Geo referencing & Map projections
2009/2010 CGI GIRS ©
Overview •Georeference Geo information process
• systems • ellipsoid / geoid • datums / reference surfaces • sea level •Map projections
• properties • projection types • UTM • coordinate systems Geo reference systems Geo Reference Systems
earth something to refer to coordinates
physical reality< relation > geometrical abstractions Garden maintenance objects need a reference
Y
X History
Local (for at least 21 centuries ) National (since mid 19 th century (NL) ) Continental (since mid 20 th century ) Global (since 1970 / GPS, 1989 ) Geo referencing (in brief)
Georeferencing: Geometrically describing locations on the earth surface by means of earth fixed coordinates Geographic coordinate systems
Location on the earth in Longitude and Latitude (e.g. 51°58' N 5°40' E )
Latitude parallels North South Longitude meridians East West
Its not based on a Cartesian plane but on location on the earth surface (spherical coordinate system) Latitude Longitude
Geographic coordinates
Angular measures Degrees minutes second o Lat 51 ’ 59’ 14.5134” o Lon 5 ’ 39’ 54.9936” Decimal Degrees (DD) Lat 51.98736451427008 Lon 5.665276050567627 Model of the earth Spheroid and datum
Spheroid (ellipsoid) approximates the shape of the earth Geodetic datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth. Datum WGS 1984 (world application) Horizontal and vertical models
One location :
Horizontal datum: (ellipsoid ) for position ‘egg’ mathematical model
Vertical datum: (geoid ) for elevation physical model ‘potato’ Rotating potato Mean gravity level at mean sea level Tom & Jerry Geoid undulation (global) http://www.csr.utexas.edu/grace/gravity/gravity_definition.html
–120 m 0 m 80 m
Two different abstract models
One location , but yet:
Two different positions
Two different ‘heights’: orthometric (related to geoid) = H geodetic (related to ellipsoid) = h = H+N geoid undulation = N (‘potato minus egg’)
Map ‘Jumping’ Difference in ‘Mean Sea Levels’ 2
Netherlands — Belgium
Average tide Average low tide IJmuiden (North Oostende (Dover Sea) Channel)
A visible elevation jump of +2.34 m from Netherlands to Belgium ???? Difference in ‘Mean Sea Levels’
Differences between Height Reference Levels within Europe Many different ellipsoids (a small selection)
Datum: mathematical model of the Earth to serve as reference
Ellipsoid Major axis. Unit of Flattening name a measure 1/f
Clarke 61866 378 206.4 294.978 m 698 2 Bessel 61841 377 397.155 299.152 m 812 85 Everest 1830 (India) 6 377 276.3458 300.801 m 7 GRS80 (New Intern’l) 6 378 137 298.257 m 222 100 882 7 WGS84 6 378 137 298.257 m 223 563
Various ellipsoids; selection adopted from M. Hooijberg, Practical Geodesy, 1997, p35 37 Question
Is it possible to have different coordinates for the same location? Examples (Bellingham, Washington)
NAD 1927 Lat 122.466903686523 Lon 48.7440490722656 NAD 1983 Lat 122.46818353793 Lon 48.7438798543649 WGS 1984 Lat 122.46818353793 Lon 48.7438798534299 Projections
Attemp to portray (a portion of) the earth on a flat surface From spherical coordinate system to a planar (Cartesian) coordinate system.
Always lead to distortions Map projection 16 th century Waldseemuller Type of projection (projection surface) Projection plane Planar
Cylindrical
Conical Map projections
Mathematical projections (abstract) from an ellipsoid to a map plane
Numerous projections Projection plane always flat Cartesian coordinates Countries uses own projections Always purposely designed
Type of map projections Grouping by preserved properties:
conformal : preserves local angles and shapes – global equivalent : represents areas in correct relative size – global equidistant : maintains consistency of scale for certain distances local azimuthal : retains certain accurate directions – local … but never conformal and equivalent Properties
Tissot indicatrices: to show the distortion of parts of a map Cylindrical projections
Conformal
Equidistant
Equivalent Cylindrical projections
Equal area
conformal at Equator
conformal at higher latitudes (N & S) What is the projection type? What is the projection type? What is the projection type? Conical projections ... … defined for USA
Conformal ( Lambert ) Equal area ( Albers ) Equidistant ... … a confusing concept , because:
means “equal in distance ” distance on earth surface equal to distance in map projection plane (scale 1:1) but only applied to specific directions “all” directions to a single point , or “all” perpendiculars to a single line
An equidistant projection has NO uniform scale Great Circle (azimuthal) Great Circle (equidistance) Dutch map grid
Datum point: Amersfoort Bessel 1841 ellipsoid Projection: Planar Conformal Azimuthal False origin: X = – 155.000 m Y = – 463.000 m
UTM 1
Universal Transverse Mercator
60 zones 6 degrees UTM zones UTM 2
M: Mercator projection T: transverse (cylinder axis in Equator plane) U: universal (60 projection zones of 6 degree latitude) 1 Central line per zone 2 standard lines per zone (180 km to the west and the east of central line) False Easting and False Northing UTM ... … a source of much confusion as UTM stands for different things:
1. UTM projection can be defined with different datums (ellipsoids) 2. UTM grid can be defined on other projections than UTM
With UTM coordinates always check ellipsoid and projection Dutch topographic map (1996)
Civil Bessel ellipsoid RD map grid
Military WGS 84 ellipsoid (formerly Hayford) UTM map grid UTM background http://www.dmap.co.uk/utmworld.htm UTM Grid Zones of the World http://www.maptools.com/UsingUTM/ Using UTM Coordinate system Coordinates
Coordinates in a map projection plane :
Geographic coordinates angle East/West from 0 meridian (longitude) angle North/South from Equator (latitude)
Cartesian coordinates distance from Y axis (X coordinate) distance from X axis (Y coordinate) Dutch example Meta data of Dutch Topographic data maps
PROJCS["Rijksdriehoekstelsel_New", GEOGCS["GCS_Amersfoort", DATUM["D_Amersfoort", SPHEROID["Bessel_1841",6377397.155,299.1528128]], PRIMEM["Greenwich",0.0], UNIT["Degree",0.0174532925199433]], PROJECTION["Double_Stereographic"], PARAMETER["False_Easting",155000.0], PARAMETER["False_Northing",463000.0], PARAMETER["Central_Meridian",5.38763888888889], PARAMETER["Scale_Factor",0.9999079], PARAMETER["Latitude_Of_Origin",52.15616055555555], UNIT["Meter",1.0]] longitude of center of projection 5 23 15,5006 DMS latitude of center of projection 52 09 22,1841 DMS radius of sphere of reference 6370997 datum WGS 1984 Summary
Georeferencing Geometry
Plane projection (flat earth model) vs. Spherical projection (round earth model) Coordinate systems Geographic coordinates (latitude and longitude) Geocentric coordinates (X, Y, Z – mass centre of the earth) Cartesian coordinates
Datums Horizontal and Vertical references Ellipsoid / Geoid / Mean Sea Level
Vertical elevation / Geoid undulation Role of Gravity
Map projections Properties: shape, area, distance, angle UTM, RD, false origin Study materials:
Theory Chang, 2008 Chapter 2: Coordinate systems
Practical: Exercise Module 3: ‘Map projections’
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