You will want to pay attention…You will want to pay attention…

there will be a test on this material!!!there will be a test on this material!!!

The Exhilarating World of The Exhilarating World of Geodesy and Map Geodesy and Map

ProjectionsProjections

Geodesy: measuring the EarthGeodesy: measuring the Earth Geodesy: Geodesy: a branch of earth sciences, is the a branch of earth sciences, is the

scientific discipline that deals with the scientific discipline that deals with the measurement and representation of the Earth, measurement and representation of the Earth, including its gravity field, in a three-dimensional including its gravity field, in a three-dimensional time varying space.time varying space.

Geodesy deals with the determination of the Geodesy deals with the determination of the earth's shape and size, as well as its gravity field, earth's shape and size, as well as its gravity field, i.e. the measurement of gravitational i.e. the measurement of gravitational acceleration. acceleration.

The knowledge of the gravity field is important, The knowledge of the gravity field is important, because almost every geodetic measurement is because almost every geodetic measurement is closely related to gravity, e.g. instruments have closely related to gravity, e.g. instruments have to be leveled along the a horizontal surface. to be leveled along the a horizontal surface.

Calculating Routes on the Earth’s SurfaceCalculating Routes on the Earth’s Surface Calculations however (including calculations of a Calculations however (including calculations of a

route for high-speed trains) do not use the actual route for high-speed trains) do not use the actual shape of the earth, but mathematically defined shape of the earth, but mathematically defined surfaces and bodies such as planes, spheres or surfaces and bodies such as planes, spheres or ellipsoids of rotation. ellipsoids of rotation.

The difference between reality and these The difference between reality and these simplified mathematical models is shown in the simplified mathematical models is shown in the figure below.figure below.

http://www.gug.bv.tum.de/seiten-e/technik/physik.html

Geodesy and GPSGeodesy and GPS It is critical to know about the difference between heights It is critical to know about the difference between heights

above sea level (which are related to the gravitational field above sea level (which are related to the gravitational field and thus the only way to determine the slope) and the and thus the only way to determine the slope) and the ellipsoidal heights, which are a result of GPS ellipsoidal heights, which are a result of GPS measurements. measurements.

Geodesy provides information about the reference surface Geodesy provides information about the reference surface of the heights above sea level - the so-called geoid. The of the heights above sea level - the so-called geoid. The geoid is represented as the surface of an imaginary, calm geoid is represented as the surface of an imaginary, calm sea, continued below the continents. sea, continued below the continents.

It is the connection between the heights measured with It is the connection between the heights measured with GPS and heights above sea level, used in national vertical GPS and heights above sea level, used in national vertical control networks.control networks.

http://www.gug.bv.tum.de/seiten-e/technik/physik.html

Earth as a GeoidEarth as a Geoid

Earth has a dynamic Earth has a dynamic surface and complex surface and complex structure. structure.

A Geoid is too complex a A Geoid is too complex a shape for daily needs so shape for daily needs so easier to think of Earth easier to think of Earth as an ellipsoidas an ellipsoid

http://www.hydrology.uni-kiel.de/lehre/vorlesung/ws04-05/vl_msc0104_02.pdf

Geoid-Spheroid-EllipsoidGeoid-Spheroid-Ellipsoid

A GEOID is the earth’s actual shape A GEOID is the earth’s actual shape (including elevation above/below sea level)(including elevation above/below sea level)

A SPHEROID is an ellipsoid that A SPHEROID is an ellipsoid that approximates the shape of a sphereapproximates the shape of a sphere

An ELLIPSOID is created by rotating an An ELLIPSOID is created by rotating an ellipse about either major axis or minor axisellipse about either major axis or minor axis

Earth as Reference EllipsoidEarth as Reference Ellipsoid Ellipsoid defined by an Ellipsoid defined by an

equatorial radius, polar equatorial radius, polar radius and the reciprocal radius and the reciprocal of the flatteningof the flattening

Ellipsoid approximates Ellipsoid approximates the geoid in size and the geoid in size and positionposition

Different ellipsoids in Different ellipsoids in use. They differ in use. They differ in equatorial radius and equatorial radius and flattening as well as flattening as well as positioning of their positioning of their center.center.

Geoid with different elipsoids and different reference locations

Graticule: parallels and meridiansGraticule: parallels and meridians System of System of

imaginary imaginary intersecting lines intersecting lines was created based was created based on 360 degree on 360 degree Babylonian system Babylonian system for dividing a circle for dividing a circle or sphereor sphere

Map projections are Map projections are based on:based on:• Central MeridiansCentral Meridians• Standard ParallelsStandard Parallels

The Graticule …ProjectedThe Graticule …Projected

What is a Map Projection?What is a Map Projection?

A map is a flat A map is a flat representation of a representation of a globeglobe

A map projection is A map projection is a systematic a systematic transfer of points on transfer of points on a curved surface to a curved surface to a flat projection a flat projection surfacesurface

SSADDSSADD: 5 Key Properties of Maps: 5 Key Properties of Maps

Scale:Scale: relationship of distance and area relationship of distance and area on Earth to distance and area on mapon Earth to distance and area on map

Shape:Shape: shape is preserved when the scale shape is preserved when the scale of any point on the map is the same in any of any point on the map is the same in any direction direction

Area:Area: proportional relationship between proportional relationship between study region and area of the Earth that it study region and area of the Earth that it representsrepresents

Distance:Distance: length from center of the length from center of the projection to any other place on the mapprojection to any other place on the map

DirectionDirection: angles from a point on a line to : angles from a point on a line to another point are portrayed correctly in all another point are portrayed correctly in all directionsdirections

Why use Map Projections?Why use Map Projections?

GIS and paper maps are flat and more GIS and paper maps are flat and more convenient than 3D models for most convenient than 3D models for most applicationsapplications

Scanning and digitizing maps is a big Scanning and digitizing maps is a big source of spatial data used in GISsource of spatial data used in GIS

Most common spatial data models are flat Most common spatial data models are flat and cannot be created on curved surfaceand cannot be created on curved surface

Earth has to be projected to see all of it Earth has to be projected to see all of it Much easier to measure distance on a Much easier to measure distance on a

planeplane

Problems with Map ProjectionsProblems with Map Projections

Maps can preserve some of the Maps can preserve some of the properties but not allproperties but not all

No projection can retain more than No projection can retain more than one of these properties over large one of these properties over large portion of globeportion of globe

Every map projection distorts the Every map projection distorts the earth is several waysearth is several ways

Decisions of which projection to use Decisions of which projection to use depends on reducing distortiondepends on reducing distortion

Projection ParametersProjection Parameters

Projection Center: point of projectionProjection Center: point of projection Projection Families: Developable Projection Families: Developable

SurfacesSurfaces Projection Aspect: orientation of Projection Aspect: orientation of

developable surfacesdevelopable surfaces Location of developable surfaceLocation of developable surface

Projection CentersProjection Centers

Gnomonic: Gnomonic: projection point projection point from Earth’s from Earth’s centercenter

Stereographic: Stereographic: at antipodal at antipodal surfacesurface

Orthographic: Orthographic: at infinityat infinity

3 Families of Projections3 Families of Projections

CylindricalCylindrical ConicalConical PlanarPlanar

Developable surface: 2 D surface upon which map information is projected. Can be unrolled without distortion although projection will contain distortions

Cylindrical ProjectionsCylindrical Projections Used by Used by

mariners for mariners for navigationnavigation

Meridians run Meridians run north - southnorth - south

Parallels runParallels run east- westeast- west True at equator True at equator

and distortion and distortion increases increases towards the towards the polespoles

Conical ProjectionsConical Projections

Used for mid Used for mid latitude mapslatitude maps

True at areas True at areas between standard between standard parallelsparallels

Planar ProjectionsPlanar Projections Used to navigate Used to navigate

flight routesflight routes Preserves Great Preserves Great

Circle LinesCircle Lines In polar aspect, In polar aspect,

these maps project these maps project meridians as meridians as straight lines straight lines radiating from the radiating from the poles and parallels poles and parallels as complete circles as complete circles centered at the polecentered at the pole

True at poles and True at poles and distortions increases distortions increases outwardsoutwards

3 basic rules for choosing 3 basic rules for choosing projection familyprojection family

4 Types of Projection Aspect4 Types of Projection Aspect

Normal: oriented Normal: oriented with polar axiswith polar axis

Transverse: Transverse: perpendicular to perpendicular to polar axispolar axis

Polar: centered Polar: centered on N/S Poleson N/S Poles

Oblique: all Oblique: all othersothers

Location of Developable SurfaceLocation of Developable Surface

Tangent: DS Tangent: DS touches the touches the globeglobe

Secant: DS Secant: DS cuts into the cuts into the globeglobe

Map Property PreservationMap Property Preservation

If a projection preserves…If a projection preserves…•SHAPESHAPE it is called it is called CONFORMALCONFORMAL . . •AREAAREA is called is called EQUAL-AREAEQUAL-AREA or or

Equivalent. Equivalent. •DISTANCEDISTANCE it is called it is called EQUIDISTANTEQUIDISTANT•DIRECTIONDIRECTION it is called it is called AZIMUTHALAZIMUTHAL

Tissot’s Indicatrix: Graphical Tool to Tissot’s Indicatrix: Graphical Tool to Analyze Projection PropertiesAnalyze Projection Properties

http:www.jhlabs.com/java/maps/projhttp:www.jhlabs.com/java/maps/proj

Example: Mercator ProjectionExample: Mercator Projection CylindricalCylindrical ConformalConformal Areas not preserved and increase Areas not preserved and increase

towards the top and bottom of the towards the top and bottom of the mapmap

Preserves true-direction along Preserves true-direction along graticule linesgraticule lines

Used for ocean navigationUsed for ocean navigation

Mercator ProjectionMercator Projection

http:www.jhlabs.com/java/maps/projhttp:www.jhlabs.com/java/maps/proj

Example: Lambert Conformal Example: Lambert Conformal Conical Conical

ConicalConical ConformalConformal Preserves Preserves

shape of shape of geographic geographic featuresfeatures

Useful in Useful in mapping mid mapping mid latitudeslatitudes

Lambert Conformal ConicalLambert Conformal Conical

http:www.jhlabs.com/java/maps/projhttp:www.jhlabs.com/java/maps/proj

Example: Orthographic AzimuthalExample: Orthographic Azimuthal

PlanarPlanar AzimuthalAzimuthal Equatorial or Equatorial or

Oblique AspectsOblique Aspects Azimuthal not Azimuthal not

suitable for suitable for displaying entire displaying entire Earth in one Earth in one viewview

Orthographic AzimuthalOrthographic Azimuthal

http:www.jhlabs.com/java/maps/projhttp:www.jhlabs.com/java/maps/proj

Robinson ProjectionRobinson Projection

• ‘Looks’ Balanced

•Used by NGS

Distance

Shape

Direction

are all distorted but…

http:www.jhlabs.com/java/maps/projhttp:www.jhlabs.com/java/maps/proj

Projection SystemsProjection Systems A A Projected Coordinate SystemProjected Coordinate System

is a projection based on two is a projection based on two different projections depending on different projections depending on the shape of the region it describesthe shape of the region it describes

State Plane Coordinate System State Plane Coordinate System (SPCS)(SPCS)• States extending east to west, States extending east to west,

uses Lambert conformal conical uses Lambert conformal conical projectionprojection

• States extending north to south, States extending north to south, uses tranverse cylindrical uses tranverse cylindrical Mercator projectionMercator projection

• Measured in feetMeasured in feet• Minimizes distortions within 1 Minimizes distortions within 1

footfoot

Projection SystemsProjection Systems Universal Tranverse Universal Tranverse

Mercator Coordinate Mercator Coordinate System (UTM)System (UTM)• Uses 60 zones, each Uses 60 zones, each

6 degrees of 6 degrees of longitude widelongitude wide

• Measured in metersMeasured in meters• Uses a secant Uses a secant

variation variation • Minimizes distortion Minimizes distortion

< 1meter within each < 1meter within each zone zone

Unprojected vs. Undefined DataUnprojected vs. Undefined Data

UnprojectedUnprojected geographic coordinate geographic coordinate system allows more flexibility in setting system allows more flexibility in setting ArcMap’s data frame coordinate system to ArcMap’s data frame coordinate system to suit analysis needssuit analysis needs

Undefined Undefined coordinate system is missing coordinate system is missing files to enable ArcMap to read and files to enable ArcMap to read and reference them with other data layers. You reference them with other data layers. You will need to define the coordinate system will need to define the coordinate system to fully use the file in an ArcMap project.to fully use the file in an ArcMap project.

Final ThoughtsFinal Thoughts

Map projections are critical for transferring Map projections are critical for transferring 3D globe onto 2D flat surface3D globe onto 2D flat surface

Many types of projections used for different Many types of projections used for different purposespurposes

Need to understand map projections to Need to understand map projections to work with multiple layer files in GIS to make work with multiple layer files in GIS to make each layer ‘fit’ with the other.each layer ‘fit’ with the other.

Go to JH Labs website and explore more Go to JH Labs website and explore more unusual map projections. Bring a copy of unusual map projections. Bring a copy of your favorite unusual projection with a your favorite unusual projection with a description of which properties are description of which properties are preserved and which are distorted. preserved and which are distorted.

AssignmentAssignment Go to JH Labs website Go to JH Labs website ((JH Labs: Java Map Projection JH Labs: Java Map Projection

Library http:www.jhlabs.com/java/maps/proj)Library http:www.jhlabs.com/java/maps/proj)

and explore more unusual map projections. and explore more unusual map projections. Bring a copy of your favorite unusual projection with a Bring a copy of your favorite unusual projection with a

description of which properties are preserved and which are description of which properties are preserved and which are distorted.distorted.

Go online to search how geodesy is used in making maps, Go online to search how geodesy is used in making maps, refining measurements of earth’s surface, navigation refining measurements of earth’s surface, navigation systems, or another interesting aspect of how it is used by systems, or another interesting aspect of how it is used by scientists and engineers. Write a one page (double spaced scientists and engineers. Write a one page (double spaced 12 font) summary of the information you found. Provide the 12 font) summary of the information you found. Provide the website URLs and any images that will help explain your website URLs and any images that will help explain your findings.findings.

Be prepared to share your projection selection and your Be prepared to share your projection selection and your geodesy research summary with a small group.geodesy research summary with a small group.

Quiz MaterialQuiz Material Know definitions for geoid, spheroid, ellipsoidKnow definitions for geoid, spheroid, ellipsoid Know definition of geodesy and ‘map projection’Know definition of geodesy and ‘map projection’ Know definitions of the 5 Key Properties of Maps Know definitions of the 5 Key Properties of Maps

(SSADD)(SSADD) Know at least one reason for using map projections Know at least one reason for using map projections

and at least one problem with map projectionsand at least one problem with map projections Know 3 types of projection centersKnow 3 types of projection centers Know 3 families of projectionKnow 3 families of projection Name 3 specific map projections and the Name 3 specific map projections and the

characteristics of one of them (pros and cons)characteristics of one of them (pros and cons) Name one example of a Projected Coordinate SystemName one example of a Projected Coordinate System

Resources used for presentationResources used for presentation

JH Labs: Java Map Projection Library JH Labs: Java Map Projection Library http:www.jhlabs.com/java/maps/projhttp:www.jhlabs.com/java/maps/proj

Information on Geodesy and Geoinfomatics Engineering Information on Geodesy and Geoinfomatics Engineering http://www.uni-stuttgart.de/studieren/angebot/geodaesie/index.en.hhttp://www.uni-stuttgart.de/studieren/angebot/geodaesie/index.en.html#diplomatml#diploma

Geodesy and Geoinformaiton Geodesy and Geoinformaiton http://www.gug.bv.tum.de/seiten-e/technik/physik.htmlhttp://www.gug.bv.tum.de/seiten-e/technik/physik.html

Hydrology and Water Management Ecology Centre: Hydrology and Water Management Ecology Centre: http://www.hydrology.uni-kiel.de/lehre/vorlesung/ws04-05/vl_msc01http://www.hydrology.uni-kiel.de/lehre/vorlesung/ws04-05/vl_msc0104_02.pdf04_02.pdf

GEOG101: GEOG101: http://faculty.winthrop.edu/storiec/files/GEOG101/lectures/05-GEOG1http://faculty.winthrop.edu/storiec/files/GEOG101/lectures/05-GEOG101-MapsGIS.pdf01-MapsGIS.pdf

Kate Beard’s SIE 509 Principles of GIS: Map ProjectionsKate Beard’s SIE 509 Principles of GIS: Map Projections higheredbcs.wiley.com/legacy/college/strahler/0471480533/higheredbcs.wiley.com/legacy/college/strahler/0471480533/

student_pres/ch03.ppt – student_pres/ch03.ppt – http://www.biology.ualberta.ca/facilities/gis/uploads/instructions/http://www.biology.ualberta.ca/facilities/gis/uploads/instructions/

5_GCP_Fall2004.pdf5_GCP_Fall2004.pdf