1. Map Projections and Coordinate Systems
Surveying 101 for GIS Professionals
2013 Kentucky GIS Conference
Jeremy Gould – Kentucky Transportation Cabinet 1 1

2. Agenda Geographic Coordinate Systems Ellipsoids Geoid
Horizontal Datums
Projected Coordinate Systems
Project Datum Factors
Vertical Datums

3. 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 (λ,φ, γ) where:
λ= +/- degrees longitude
Φ= +/-degrees latitude
γ= + radial distance from center

4. Geographic Coordinate Systems
Kentucky
(-85.3 °,37.5 °)
(85.3 ° W, 37.5 ° N)
Equator
0° latitude
Prime Meridian
0° longitude

5. 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

6. Geoid
The geoid is an equipotential gravimetric surface resulting in an irregular and non-mathematical approximation of the earth’s 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

7. Geoid
Gravity Recovery And Climate Experiment (GRACE) Gravimeters

8. Ellipsoids There are Global Ellipsoids and Regional (local) Ellipsoids
Two Global ellipsoids are GRS80 and WGS84

9. 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.

10. Ellipsoid, Geoid, and Datum
GRS80 Ellipsoid
(NAD’83)
CLARKE 1866 Ellipsoid
(NAD’27)
GEOID
Earth Mass Center
Approximately 236 meters

11. 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 100’s of meters

12. Horizontal Datums Geographic Position (Lat-Long)
(variations between datums for same position)
Example:
Datum 1 may have a long-lat of
( °, °)
Datum 2 may have a long-lat of
( °, °)
The same point has different coordinates because of the shift/rotation of the ellipsoid

13. 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).

14. Projected Coordinate Systems
So how do we get from our Geographic Coordinates to a Projected Coordinate System?

15. Projected Coordinate Systems
Cylindrical
Conical
Planar

16. Projected Coordinate Systems
Transverse Mercator Projection
SF < 1
Practical Limit
of Projection
(SF  k0)
SF > 1
Axis of
Cylinder
Grid Origin
Intersection of Ellipsoid
and Projection Cylinder
(SF = 1)
Central Meridian
(SF = k0)
Polar Axis

17. Universal Transverse Mercator Coordinate System

18. Projected Coordinate Systems
KENTUCKY PROJECTIONS UTM Zones 16 & 17 Transverse Mercator (Secant Cylinder)
UTM Zone 16
UTM Zone 17

19. Projected Coordinate Systems
Lambert Conic Projection (Northern Hemisphere)
Polar Axis
North Standard Parallel (SF = 1)
Central Meridian
South Standard Parallel (SF = 1)
Parallel of Grid Origin (Base Parallel)

20. State Plane Coordinate Systems
State Plane zones are sometimes identified by the Federal Information Processing System (FIPS) Codes as shown below

21. Projected Coordinate Systems
KENTUCKY PROJECTIONS North and South State Plane Lambert Conformal Conic (Secant Cone)
State Plane South Zone
State Plane North Zone

22. Projected Coordinate Systems
KENTUCKY SINGLE ZONE PROJECTION

23. Projected Coordinate Systems
KENTUCKY SPCS – NORTH AND SOUTH ZONES
NORTH ZONE
SOUTH ZONE

24. Projected Coordinate Systems
Kentucky Projections NAD83 State Plane Coordinate System (Lambert Conformal Conic)
Parameter
Single Zone
North Zone
South Zone
Central Meridian
85° 45’ W
84° 15’ 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
False Northing
1,000,000 m
0 m
500,000 m
False Easting
1,500,000 m
Linear unit of measure for all zones is the U.S. Survey Foot (USFt)
(1 USFt = meters)

25. Projected Coordinate Systems
COORDINATE SPACE COMPARISON
1,500,000 m ft
1,250,000 m ft
NAD'83 SINGLE ZONE
1,000,000 m ft
NORTHING
750,000 m ft
NAD'83 SOUTH ZONE
500,000 m ft
NAD'83 NORTH ZONE
250,000 m ft
NAD'27 NORTH ZONE
NAD'27 SOUTH ZONE
0 m
0 ft
0 m
0 ft
250,000 m ft
500,000 m ft
750,000 m ft
1,000,000 m ft
1,250,000 m ft
1,500,000 m ft
1,750,000 m ft
2,000,000 m ft
EASTING

26. Projected Coordinate Systems
Equatorial Plane
Topographic Surface (Ground)
Ellipsoid E1
Axis of Rotation S1 G1 G2 E2 S2 G3 E3 S3
E1 < G1 < S1
G2 < E2 < S2
E3 < S3 < G3
Projection Grid
North Standard Parallel
South Standard Parallel
E = Distance on ellipsoid G = Distance on grid S = Distance on surface
SF = Grid Scale Factor  = Geodetic latitude
SF=1
SF<1
SF>1

27. 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.

28. Project Datum Factor Example

29. Project Datum Factor Example
0’s
Inverse of PDF 1/

30. Project Datum Factor Example

31. 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

32. Conversion Among Coordinate Systems
Inverse of PDF
Inverse of PDF

33. Vertical Datums
Many Vertical Datums
GPS provides Elipsoid height

34. Summary Geographic Coordinate Systems Ellipsoids Geoid
Horizontal Datums
Projected Coordinate Systems
Project Datum Factors

35. References http://kartoweb.itc.nl/geometrics/index.html
Basic GIS Coordinates, Second Edition: Jan Van Sickle

36. Hopefully after this talk your project won’t look like this.
Questions?
Hopefully after this talk your project won’t look like this.