Basic Coordinate Systems
Grid Systems
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
(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
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
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
= 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
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. 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
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
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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
– Images:
• Peter H. Dana, Department of Geography, The University of Texas at Austin
• http://upload.wikimedia.org/wikipedia/commons/a/ab/WorldMapLongLat-eqcircles-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