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Geo Referencing &Map projections
CGI-GIRS ©1011
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Where are you ?
31UFT8361
174,7 441,2
51°58' NB 5°40' OL
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Who are they ?
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Do geo data describe Earth’s phenomena perfectly?
• Map projections
• geometric properties
• projection types
• UTM
• coordinate systems
Geo-data cycle• Georeference•geodetic datum /
reference surfaces
• ellipsoid / geoid
• sea level
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Geo-reference systemsGeo - Reference - Systems
earth something to refer to coordinates
physical reality geometrical abstractions< relation >
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Geodetic Highlights
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Geographic coordinate systems
Location on the earth in Latitude and Longitude (e.g. 51°58' N 5°40' E )
Latitude based on parallels gives North SouthpalabreLongitude based on meridians gives East-Westmelole
Its not based on a Cartesian plane but on location on the earth surface (spherical coordinate system) from the earth’s centre
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Latitude Longitude
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Geographic coordinatesAngular measures
Degrees-minutes-secondLat 51o’ 59’ 14.5134”
( = degrees, minutes, seconds)Lon 5o’ 39’ 54.9936”
Decimal Degrees (DD)Lat 51.98736451427008
(= degrees + minutes/60+ seconds/3600)Lon 5.665276050567627
Radian1 radian= 57,2958 o
1 degree = 0,01745 rad
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Coordinates
Geographic coordinatesangle 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)
Planar | Projected
Coordinates in a map projection plane:
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Garden maintenance objects need a reference
X
Y
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Map projection 16th century Waldseemuller
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From ‘round earth’ to ‘flat earth’
DistanceAngleAreaShape
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What Projection ?
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Map projections
Mathematical projections (abstract) from an ellipsoid to a map plane
Numerous projectionsProjection plane always flatCartesian coordinatesEvery country uses own projectionsAlways purposely designed
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Type of map projectionsGrouping by preserved properties:
conformal: preserves local 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 for all together
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Properties
Tissot indicatrices:to show the distortionof parts of a map
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Type of projection (projection surface)Projection plane Azimuthal
Cylindric
Conic
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Type of projection: aspect • normal: Axis of Globe and Axis of Plane: identical• transversal: Axis of Globe and Axis of Plane: perpendicular• oblique: angles between normal and transversal
normal transversal oblique
• simple case : 1 line of tangency (1 : 1 scale) • secant case : 2 lines of tangency
Standard line
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Cylindrical projections
Conformal
Equidistant
Equal area
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Cylindrical projections
conformal at Equator
conformal at higher latitudes (N & S)
Equal area
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Conical projections ...
Conformal (Lambert)Equal area (Albers)
… defined for USA
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Why many types of projections?
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What projection ?
- Standard line, line of tangency
Criteria - Extent of Area, Precision
- Area, Conformal, Distance
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Mercator projection - great circle
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UTMM: Mercator projectionT: transverse (cylinder axis perpendicular to globe axis)U: universal (60 projection zones of 6 degree latitude)
1 Central line per zone2 Standard lines per zone (180 km to the west and the east of central line)
False Easting and False Northing
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UTM zones
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UTM ...
1. UTM projectioncan be defined with different datums (ellipsoids)
2. UTM gridcan be defined on other projections than UTM
… a source of much confusion
as UTM stands for different things:
With UTM coordinates
always check ellipsoid and projection
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Geometry as displayed on maps
LL-graticule (degrees)meridians (E or W)parallels (N or S)suits positioning only
XY-grid (kilometres)square rastersuits geometric calculations as well
Map sheet or screen (material) shows:
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Dutch topographic map (1996)
CivilBessel ellipsoidRD map grid
MilitaryWGS 84 ellipsoid (formerly Hayford)UTM map grid
Map Scale
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UTM background
http://www.dmap.co.uk/utmworld.htm
UTM Grid Zones of the World
http://www.maptools.com/UsingUTM/
Using UTM Coordinate system
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Dutch example
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Dutch Reference
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Dutch map grid
Datum : AmersfoortEllipsoid: Bessel 1841 Projection: secant azimuthalstereographicFalse origin:
X = – 155.000 mY = – 463.000 m
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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]]
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Geo-reference systemsGeo - Reference - Systems
earth something to refer to coordinates
physical reality geometrical abstractions< relation >
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Georeferencing in a nutshell
Georeferencing is:Geometrically describing 3D-locations on the earth surface by means of earth-fixed coordinates
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‘Good’ old days
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Combination of reference systems
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History of geodetic datums
Local (for at least 21 centuries)National (since mid 19th century (NL))Continental (since mid 20th century)Global (since 1970 / GPS, 1989)
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‘Good’ new days
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Georeferencing is about … (1)
Positions viaangles (triangulation)lengths (distances)time (GPS)
Elevations viavertical distances (between gravity level surfaces)
Measurements in the real world (material)
to acquire:
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Georeferencing is about … (2)
Horizontal: smooth ellipsoidfor positions
Vertical: irregular geoidfor elevations
Abstract reference surfaces for:
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Geodetic Datum and Spheroid
Geodetic datum is the basis for geographical coordinates of a location which defines the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth. Spheroid (ellipsoid) approximates the shape of the earthDatum Example: WGS 1984 (world application)
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Many Models of the earth
Variables: a ~ 6378 km; b ~6356 km
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Many different ellipsoids (a small selection)
Ellipsoid Major axis. Unit of Flattening
name a measure 1/f
Clarke 1866 6 378 206.4 m 294.978 698 2
Bessel 1841 6 377 397.155 m 299.152 812 85
Everest 1830 (India) 6 377 276.3458 m 300.801 7
GRS80 (New Intern’l) 6 378 137 m 298.257 222 100 882 7
WGS84 6 378 137 m 298.257 223 563
Various ellipsoids; selection adopted from M. Hooijberg, Practical Geodesy, 1997, p35-37
Datum: mathematical model of the Earth to serve as reference
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Meridians of Europe
Santa Maria degli Angeli e dei MartiriClementus XI - 1702
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Question
Is it possible to have different coordinates for the same location?
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Examples (Bellingham, Washington)
NAD 1927Lat -122.466903686523 Lon 48.7440490722656
NAD 1983Lat -122.46818353793Lon 48.7438798543649
WGS 1984Lat -122.46818353793Lon 48.7438798534299
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Horizontal and vertical models
Horizontal datum: (ellipsoid) for position
mathematical model
Vertical datum: (geoid) for elevation
physical model
One location:
‘egg’
‘potato’
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Map ‘Jumping’
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Difference in ‘Mean Sea Levels’ 2
Average height tide Den Helder(North Sea)
Average low tide Oostende (Dover Channel)
Netherlands — Belgium
A visible elevation jump of
From +2.30 m, via +2.34 into +2.426 mfrom Netherlands to Belgium ????
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Difference in ‘Mean Sea Levels’Differences between Height Reference Levels within Europe
see Augath, Ihde, 2002
page GRS-10306
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Two different abstract models
Two different positions
Two different ‘heights’:orthometric (related to geoid) = H (plumb line)geodetic (related to ellipsoid) : h = H+N (normal line)
geoid undulation = N (‘potato minus egg’)
One location, but yet:
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Rotating potatoMean gravity level at mean sea level
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Geoid undulation (global)
–120 m 0 m 80 m
http://www.csr.utexas.edu/grace/gravity/gravity_definition.html
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Towards a very accurate geoid (GRACE)
twin satellites (‘Tom & Jerry’)
launched March 2002 detailed measurements of Earth's gravity field
Orbiting Twins - The GRACE satellites
NASA http://www.csr.utexas.edu/grace/
GRACE animation with oral explanationhttp://www.csr.utexas.edu/grace/gallery/animations/measurement/measurement_wm.html
ESA http://www.esa.int/esaLP/ESAYEK1VMOC_LPgoce_0.html
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SummaryGeoreferencingGeometry
Plane projection (flat earth model) vs. Spherical projection (round earth model)Coordinate systems
Geographic coordinates (latitude and longitude)Cartesian coordinates (x, y) - projected
DatumsHorizontal and Vertical references
Ellipsoid / Mean Sea LevelGeoid
Vertical elevation / Geoid undulationRole of Gravity
Map projectionsProperties: shape, area (size), distance (size), angle (orientation)UTM, RD, false originGrid, graticule
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Something to refer to
Geographic coordinates(RD) cartesian coordinates
Earth Spheroid ProjectedMap
MapGrid
MathematicalRepresentation
Geo Datum
Map Projection
Plane OrientationDistortion
ReferenceTransformation
GridFalse Origin
Horizontal reference !!
Principal scale Local scale Map scale
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Study materials:
© Wageningen UR
Theory Chang, 2006, 2008 | 2010Chapter 2: Coordinate systems (except: 2.4.2;2.4.3; 2.4.4 )|
Practical: Exercise Module 3: ‘Map projections’
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Equidistant ...
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
… a confusing concept, because:
An equidistant projection has NO uniform scale
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Why horizontal and vertical differentiation?
Horizontal deviationexponential increase of dD/D dD=1*10-6 * D3
1 mm / 1 km1 m
Example: distance D = 100 km:
Vertical deviationdH (mm) = 7,8mm/km * D2
dH (mm) = 78 * D2
780 m
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