1. Geographic Datums & Coordinates
Datums and Geographic Reference Frames
M. Helper,3/6/03
Geographic Datums & Coordinates
What is the shape of the earth?
Why is it relevant?
M. Helper
GEO420k, UT Austin
GEO 420k, UT Austin

2. Make a Map, Graph the World
Datums and Geographic Reference Frames
M. Helper,3/6/03
Make a Map, Graph the World
What determines spacing of 30o increments of Lat. & Lon. ?
Dimensions and shape of earth (= DATUM)
Map Projection
Map Scale
Austin: (-97.75, 30.30)
X-axis
Y-axis
Graph shows 30o increments of Lat. & Lon. at ~ 1:385,000,000
M. Helper
GEO420k, UT Austin
GEO 420k, UT Austin

3. The Figure of the Earth Models Sphere with radius of ~6378 km
Ellipsoid (or Spheroid) with equatorial radius (major axis) of ~6378 km and polar radius (minor axis) of ~6357 km
Difference of ~21 km is usually expressed as the “flattening” (f ) ratio of the ellipsoid:
f = difference/major axis = ~1/300 for earth
M. Helper
GEO420k, UT Austin

4. Ellipsoid / Spheroid
Rotate an ellipse around an axis (c.f. Uniaxial indicatrix of optical mineralogy)
Rotation axis
a = Major axis
b = Minor axis
X, Y, Z = Reference frame
M. Helper
GEO420k, UT Austin

5. Standard Earth Ellipsoids
Major Axis a (km)
Minor Axis b (km)
Flattening (1/f)
Clark (1886) 6, 6,
294.98
GRS 80 6, 6,
298.57
M. Helper
GEO420k, UT Austin

6. Datums and Geographic Reference Frames
M. Helper,3/6/03
Horizontal Datums
Datum = ellipse and axis of rotation.
Common North American datums:
NAD27 (1927 North American Datum)
Clarke (1866) ellipsoid, non-geocentric axis of rotation*
NAD83 (1983 North American Datum)
GRS80 ellipsoid, non-geocentric axis of rotation
WGS84 (1984 World Geodetic System)
GRS80 ellipsoid, nearly identical to NAD83
Other datums in use globally
* Selection of a non-geocentric axis of rotation allows closer agreement between the geoid and ellipsoid – see notes below.
M. Helper
GEO420k, UT Austin
GEO 420k, UT Austin

7. Datum “shifts”
Coordinate shift by use of improper datum can result in horizontal positioning errors as great as 800 m
An example compares the WGS84 location of the Texas state capitol dome to 13 other datums.
M. Helper
GEO420k, UT Austin

8. Latitude and Longitude
+30o (North) Latitude
-30o (West) Longitude
M. Helper
GEO420k, UT Austin

9. Latitude facts:
Lines of latitude (parallels) are evenly spaced (small circles) from 0o at equator (a great circle) to 90o at poles.
60 nautical miles (~ 110 km)/1o, ~1.8 km/minute and ~ 30 m/second of latitude.
N. latitudes are positive (+f), S. latitudes are negative (-f).
M. Helper
GEO420k, UT Austin

10. Longitude facts:
Lines of longitude (meridians) converge at the poles; the distance of a degree of longitude varies with latitude.
Zero longitude is the Prime (Grenwich) Meridian (PM); longitude is measured from 0-180o east and west of the PM.
East longitudes are positive (+l), west longitudes are negative (-l).
P.M.
180o
M. Helper
GEO420k, UT Austin

11. Vertical Datums Sea Level (MSL), Geoid
Geoid = surface of constant gravitational potential that best fits MSL
governed by mass distribution of earth
Ellipsoid (HAE = Height above ellipsoid)
Geometric surface
Datum used by most GPS receivers
M. Helper
GEO420k, UT Austin

12. Sea Level (MSL), Geoid
Measure ht. of sea surface (via satellites) and connect with costal surveys on land to get geoid.
Sea “Level” (geoid) not level; as much as 700 m of relief globally.
Earth Surface
Ellipsoid
Geoid
M. Helper
GEO420k, UT Austin

13. Geoid, Ellipsoid and Elevation (z)
Height above MSL (Orthometric height)
H.A.E.
Geoid height = H.A.E.
Earth Surface
Geoid (~MSL)
Ellipsoid
Geoid Height
M. Helper
GEO420k, UT Austin

14. Geoid of the conterminous US
GEOID99 heights (= Geoid – Ellipsoid) range from a low of m (magenta) in the Atlantic Ocean to a high of 3.23 m (red) in the Labrador Strait.
Source: NGS at
M. Helper
GEO420k, UT Austin

15. To convert HAE to orthometric (elev. above MSL) height:
Need accurate model of geoid height (e.g. N.G.S. GEOID99)
GEOID99 has 1 x 1 minute grid spacing
Compute difference between HAE and Geoid height (online here for US)
Current model allows conversions accurate to ~ 5 cm
More precise orthometric heights require local gravity survey
M. Helper
GEO420k, UT Austin

16. How do we get from 3D earth models to 2D maps?
Map Projections – transforming a curved surface to a flat graph
Rectangular coordinate systems for smaller regions – UTM, SPCS, PLS
M. Helper
GEO420k, UT Austin

17. Laying the earth flat How?
Projections – transformation of curved earth to a flat map; systematic rendering of the lat. & lon. graticule to rectangular coordinate system.
Scale 1: 42,000,000
Scale Factor
(for specific line(s))
Earth
Globe
Map
Peters Projection
Globe distance Earth distance
Map distance Globe distance
M. Helper
GEO420k, UT Austin

18. Laying the earth flat
Systematic rendering of Lat. (f) & Lon. (l) to rectangular (x, y) coordinates: y
0, 0 x
Geographic Coordinates (f, l)
Projected Coordinates (x, y)
Map Projection
M. Helper
GEO420k, UT Austin

19. Laying the earth flat “Geographic” display – no projection
x , y = f , l
coords. have same scale and spacing
M. Helper
GEO420k, UT Austin

20. Laying the earth flat How? Projection types: Orthographic Gnomonic
Stereographic a A’ A’ A’ a a T’ T’ T’ T T T b B’ B’ b b B’
M. Helper
GEO420k, UT Austin

21. Developable Surfaces Surface for projection:
Plane (azimuthal projections)
Cylinder (cylindrical projections)
Cone (conical projections)
Cylinder and cone produce a line of intersection (standard parallel) rather than at a point
Standard Parallel T’
M. Helper
GEO420k, UT Austin

22. 3 orientations for developable surfaces
Normal
Transverse
Oblique
M. Helper
GEO420k, UT Austin

23. Tangent or Secant?
Developable surfaces can be tangent at a point or line, or secant if they penetrate globe
Secant balances distortion over wider region
Secant cone & cylinder produce two standard parallels
Standard Parallels
M. Helper
GEO420k, UT Austin

24. Projection produces distortion of:
Distance
Area
Direction
Proximity
Shape
Distortions vary with scale; minute for large-scale maps (e.g. 1:24,000), gross for small-scale maps (e.g. 1: 5,000,000)
Goal: find a projection that minimizes distortion of property of interest
M. Helper
GEO420k, UT Austin

25. Where’s the distortion?
No distortion along standard parallels, secants or point of tangency.
For tangent projections, distortion increases away from point or line of tangency.
For secant projections, distortion increases toward and away from standard parallels.
Secant line
M. Helper
Tangent
Secant
GEO420k, UT Austin

26. What needs to be specified?
Geographic (unprojected)
Lambert Conformal Conic
Horizontal Datum
Origin Coordinates
Secant Locations
Origin X, Y Values
M. Helper
GEO420k, UT Austin

27. Projections in common use, US
Lambert Conformal Conic
Projection used by USGS for most maps of conterminous US (E-W extent is large)
Used by SPCS for state zones that spread E-W (Texas)
Conformal
M. Helper
GEO420k, UT Austin

28. Projections in common use, US
Cylindrical
Transverse Mercator – basis for UTM coordinate system and State Plane Coordinate Systems that spread N-S
Standard Parallels 3o apart
M. Helper
GEO420k, UT Austin

29. Rectangular Coordinate Systems
Universal Transverse Mercator (UTM)
US military developed for global cartesian reference frame.
State Plane Coordinate System (SPCS)
Coordinates specific to states; used for property definitions.
Public Land Survey System (PLS)
National system once used for property description
no common datum or axes, units in miles or fractional miles.
M. Helper
GEO420k, UT Austin

30. UTM Coordinate System
T. M. secant projection is rotated about vertical axis in 6o increments to produce 60 UTM zones.
(x)
(Y)
Rotate in 6o increments
UTM Zone is 6o wide
M. Helper
GEO420k, UT Austin

31. UTM Coordinate System Zone boundaries are parallel to meridians.
Zones numbered from 180o (begins zone 1) eastward and extend from 80o S to 84o N.
UTM Zones 20 9 10 19 11 12 18 13 14 15 16 17
M. Helper
GEO420k, UT Austin

32. UTM Coordinate System
(x)
(Y)
Central meridian of each zone in US has a scale factor of (max. distortion).
Secants are 1.5o on either side of the central meridian.
M. Helper
GEO420k, UT Austin

33. UTM Coordinate System
Locations are given in meters from central meridian (Easting) and equator (Northing).
(-) Eastings avoided by giving X value of 500,000 m (“false easting”) to the Central Meridian
In S. hemisphere, equator is given “false northing” of 10,000,000 m to avoid (-) Northings. y x
N. Hemisphere origin is (500,000m, 0)
S. Hemisphere origin is (500,000m, 10,000,000m)
M. Helper
GEO420k, UT Austin

34. UTM Coordinate System UTM Coordinates for central Austin:
Central Meridian (X = 500,000 m) Y
Zone 14
Austin
99oW
Y = 3,000,000 mN
UTM Coordinates for central Austin:
Zone ,000 mE, 3,350,000 mN
M. Helper
GEO420k, UT Austin

35. State Plane Coordinate System (SPCS)
Developed in 1930’s to provide states a reference system that was tied to national datum (NAD27); units in feet.
Updated to NAD83, units in meters; some maps still show SPCS NAD27 coordinates.
Larger states divided into several zones.
X, Y coordinates are given relative to origin outside of zone; false eastings and northings different for each zone.
M. Helper
GEO420k, UT Austin

36. Austin: Central Zone ~ 944,000mE ~ 3,077,000mN
Texas NAD83 SPCS
Austin: Central Zone ~ 944,000mE ~ 3,077,000mN
Zone Code
Stand. Parallels
Origin
F. Easting F. Northing
4201 North
200,000 1,000,000
4202 N. Cent.
600,000 2,000,000
4203 Central
700,000 3,000,000
4204 S. Cent.
600,000 4,000,000
4205 South
500,000 5,000,000 Y
Austin X
M. Helper
GEO420k, UT Austin

37. Public Land Survey System (PLS)
System developed to survey and apportion public lands in the US, c. ~1800?
Coordinate axes are principle baselines and meridians, which are distributed among the states.
Grid system based on miles and fractional miles from baseline and meridian origin.
Not in Texas or original 13 states
M. Helper
GEO420k, UT Austin

38. Public Land Survey System (PLS)
Step 2
Step 1
Section 33
Center Sec. 33
Step 3
T2S, R1W, Section 33
M. Helper
GEO420k, UT Austin

39. Summary
Projections transform geographic coordinates (f, l) to cartesian (x, y).
Projections distort distance, area, direction and shape to greater or lesser degrees; choose projection that minimizes the distortion of the map theme.
Points of tangency, standard parallels and secants are areas of no distortion.
A conformal map has the same scale in all directions.
M. Helper
GEO420k, UT Austin

40. Summary (cont.) Projection characteristics are classified by:
Light source location
Gnomonic
Stereographic
Orthographic
Developable surface
Plane (azimuthal)
Cylinder (cylindrical)
Cone (conic)
Orientation
Normal
Transverse
Oblique
M. Helper
GEO420k, UT Austin