Projections and Datums

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Projections and Datums
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The Global Grid

• The global grid system constructed using two
  natural reference features on earth
• The two natural reference features are the
  earths axis and the equator

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Meridians and Parallels

• Any circle that lies in a plane passing through
  the center of the earth is a great circle
• The equator is a great circle bisecting the earth
  midway between the poles
• A special kind of great circle is one that passes
  through the poles

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Meridians and Parallels cont.

• Half of one of these great circles passing from
  pole to pole is called a meridian
• Circles which do not lie in planes containing the
  center of the earth are small circles
• Small circles lying in planes parallel to the
  equator are called parallels

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Latitude and Longitude

• This locational grid system is built using
  parallels and meridians
• Longitude is measured with respect to an
  arbitrary meridian the Greenwich, or prime
  meridian
• This is defined as zero degrees long.

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Longitude

• Measured with respect to the prime meridian
• Is defined by the angle made by the point of
  interest, the center of the earth, and the prime
  meridian
• The angle is measured along the parallel
  containing the point of interest

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Longitude cont.

• Measured in degrees, minutes, seconds East or
  West of the Prime Meridian
• 180 degrees E/W is the foundation for the
  International Dateline
• Distance between lines of longitude lessens from
  equator to poles as lines of longitude converge
  towards poles

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Latitude

• Measured in same units as Longitude
• The equator is 0 degrees latitude, poles are 90
  degrees north and south of the equator
• Angle is measured from the point of interest
  through the center of the earth to the equator
• Measured along the meridian containing the point
  of interest

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Lat/Long

• Coordinate usually stated as e.g.
• Lat 47 deg 35 25 N Long 117 deg 59 32 W

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Projections

• The spherical grid must somehow be represented on
  flat maps
• We envisage this by shining a light bulb through
  a gridded transparent earth surrounded by a
  cylindrical piece of paper
• Trace the projected grid on the paper, open the
  paper and we have a cylindrical projection

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Cylindrical Projection

• A cylindrical projection results in straight,
  parallel meridians and parallels
• Mercator projection is a famous example
• The straight meridians provide good navigation
  grids

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Other Projections

• Other classic types of projection include the
  conic projection and polar projection
• All projections involve compromise
• Distortions of shape, distance, area occur to
  different extents depending on the projection

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Projection Compromises

• A projection which preserves shape is conformal
• A projection which preserves area is equivalent
• Most projections are a compromise e.g. Robinson
  used by Rand McNally

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Projection Compromises

• The Mercator Projection is conformal but makes
  Greenland look as big as Africa
• Many projections have been created for different
  purposes
• All are mathematical constructs

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A useful projection

• The Universal Transverse Mercator Projection
• A cylindrical projection where the conceptual
  light bulb is shone through a chosen meridian
  perpendicular to the earths axis

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UTM

• UTM projections are useful because they provide a
  decimal grid of eastings and northings
• Easting distance in meters east of reference
  meridian
• Northing distance in meters north of equator (in
  our hemisphere)

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UTM Grids

• 60 UTM zones around the earth
• Areas north and south of 80 degrees have a
  similar system called UPS
• Washington is in UTM zone 11 N
• Many find the decimal coordinates easier to work
  with than lat/long

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State Plane

• Although 124,000 quad maps show ticks for the
  UTM grid
• They are actually projected using the Lambert
  Conformal Conic Projection
• The projection occurs along a parallel and is
  used for states which are longer in the east/west
  direction

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State Planes

• States longer in the north/south direction use
  transverse mercator
• Alaska uses an oblique mercator
• Washington has two zones N and S in the State
  Plane system

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Washington State Plane

• State Plane Zone N has its origin of projection
  at lat 47 deg 0 N
• State Plane Zone S has its origin of projection
  at lat 45 deg 30 N
• The variations in types of projections for each
  state arose in an effort to maintain a minimum
  accuracy level in conformal projections for each
  state

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Lambert Conformal Conic

• Ticks for this projection are shown on the
  124,000 quad in feet

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Datums

• A datum is a representation of the shape of the
  surface of the earth for a restricted area
• One which was defined in 1927 is called North
  American Datum 27 (NAD 27)
• Subsequently we had NAD 83

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Datums cont.

• NAD 27 and NAD 83 are seen on quad maps depending
  on when they were last revised
• WGS 84, a datum used by GPS systems can be
  considered as more or less equivalent to NAD 83

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Datum Conflicts

• Superimposing a set of data tied to the NAD 27
  datum on a set of NAD 83 data can lead to errors
  of the order of 500 feet

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Township/Range

• Also called the public lands survey system
• Shown on 124,000 quads
• Not a mathematical projection system and not
  useful for locating a point

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Summary

• Projections arise from mathematical constructs
  used to convert a spherical into a two
  dimensional grid
• All projections incorporate distortion
• Datums arise from constructs which try to define
  the shape of the earths surface in a region

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Implications for GIS

• All data layers in the GIS database must use the
  same projection
• All data layers in the GIS database must use the
  same datum
• The UTM projection system is often found useful
  because of its easy decimal XY coordinate system