Geo Referencing &Map projections

CGI-GIRS ©0910

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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

• properties

• projection types

• UTM

• coordinate systems

Geo-data cycle•Georeference

• systems

• ellipsoid / geoid

• datum / reference surfaces

• 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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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 certaindistances - 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

Cylindrical

Conical

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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

• simple case : 1 line of tangency (1 : 1 scale) • secant case : 2 lines of tangency

Standard line

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Why many types of projections?

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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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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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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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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)

Coordinates in a map projection plane:

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Geographic coordinate systems

Location on the earth in Longitude and Latitude (e.g. 51°58' N 5°40' E )

Longitude based on parallels gives East-WestLatitude based on meridians gives North South

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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Geodetic Highlights

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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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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 example

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Dutch Reference

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Dutch map grid

Datum point: AmersfoortDatum: Bessel 1841 ellipsoidProjection: secant azimuth.False 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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History

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’ old days

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Combination of reference systems

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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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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) = Hgeodetic (related to ellipsoid) = h = H+N

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)Geocentric coordinates (X, Y, Z – mass centre of the earth)Cartesian coordinates Grids

DatumsHorizontal and Vertical references

Ellipsoid / Geoid / Mean Sea Level

Vertical elevation / Geoid undulationRole of Gravity

Map projectionsProperties: shape, area, distance, angleUTM, RD, false origin

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Something to refer to

Geographic coordinatesRD coordinates

Earth Spheroid ProjectedMap

GriddedMap

MathematicalRepresentation

Geo Datum

Map Projection

Plane OrientationDistortion

ReferenceTransformation

GridFalse Origin

Horizontal reference !!Principal scale Local scale Map scale

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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