1. Introduction to GIS
Map Projections

3. Earth’s shape Surprise! It’s not a perfect sphere Earth is an…
Oblate spheroid
Oblate ellipsoid
Geoidal
Earth’s shape

4. Geographic Coordinate System (GCS)

5. GCS An unprojected coordinate system
uses latitude and longitude to define the locations of points on a sphere or spheroid
Covers entire earth with one system and a single origin
Used when a single coordinate system is needed for entire earth
Since latitude and longitude are angular measurements they are not suitable for measuring distances.
GCS

6. GCS LATITUDE LONGITUDE ORIGIN the equator is the origin for latitude
1 degree of latitude is ALWAYS 69 miles (111km)
LONGITUDE
Greenwich, England, is the origin for longitude.
1 degree of longitude is 69 miles (111km) at the equator
1 degree of longitude is 0 miles at the poles
ORIGIN
single origin is off the coast of Africa
GCS

8. Latitude and longitude are angles expressed in degrees, minutes, and seconds
1 degree = 60 minutes
1 minute = 60 seconds
125°30’ 45’’
= / /60/60 =
It’s about the angles

10. A datum is a mathematical representation (model, a set of reference points) of the shape of the Earth’s surface
It serves as the reference or base for calculating the Geographic Coordinate of a location.
a datum is a set of reference points on the earth's surface against which position measurements are made, and (often) an associated model of the shape of the earth (ellipsoid) to define a geographic coordinate system.
Datum for GCS

11. Datum for GCS Two kinds of datum:
A global/geocentric datum: is centered on the earth's center of mass.
World Geodetic System of 1984 (WGS 84).
A local datum: is slightly offset to a convenient location in order to accommodate a particular region of study.
The North American Datum of 1927 (NAD27)
The North American Datum of 1983 (NAD83)
Datum for GCS

12. A datum is a mathematical representation of the shape of the Earth’s surface.
A datum is defined by a spheroid, which approximates the shape of the Earth and the spheroid’s position relative to the center of the Earth.
There are many spheroids that represent the shape of the Earth and many more datums based on them.
A horizontal datum provides a frame of reference for measuring locations on the surface of the Earth.
A local datum aligns its spheroid to closely fit the Earth’s surface in a particular area, its origin point is located on the surface of the Earth.
Datum

13. North American Datum of 1927 (NAD27) is a datum based on the Clarke ellipsoid of 1866.  The reference or base station is located at Meades Ranch in Kansas. There are over 50,000 surveying monuments throughout the US and these have served as starting points for more local surveying and mapping efforts.  Use of this datum is gradually being replaced by the North American Datum of 1983.
North American Datum of 1983 (NAD83) is an earth-centered datum based on the Geodetic Reference System of The size and shape of the earth was determined through measurements made by satellites and other sophisticated electronic equipment; the measurements accurately represent the earth to within two meters. 
North American Datums

14. Projections

15. Projection is the process that transforms three-dimensional space onto a two-dimensional map.
Projections

16. Map Projections a Map Projection Scale change Map Coordinates
this is what gets us flat
Scale change
zoom into the area of interest
Map Coordinates
this helps us locate things on the map
Map Projections

17. Projection is the process that transforms three-dimensional space onto a two-dimensional map.
Projections are done through mathematical principles of geometry and trigonometry that recreate the physical projection of light through the globe
What is the goal?
To minimize the distorting effects of projections on the true representation of spatial phenomena
Projections

18. ANY projected flat map distorts reality by compromising on one of the following:
Shape [S]
Area [A]
Distance [D]
Direction [D]
This makes geographers and GIS experts very [SADD]…
There are names for the different classes of projections that minimize distortion. Those that minimize distortion:
in shape: conformal.
in distance: equidistant.
in area: equal-area.
in direction: true-direction.
Projections

19. Shapes vs Sizes

20. Distortions

21. Equi-rectangular

22. Peters

23. Mercator

24. “A set of techniques developed by cartographers to depict with reasonable accuracy the spherical earth in two-dimensional media.”
Cylindrical (regular or transverse)
conic
azimuthal
The Flat Surface

25. The Mercator projection is also known as the cylindricalprojection and is shown in the illustration here. Note that it is as if a cylindrical piece of paper is wrapped around the globe. If a light bulb were inside the globe, the outlines of the continents and latitude and longitude lines will be "projected" onto the paper. You would then trace these lines and create the map when you open up the paper. It is important to see that where the paper is in contact with the globe the transfer of information to the map is very accurate. As the distance between the paper and the globe increases, the amount of distortion in the shapes of the landmasses also increases. Therefore, with the Mercator projection, the map is most accurate at the equator and the worst at the poles. Look how excessively large Antarctica is!
parallels and meridians are perpendicular on this map
best accuracy at equator, worst representation at the poles
map is used in navigation: straight lines on this map are rhumb lines - lines of constant compass bearing (not the shortest route). Rhumb lines are also known as loxodromes.
Great circle routes (shortest route between two points) are curved on this map.
Mercator

26. The Polar Projection (also known as the Plane or Gnomonic Projection)
The Polar Projection (also known as the Plane or Gnomonic Projection).  Produced by placing our piece of paper on either pole.
parallels are shown as circles around the pole
meridians are straight lines radiating from the pole like the spokes of a wheel
distorts near the equator
only shows one hemisphere at a time so if you want to show the entire world, you would need two maps
Great circle routes on this map are straight lines, rhumb lines are curved.
Polar

27. The Conic Projection is centered on the mid-latitudes so there is least distortion there. Make a cone and place it on the globe.
parallels are curved
meridians appear straight and converge towards the pole
good map projection if you are going to show features in the mid-latitudes, like the United States. 
Conic

28. Coordinate Systems…

29. Different coordinate systems have different origins (0,0)
Different coordinate systems cover all or only part of the earth
Different coordinate systems have different units of measurement (e.g. feet, meters, degrees)
A coordinate system is a means for identifying a point on the earth on a planimetric map.
Coordinate Systems

30. 3 Main Coordinate Systems
Geographic Coordinate System (GCS);
map units in decimal degrees.
Universal Transverse Mercator (UTM);
map units in meters.
State Plane Coordinate System (SPCS);
preferred map units in U.S. Survey Foot.
3 Main Coordinate Systems

31. UNIVERSAL TRANSVERSE MERCATOR (UTM)

32. UTM provides georeferencing at high levels of precision for the entire globe
covers the entire earth in 60 zones, each 6 degrees wide
commonly used by environmental scientists, the military and other professions who need to work at the local level but also need their maps to coordinate with other areas on earth.
80 degrees S to 84 degrees N used due to deviation on the two ends
UTM

34. UTM (cont’d) 10 zones (10-19) cover the continental US
Each 6 degree zone is split in two: North Zone and South Zone
Origin (0,0) is at South West of each zone (avoids negative coordinates
UTM is measured in meters, i.e. how many meters east and north from origin?
UTM (cont’d)

35. UTM Zones in California

36. State Plane Coordinate System (SPCS)

37. SPCS developed by the US Coast Guard and Geodetic Survey
used only in the US
about 120 zones to cover the entire United States
each zone has its own coordinate system
similar coordinate systems are used around the world
SPCS

38. State Plane Coordinate System (SPCS)
Wisconsin (left) has 3 zones
each zone has its origin (0,0) in the south west corner so that all coordinates in the zone have positive values
SPCS is measured in feet
a point is located based on how many feet east and north or origin
zones are defined by political boundaries
State Plane Coordinate System (SPCS)

39. State Planes in California
CALIFORNIA ZONE I FIPSZONE: UTM ZONE: 10
DEL NORTE, HUMBOLDT, LASSEN, MODOC, PLUMAS, SHASTA, SISKIYOU, TEHAMA, TRINITY
CALIFORNIA ZONE II FIPSZONE: 0402 UTM ZONES: 10 & 11
ALPINE, AMADOR, BUTTE, COLUSA, EL DORADO, GLENN, LAKE, MENDOCINO, NAPA NEVADA, PLACER, SACRAMENTO, SIERRA, SOLANO, SONOMA, SUTTER, YOLO, YUBA
CALIFORNIA ZONE III FIPSZONE: 0403 UTM ZONES: 10 & 11
ALAMEDA, CALAVERAS, CONTRA COSTA, MADERA, MARIN, MARIPOSA, MERCED, MONO, SAN FRANCISCO SAN JOAQUIN, SAN MATEO, SANTA CLARA, SANTA CRUZ, STANISLAUS, TUOLUMNE
CALIFORNIA ZONE IV FIPSZONE: 0404 UTM ZONES: 10 & 11
FRESNO, INYO, KINGS, MONTEREY, SAN BENITO, TULARE
CALIFORNIA ZONE V FIPSZONE: 0405 UTM ZONES: 10 & 11
KERN, LOS ANGELES, SAN BERNARDINO, SAN LUIS OBISPO, SANTA BARBARA, VENTURA
CALIFORNIA ZONE VI FIPSZONE: 0406 UTM ZONE: 11
IMPERIAL, ORANGE, RIVERSIDE, SAN DIEGO
State Planes in California

41. UTM vs State Plane Both based on zones
UTM zones follow lines of latitude and longitude
state plane zones generally follow political boundaries
UTM not as accurate as SPCS
UTM vs State Plane

42. Who cares? I’m not a cartographer, I’m a planner!
ArcGIS…

43. ArcGIS Everything in ArcGIS is based on an “X” and a “Y”
If your data does not have a defined projection, you can “define” it (but you need to know what it is!)
If your data has a different projection than your other data, you need to “project” it to one common projection
In other words… one project = one projection
ArcGIS

45. ArcGIS The “Define Projection” tool: The “Feature/Project” tool:
Assign the correct projection to the data layer
ArcMap, select Catalog window > Toolboxes > System Toolboxes
The “Feature/Project” tool:
Creates a NEW copy of the data in the coordinate system you have selected
ArcGIS

46. On-the-fly projection eliminates the need to change the projection of the data in ArcGIS
A data frame’s projection can be pre-set by the user or ArcMap will default to the projection of the first layer added
If re-projection or projection of the data is needed, ArcToolbox provides the tools
Projections in ArcGIS

48. If you don't believe any of this…

49. Join the Flat Earth Society !

50. Recommended reading…

51. DeMers, Michael N., Fundamentals of Geographic Information Systems. New York: John Wiley & Sons, Inc.
Krygier, John and Wood, Denis, Making Maps. New York: The Guilford Press.
Georeferencing, Projections. Retrieved from
Maher, Margaret M., Lining Up Data in ArcGIS. Redlands, California: ESRI PRESS.
Sources