Basic Coordinate Systems Grid Systems RG 620 May 09, 2013 Institute of Space Technology, Karachi RG 620 May 09, 2013 Institute of Space Technology, Karachi

Coordinate Systems After projection it is necessary to set up a coordinate system on the map that will allow a point to be described in X-Y space (or northing and easting) To describe a location in a universally understandable manner a grid system is necessary For a useful grid it is necessary for it to define an origin and a uniform grid spacing There are several types of Coordinate System to represent the Earth’s surface

Coordinate Systems Some commonly used Coordinate Systems are: –Geographic Latitude and Longitudes are used –UTM Shape is preserved and precise measurements in meter –State Plane Local surveying (with minimum distortion)

Geographic Coordinate System (WGS84 datum)

Universal Transverse Mercator Coordinate System Global coordinate system Globe is divided into narrow longitude zones Best used for north-south oriented areas (little distortion in this direction) Successive swaths of relatively undistorted regions created by changing the orientation of the cylinder slightly These swaths are called UTM zones Each zone is six degrees of longitude wide Total 60 zones

Universal Transverse Mercator Coordinate System These zones are numbered from west to east Zone 1 begins at the International Date Line (180 0 W), Zone 2 at 174°W and extends to 168°W Each Zone is further divided into Eastern and Western halves by drawing a center line called Central Meridian Zones are further split north and south of the equator

Universal Transverse Mercator Coordinate System At equator a zone is about 40,000/60 = 667 Km wide Any point can be described by ‘Easting’ and ‘Northing’ values Northing is the distance to the equator, while easting is the distance to the "false easting", which is uniquely defined in each UTM zone The equator is used as the northing origin for all north zones (northing value of zero) South zones have a false northing value added to ensure all coordinates within a zone are positive For UTM south zones, the northing values at the equator are set to equal 10,000,000 meters

UTM – Easting and Northing

Universal Transverse Mercator Coordinate System Important thing to remember Coordinate values are discontinuous across UTM zone boundaries, therefore, analyses are difficult across zonal boundaries

Horizontal Zoning Latitudes are divided into zones lettered from A at the South Pole to Z at the North Pole Spacing is not regular throughout A and B zones are within the south circle of 80 degrees Zones Y and Z cover the north polar region north of 84 Rest of the zones extend from 80 degrees south latitude to 84 degrees north latitude degrees Zone X is 12 degrees wide (from 72 to 84 degrees North) I and O not used Rest of the zones are 8 degree wide Zone M and N are just South and North of Equator respectively

UTM Zones

UTM Zones - Pakistan

UTM – Finding Grid Zone Finding Grid Zone for any Latitude In calculation take west longitude as (-) negative and east longitude as (+) positive Add 180 and divide by 6 Round off the resultant value to the next higher number Example: Greenwich Prime Meridian is at …….. Longitude?

Measuring Distance Distortion Comparing map distance with the Great Circle Distance Remember the Example from Text Book where the Great Circle Distance between two point A and B was = KM Identify coordinates of the equivalent points on UTM grid Calculate the distance between these points Negative scale distortion when features are compresses or reduced in size Positive scale distortion when features are expanded

Grid Distance

State Plane Coordinate (SPC) Systems Standard set of projections for the United States developed in 1930’s Specifies positions in Cartesian coordinate systems for each state Used for local surveying and engineering applications Points are projected from their geodetic latitudes and longitudes to x and y coordinates in the State Plane systems Conformal mapping system for US with a maximum scale distortion of one part in 10,000

State Plane Coordinate Systems Large states are divided into zones to limit distortion error and maintain said accuracy One or more zones in each state with slightly different projection in each zone Boundaries of zones follow state and county lines The number of zones in each state is determined by the area the state covers The number of zones ranges from 1 to 10 (in Alaska) Each zone has a unique central meridian

State Plane Coordinate Systems Zones have different projections –Lambert Conformal Conic: for states that are longer east– west, such as Tennessee, Kentucky, North Carolina, Virginia, etc. –Transverse Mercator projection: for states that are longer north–south, such as Illinois, Arizona, New Hampshire, etc. –The Oblique Mercator projection: for the panhandle of Alaska (AK zone 1) because it lays at an angle

State Plane 1927 vs Originally based on the North American Datum of 1927 and the measurement unit was feet Now being converted to North American Datum of 1983 (NAD83) (will use meters as unit of measure) Due to datum change some zones are redefined

State Plane Zone Boundaries NAD83

Alaska State Plane Zones

Variation between Datums Reference: David Corner

Reference: David Conner National Geodetic Survey, 2003

Conversion Among Coordinate Systems

References – – – – –Images: Peter H. Dana, Department of Geography, The University of Texas at Austin circles-tropics-non.pnghttp://upload.wikimedia.org/wikipedia/commons/a/ab/WorldMapLongLat-eq- circles-tropics-non.png gifhttp:// gif