Geo Referencing &Map projections

CGI-GIRS ©1011

2/60

Where are you ?

31UFT8361

174,7 441,2

51°58' NB 5°40' OL

3/60

Who are they ?

4/60

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

5/60

Geo-reference systemsGeo - Reference - Systems

earth something to refer to coordinates

physical reality geometrical abstractions< relation >

6/60

Geodetic Highlights

7/60

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

8/60

Latitude Longitude

9/60

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

10/60

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:

11/60

Garden maintenance objects need a reference

X

Y

12/60

Map projection 16th century Waldseemuller

13/60

From ‘round earth’ to ‘flat earth’

DistanceAngleAreaShape

14/60

What Projection ?

15/60

Map projections

Mathematical projections (abstract) from an ellipsoid to a map plane

Numerous projectionsProjection plane always flatCartesian coordinatesEvery country uses own projectionsAlways purposely designed

16/60

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

17/60

Properties

Tissot indicatrices:to show the distortionof parts of a map

18/60

Type of projection (projection surface)Projection plane Azimuthal

Cylindric

Conic

19/60

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

20/60

Cylindrical projections

Conformal

Equidistant

Equal area

21/60

Cylindrical projections

conformal at Equator

conformal at higher latitudes (N & S)

Equal area

22/60

Conical projections ...

Conformal (Lambert)Equal area (Albers)

… defined for USA

23/60

Why many types of projections?

24/60

What projection ?

- Standard line, line of tangency

Criteria - Extent of Area, Precision

- Area, Conformal, Distance

25/60

Mercator projection - great circle

26/60

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

27/60

UTM zones

28/60

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

29/60

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:

30/60

Dutch topographic map (1996)

CivilBessel ellipsoidRD map grid

MilitaryWGS 84 ellipsoid (formerly Hayford)UTM map grid

Map Scale

31/60

UTM background

http://www.dmap.co.uk/utmworld.htm

UTM Grid Zones of the World

http://www.maptools.com/UsingUTM/

Using UTM Coordinate system

32/60

Dutch example

33/60

Dutch Reference

34/60

Dutch map grid

Datum : AmersfoortEllipsoid: Bessel 1841 Projection: secant azimuthalstereographicFalse origin:

X = – 155.000 mY = – 463.000 m

35/60

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]]

36/60

Geo-reference systemsGeo - Reference - Systems

earth something to refer to coordinates

physical reality geometrical abstractions< relation >

37/60

Georeferencing in a nutshell

Georeferencing is:Geometrically describing 3D-locations on the earth surface by means of earth-fixed coordinates

38/60

‘Good’ old days

39/60

Combination of reference systems

40/60

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)

41/60

‘Good’ new days

42/60

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:

43/60

Georeferencing is about … (2)

Horizontal: smooth ellipsoidfor positions

Vertical: irregular geoidfor elevations

Abstract reference surfaces for:

44/60

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)

45/60

Many Models of the earth

Variables: a ~ 6378 km; b ~6356 km

46/60

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

47/60

Meridians of Europe

Santa Maria degli Angeli e dei MartiriClementus XI - 1702

48/60

Question

Is it possible to have different coordinates for the same location?

49/60

Examples (Bellingham, Washington)

NAD 1927Lat -122.466903686523 Lon 48.7440490722656

NAD 1983Lat -122.46818353793Lon 48.7438798543649

WGS 1984Lat -122.46818353793Lon 48.7438798534299

50/60

Horizontal and vertical models

Horizontal datum: (ellipsoid) for position

mathematical model

Vertical datum: (geoid) for elevation

physical model

One location:

‘egg’

‘potato’

51/60

Map ‘Jumping’

52/60

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 ????

53/60

Difference in ‘Mean Sea Levels’Differences between Height Reference Levels within Europe

see Augath, Ihde, 2002

page GRS-10306

54/60

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:

55/60

56/60

Rotating potatoMean gravity level at mean sea level

57/60

Geoid undulation (global)

–120 m 0 m 80 m

http://www.csr.utexas.edu/grace/gravity/gravity_definition.html

58/60

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

59/60

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

60/60

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

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’

62/60

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

63/60

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

64/60