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Geo Referencing & Map Projections

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Geo Referencing & Map Projections 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 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 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.
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