian of a zone is given 2,000,000ft Easting False ► 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. Datum ► Vertical datum: is the zero surface from which all elevations or heights are measured

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

4. 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 ► Azimuthal ► Conic http://exchange.manifold.net

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

Conformal –

preserves shape

Equivalent -

preserves area

Equivalent -

preserves area

Compromise -

preserves neither courtesy: Mary Ruvane, http://ils.unc.edu/

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 TM as a means of projection

► Chapter 2 Readings

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