Published on November 15, 2007
GEOL 403/503 Principles of GIS: GEOL 403/503 Principles of GIS Bhushan Gokhale Ted Dunsford Fall 2007 Lecture 4: Geodesy, Datums, Map Projections and Coordinate Systems: Lecture 4: Geodesy, Datums, Map Projections and Coordinate Systems Spatial Data: Spatial Data GIS is different than other information systems because it contains spatial data Spatial data Co-ordinates that define the location, shape & extent of geographic objects For effective use of GIS we must understand How co-ordinate systems are established How cordinates are measured The Problem…: The Problem… People understand geography in a “Cartesian” coordinate system on a flat earth… We see a flat Earth, but the Earth is curved! Flat maps distort geometry Straight lines appear curved, etc… Irregular nature of the Earth’s shape Earth isn’t actually a sphere Geodesy Basics: Geodesy Basics Geodesy: the science of measuring the shape of the Earth Early History: Shape Pythagoras (sphere), Anaximenes (rectangular box) Early History: Size Eratosthenes (well), Posidonius (stars), Ptolemy Measuring the Earth’s Circumference: Measuring the Earth’s Circumference Eratosthenes measured the circumference of the Earth using basic principles of geometry Bolstad,2005 Estimation of the Earth’s Radius & Circumference: Estimation of the Earth’s Radius & Circumference Bolstad,2005 Posidonius estimated the circumference of the Earth by measuring angles to a star near the horizon Earth Size: Earth Size Defining the Earth’s Shape: Defining the Earth’s Shape Ellipsoid The Earth revolves easterly on its axis, generating centrifugal force, causing a bulge in the middle and flattening at the poles Geoid Representation of the Earth as an equigravitational surface Due to variations in gravity, the geoid does not follow the ellipsoid exactly (100 m deviation) Geoid height – difference between ellipsoid and geiod (geoid undulation) Bolstad,2005 Ellipsoidal Earth: Ellipsoidal Earth It is not practical to mathematically define every area of the Earth. An ellipse is a mathematical model that approximates the Earth’s size and shape The major axis lies in the earth’s equatorial plane while the minor axis is coincident with the earth’s spin axis Ellipsoid is generated by rotating an ellipse around the center of the Earth, using the semi-minor and semi-major axes, along with the flattening ratio Bolstad,2005 Ellipsoidal model of the Earth’s shape Why Different Ellipsoids?: Why Different Ellipsoids? Better methods for approximating the surface of the Earth Developed from different areas of the Earth Just an approximation… Geoid, Ellipsoid, and Topographic Surface: Geoid, Ellipsoid, and Topographic Surface Geoid – the equipotential surface of the earth Due to variations in gravity, the geoid does not follow the ellipsoid exactly (100 m deviation over most of the earth) Geoidal height – difference between ellipsoid and geiod (geoid undulation) Bolstad,2005 Geoidal Heights across the Globe: Geoidal Heights across the Globe Bolstad,2005 A & B - Large positive values , C - Large negative value Geographic Coordinate System: Geographic Coordinate System A geographic coordinate system uses a 3 dimensional sphere to define locations on the Earth. Locations are referenced by longitude and latitude. Bolstad,2005 Magnetic North Pole vs. Geographic North Pole: Magnetic North Pole vs. Geographic North Pole Bolstad,2005 Angular difference between the two directions is known as declination and it varies around the globe Specifications of the map projections and coordinate systems are always in reference to the geographic North Pole Parallels and Meridians: Parallels and Meridians Meridians are also known as lines of longitude Example is the Prime / Greenwich meridian Parallels are also known as lines of latitude Example is the equator Bolstad,2005 Spherical vs. Cartesian Geographical Coordinates: Notice the distortion of the circles near the North pole Spherical vs. Cartesian Geographical Coordinates Bolstad,2005 Datum: Datum The ellipsoid is a mathematical model that describes the shape of the Earth. A datum defines the position of the ellipsoid relative to the center of the Earth provides a frame of reference for measuring locations on the surface of the Earth aligns its spheroid to closely fit the Earth’s surface in a particular area © ESRI, ARC/INFO Help Bolstad,2005 Horizontal Datum Defined:: Horizontal Datum - A base reference for a coordinate system. It includes the latitude and longitude and orientation of an initial point of origin and an ellipsoid that models the surface of the earth in the region of interest. Horizontal Datum Defined: Y Prime Meridian X Z Slide21: Satellite Observations of the Earth European Remote Sensing satellite, ERS-1 from 780Km ERS-1 depicts the earth’s shape without water and clouds. This image looks like a sloppily pealed potato, not a smoothly shaped ellipse. Satellite Geodesy has enabled earth scienetists to gain an accurate estimate (+/- 10cm) of the geocentric center of the of the earth. A worldwide horizontal datum requires an accurate estimation of the earth’s center Datums: Datums North American Datums NAD27 (North American Datum of 1927) NAD83 (North American Datum of 1983) World Datums WGS84 (World Geodetic System of 1984) Used for GPS Other Datums European Datum of 1979 Ordnance Survey Datum of Great Britain, 1936 Australian Geodetic Datum, 1984 Horizontal Datums: Horizontal Datums Global replaces regional datums with a common, accurate standard One system for maps of the entire planet Regional vs. Global Approach Projection: Projection Why we make maps Globes are expensive to make, and cumbersome to carry in a briefcase!! Distortions are inherent when features on the earth surface are shown on a flat map sheet Orange Peel Example Bolstad,2005 Concept of a Projection: Concept of a Projection A systematic rendering of a graticule Projection Surfaces Developable Surfaces Cone Cylinder Plane Different projections create different distortions © ESRI, ArcView Help Planar Projections: Planar Projections Project map data onto a flat surface touching the globe Usually tangent to the globe, but may be secant Tangent point is focus of the projection Conic Projections: Conic Projections Conic Projection - tangent to the globe along a line of latitude distortion increases away from the standard parallel Conic projections are used for mid-latitude zones that have an east-to-west orientation Somewhat more complex conic projections contact the global surface at two locations called secant conic projections Bolstad,2005 Cylindrical Projections: Cylindrical Projections Mercator is most common cylindrical projection Equator is typically the line of tangency Meridians are of equal space, lines of latitude increases toward poles Displays true direction along straight lines Transverse projections use meridian lines as tangent point, therefore, North/South lines are preserved Bolstad,2005 Common Types of Projections: Common Types of Projections Conformal Projections Conformal projections preserve local shape. They show the perpendicular graticule lines intersecting at 90 degree angles However, an area may become more distorted to maintain the angles Equal Area Projections preserve the area of features. Other properties such as shape, angle, and scale are distorted. Equidistant projections preserve distances between certain points. Scale is not maintained correctly, however, typically one or more lines has its scale maintained. Bolstad,2005 Major Properties of Projections: Major Properties of Projections Conformality – retention of correct angles. Preserves shape, but not size. Also allows for accurate directions Equivalence – retains unit area. Good for measuring area phenomena (amount of arable land). There are scale changes however, and changes in shape Projection Effects: Projection Effects Conformal projections Mercator, Lambert conformal Equivalence Sinusoidal Equidistance azimuthal Coordinate Systems: Coordinate Systems Universal Transverse Mercator (UTM) is an international metric coordinate system that covers the entire earth. It has the advantage of being mathematically consistent and well defined for the entire earth. Local coordinate systems are often used to fit mapping needs for a particular region. Universal Transverse Mercator: Bolstad,2005 Universal Transverse Mercator Based on transverse Mercator projection Covers Earth surface between 80o South and 84o North 60 north-south zones 6 degrees of longitude wide Each zone overlaps ½ degree into the adjoining zones False origin of 500,000 meters west of the central meridian of each UTM zone UTM Zone 11N: UTM Zone 11N Bolstad,2005 State Plane Coordinate Systems: State Plane Coordinate Systems A rectangular coordinate system that is individually applied to each of the United States Designed to simplify local surveys and tie them in to a national geodetic network. System uses plane coordinates Therefore, curvature of the earth is not taken into account as the errors are minimal Projection from One System to Another: Projection from One System to Another Summary : Summary Datums: Datums A datum contains a reference ellipsoid. Each reference ellipsoid can be described by it’s: starting point degree of flattening (ratio of axes) Projections...: Projections... The process of fitting a spherical object to a flat surface. Three basic types Azimuthal (plane) Cylindrical Conic A Simulation: A Simulation Azimuthal Cylindrical Conic Projection orientations: Projection orientations Equatorial Transverse Oblique The four Properties: The four Properties Distance Direction Shape Area Coordinate System: Coordinate System Uniformly measures the earth’s surface… Coordinate systems have an origin... Basic coordinate systems: Basic coordinate systems Geographic Universal Transverse Mercator Military Grid State Plane All have advantages and disadvantages!