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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: EllipsoidAlso referred to as Spheroid, although Earth is not a sphere but is bulging at the equator and flattened at the polesFlattening is about 21.5 km difference between polar radius and equatorial radiusEllipsoid model necessary for accurate range and bearing calculation over long distances GPS navigationBest 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: DatumA mathematical model that describes the shape of the ellipsoidCan be described as a reference mapping surfaceDefines 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 measurementsDatums are the basis for coordinate systemsLarge diversity of datums due to high precision of GPSAssigning the wrong datum to a coordinate system may result in errors of hundreds of meters
Commonly used datums
Datum Spheroid Region of use
NAD 27 Clark 1866Canada, US, Atlantic/Pacific Islands,
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
ProjectionMethod of representing data located on a curved surface onto a flat planeAll projections involve some degree of distortion of:
DistanceDirectionScaleAreaShape
Determine which parameter is importantProjections 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!
Cylindrical:
used for entire world
parallels and meridians form straight lines
Tangency: only one point touches surface
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)
Secant at 2 standard parallels
Distorts scale and distance, except along standard parallels
Areas are proportional
Directions are true in limited areas
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
Azimuthal:
Often used to show air route distances
Distances measured from center are true
Distortion of other properties increases away from the center point
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
Orthographic:
Used for perspective views of hemispheres
Area and shape are distorted
Distances true along equator and parallels
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 RelationshipsConformality
Scale is the same in every directionParallels and meridians intersect at right anglesShapes and angles are preservedUseful for large scale mappingExamples: Mercator, Lambert Conformal Conic
EquivalenceMap area proportional to area on the earthShapes are distortedIdeal for showing regional distribution of geographic phenomena (population density, per capita income)Examples: Albers Conic Equal Area, Lambert Azimuthal Equal Area, Peters, Mollweide)
Mathematical RelationshipsEquidistance
Scale is preserved Parallels are equidistantly placedUsed for measuring bearings and distances and for representing small areas without scale distortionLittle angular distortionGood compromise between conformality and equivalenceUsed in atlases as base for reference maps of countriesExamples: Equidistant Conic, Azimuthal Equidistant
CompromiseCompromise between conformality, equivalence and equidistanceExample: 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 spaceNeeded to measure distance and area on a mapRectangular grid systems were used as early as 270 ADCan 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 systemDeveloped in the ’30s, based on NAD27Provide local reference systems tied to a national datumUnits are feetSome larger states have several zonesProjections used vary depending on east-west or north-south extent of state
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 collarUTM tic marks are blue and 1000 m apartSPCS tics are black, extend out beyond the map collar, and are 10,000 ft apart
Which tic marks belong to which grid?
Other systems
Global systemsMilitary 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
MetadataData about dataMay be missing
HeaderOpened with text editor
SoftwareSome allow it, some don’t
ComparisonOverlay may show discrepanciesIf 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, regionLocation: polar, equatorialAxis: N-S, E-W
Select Lambert Conformal Conic for conformal accuracy and Albers Equal Area for areal accuracy for E-W axis in temperate zonesSelect UTM for conformal accuracy for N-S axisSelect 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.