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

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Datums and ProjectionsHow to fit a globe onto a
2-dimensional surface
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Overview

• Ellipsoid
• Spheroid
• Geoid
• Datum
• Projection
• Coordinate System

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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

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• 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

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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

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Commonly used datums
GPS is based on WGS 84 system GRS 1980 and
WGS 84 define the earths shape by measuring and
triangulating from an outside perspective, origin
is earths center of mass
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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

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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
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Other Projections

• Pseudocylindrical
• Unprojected or Geographic projection
  Latitude/Longitude
• There are over 250 different projections!

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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
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Cylindrical projection
Shapes and angles within small areas are true
(7.5 Quad) Distances only true along equator
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Conical can only represent one hemisphere often
used to represent areas with east-west extent
(US)
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Albers is used by USGS for state maps and all US
maps of 12,500,000 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
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Azimuthal Often used to show air route
distances Distances measured from center are
true Distortion of other properties increases
away from the center point
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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
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Pseudocylindrical Used for world maps Straight
and parallel latitude lines, equally spaced
meridians Other meridians are curves
Scale only true along standard parallel of 4044
N and 4044 S
Robinson is compromise between conformality,
equivalence and equidistance
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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)

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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

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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.

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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

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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

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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

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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)
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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

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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

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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)

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Determining datum or projection for existing data

• Metadata
• Data about data
• May be missing
• Header
• Opened with text editor
• Software
• Some allow it, some dont
• 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

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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

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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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