Map Projections and Coordinate Systems

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Map Projections and Coordinate Systems

• Surveying 101 for GIS Professionals
• 2013 Kentucky GIS Conference
• Jeremy Gould Kentucky Transportation Cabinet

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Agenda

• Geographic Coordinate Systems
• Ellipsoids
• Geoid
• Horizontal Datums
• Projected Coordinate Systems
• Project Datum Factors

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Geographic Coordinate Systems

• Geographic Coordinates Systems use radial
  coordinates to locate a point on a specifically
  defined sphere (ellipse). These are called
  spherical coordinates.

Cartesian point P can also be represented in
spherical coordinates (?,f, ?) where ? /-
degrees longitude F /-degrees latitude ?
radial distance from center
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Geographic Coordinate Systems
Kentucky (-85.3 ,37.5 ) (85.3 W, 37.5 N)
Equator 0 latitude
Prime Meridian 0 longitude
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Ellipsoids

• Ellipsoids are flattened spheroids that when
  referenced to the earth can be rotated and/or
  shifted to best fit the earth (geoid) either in
  part or in whole

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Geoid

• The geoid is an equipotential gravimetric surface
  resulting in an irregular and non-mathematical
  approximation of the earths size and shape
  relative to a base of reference that best fits
  global mean sea level in a least squares sense
• The geoid is a 3 dimensional surface along which
  the pull of gravity is a specified constant
• The geoid is a measured and interpolated surface
  and not a mathematically defined surface
• Differences in the density of the Earth cause
  variation in the strength of the gravitational
  pull, in turn causing regions to dip or bulge
  above or below the reference ellipsoid

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Geoid
Gravity Recovery And Climate Experiment
(GRACE)Gravimeters
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Ellipsoids
There are Global Ellipsoids and Regional (local)
Ellipsoids Two Global ellipsoids are GRS80 and
WGS84
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Horizontal Datums

• A datum is a reference surface
• A geodetic datum consists of two major components
• Ellipsoid with a spherical coordinate system and
  origin
• Set of points and lines that have been surveyed
• A geodetic datum is a three dimensional Euclidian
  reference frame defined relative to an associated
  ellipsoid oriented to achieve a best fit
  statistical approximation of the geoid either in
  part or in whole.
• The North American Datum (NAD) has been defined
  by two different ellipsoids, the Clarke ellipsoid
  of 1866, which was oriented to best fit the North
  American continent and is the basis of NAD27, and
  the Global Reference System ellipsoid of 1980
  (GRS80) which is a globally defined ellipsoid and
  the basis of NAD83.

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Ellipsoid, Geoid, and Datum
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Horizontal Datums

• Lat and Long locations of given benchmarks in the
  NAD27 datum will likely be different from the lat
  and long of that same benchmark in the NAD83 or
  WGS84 datum's.
• The monumented points do not move
• This is described as a datum shift
• Shift in coordinate locations from WGS84 to NAD83
  is often less than 1 meter
• Datum shifts between NAD27 and NAD83 are often
  100s of meters

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Horizontal Datums

• Geographic Position (Lat-Long)
• (variations between datums for same position)

Example Datum 1 may have a long-lat of (-85.31
, 37.55 ) Datum 2 may have a long-lat
of (-85.30 , 37.54 ) The same point has
different coordinates because of the
shift/rotation of the ellipsoid
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Projected Coordinate Systems

• A mapping projection is a geometric tool that
  allows a portion of a spherical surface to be
  represented on a two dimensional surface such as
  a flat sheet of paper or computer screen in a
  spatially consistent manner.
• A State Plane Coordinate System is a specialized
  mapping projection that allows direct conversion
  between spherical geographic coordinates of
  latitude (?) and longitude (?), and rectangular
  Cartesian coordinates of northing (y) and easting
  (x).

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Projected Coordinate Systems

• So how do we get from our Geographic Coordinates
  to a Projected Coordinate System?

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Projected Coordinate Systems
Cylindrical Conical Planar
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Projected Coordinate Systems

• Transverse Mercator Projection

SF lt 1
Practical Limit of Projection (SF ? k0)
SF gt 1
Axis of Cylinder
Grid Origin
Intersection of Ellipsoid and Projection
Cylinder (SF 1)
Central Meridian (SF k0)
Polar Axis
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Universal Transverse Mercator Coordinate System
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Projected Coordinate Systems
KENTUCKY PROJECTIONSUTM Zones 16 17Transverse
Mercator (Secant Cylinder)
UTM Zone 17
UTM Zone 16
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Projected Coordinate Systems

• Lambert Conic Projection (Northern Hemisphere)

North StandardParallel (SF 1)
Polar Axis
Central Meridian
South StandardParallel (SF 1)
Parallel ofGrid Origin(Base Parallel)
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State Plane Coordinate Systems

• State Plane zones are sometimes identified by the
  Federal Information Processing System (FIPS)
  Codes as shown below

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Projected Coordinate Systems
KENTUCKY PROJECTIONSNorth and South State
PlaneLambert Conformal Conic (Secant Cone)
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Projected Coordinate Systems
KENTUCKY SINGLE ZONE PROJECTION
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Projected Coordinate Systems
KENTUCKY SPCS NORTH AND SOUTH ZONES
NORTH ZONE
SOUTH ZONE
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Projected Coordinate Systems
Kentucky ProjectionsNAD83 State Plane Coordinate
System(Lambert Conformal Conic)
Parameter Single Zone North Zone South Zone
Central Meridian 85 45 W 84 15 W 85 45 W
North Std Parallel 38 40 N 38 58 N 37 56 N
South Std Parallel 37 05 N 37 58 N 36 44 N
Base Parallel 36 20 N 37 30 N 36 20 N
False Northing 1,000,000 m 0 m 500,000 m
False Easting 1,500,000 m 500,000 m 500,000 m
Linear unit of measure for all zones is the U.S.
Survey Foot (USFt) (1 USFt .3048006096012
meters)
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Projected Coordinate Systems
COORDINATE SPACE COMPARISON
1,500,000 m
4921245 ft
1,250,000 m
4101038 ft
NAD'83 SINGLE ZONE
1,000,000 m
328083 ft
NORTHING
750,000 m
2460623 ft
NAD'83 SOUTH ZONE
500,000 m
1640415 ft
NAD'83 NORTH ZONE
250,000 m
820207 ft
NAD'27 NORTH ZONE
NAD'27 SOUTH ZONE
0 m
0 ft
0 m
0 ft
820207 ft
250,000 m
500,000 m
750,000 m
328083 ft
1640415 ft
5741453 ft
2460623 ft
4101038 ft
4921245 ft
6561660 ft
1,000,000 m
1,250,000 m
1,500,000 m
1,750,000 m
2,000,000 m
EASTING
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Projected Coordinate Systems
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Project Datum Factor

• A Project Datum Factor (PDF) converts grid
  distances (state plane coordinates) to
  ground/surface distances.
• If you were to use a total station to measure
  distance between two points on the ground and
  then used GPS to measure the location of the same
  two points and calculate the distance between
  those two points on the state plane grid, the two
  distances would be close but not exactly the
  same.  This is due to the curvature of the earth
  combined with the elevation above sea level of
  the project location.  The grid (state plane
  projection) is trying to represent the elevated,
  curved surface of the earth on a flat plane at
  sea level.
• The PDF was more prevalent before GPS became
  popular because total stations were the primary
  tools used for surveying.
• Projects were designed using the PDF. This
  allowed surveyors in the field to measure
  directly from the designed plans, without having
  to apply the PDF on the fly in the field.

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Project Datum Factor Example
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Project Datum Factor Example
0s
Inverse of PDF 1/1.000059148
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Project Datum Factor Example
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Conversion Among Coordinate Systems

• Exact or approximate mathematical formulas have
  been developed to convert to and from geographic
  coordinates (lat and long) to all commonly used
  coordinate projections
• Care must be taken when converting among
  projections that use different datums
• A datum transformation must be used to convert
  from one geographic coordinate system to another

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Conversion Among Coordinate Systems
Inverse of PDF
Inverse of PDF
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Summary

• Geographic Coordinate Systems
• Ellipsoids
• Geoid
• Horizontal Datums
• Projected Coordinate Systems
• Project Datum Factors

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References

• http//kartoweb.itc.nl/geometrics/index.html
• http//resources.arcgis.com/en/help/main/10.1/inde
  x.html//003r00000001000000
• http//training.esri.com/gateway/index.cfm?facata
  log.webCourseDetailcourseid24
• http//www.agc.army.mil/Missions/Corpscon.aspx
• Basic GIS Coordinates, Second Edition Jan Van
  Sickle

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Questions?

• Hopefully after this talk your project wont look
  like this.