1. Map Projections and Georeferencing

2. © Paul Bolstad, GIS Fundamentals
Coordinate Systems
A geographical coordinate system uses a three-dimensional spherical surface to define locations on the earth.
Divides space into orderly structure of locations.
Two types: cartesian and angular (spherical)
© Paul Bolstad, GIS Fundamentals

3. Parallels and Meridians
Meridians are great circles of constant longitude
Example is the prime meridian
Parallels are circles of constant latitude
Example is the equator
latitude (φ): angular distance from equator
longitude (λ): angular distance from standard meridian
St. Louis 38° 39' N 90° 38' W
New York 40° 47' N 73° 58' W
Los Angeles 34° 3' N 118° 14' W
Rome 41° 48' N  12° 36' E
Sydney 33° 52' S  151° 12' E

4. Earth’s Shape
The shape of earth can be approximated as a sphere or spheroid. Most often it is modeled as a spheriod. a b
WGS 84 (World Geodetic System of 1984)
a = km
b = km
flattening = 1/ =

5. Earth’s Expanding Waistline
From the Chronicle of Higher Education Jan 17, 2003

6. Datum
While a spheroid approximates the shape of the earth, a datum defines the position of the ellipsoid relative to the center of the Earth
The datum provides a frame of reference for measuring locations on the surface of the Earth
A datum is chosen to align a spheroid to closely fit the Earth’s surface in a particular area

7. Datums
It is important to ensure that the datum of a dataset matches with the datum setting of your GIS and with other data sets being used.

8. From one two-dimensional coordinate system to another
Map Transformations
From one two-dimensional coordinate system to another

9. Distance Calculations
The distance between two points on a flat plane can be calculated as the square of the coordinate differences summed. 1 2 1 2
Great circle distance is the distance of the arc formed by the plane intersecting the two points and the center of the sphere.
Radius = 6378 km

10. Map Projections: Flattening the Earth
A map projection
is the orderly transfer of positions of places on the surface of the earth to corresponding points on a flat map.
is the systematic arrangement of the earth’s parallels and meridians onto a plane surface.
uses mathematical formulas to relate spherical coordinates on the globe to flat, planar coordinates.

11. Distortion All projections introduce distortions in the map.
Some projections minimize distortions in some of these properties at the expense of maximizing errors in others.
Some projections are attempts to only moderately distort all of these properties.
The map properties that are distorted during projection are:
On Earth
On Map
Distance (length)
Angle
Area
Scale
Shape

12. Projection Types Three general types of projections:
Equal area – the ratio of areas on the earth and on the map are constant. Shape, angle, and scale are distorted.
Conformal – the shape of any small surface of the map is preserved in its original form. If meridians and parallel lines are at 90-degree angles, then angles are also preserved.
Equidistant - preserve distances between certain points. Scale is not maintained correctly, however, typically one or more lines has its scale maintained.

13. Conceptualizing Projections
Projections can be conceptualized by the placement of paper on or around a globe.
The “location” of the paper is a factor in defining the projection. The paper can be either tangent or secant.

14. Azimuthal or Plane Projection
With Azimuthal projections, the spherical (globe) grid is projected onto a flat plane, thus it is also called a plane projection.
Planar projections are used most often for polar regions
Lambert Azimuthal Equal-area
Polar
Equatorial

15. Cylindrical Projections
Equator is typically the line of tangency
Meridians are of equal space, lines of latitude increases toward poles
Conformal and displays true direction along straight lines
Transverse projections use meridian lines as tangent point, therefore, North/South lines are preserved
Cylindrical projections are typically used to represent the entire world.
Mercator is most common cylindrical projection
x = λR
y = 2R tan (φ /2)

16. Conic Projections
Conic Projection - tangent to the globe along a line of latitude
distortion increases away from the standard parallel
The normal aspect is the north or south pole where the axis of the cone (the point) coincides with the pole.
Conic projections can only represent one hemisphere, or a portion of one hemisphere, for the cone does not extend far beyond the center of the sphere.
Conic projections are often used to project areas that have a greater east-west extent than north-south, such as the United States.
Secant Conic projections have two standard parallels which results in less distortion

17. Projection Aspects Normal
The standard aspect for a projection. For Equatorial Cylindrical projections the normal is equatorial. For Azimuthal projections normal is polar.
Transverse
The transverse aspect places the projection surface 90 degrees from the normal position, e.g., for a Polar Azimuthal projection the equator would be the transverse aspect, while for an Equatorial Cylindrical projection the poles would be the transverse aspect.
Oblique
The oblique aspect of a projection surface is placed above or on any position between, but not including, the equator and the poles. It may be centered on a parallel or on a meridian.

18. The “Unprojected” Projection
Assigns latitude to the y axis and longitude to the x axis
A type of cylindrical projection
Is neither conformal nor equal area
As latitude increases, lines of longitude are much closer together on the Earth, but are the same distance apart on the projection
Also known as the Plate Carrée or Cylindrical Equidistant Projection or
Geographic Projection

19. Comparing Projections

20. Pseudocylindrical Projections
Bonne

21. Universal Transverse Mercator (UTM)
Implemented as an internationally standard coordinate system
Initially devised as a military standard
Uses a system of 60 zones
Maximum distortion is 0.04%
Transverse Mercator because the cylinder is wrapped around the Poles, not the Equator
Zones are each six degrees of longitude numbered from west to east

22. Military Grid Coordinate System
The Military grid divides the UTM coordinate system into 6X8 degree cells and subdivides each of those cells with lettering and a number system

23. State Plane Coordinates
Defined in the US by each state
Some states use multiple zones
Several different types of projections are used by the system
Provides less distortion than UTM
Preferred for applications needing very high accuracy, such as surveying

24. Time Zones Greenwich Mean Time (GMT)
Each Time Zone is measured relative to Greenwich, England.
St. Louis is GMT -6
(GMT -5 during daylight savings [Apr-Oct])

25. Non-projected Georeferencing
Is essential in GIS, since all information must be linked to the Earth’s surface
The method of georeferencing must be:
Unique, linking information to exactly one location
Shared, so different users understand the meaning of a georeference
Persistent through time, so today’s georeferences are still meaningful tomorrow
A georeference may be unique only within a defined domain, not globally
There are many instances of Springfield in the U.S., but only one in any state
The meaning of a reference to London may depend on context, since there are smaller Londons in several parts of the world

26. Georeferences as Measurements
Some georeferences are metric
They define location using measures of distance from fixed places
E.g., distance from the Equator or from the Greenwich Meridian
Others are based on ordering
For example street addresses in most parts of the world order houses along streets
Others are only nominal
Placenames do not involve ordering or measuring

27. Converting Georeferences
GIS applications often require conversion of projections and ellipsoids
These are standard functions in popular GIS packages
Street addresses must be converted to coordinates for mapping and analysis
Using geocoding functions
Placenames can be converted to coordinates using gazetteers
Gazetteers provide information about geographical areas or locations using place names and can be linked to coordinate systems .

28. Map Projection References
Understanding Map Projections
Melita Kennedy and Steve Kopp
Environmental Systems Research Institute, Inc
2000
Introduction to Map Projections (
Peter H. Dana
Department of Geography
University of Texas at Austin
Map Projections (
Carlos A. Furuti
Prógonos Consulting

29. Summary
Projections are needed to represent 3-D surface on a flat plane
There are hundreds of projections – choose the one that fits your mapping purpose best
- preserve distance
- preserve shape
- preserve direction
Choosing a coordinate system is also important (if you have are mapping a dataset, you should know it’s projection and coordinate system)
Different coordinate systems use different datums in order to approximate the shape of the earth.

30. A geodatabase has three primary components feature classes
ArcGIS Geodatabases
A geodatabase has three primary components
feature classes
feature datasets
nonspatial tables.
A feature class is a collection of features that share the same geometry type (point, line, or polygon) and spatial reference.
A feature dataset is a collection of feature classes. All the feature classes in a feature dataset must have the same spatial reference.
A nonspatial table contains attribute data that can be associated with feature classes.
All three components are created and managed in ArcCatalog.
Vector data is stored in the database, while raster data is referenced.

32. Relational Database Example #1

33. Data Needed this Week Folders: GIStutorial\MaricopaCounty
Gistutorial\RochesterNY
Gistutorial\World
Gistutorial\AlleghenyCounty
Files:
Tutorial4-2.mxd