1. Nicholas A. Procopio, Ph.D, GISP
Environmental GIS
Nicholas A. Procopio, Ph.D, GISP

2. Ptolemy’s Projection
URL:

3. The Size and Shape of the Earth
Earth’s ellipsoid is about 1/300 off from the sphere
Clarke, Getting Started with Geographic Information Systems, prentice-Hall, 2001

4. Geodetic Datum
An estimate of the ellipsoid allows calculation of the elevation of every point on earth, including sea level, and is often called a datum

5. Geodetic Datum Definition
The National Geodectic Survey defines a geodetic datum as “a set of constants specifying the coordinate system used for geodetic control, i.e., for calculating the coordinates of points on the Earth”
Base reference level for the third dimension of elevation for the earth’s surface
Can depend on the ellipsoid, the earth model, and the definition of sea level
Recent datums use the center of the earth as a reference point rather than a point on the ground surface

6. Geodetic Datum
Hundreds of different datums have been used to frame position descriptions since the first estimates of the earth's size were made
Different nations and agencies use different datums as the basis for coordinate systems used to identify positions in geographic information systems, precise positioning systems, and navigation systems
Referencing geodetic coordinates to the wrong datum can result in position errors of hundreds of meters

7. Importance of Datums
Referencing geodetic coordinates to the wrong datum can result in position errors of hundreds of meters
Different nations and agencies use different datums as the basis for coordinate systems used to identify positions in geographic information systems, precise positioning systems, and navigation systems

8. Variations in Datums
Elevations referenced to a sphere, ellipsoid, geoid, or local sea level will all be different
Even horizontal locations may vary

9. Clarke Ellipsoid
In 1866, the US was mapped based on an ellipsoid measured by Sir Alexander Ross Clarke
Ellipsoid derived from measurements taken in Europe, Russia, India, South Africa, and Peru
The Clarke ellipsoid had an equatorial radius of 6,378,206.4 meters and a polar radius of 6,356,538.8 meters

10. Clarke Ellipsoid
In 1924, a simpler measure of 1/297 was adopted as the international standard
The US adopted the older values and became known as the North American Datum 1927 (NAD 1927)

11. NAD 1927
A horizontal control datum for the U.S. defined by a location and azimuth on the Clarke spheroid of 1866, with an origin at the survey station Meades Ranch, Kansas
Geoidal height at Meades Ranch was assumed to be zero

12. NAD 1983
Horizontal control datum for the U.S., Canada, Mexico, and Central America, based on a geocentric origin
Based on measurements taken in 1980 and accepted internationally as the geodetic reference system (GRS80 ellipsoid)

13. NAD 1928 vs. NAD 1983 NAD 27 based on Clarke Ellipsoid of 1866
NAD 27 computed with a single survey point (Meades Ranch) as the datum point
Difference about 300m in places
NAD 83 based on the Geodetic Reference System (GRS) of 1980
NAD 83 computed as a geocentric reference system with no datum point
Difference about 300m in places

14. World Geodetic System
U.S. military references an ellipsoid known as the GRS80 ellipsoid
Refined the values slightly in 1984 to make the world geodetic system (WGS84)
Significant because of GPS

15. Vertical Datums A level surface to which heights are referenced
National Geodetic Vertical Datum of 1929 (NGVD 29) - vertical control datum in the U.S.
NGVD 29 is defined by the observed (fixed) heights of MSL at 26 tide gauges and by the set of elevations of all benchmarks resulting from the adjustment

16. Vertical Datums
North American Vertical Datum of 1988 (NAVD 88) - vertical control datum est. in 1991 by the minimum-constraint adjustment of the Canadian-Mexican-U.S. leveling observations
Held fixed the height of the primary tidal benchmark at Father Point/Rimouski, Quebec, Canada.

17. Map Projections
Cartographer’s tool for taking curved surface of reality (the globe) and placing it on a flat surface such as a piece of paper or a computer screen

18. Projection Importance
Maps are a common source of input data for a GIS
It is not uncommon to input various maps into a GIS that are based on individual projections
In order to maintain accuracy of the input data, the input maps must be referenced from the same projection

19. Importance of Understanding Projections
When displaying various data, it is important that they are all referenced to the same coordinate system
Data displayed in varying coordinate systems will be located incorrectly relative to each other
Very important factor data accuracy is critical

20. Global Projections The most complete projection is the globe
Scale remains constant everywhere
Little to no distortion

21. Map Projections
A map projection is used to portray all or part of the round Earth on a flat surface
Every map projection will distort one or more of the following attributes:
Shape
Area
Distance
Direction

22. Distortion of Map Projections
No flat map can be simultaneously conformal (shape-preserving) and equal-area (area-preserving) in every point
In most projections, at least one specific region (usually the center of the map) suffers little or no distortion
If the represented region is small enough (and if necessary suitably translated in an oblique map), the projection choice may be of little importance

23. Distortion of Map Projections
Summary
Projections that minimize distortion of shape are referred to as conformal
Projections that minimize distortion of area are referred to as equal-area
Projections that minimize distortion of distance are referred to as equidistant
Projections that minimize distortion of direction are referred to as true-direction

24. Projection Distortion
Some projections minimize distortions in some of these properties at the expense of maximizing errors in others
Others attempt to only moderately distort all of these properties
Every projection has its own set of advantages and disadvantages

25. Types of Map Projections
Conformal
The scale of a map at any point on the map is the same in any direction
Meridians (longitude) and parallels (latitude) intersect at right angles
Shape is preserved locally on conformal maps
Found mostly for maps used for measuring directions, because they preserve directions around any given point
Examples - Lambert Conformal Conic & the Mercator projections

26. Lambert Conformal Projection
URL:

27. Mercator Projection
URL

28. Types of Projections Equivalent (Equal-Area)
Preserves the property of area
All parts of the earth’s surface are shown with the correct area
Examples – Albers and Sinusoidal

29. Albers Projection
URL;

30. Types of Map Projections
Equidistant
Portrays distances from the center of the projection to any other place on the map
Useful only if distances are critical
Infrequently used in GIS
Simple conic & azimuthal equidistant projections

31. The basis for three types of map projections—cylindrical, planar, and conic.
In each case a sheet of paper is wrapped around the Earth, and positions of objects on the Earth’s surface are projected onto the paper. The cylindrical projection is shown in the tangent case, with the paper touching the surface, but the planar and conic projections are shown in the secant case, where the paper cuts into the surface.
(Reproduced by permission of Peter H. Dana)

32. Examples of some common map projections
The Mercator projection is a tangent cylindrical type, shown here in its familiar equatorial aspect (cylinder wrapped around the equator).
The Lambert Conformal Conic projection is a secant conic type. In this instance, the cone onto which the surface was projected intersected the Earth along two lines of latitude: 20 North and 60 North.

33. (A) The so-called unprojected or Plate Carrée projection, a tangent cylindrical projection formed by using longitude as x and latitude as y.
(B) A comparison of three familiar projections of the United States. The Lambert Conformal Conic is the one most often encountered when the United States is projected alone and is the only one of the three to curve the parallels of latitude, including the northern border on the 49th Parallel.

34. Coordinate Systems

35. A Cartesian coordinate system, defining the location of the blue cross in terms of two measured distances from the origin, parallel to the two axes

36. Coordinate Systems
Relative location - references to locations given with respect to another place
Absolute location – a location in geographic space given with respect to a known origin and standard measurement system, such a coordinate system

37. Locations to Numbers
We must choose a standard way to encode locations on the earth
Locations on paper map can be given in map millimeters or inches starting at the lower left-hand corner 
Locations can then be given in (x, y) format – east-west followed by north-south 
Standard ways of listing coordinates are then called coordinate systems

38. Locations to Numbers
A system with all the necessary components to locate a position in 2- or 3-dimensional space; that is, an origin, a type of unit distance, and two axes
Many different coordinate systems, based on a variety of geodetic datums, units, projections, and reference systems in use today

39. Coordinate Systems Latitude and Longitude
Most common coordinate system
The Prime Meridian and the Equator are the reference planes used to define latitude and longitude
Hurvitz, P., University of Washington, CFR 250 Lecture Notes,

40. Latitude and Longitude
Start with a line connecting N and S pole through the point
The line is called a meridian
Latitude measures angle between the point and the equator along the meridian
Longitude measures the angle on the equatorial plane between the meridian of the point and the central meridian (through Greenwich, England)

41. Coordinate Systems Universal Transverse Mercator
Earth divided into pole-to-pole zones
Zones are each 6o of longitude wide
First zone starts at 180oW, at the international date line and runs east (180oW to 174oW)
Final zone (zone 60) runs from 174oE to the date line

42. The system of zones of the Universal Transverse Mercator system
The system of zones of the Universal Transverse Mercator system. The zones are identified at the top. Each zone is six degrees of longitude in width
(Reproduced by permission of Peter H. Dana)

43. Universal Transverse Mercator
URL:

44. UTM Zones for the United States
URL:

45. Northings and Eastings
Earth ~40,000,000 m around, thus northings in a zone go from 0 to 10 million meters
Southern hemisphere – 0 northing is the South Pole; 10 million meter northing at equator
Northern hemisphere – 0 northing at equator and 10 million meter northing at North Pole
Eastings
False origin established beyond the westerly limit of each zone (about half a degree)
Central meridian has an easting of 500,000m
Advantages:
Allows overlap between zones for mapping purposes
Gives all eastings positive numbers

46. UTM Zones
Clarke, Getting Started with Geographic Information Systems, prentice-Hall, 2001

47. UTM Advantages Frequently used Consistent for the globe
Provides a universal approach to accurate georeferencing

48. UTM Disadvantages Not used beyond 84oN & 80oS
Full georeference requires the zone number, easting and northing (unless the area of the data base falls completely within a zone)
Rectangular grid superimposed on zones defined by meridians causes axes on adjacent zones to be skewed with respect to each other
problems arise in working across zone boundaries
no simple mathematical relationship exists between coordinates of one zone and an adjacent zone

49. Coordinate Systems State Plane Coordinate System
Based on both the transverse Mercator & the Lambert conformal conic projections w/ units in feet (metric versions now as well)
Based upon a different map of each state
E-W elongated states drawn on a Lambert conformal conic projection
N-S elongated states drawn on a transverse Mercator projection
Except Alaska – Lambert conformal conic, transverse Mercator, & oblique Mercator

50. Coordinate Systems State Plane Coordinate System
Based upon a different map of each state
E-W elongated states drawn on a Lambert conformal conic projection
N-S elongated states drawn on a transverse Mercator projection
Except Alaska – Lambert conformal conic, transverse Mercator, & oblique Mercator

51. State Plane Coordinate System
URL:

52. Coordinate Systems State Plane Coordinate System
Each zone has an arbitrarily determined origin that is usually some given number of feet west and south of the southernmost point on the map
Means that the eastings and northings all come out as positive numbers
System then simply gives eastings and northings in feet

53. State Plane Advantages
Slightly more precise than UTM
Foot rather than meter scale
SPCS can be more accurate over small areas
SPCS is used by surveyors all over the U.S.

54. State Plane Disadvantages
Lack of universality
Problems may arise at the boundaries of projections

55. Military Grid Coordinate System
Adopted by U.S. Army in 1947 
Uses a lettering & numbering system 
West to east zones numbered from 1 to 60
Within zones, 8o strips of latitude lettered from C (80o to 72o S) to X (72o to 84o N)

56. Military Grid Coordinate System
Clarke, Getting Started with Geographic Information Systems, prentice-Hall, 2001

57. Set coordinates to Lat/Long

58. Set coordinates to State Plane

59. Set coordinates to UTM