Geo�referencing &

Map projections

2009/2010 CGI�GIRS©

Overview

•Map projections

• properties

• projection types

• UTM

• coordinate systems

Geo�information process•Georeference

• systems

• ellipsoid / geoid

• datums / reference surfaces

• sea level

Geo�reference systems

Geo � Reference � Systems

earth something to refer to coordinates

physical reality geometrical abstractions< relation >

Garden maintenance objects need a reference

X

Y

History

� Local (for at least 21 centuries)

� National (since mid 19th century (NL))

� Continental (since mid 20th century)

� Global (since 1970 / GPS, 1989)

Geo�referencing (in brief)

� Georeferencing:

� Geometrically describing locations on the earth surface by means of earth�fixed coordinates

Geographic coordinate systems

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

� Latitude � parallels � North South

� Longitude � meridians � East�West

� Its not based on a Cartesian plane but on location on the earth surface (spherical coordinate system)

Latitude

Longitude

Geographic coordinates

� Angular measures

� Degrees�minutes�second

� Lat 51o’ 59’ 14.5134”

� Lon 5o’ 39’ 54.9936”

� Decimal Degrees (DD)

� Lat 51.98736451427008

� Lon 5.665276050567627

Model of the earth

Spheroid and datum

� Spheroid (ellipsoid) approximates the shape of the earth

� Geodetic datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth.

� Datum WGS 1984 (world application)

Horizontal and vertical models

� Horizontal datum: (ellipsoid) for position

� mathematical model

� Vertical datum: (geoid) for elevation

� physical model

One location:

‘egg’

‘potato’

Rotating potatoMean gravity level at mean

sea level

Tom & Jerry

Geoid undulation (global)

–120 m 0 m 80 m

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

Two different abstract models

� Two different positions

� Two different ‘heights’:� orthometric (related to

geoid) = H

� geodetic (related to ellipsoid) = h = H+N

� geoid undulation = N (‘potato minus egg’)

One location, but yet:

Map ‘Jumping’

Difference in ‘Mean Sea Levels’ 2

� Average tide IJmuiden (North Sea)

� Average low tide Oostende (Dover Channel)

Netherlands — Belgium

A visible elevation jump of

+2.34 m

from Netherlands to Belgium ????

Difference in ‘Mean Sea Levels’

Differences between Height Reference Levels within Europe

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

Question

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

Examples (Bellingham, Washington)

� NAD 1927

� Lat �122.466903686523

� Lon 48.7440490722656

� NAD 1983

� Lat �122.46818353793

� Lon 48.7438798543649

� WGS 1984

� Lat �122.46818353793

� Lon 48.7438798534299

Projections

� Attemp to portray (a portion of) the earth on a flat surface

� From spherical coordinate system to a planar (Cartesian) coordinate system.

� Always lead to distortions

Map projection 16th century

Waldseemuller

Type of projection (projection surface)

Projection plane Planar

Cylindrical

Conical

Map projections

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

� Numerous projections

� Projection plane always flat

� Cartesian coordinates

� Countries uses own projections

� Always purposely designed

Type of map projections

Grouping by preserved properties:

� conformal: preserves local angles and 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 conformal and equivalent

Properties

� Tissot indicatrices:to show the distortionof parts of a map

Cylindrical projections

� Conformal

� Equidistant

� Equivalent

Cylindrical projections

� conformal at Equator

� conformal at higher latitudes (N & S)

Equal area

What is the projection type?

What is the projection type?

What is the projection type?

Conical projections ...

� Conformal (Lambert)

� Equal area (Albers)

… defined for USA

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

Great Circle (azimuthal)

Great Circle (equidistance)

Dutch map grid

� Datum point: Amersfoort

� Bessel 1841 ellipsoid

� Projection: Planar

� Conformal

� Azimuthal

� False origin:

� X = – 155.000 m

� Y = – 463.000 m

UTM 1

� Universal

� Transverse

� Mercator

� 60 zones

� 6 degrees

UTM zones

UTM 2

� M: Mercator projection� T: transverse (cylinder axis in Equator plane)� U: universal (60 projection zones of 6 degree latitude)� 1 Central line per zone� 2 standard lines per zone (180 km to the west and the east of central line)� False Easting and False Northing

UTM ...

� 1. UTM projection

� can be defined with different datums (ellipsoids)

� 2. UTM grid

� can 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

Dutch topographic map (1996)

� Civil

� Bessel ellipsoid

� RD map grid

� Military

� WGS 84 ellipsoid (formerly Hayford)

� UTM map grid

UTM background

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

UTM Grid Zones of the World

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

Using UTM Coordinate system

Coordinates

� Geographic coordinates

� angle 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:

Dutch example

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]]� longitude of center of projection 5 23 15,5006 DMS� latitude of center of projection 52 09 22,1841 DMS� radius of sphere of reference 6370997� datum WGS 1984

Summary

� Georeferencing� Geometry

� 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

� Datums� Horizontal and Vertical references

� Ellipsoid / Geoid / Mean Sea Level

� Vertical elevation / Geoid undulation� Role of Gravity

� Map projections� Properties: shape, area, distance, angle� UTM, RD, false origin

Study materials:

© Wageningen UR

Theory Chang, 2006

Chapter 2: Coordinate systems

Practical: Exercise Module 3: ‘Map projections’

Georeferencing is about … (1)

� Positions via� angles (triangulation)

� lengths (distances)

� time (GPS)

� Elevations via� vertical distances

(between gravity level surfaces)

Measurements in the real world (material)

to acquire:

‘Good’ old days

Combination of reference systems

‘Good’ new days