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Basic Coordinate Systems

Basic Coordinate Systems. Grid System RG 620 April 20, 2016 Institute of Space Technology, Karachi. Coordinates are not certain !!. Even if their figures are precise. Example.

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Basic Coordinate Systems

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  1. Basic Coordinate Systems Grid System RG 620 April 20, 2016 Institute of Space Technology, Karachi

  2. Coordinates are not certain!! Even if their figures are precise

  3. Example • In 1937 the United States Coast and Geodetic Survey set Youghall at latitude 40º 25' 33.504"N and longitude 108º 45' 55.378"W • In November of 1997Youghall suddenly got a new coordinate, 40º 25' 33.39258"N and 108º 45' 57.78374"W • Had Youghall actually moved at all? • Of course it did no such thing, the station is right where it has always been • Its datum changed !!!!!! • Originally, in1937 latitude and longitude for Youghall was based on the North American Datum 1927 • In 1997 the basis of the coordinate of Youghall became the North American Datum 1983 (NAD83)

  4. Coordinates without a specified datum, are vague…..

  5. Reference: David Conner National Geodetic Survey, 2003

  6. 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

  7. Coordinate Systems • The method of projection, onto a simple flat plane, is based on the idea that a small section of the Earth, as with a small section of the orange, conforms so nearly to a plane that distortion on such a system is negligible • Mapping a considerable portion of the Earth using a large number of small individual planes • Offers the convenience of working in plane Cartesian coordinates and still keep distortion at manageable levels • Note: when these planes are brought together they cannot be edge-matched accurately

  8. 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)

  9. Geographic Coordinate System (WGS84 datum)

  10. 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 1 part in 10,000

  11. 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

  12. False Easting and Northing?

  13. 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

  14. State Plane 1927 vs. 1983 • 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

  15. Scale Factor Where K is the scale factor for a line, K1 is the scale factor at one end of the line and K2 is the scale factor at the other end of the line.

  16. Scale Factor • Scale factor varies with the latitude in the Lambert projection. • Distortion lessens and the scale factor approaches 1 as a line nears a ______??

  17. 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 _?_____zones • Error is less than 0.04%

  18. Universal Transverse Mercator Coordinate System • These zones are numbered from west to east • Zone 1 begins at the International Date Line (1800 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

  19. 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

  20. UTM – Easting and Northing

  21. The UTM secant projection gives approximately 180 kilometers between the lines of exact scale where the cylinder intersects the ellipsoid (total = 360 km). The scale factor grows from 0.9996 along the central meridian of a UTM zone to 1.00000 at 180 km to the east and west. In state plane coordinates, the scale factor is usually no more than 1 part in 10,000. In UTM coordinates it can be as large as 1 part in 2,500.

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

  23. 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

  24. UTM Zones

  25. UTM Zones

  26. UTM Zones - Pakistan

  27. 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 • For example, Denver, Colorado is near 105° W. Longitude, -105°. -105° + 180° = 75° 75°/ 6 = 12.50 Round up to 13 • Example 2: Greenwich Prime Meridian is at …….. Longitude?

  28. Quiz

  29. 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 = 412.906 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

  30. Grid Distance

  31. Variation between Datums Reference: David Corner

  32. Conversion Among Coordinate Systems

  33. References • http://www.ncgia.ucsb.edu/giscc/units/u013/u013_f.html • http://geography.about.com/od/locateplacesworldwide/a/latitude.htm • http://webhelp.esri.com/arcgisdesktop/9.2/ • http://www.uwgb.edu/DutchS/FieldMethods/UTMSystem.htm • http://www.pdhcenter.com/courses/l117/l117content.pdf • Images: • Peter H. Dana, Department of Geography, The University of Texas at Austin • http://upload.wikimedia.org/wikipedia/commons/a/ab/WorldMapLongLat-eq-circles-tropics-non.png • http://www.ncgia.ucsb.edu/education/curricula/giscc/units/u013/figures/figure10.gif • http://www.ncgia.ucsb.edu/giscc/units/u013/u013_f.html • http://www.worldatlas.com/aatlas/imageg.htm • http://www-istp.gsfc.nasa.gov/stargaze/Slatlong.htm • http://www.esri.com/news/arcuser/0703/geoid1of3.html • http://www.pdhcenter.com/courses/l117/l117content.pdf

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