Geo Referencing & Map projections

CGI-GIRS ©0910 Where are you ?

31UFT8361

174,7 441,2

51°58' NB 5°40' OL

2/60 Who are they ?

3/60 Do geo data describe Earth’s phenomena perfectly? •Georeference Geo-data cycle

• systems • ellipsoid / geoid • geodetic datum / reference surfaces •sea level • Map projections

• properties • projection types •UTM • coordinate systems

4/60 Geo-reference systems Geo - Reference - Systems

earth something to refer to coordinates

physical reality< relation > geometrical abstractions

5/60 Geodetic Highlights

6/60 Geographic coordinate systems

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

„ Latitude Î based on parallels Î gives North South palabre „ Longitude Î based on meridians Î gives East-West melole

„ Its not based on a Cartesian plane but on location on the earth surface (spherical coordinate system) from the earth’s centre

7/60 Latitude Longitude

8/60 Geographic coordinates Angular measures „ Degrees-minutes-second o z Lat 51 ’ 59’ 14.5134” ( = degrees, minutes, seconds) o z Lon 5 ’ 39’ 54.9936” „ Decimal Degrees (DD) z Lat 51.98736451427008 (= degrees + minutes/60+ seconds/3600) z Lon 5.665276050567627 „ Radian o z 1 radian= 57,2958 z 1 degree = 0,01745 rad

9/60 Coordinates

Coordinates in a map projection plane:

„ Geographic coordinates z angle East/West from 0-meridian (longitude) z angle North/South from Equator (latitude)

„ Cartesian coordinates z distance from Y-axis (X-coordinate) z distance from X-axis (Y-coordinate)

10/60 Garden maintenance objects need a reference

Y

X

11/60 Map projection 16th century Waldseemuller

12/60 From ‘round earth’ to ‘flat earth’

„ Distance „ Angle „ Area „ Shape

13/60 What Projection ?

14/60 Map projections

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

z Numerous projections z Projection plane always flat z Cartesian coordinates z Every country uses own projections z Always purposely designed

15/60 Type of map projections Grouping 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

16/60 Properties

„ Tissot indicatrices: to show the distortion of parts of a map

17/60 Type of projection (projection surface) Projection plane Azimuthal

Cylindrical

Conical

18/60 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

Standard line

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

normal transversal oblique

19/60 Why many types of projections?

20/60 Cylindrical projections

„ Conformal

„ Equidistant

„ Equal area

21/60 Cylindrical projections

Equal area

„ conformal at Equator

„ conformal at higher latitudes (N & S)

22/60 Conical projections ... … defined for USA

„ Conformal (Lambert) „ Equal area (Albers)

23/60 What projection ? Criteria - Extent of Area, Precision - Area, Conformal, Distance

- Standard line, line of tangency

24/60 Mercator projection - great circle

25/60 UTM „ M: Mercator projection „ T: transverse (cylinder axis perpendicular to globe axis) „ U: universal (60 projection zones of 6 degree latitude) z 1 Central line per zone z 2 Standard lines per zone (180 km to the west and the east of central line) „ False Easting and False Northing

26/60 UTM zones

27/60 UTM ... … a source of much confusion as UTM stands for different things:

„ 1. UTM projection z can be defined with different datums (ellipsoids) „ 2. UTM grid z can be defined on other projections than UTM

With UTM coordinates always check ellipsoid and projection

28/60 Geometry as displayed on maps

Map sheet or screen (material) shows:

„ LL-graticule (degrees) z meridians (E or W) z parallels (N or S) z suits positioning only

„ XY-grid (kilometres) z square raster z suits geometric calculations as well

29/60 Dutch topographic map (1996) Map Scale

„ Civil z Bessel ellipsoid z RD map grid

„ Military z WGS 84 ellipsoid (formerly Hayford) z UTM map grid

30/60 UTM background

http://www.dmap.co.uk/utmworld.htm UTM Grid Zones of the World

http://www.maptools.com/UsingUTM/ Using UTM Coordinate system

31/60 Dutch example

32/60 Dutch Reference

33/60 Dutch map grid

„ Datum : Amersfoort „ Ellipsoid: Bessel 1841 „ Projection: secant azimuthal stereographic „ False origin: z X = – 155.000 m z Y = – 463.000 m

34/60 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]]

35/60 Geo-reference systems Geo - Reference - Systems

earth something to refer to coordinates

physical reality< relation > geometrical abstractions

36/60 Georeferencing in a nutshell

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

37/60 ‘Good’ old days

38/60 Combination of reference systems

39/60 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)

40/60 ‘Good’ new days

41/60 Georeferencing is about … (1) Measurements in the real world (material) to acquire:

„ Positions via z angles (triangulation) z lengths (distances) z time (GPS)

„ Elevations via z vertical distances (between gravity level surfaces)

42/60 Georeferencing is about … (2)

Abstract reference surfaces for:

„ Horizontal: smooth ellipsoid for positions „ Vertical: irregular geoid for elevations

43/60 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 earth „ Datum Example: WGS 1984 (world application)

44/60 Many Models of the earth

Variables: a ~ 6378 km; b ~6356 km

45/60 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

GRS80 (New Intern’l) 6 378

WGS84 6 378 137 298.257 m 223 563 377 276.3458 300.801 m 7 Various ellipsoids; selection adopted from M.

137 298.257 m 222 100 882 7

Hooijberg, Practical Geodesy, 1997, p35-37 46/60 Meridians of Europe

„ Santa Maria degli Angeli e dei Martiri „ Clementus XI - 1702

47/60 Question

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

48/60 Examples (Bellingham, Washington)

„ NAD 1927 z Lat -122.466903686523 z Lon 48.7440490722656 „ NAD 1983 z Lat -122.46818353793 z Lon 48.7438798543649 „ WGS 1984 z Lat -122.46818353793 z Lon 48.7438798534299

49/60 Horizontal and vertical models

One location:

„ Horizontal datum: (ellipsoid) for position ‘egg’ z mathematical model

„ Vertical datum: (geoid) for elevation z physical model ‘potato’

50/60 Map ‘Jumping’

51/60 Difference in ‘Mean Sea Levels’ 2

Netherlands — Belgium

„ Average height „ Average low tide tide Den Helder Oostende (Dover (North Sea) Channel)

A visible elevation jump of From +2.30 m, via +2.34 into +2.426 m from Netherlands to Belgium ????

52/60 Difference in ‘Mean Sea Levels’ Differences between Height Reference Levels within Europe

see Augath, Ihde, 2002 page GRS-10306

53/60 Two different abstract models

One location, but yet:

„ Two different positions

„ Two different ‘heights’: z orthometric (related to geoid) = H (plumb line) z geodetic (related to ellipsoid) : h = H+N (normal line) „ geoid undulation = N (‘potato minus egg’)

54/60 55/60 Rotating potato Mean gravity level at mean sea level

56/60 Geoid undulation (global) http://www.csr.utexas.edu/grace/gravity/gravity_definition.html

–120 m 0 m 80 m

57/60 Towards a very accurate geoid (GRACE)

NASA http://www.csr.utexas.edu/grace/

ESA http://www.esa.int/esaLP/ESAYEK1VMOC_LPgoce_0.html

„ twin satellites (‘Tom & Jerry’) „ launched March 2002

„ detailed measurements of Earth's gravity field Orbiting Twins - The GRACE satellites GRACE animation with oral explanation http://www.csr.utexas.edu/grace/gallery/animations/measurement/measurement_wm.html

58/60 Summary

„ Georeferencing „ Geometry

„ Plane projection (flat earth model) vs. Spherical projection (round earth model) „ Coordinate systems z Geographic coordinates (latitude and longitude) z Cartesian coordinates (x, y)

„ Datums „ Horizontal and Vertical references z Ellipsoid / Mean Sea Level z Geoid

„ Vertical elevation / Geoid undulation „ Role of Gravity

„ Map projections z Properties: shape, area, distance, angle z UTM, RD, false origin z Grid, graticule

59/60 Something to refer to

„ Geographic coordinates „ RD coordinates Horizontal reference !!

Principal scale Local scale Map scale

Earth Spheroid Projected Gridded Map Map

Mathematical Map Reference Representation Projection Transformation

Geo Datum Plane Grid Orientation False Origin Distortion

60/60 Study materials:

Theory Chang, 2006, 2008 | 2010 Chapter 2: Coordinate systems (except: 2.4.2;2.4.3; 2.4.4 )|

Practical: Exercise Module 3: ‘Map projections’

©Wageningen UR Equidistant ... … a confusing concept, because:

„ means “equal in distance” z distance on earth surface equal to distance in map projection plane (scale 1:1) „ but only applied to specific directions z “all” directions to a single point, or “all” perpendiculars to a single line

An equidistant projection has NO uniform scale

62/60 Why horizontal and vertical differentiation? Example: distance D = 100 km:

„ Horizontal deviation z exponential increase of dD/D z dD=1*10-6 * D3 z 1 mm / 1 km z 1 m

„ Vertical deviation z dH (mm) = 7,8mm/km * D2 z dH (mm) = 78 * D2 z 780 m

63/60 64/60