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					Datums and Projections:
How to fit a globe onto a
2-dimensional surface
Overview
 Ellipsoid
 Spheroid
 Geoid
 Datum
 Projection
 Coordinate System
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
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
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
Commonly used datums

   Datum            Spheroid                  Region of use

                                     Canada, US, Atlantic/Pacific Islands,
    NAD 27           Clark 1866
                                              Central America

    NAD 83            GRS 1980          Canada, US, Central America

    WGS 84            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
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
Projections
  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
Other Projections
 Pseudocylindrical
 Unprojected or Geographic projection:
 Latitude/Longitude
 There are over 250 different projections!
 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
                       Cylindrical
                       projection




Shapes and angles
within small areas
are true (7.5’ Quad)
Distances only true
along equator
Conical:
can only represent one hemisphere
often used to represent areas with
east-west extent (US)
                               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
Azimuthal:
Often used to show air
route distances
Distances measured
from center are true
Distortion of other
properties increases
away from the center
point
                                                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
                         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
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)
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
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.
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
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
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
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 447825 (6 digits)
Northing 5432953 (7 digits)
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
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
Other systems
 Global 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)
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
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
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.

				
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