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 and a distance in the direction

2. Coordinate Systems Rectangular 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

Latitude and Longitude Lines of Longitude (North/South - meridians) 900 latitude Lines of Latitude (East/West - parallels) Central Parallel 00 Prime Meridian 00 courtesy: Mary Ruvane, http://ils.unc.edu/

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 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 60 longitude 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 671,000m Easting, 4,749,000m Northing

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 2,000,000ft 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. 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

Readings Chapter 2

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