1. Datums and Projections: How to fit a globe onto a 2-dimensional surface

2. Overview
Ellipsoid
Spheroid
Geoid
Datum
Projection
Coordinate System

3. Definitions: Ellipsoid
Also referred to as Spheroid, although Earth is not a sphere but is bulging at the equator and flattened at the poles
Flattening is about 21.5 km difference between polar radius and equatorial radius
Ellipsoid model necessary for accurate range and bearing calculation over long distances  GPS navigation
Best models represent shape of the earth over a smoothed surface to within 100 meters

6. WGS 84 Geoid defines geoid heights for the entire earth
Geoid: the true 3-D shape of the earth considered as a mean sea level extended continuously through the continents
Approximates mean sea level
WGS 84 Geoid defines geoid heights for the entire earth

8. Definition: Datum
A mathematical model that describes the shape of the ellipsoid
Can be described as a reference mapping surface
Defines the size and shape of the earth and the origin and orientation of the coordinate system used.
There are datums for different parts of the earth based on different measurements
Datums are the basis for coordinate systems
Large diversity of datums due to high precision of GPS
Assigning the wrong datum to a coordinate system may result in errors of hundreds of meters

9. Commonly used datums Datum Spheroid Region of use
NAD 27
Clark 1866
Canada, US, Atlantic/Pacific Islands, Central America
NAD 83
GRS 1980
Canada, US, Central America
WGS 84
Worldwide
GPS is based on WGS 84 system
GRS 1980 and WGS 84 define the earth’s shape by measuring and triangulating from an outside perspective, origin is earth’s center of mass

10. Projection
Method of representing data located on a curved surface onto a flat plane
All projections involve some degree of distortion of:
Distance
Direction
Scale
Area
Shape
Determine which parameter is important
Projections can be used with different datums

11. Projections Planar or azimuthal Conic Cylindrical
The earth is “projected” from an imaginary light source in its center onto a surface, typically a plate, cone, or cylinder.
Planar or azimuthal
Conic
Cylindrical

12. Other Projections Pseudocylindrical
Unprojected or Geographic projection: Latitude/Longitude
There are over 250 different projections!

13. Cylindrical: used for entire world
Tangency: only one point touches surface
Cylindrical:
used for entire world
parallels and meridians form straight lines
Secancy: projection surface cuts through globe, this reduces distortion of larger land areas

14. Cylindrical projection
Shapes and angles within small areas are true (7.5’ Quad)
Distances only true along equator

15. Conical: can only represent one hemisphere
often used to represent areas with east-west extent (US)

16. Lambert is used in State Plane Coordinate System
Albers is used by USGS for state maps and all US maps of 1:2,500,000 or smaller
96 degrees W is central meridian
Lambert is used in State Plane Coordinate System
Secant at 2 standard parallels
Distorts scale and distance, except along standard parallels
Areas are proportional
Directions are true in limited areas

17. Azimuthal: Often used to show air route distances
Distances measured from center are true
Distortion of other properties increases away from the center point

18. Orthographic:
Used for perspective views of hemispheres
Area and shape are distorted
Distances true along equator and parallels
Lambert:
Specific purpose of maintaining equal area
Useful for areas extending equally in all directions from center (Asia, Atlantic Ocean)
Areas are in true proportion
Direction true only from center point
Scale decreases from center point

19. Scale only true along standard parallel of 40:44 N and 40:44 S
Pseudocylindrical:
Used for world maps
Straight and parallel latitude lines, equally spaced meridians
Other meridians are curves
Scale only true along standard parallel of 40:44 N and 40:44 S
Robinson is compromise between conformality, equivalence and equidistance

20. Mathematical Relationships
Conformality
Scale is the same in every direction
Parallels and meridians intersect at right angles
Shapes and angles are preserved
Useful for large scale mapping
Examples: Mercator, Lambert Conformal Conic
Equivalence
Map area proportional to area on the earth
Shapes are distorted
Ideal for showing regional distribution of geographic phenomena (population density, per capita income)
Examples: Albers Conic Equal Area, Lambert Azimuthal Equal Area, Peters, Mollweide)

21. Mathematical Relationships
Equidistance
Scale is preserved
Parallels are equidistantly placed
Used for measuring bearings and distances and for representing small areas without scale distortion
Little angular distortion
Good compromise between conformality and equivalence
Used in atlases as base for reference maps of countries
Examples: Equidistant Conic, Azimuthal Equidistant
Compromise
Compromise between conformality, equivalence and equidistance
Example: Robinson

23. Projections and Datums
Projections and datums are linked
The datum forms the reference for the projection, so...
Maps in the same projection but different datums will not overlay correctly
Tens to hundreds of meters
Maps in the same datum but different projections will not overlay correctly
Hundreds to thousands of meters.

24. Coordinate System
A system that represents points in 2- and 3- dimensional space
Needed to measure distance and area on a map
Rectangular grid systems were used as early as 270 AD
Can be divided into global and local systems

25. Geographic coordinate system
Global system
Prime meridian and equator are the reference planes to define spherical coordinates measured in latitude and longitude
Measured in either degrees, minutes, seconds, or decimal degrees (dd)
Often used over large areas of the globe
Distance between degrees latitude is fairly constant over the earth
1 degree longitude is 111 km at equator, and 19 km at 80 degrees North

26. Universal Transverse Mercator
Global system
Mostly used between 80 degrees south to 84 degrees north latitude
Divided into UTM zones, which are 6 degrees wide (longitudinal strips)
Units are meters

27. Eastings are measured from central meridian (with 500 km false easting for positive coordinates) Northing measured from the equator (with 10,000 km false northing)
Easting (6 digits) Northing (7 digits)

28. State Plane Coordinate System
Local system
Developed in the ’30s, based on NAD27
Provide local reference systems tied to a national datum
Units are feet
Some larger states have several zones
Projections used vary depending on east-west or north-south extent of state

31. Which tic marks belong to which grid?
Each of the three coordinate systems (Lat/Long, UTM, and SPCS) have their own set of tick marks on 7½ minute quads:
Lat/Long tics are black and extend in from the map collar
UTM tic marks are blue and 1000 m apart
SPCS tics are black, extend out beyond the map collar, and are 10,000 ft apart

32. Other systems Global systems Local systems
Military grid reference system (MGRS)
World geographic reference system (GEOREF)
Local systems
Universal polar stereographic (UPS)
National grid systems
Public land rectangular surveys (township and sections)

33. Determining datum or projection for existing data
Metadata
Data about data
May be missing
Header
Opened with text editor
Software
Some allow it, some don’t
Comparison
Overlay may show discrepancies
If locations are approx. 200 m apart N-S and slightly E-W, southern data is in NAD27 and northern in NAD83

34. Selecting Datums and Projections
Consider the following:
Extent: world, continent, region
Location: polar, equatorial
Axis: N-S, E-W
Select Lambert Conformal Conic for conformal accuracy and Albers Equal Area for areal accuracy for E-W axis in temperate zones
Select UTM for conformal accuracy for N-S axis
Select Lambert Azimuthal for areal accuracy for areas with equal extent in all directions
Often the base layer determines your projections

35. Summary
There are very significant differences between datums, coordinate systems and projections,
The correct datum, coordinate system and projection is especially crucial when matching one spatial dataset with another spatial dataset.