1. Projections and Coordinate Systems, Continued
------Using GIS--
Introduction to GIS
Lecture 10:
Projections and Coordinate Systems, Continued
By Austin Troy

2. Datums Necessary for understanding coordinate systems
Introduction to GIS
Datums
Necessary for understanding coordinate systems
Definition: a three dimensional surface from which latitude, longitude and elevation are calculated
Datum roughly approximates the surface of the earth at some mean sea level value
Interesting fact: before satellites, datums were known to all be wrong, but geodesists agreed how to be wrong

3. Introduction to GIS
Datums vs. spheroids
A datum is essentially the model that is used to translate a spheroid into locations on the earth
A different datum is generally used for each spheroid.
Prior to satellites, datums were realized by referenced survey monuments (250,000+) with known position. These monuments were connected by a network of measurements enabling the computation of a position.
Based on that survey, a location was chosen where the spheroid meets the earth. That translation between model and reality is the datum

4. Introduction to GIS
Datums as a point
In the old days, determined the lat/long of a location by measuring it relative to a known reference point
That reference point was known in relation to another reference point.
The datum is essentially the “ultimate reference point.”
In the old days, they used pendulums, magnetometers, sextants, etc. to try to determine its precise location.
Eventually the whole system of linked reference and subrefence points came to be known as the datum.

5. Surface Based Datums These pre-satellite datums are surface based.
Introduction to GIS
Surface Based Datums
These pre-satellite datums are surface based.
A given datum has the spheroid meet the earth in a specified location somewhere.
Datum is most accurate near the touching point, less accurate as move away (remember, this is different from a projection surface because the ellipsoid is 3D)
Different surface datums can result in different lat/long values for the same location on the earth.
So, just giving lat and long is not enough!!!

6. Satellite Based Datums
Introduction to GIS
Satellite Based Datums
The errors of these datums stem from fact they used the surface of the earth as the reference point
With satellite measurements the center of the spheroid can be matched with the center of the earth.
This gives a spheroid that when used as a datum correctly maps the earth such that all Latitude/Longitude measurements from all maps created with that datum agree.

7. Introduction to GIS
Common Datums
Previously, the most common spheroid was Clarke 1866; the North American Datum of 1927 (NAD27) is based on that spheroid, and has its center in Kansas.
A newer, satellite measured spheroid is the World Geodetic System 1984 (WGS84) spheroid, which is more or less identical to Geodetic Reference System 1980 (GRS80). The GPS system uses WGS84.
NAD83 is based on these spheroids and is measured from the center of the spheroid, rather than the surface.
WGS84 is considered to be a datum and a spheroid

8. Spheroids and Datums Spheroids
Introduction to GIS
Spheroids and Datums
Spheroids
GRS Satellite derived - Ellipsoid Centered - NAD 1983
WGS Satellite derived - Ellipsoid Centered – WGS 1984
Clarke Initial point - origin Meads Ranch, Kansas - NAD 1927
Everest 1830 Initial point - India 1960
Additional WGS-84 based datums exist in other parts of the world, like the Geocentric Datum of Australia (GDA 94)
Major Datums
Click here for a listing of all world datums from Peter Dana

9. Datums NAD83 is superior to NAD 27 because: NAD83 is more accurate
Introduction to GIS
Datums
NAD83 is superior to NAD 27 because:
NAD83 is more accurate
NAD27 can result in a significant horizontal shift
The error in going from a surface-oriented datum to a spheroid-based datum is called datum shift
That error varies with location: 10 to 100 m in the cont. US, 400 m in Hawaii, 35 m in Vermont

10. Datums-things to remember
Introduction to GIS
Datums-things to remember
Lat/long coordinates calculated with one datum are valid only with reference to that datum.
This means those coordinates calculated with NAD 27 are in reference to a NAD 27 earth surface, not a NAD 83 earth surface.
To be viewed in NAD 83, their position must be recalculated and they will be given new coordinates.

11. Introduction to GIS
Coordinate Systems
Map projections, like we discussed in last lecture provide the means for viewing small-scale maps, such as maps of the world or a continent or country (1:1,000,000 or smaller)
Plane coordinate systems are typically used for much larger-scale mapping (1:100,000 or bigger)

12. Introduction to GIS
Coordinate Systems
Projections are designed to minimize distortions of the four properties we talked about, because as scale decreases, error increases
Coordinate systems are more about accurate positioning (relative and absolute positioning)
To maintain their accuracy, coordinate systems are generally divided into zones where each zone is based on a separate map projection

13. Introduction to GIS
Coordinate Systems
The four most commonly used coordinate systems in the US:
Universal Transverse Mercator (UTM) grid system
The Universal Polar Stereographic (UPS) grid system
State Plane Coordinate System (SPC)
And the Public Land Survey System (PLSS)

14. UTM Universal Transverse Mercator is a very common projection
Introduction to GIS
UTM
Universal Transverse Mercator is a very common projection
UTM is based on the Transverse Mercator projection (remember, that’s using a cylinder turned on its side)
It generally uses either the NAD 27 or NAD83 datums, so you will often see a layer as projected in “UTM83” or “UTM27”

15. Introduction to GIS
UTM
UTM divides the earth between 84°N and 80°S into 60 zones, each of which covers 6 degrees of longitude
Zone 1 begins at 180 ° W longitude.
World UTM zones

16. Introduction to GIS
UTM
US UTM zones

17. UTM Each UTM zone is projected separately
Introduction to GIS
UTM
Each UTM zone is projected separately
There is a false origin (zero point) in each zone
In the transverse Mercator projection, the “cylinder” touches at two secants, so there is a slight bulge in the middle, at the central meridian. This bulge is very very slight, so the scale factor is only .9996
The standard meridians, where the cylinder touches

18. Introduction to GIS
UTM
Because each zone is big, UTM can result in significant errors as get further away from the center of a zone, corresponding to the central line

19. UTM Scale factors are .9996 in the middle and 1 at the secants
Introduction to GIS
UTM
Scale factors are in the middle and 1 at the secants
Earth surface
.9996
Projection surface
Standard meridians
Central meridian

20. Introduction to GIS
UTM
In the N hemisphere, UTM coordinates are measured from a false origin at the equator and 500,000 meters west of the central meridian
In the S hemisphere, they are measured from a false origin 10,000,000 meters south of the equator and 500,000 meters west of the central meridian
Accuracy: 1 in 2,500

21. Introduction to GIS
UTM
UTM is used for large scale mapping applications the world over, when the unit of analysis is fairly small, like a state
For portraying large land units, like Alaska or the 48 states, a projection is usually used, like Albers Equal Area Conic

22. Introduction to GIS
UPS Grid
The Universal Polar Stereographic Grid system cover the polar areas and uses the stereographic projection, centered on the pole
Used to divide the polar area into a series of 100,000 meter squares

23. Introduction to GIS
SPC System
State Plane Coordinate System is one of the most common coordinate systems in use in the US
It was developed in the 1930s to record original land survey monument locations in the US
More accurate than UTM, with required accuracy of 1 part in 10,000
Hence, zones are much smaller—many states have two or more zones

24. Introduction to GIS
SPC System
Transverse Mercator projection is used for zones that have a north south access.
Lambert conformal conic is used for zones that are elongated in the east-west direction. Why?
Units of measurement are feet, which are measured from a false origin.
SPC maps are found based on both NAD 27 and NAD 83, like with UTM, but SPC 83 is in meters, while SPC 27 is in feet

25. Introduction to GIS
SPC System
Note how a conic projection is used here, since the errors indicate an east-west central line
Polygon errors-state plane

26. SPC System Many States have their own version of SPC
Introduction to GIS
SPC System
Many States have their own version of SPC
Vermont has the Vermont State Plane Coordinate System, which is in meters and based on NAD 83
In 1997, VSGI converted all their data from SPC 27 to SPC 83
Vermont uses Transverse Mercator because of its north-south orientation

27. Introduction to GIS
SPC System
Here are some State Plane zone maps

28. Introduction to GIS
SPC System
Here are some State Plane zone maps