You will want to pay attention… there will be a test on this material!!! The Exhilarating World of Geodesy and Map Projections

Geodesy: measuring the Earth Geodesy: a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravity field, in a three-dimensional time varying space. Geodesy: a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravity field, in a three-dimensional time varying space. Geodesy deals with the determination of the earth's shape and size, as well as its gravity field, i.e. the measurement of gravitational acceleration. Geodesy deals with the determination of the earth's shape and size, as well as its gravity field, i.e. the measurement of gravitational acceleration. The knowledge of the gravity field is important, because almost every geodetic measurement is closely related to gravity, e.g. instruments have to be leveled along the a horizontal surface. The knowledge of the gravity field is important, because almost every geodetic measurement is closely related to gravity, e.g. instruments have to be leveled along the a horizontal surface.

Calculating Routes on the Earth’s Surface Calculations however (including calculations of a route for high-speed trains) do not use the actual shape of the earth, but mathematically defined surfaces and bodies such as planes, spheres or ellipsoids of rotation. Calculations however (including calculations of a route for high-speed trains) do not use the actual shape of the earth, but mathematically defined surfaces and bodies such as planes, spheres or ellipsoids of rotation. The difference between reality and these simplified mathematical models is shown in the figure below. The difference between reality and these simplified mathematical models is shown in the figure below.

Geodesy and GPS It is critical to know about the difference between heights above sea level (which are related to the gravitational field and thus the only way to determine the slope) and the ellipsoidal heights, which are a result of GPS measurements. It is critical to know about the difference between heights above sea level (which are related to the gravitational field and thus the only way to determine the slope) and the ellipsoidal heights, which are a result of GPS measurements. Geodesy provides information about the reference surface of the heights above sea level - the so-called geoid. The geoid is represented as the surface of an imaginary, calm sea, continued below the continents. Geodesy provides information about the reference surface of the heights above sea level - the so-called geoid. The geoid is represented as the surface of an imaginary, calm sea, continued below the continents. It is the connection between the heights measured with GPS and heights above sea level, used in national vertical control networks. It is the connection between the heights measured with GPS and heights above sea level, used in national vertical control networks.

Earth as a Geoid Earth has a dynamic surface and complex structure. A Geoid is too complex a shape for daily needs so easier to think of Earth as an ellipsoid kiel.de/lehre/vorlesung/ws04-05/vl_msc0104_02.pdf kiel.de/lehre/vorlesung/ws04-05/vl_msc0104_02.pdf

Geoid-Spheroid-Ellipsoid A GEOID is the earth’s actual shape (including elevation above/below sea level) A GEOID is the earth’s actual shape (including elevation above/below sea level) A SPHEROID is an ellipsoid that approximates the shape of a sphere A SPHEROID is an ellipsoid that approximates the shape of a sphere An ELLIPSOID is created by rotating an ellipse about either major axis or minor axis An ELLIPSOID is created by rotating an ellipse about either major axis or minor axis

Earth as Reference Ellipsoid Ellipsoid defined by an equatorial radius, polar radius and the reciprocal of the flattening Ellipsoid defined by an equatorial radius, polar radius and the reciprocal of the flattening Ellipsoid approximates the geoid in size and position Ellipsoid approximates the geoid in size and position Different ellipsoids in use. They differ in equatorial radius and flattening as well as positioning of their center. Different ellipsoids in use. They differ in equatorial radius and flattening as well as positioning of their center. Geoid with different elipsoids and different reference locations

Graticule: parallels and meridians System of imaginary intersecting lines was created based on 360 degree Babylonian system for dividing a circle or sphere System of imaginary intersecting lines was created based on 360 degree Babylonian system for dividing a circle or sphere Map projections are based on: Map projections are based on: Central MeridiansCentral Meridians Standard ParallelsStandard Parallels

The Graticule …Projected

What is a Map Projection? A map is a flat representation of a globe A map is a flat representation of a globe A map projection is a systematic transfer of points on a curved surface to a flat projection surface A map projection is a systematic transfer of points on a curved surface to a flat projection surface

SSADD: 5 Key Properties of Maps Scale: relationship of distance and area on Earth to distance and area on map Scale: relationship of distance and area on Earth to distance and area on map Shape: shape is preserved when the scale of any point on the map is the same in any direction Shape: shape is preserved when the scale of any point on the map is the same in any direction Area: proportional relationship between study region and area of the Earth that it represents Area: proportional relationship between study region and area of the Earth that it represents Distance: length from center of the projection to any other place on the map Distance: length from center of the projection to any other place on the map Direction: angles from a point on a line to another point are portrayed correctly in all directions Direction: angles from a point on a line to another point are portrayed correctly in all directions

Why use Map Projections? GIS and paper maps are flat and more convenient than 3D models for most applications GIS and paper maps are flat and more convenient than 3D models for most applications Scanning and digitizing maps is a big source of spatial data used in GIS Scanning and digitizing maps is a big source of spatial data used in GIS Most common spatial data models are flat and cannot be created on curved surface Most common spatial data models are flat and 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 plane Much easier to measure distance on a plane

Problems with Map Projections Maps can preserve some of the properties but not all Maps can preserve some of the properties but not all No projection can retain more than one of these properties over large portion of globe No projection can retain more than one of these properties over large portion of globe Every map projection distorts the earth is several ways Every map projection distorts the earth is several ways Decisions of which projection to use depends on reducing distortion Decisions of which projection to use depends on reducing distortion

Projection Parameters Projection Center: point of projection Projection Center: point of projection Projection Families: Developable Surfaces Projection Families: Developable Surfaces Projection Aspect: orientation of developable surfaces Projection Aspect: orientation of developable surfaces Location of developable surface Location of developable surface

Projection Centers Gnomonic: projection point from Earth’s center Gnomonic: projection point from Earth’s center Stereographic: at antipodal surface Stereographic: at antipodal surface Orthographic: at infinity Orthographic: at infinity

3 Families of Projections Cylindrical Cylindrical Conical Conical Planar Planar Developable surface: 2 D surface upon which map information is projected. Can be unrolled without distortion although projection will contain distortions

Cylindrical Projections Used by mariners for navigation Used by mariners for navigation Meridians run north - south Meridians run north - south Parallels run Parallels run east- west east- west True at equator and distortion increases towards the poles True at equator and distortion increases towards the poles

Conical Projections Used for mid latitude maps Used for mid latitude maps True at areas between standard parallels True at areas between standard parallels

Planar Projections Used to navigate flight routes Used to navigate flight routes Preserves Great Circle Lines Preserves Great Circle Lines In polar aspect, these maps project meridians as straight lines radiating from the poles and parallels as complete circles centered at the pole In polar aspect, these maps project meridians as straight lines radiating from the poles and parallels as complete circles centered at the pole True at poles and distortions increases outwards True at poles and distortions increases outwards

3 basic rules for choosing projection family

4 Types of Projection Aspect Normal: oriented with polar axis Normal: oriented with polar axis Transverse: perpendicular to polar axis Transverse: perpendicular to polar axis Polar: centered on N/S Poles Polar: centered on N/S Poles Oblique: all others Oblique: all others

Location of Developable Surface Tangent: DS touches the globe Tangent: DS touches the globe Secant: DS cuts into the globe Secant: DS cuts into the globe

Map Property Preservation If a projection preserves… If a projection preserves… SHAPE it is called CONFORMAL.SHAPE it is called CONFORMAL. AREA is called EQUAL-AREA or Equivalent.AREA is called EQUAL-AREA or Equivalent. DISTANCE it is called EQUIDISTANTDISTANCE it is called EQUIDISTANT DIRECTION it is called AZIMUTHALDIRECTION it is called AZIMUTHAL

Tissot’s Indicatrix: Graphical Tool to Analyze Projection Properties

Example: Mercator Projection Cylindrical Cylindrical Conformal Conformal Areas not preserved and increase towards the top and bottom of the map Areas not preserved and increase towards the top and bottom of the map Preserves true-direction along graticule lines Preserves true-direction along graticule lines Used for ocean navigation Used for ocean navigation

Mercator Projection

Example: Lambert Conformal Conical Conical Conical Conformal Conformal Preserves shape of geographic features Preserves shape of geographic features Useful in mapping mid latitudes Useful in mapping mid latitudes

Lambert Conformal Conical

Example: Orthographic Azimuthal Planar Planar Azimuthal Azimuthal Equatorial or Oblique Aspects Equatorial or Oblique Aspects Azimuthal not suitable for displaying entire Earth in one view Azimuthal not suitable for displaying entire Earth in one view

Orthographic Azimuthal

Robinson Projection ‘Looks’ Balanced Used by NGS Distance Shape Direction are all distorted but…

Projection Systems A Projected Coordinate System is a projection based on two different projections depending on the shape of the region it describes A Projected Coordinate System is a projection based on two different projections depending on the shape of the region it describes State Plane Coordinate System (SPCS) State Plane Coordinate System (SPCS) States extending east to west, uses Lambert conformal conical projectionStates extending east to west, uses Lambert conformal conical projection States extending north to south, uses tranverse cylindrical Mercator projectionStates extending north to south, uses tranverse cylindrical Mercator projection Measured in feetMeasured in feet Minimizes distortions within 1 footMinimizes distortions within 1 foot

Projection Systems Universal Tranverse Mercator Coordinate System (UTM) Universal Tranverse Mercator Coordinate System (UTM) Uses 60 zones, each 6 degrees of longitude wideUses 60 zones, each 6 degrees of longitude wide Measured in metersMeasured in meters Uses a secant variationUses a secant variation Minimizes distortion < 1meter within each zoneMinimizes distortion < 1meter within each zone

Unprojected vs. Undefined Data Unprojected geographic coordinate system allows more flexibility in setting ArcMap’s data frame coordinate system to suit analysis needs Unprojected geographic coordinate system allows more flexibility in setting ArcMap’s data frame coordinate system to suit analysis needs Undefined coordinate system is missing files to enable ArcMap to read and reference them with other data layers. You will need to define the coordinate system to fully use the file in an ArcMap project. Undefined coordinate system is missing files to enable ArcMap to read and reference them with other data layers. You will need to define the coordinate system to fully use the file in an ArcMap project.

Final Thoughts Map projections are critical for transferring 3D globe onto 2D flat surface Map projections are critical for transferring 3D globe onto 2D flat surface Many types of projections used for different purposes Many types of projections used for different purposes Need to understand map projections to work with multiple layer files in GIS to make each layer ‘fit’ with the other. Need to understand map projections to work with multiple layer files in GIS to make each layer ‘fit’ with the other. Go to JH Labs website and explore more unusual map projections. Bring a copy of your favorite unusual projection with a description of which properties are preserved and which are distorted. Go to JH Labs website and explore more unusual map projections. Bring a copy of your favorite unusual projection with a description of which properties are preserved and which are distorted.

Assignment Go to JH Labs website ( JH Labs: Java Map Projection Library Go to JH Labs website ( JH Labs: Java Map Projection Library and explore more unusual map projections. and explore more unusual map projections. Bring a copy of your favorite unusual projection with a description of which properties are preserved and which are distorted. Bring a copy of your favorite unusual projection with a description of which properties are preserved and which are distorted. Go online to search how geodesy is used in making maps, refining measurements of earth’s surface, navigation systems, or another interesting aspect of how it is used by scientists and engineers. Write a one page (double spaced 12 font) summary of the information you found. Provide the website URLs and any images that will help explain your findings. Go online to search how geodesy is used in making maps, refining measurements of earth’s surface, navigation systems, or another interesting aspect of how it is used by scientists and engineers. Write a one page (double spaced 12 font) summary of the information you found. Provide the website URLs and any images that will help explain your findings. Be prepared to share your projection selection and your geodesy research summary with a small group. Be prepared to share your projection selection and your geodesy research summary with a small group.

Quiz Material Know definitions for geoid, spheroid, ellipsoid Know 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 (SSADD) Know definitions of the 5 Key Properties of Maps (SSADD) Know at least one reason for using map projections and at least one problem with map projections Know at least one reason for using map projections and at least one problem with map projections Know 3 types of projection centers Know 3 types of projection centers Know 3 families of projection Know 3 families of projection Name 3 specific map projections and the characteristics of one of them (pros and cons) Name 3 specific map projections and the characteristics of one of them (pros and cons) Name one example of a Projected Coordinate System Name one example of a Projected Coordinate System

Resources used for presentation JH Labs: Java Map Projection Library JH Labs: Java Map Projection Library Information on Geodesy and Geoinfomatics Engineering stuttgart.de/studieren/angebot/geodaesie/index.en.html#diploma Information on Geodesy and Geoinfomatics Engineering stuttgart.de/studieren/angebot/geodaesie/index.en.html#diploma stuttgart.de/studieren/angebot/geodaesie/index.en.html#diploma stuttgart.de/studieren/angebot/geodaesie/index.en.html#diploma Geodesy and Geoinformaiton e/technik/physik.html Geodesy and Geoinformaiton e/technik/physik.htmlhttp:// e/technik/physik.htmlhttp:// e/technik/physik.html Hydrology and Water Management Ecology Centre: 05/vl_msc0104_02.pdf Hydrology and Water Management Ecology Centre: 05/vl_msc0104_02.pdf 05/vl_msc0104_02.pdf 05/vl_msc0104_02.pdf GEOG101: GEOG101-MapsGIS.pdf GEOG101: GEOG101-MapsGIS.pdf GEOG101-MapsGIS.pdf GEOG101-MapsGIS.pdf Kate Beard’s SIE 509 Principles of GIS: Map Projections Kate Beard’s SIE 509 Principles of GIS: Map Projections higheredbcs.wiley.com/legacy/college/strahler/ /student _pres/ch03.ppt – higheredbcs.wiley.com/legacy/college/strahler/ /student _pres/ch03.ppt – GCP_Fall2004.pdf GCP_Fall2004.pdf