1. Coordinate systems, Projections and Geo-referencing
Geog 413
John Masich
January 14, 2013

2. Agenda Questions from last week Modeling the Earth Projections
Geo-referencing
Article Review

3. Questions from last week

4. A quick video

5. Modeling the Earth
Geoid - surface at mean sea level and is used for measuring heights represented on maps’
Ellipsoid (Spheroid) – Measure location (latitude and longitude) of points of interest. Many different ellipsoids have been defined for the world.

6. Modeling the Earth
The earth is not a perfect sphere (don’t tell my globe that!)
Datum- a fixed, three-dimensional surface, an oblate spheroid, that is approximately the size and shape of the Earth. From this surface, Latitude, Longitude and Elevation are computed.
Reference point

7. Terrain – Represents the “actual surface of the Earth.
The relationship between;
The ellipsoid/spheriod
The Geoid
Mean Sea Level
The Terrain
Is what Geodesists study to determine measurements on the earth’s surface.
This relationship varies ...

9. Back to the datum Each country or region will develop their own datum.
NAD 83
NAD 27

10. Modeling the Earth – Geoid to Map

11. Projections
In order to display our data in the most representative manner, we project it from the GCS to some form of projection.
Projecting from a 3d model to 2d plane results in distortion
Area
Shape
Distance
Direction
We are trying to represent
this amount of the earth on
this amount of map space.

12. Classifications of Map Projections
Map projections can be described in terms of their
class (cylindrical, conical or azimuthal),
point of secancy (tangent or secant),
aspect (normal, transverse or oblique), and
distortion property (equivalent, equidistant or conformal).

13. Classes of Projections

14. Classes of Projections
Cylindrical Projection - A projection that transforms points from a spheroid or sphere onto a tangent or secant cylinder. The cylinder is then sliced from top to bottom and flattened into a plane. Conic Projection - A projection that transforms points from a spheroid or sphere onto a tangent or secant cone that is wrapped around the globe in the manner of a party hat. The cone is then sliced from the apex (top) to the bottom, and flattened into a plane. Planer Projection - A projection that transforms points from a spheroid or sphere onto a tangent or secant plane. Because its directions are often true, the planar projection is also known as an azimuthal or zenithal projection.

15. Point of Secancy (Tangent of Secant)
A projection whose surface touches the globe's without piercing it. A tangent
planar projection touches the globe at one point, while tangent conic and
cylindrical projections touch the globe along a line. At the point or line of
tangency, the projection is free from distortion.
A projection whose surface intersects the surface of a globe. A secant conic or
cylindrical projection, for example, is recessed into a globe, intersecting it at
two circles. At the lines of intersection, the projection is free from distortion.

16. Aspect
Normal
Traverse
Oblique

17. Classification of map projections
Distortion Properties
Equal area projections preserve the area of features (popular in GIS)
Conformal projections preserve the shape of small features (good for presentations) , and show local directions (bearings) correctly (useful for coastal navigation!)
Equidistant projections preserve distances (scale) to places from one point, or along a one or more lines
Scale can never be correct everywhere on any map
True direction projections preserve bearings (azimuths) either locally (in which case they are also conformal) or from center of map.

18. Equal Area Projections
Albers Conic
Lambert cylindrical Equal Area Projections
Hammer projection

19. Conformal Projection
Mercator
Lambert Conformal Conic

20. Equidistant Projections
Sinusoidal
Equi-rectangular

21. True direction
Lamberts Azimuthal

22. Some interesting map projection links
Progonos
Atlas of Canada
Radical Cartography
Kartoweb

23. How do you determine what projection to use
How will the projection of your project and data be determined
Data
Methods
Input\output
Manage your data in a manner that is the most efficient for you
Considerations
Is there a field component
What do my field staff use to collect data
How challenging will the conversion process be?
Can I automate my processes.

24. Geo-referencing

25. Georeferencing How do we make sure all our data layers line up
Georeferencing How do we make sure all our data layers line up ? Georeferencing: Aligning geographic data to a known coordinate system so it can be viewed, queried, and analyzed with other geographic data. Georeferencing may involve shifting, rotating, scaling, skewing, and in some cases warping, rubber sheeting, or orthorectifying the data.
Registration:  lining up layers with each other Rectification: The process by which the geometry of an image is made planimetric (flattened)

26. If the world was flat, we could use a simple coordinate system with 0,0 in the bottom left corner (or A1) … but alas it isn’t …
The edge of the world …

27. GCS Uses a 3d surface to define locations on the earth
This is great if we are using a globe, but impractical
Detail
Analysis
Cumbersome
Negative values
Harvard School - Projection Fundamentals
What are geographic coordinate systems? (ESRI)

28. Geographic referencing
180 E/W
PG: 54N, 123W
[54, -123]
Geographic referencing is suitable for storing global datasets, but involves negative values south and west of 0, 0
0, 0

29. Geographic referencing
Geographic is not decimal, it is sexagesimal
1 degree = 60 minutes
1 minute = 60 seconds
Decimal degrees: 58° 30’ = /60 = 0.5
Decimal degrees: 58° 36’ = /60 = 0.6
Decimal degrees: 58°36’36” = /(60*60) = 0.01
View decimal degrees on pgmap website (use Internet Explorer / Active X)

30. The main problem with geographic referencing (for GIS data display and analysis)
- 1 degree longitude varies from km (the system is not ‘rectangular’ )

31. Local example from the phone book
2007 (OK) –scale is consistent : horizontal scale is almost double
Local example from the phone book

32. 60º 55.80 Length of One Degree of Longitude
Length of a Degree of Latitude
Latitude 
Kilometres 
Miles 
Miles
0º 
111.32 
69.17  0º
110.57
68.71 
10º 
109.64 
68.13 
10º
110.61
68.73
20º 
104.65 
65.03 
20º
110.70
68.79
30º 
96.49 
59.95 
30º
110.85
68.88
40º 
85.39 
53.06 
40º
111.04
68.99
50º 
71.70 
44.55 
50º
111.23
69.12
60º 
55.80 
34.67 
60º
111.41
69.23
70º 
38.19 
23.73 
70º
111.56
69.32
80º 
19.39 
12.05 
80º
111.66
69.38
90º 
0.00 
90º
111.69
69.40
1° Longitude is half the distance at 60N ° Latitude = ~ 111km anywhere

33. Earth is not a perfect sphere, it is ellipsoidal. earth is the 'Geoid'
Earth is not a perfect sphere, it is ellipsoidal .. earth is the 'Geoid'.  The difference in the major and minor axes has been estimated since ~1830
The latest should be the most accurate, using satellite technology. The difference representing the amount of 'polar flattening' is about 1/300.
Estimated ellipsoids
Equatorial Polar
Name
Date
Radius a (metres)
Radius b (metres)
Flattening
WGS 84
1984
6,378,137
6,356,752
1/298
International
1924
6,378,388
6,356,912
1/297
Clarke
1866
6,378,206
6,356,584
1/295
Everest
1830
6,377,276
6,356,075
1/301
Each ellipsoid has a 'Datum'  =  "a set of values that serve as a base for mapping“. For Canadian / North America, we use:     a. North American Datum, NAD27 (1927) based on Clarke     b. North American Datum, NAD 83 (1983) based on WGS 1984
NAD27 was the datum for mapping over most of the 20th century
NAD83 is the datum for contemporary GIS / mapping

34. In BC we use …
UTM (Universal Transverse Mercator)
BC Albers

35. Universal Transverse Mercator (UTM) System this bit is hard so pay attention …
The world is divided into 60 x 6 º longitude strips - the width of each zone thus varies from 6 x 111km = 666 km at the equator to < 80 km at 84 ° N
They are numbered from 180 º W to 180 º E
180W
180E

36. Canada: UTM zones

37. Coordinates repeat for each zone
UTM coordinates – in metres this is the hardest part … Northings (N): from the Equator – increase to the north (to 10,000,000) Eastings (E) – based on the zone Central Meridian at 500,000
Coordinates repeat for each zone
In BC, eastings are usually between 300, ,000

38. UTM zone overlap: Topographic map with Geographic and UTM referencing
UTM zone Eastings coordinates in BC are generally between 300,000 – 700,000

39. UTM coordinates may make more sense here :
PGMAP:
(use Internet Explorer / Active X)
The UTM system works well for a local area – coordinates in metres

40. BC: UTM zones
How do we deal with multiple UTM zones: Eastings coordinates switch from ~700,000 at the east edge of one zone to ~300,000 at the west edge of the next (= same place)

41. Albers (conic) projection
e.g. Yukon Albers:

42. BC Albers projection Central meridian: 126 W
First Standard Parallel: 50N
Second Standard Parallel: 58:30N
Latitude of projection origin 45N
False northing 0
False easting (1million m)

43. Summary: BC mapping coordinates
BC geomatics industry ‘recognises’:
1. Geographic – latitude / longitude – for data storage
2. Universal Transverse Mercator (UTM): zones local / regional
3. BC Albers for provincial data
View all 3 on: (imap) (use Internet Explorer-IE) [sometimes!]
View Geographic and Albers on (use IE / Active X)

44. Multiple coordinate systems
Georeferenced data can be recognized by the coordinates
e.g. Prince George
Geographic: 53°55′01″N 122°44′58″W
UTM zone 10: 512,000 5,972,000
BC Albers: ,200, ,000
GIS software today can overlay these by projecting ‘on the fly’
Where these would plot if not properly defined: y
To be able to do analysis, layers MUST be re-projected into the same projection and datum
e.g. UTM -> Albers
NAD 27 -> NAD83
UTM A G x