Lecture 4. Coordinate Systems & Projections

Transcription

1 Lecture 4 Coordinate Systems & Projections

2 Outline Geodesy Geoids Ellipsoids Geographic Coordinate Systems Magnetic North vs. True North Datums Projections Applying Coordinate Systems and Projections

3 Why are Coordinates Important? Coordinates define the location, extent and shape of geographic objects. GEODESY: The science of measuring the shape of the earth Bolstad

4 Geoid: A three-dimensional undulating surface along which the pull of gravity is a specified constant and is deformed by the earth s rotation. Geoids

5 Ellipsoids Accepted as the best geometric model of the earth s surface. An ellipsoid is a mathematical surface defined by revolving an ellipse around its minor (polar) axis. It approximates the surface of the earth without topographic undulations. The word spheroid generally means the same thing.

6 Ellipsoids Measuring the size of the ellipsoid at different locations produced different common ellipsoids. Geoidal variation in earth s shape is the primary reason different ellipsoids are being employed in different parts of the world.

7 Common Ellipsoids Ellipsoid Semi-major axis Airy 1830, Modified Airy Australian National Bessel 1841 (Namibia) Bessel Clarke 1866, Clarke 1880, Everest (Malay. & Sing) Everest (Pakistan) Modified Fischer Krassovsky GRS South American WGS WGS * Internationally recognized ellipsoids.

8 Geographic Coordinate Systems (Spherical Coordinate Systems) While latitude and longitude can locate exact positions on the surface of the earth, they are not uniform units of measure. Only along the equator does the distance represented by one degree of longitude approximate the distance represented by one degree of latitude.

9 Recording Geographic Coordinates Two Common Methods: Degrees-minutes-seconds Ex Decimal degrees Ex

10 Magnetic vs. Geographic North Magnetic North: Where a compass points to. Geographic North Pole: Located at one of the poles of the earth s axis of rotation. They do NOT coincide. The angular difference is called magnetic declination. Maps always reference the Geographic North Pole!

11 Datums Geographic Coordinates only provide 1 exact location. The prime meridian at 0 O longitude (Greenwich Observatory). We must establish a set of points by which all other latitudes and longitudes are determined. We do this through geodetic surveys and monument points.

12 Datums Two components of a datum are: A specified ellipsoid A set of surveyed coordinate locations specifying horizontal positions (for a horizontal datum) or vertical positions (for a vertical datum) on the surface of the Earth. Most Common Datums: Datum: North American 1927 Ellipsoid: Clarke 1866 North American 1983 GRS 80 WGS 1972 WGS 72 WGS 1984 WGS 84

13 Cartesian Coordinate Systems (Projected Coordinate Systems) What are they for? Where are you right now? How far are you from some other location? Coordinate systems provide a quantitative framework for identifying your location on the earth. To overcome measurement difficulties, data is often transformed from threedimensional geographic coordinates to two-dimensional projected coordinates.

14 Projections Map Projections: The transformation of coordinate locations from the earth s curved surface onto flat maps. There are three ways to project the earth onto a developable flat surface (based on geometric shape): Azimuthal (Plane) Cylindrical (Cylinder) Conic (Cone)

15 Projections Projections with Non-Developable Surfaces: Sinusoidal Projections Mollweide Projection Created using mathematical projections from an ellipsoid. May fuse other projections to provide a more accurate global view with less distortion.

16 Classifying Projections Because all projections result in some distortion of the earth, we classify projections based on the properties they maintain: Conformal: preserves shape and direction Equivalent: preserves area Compromise: preserves neither area nor shape, preserves distance over a short area. Perspective: preserved properties varies, but for the most part all properties are distorted along the edges of the map or photo.

17 Projections A mercator projection preserves shape. (conformal) A Sinusoidal projection maintains area. (Equivalent) A Peters projection maintains area. (Equivalent) A Robinson projection does not preserve any Properties; the features look correct.

18 State Plane Coordinate System Based on Mercator and Lambert projections NAD 27 Datum FIPS Codes NAD 83 Datum Units measured in feet or meters Note: International Foot vs. US Survey Foot Los Angeles NAD27 or NAD83 Useful for mapping counties or larger areas.

19 Universal Transverse Mercator System (UTM) Global coordinate system better for areas spanning large regions. Mercator or Lambert projection applied The earth is divided into zones which are each 6 degrees of longitude wide. The origin of each zone (where the zone begins and intersects the equator) are given a false origin. Locations are then simply identified by the number of meters from the origin of the zone.

20 Applying Coordinate Systems and Projections Importance of lining up data Shapefiles have.prj files Tiff s have.tfw files Assigning projections and re-projecting data: ArcToolbox Data Management Tools Projections and Transformations How to view projection information of a layer: ArcCatalog Metadata Spatial tab. ArcMap Layer Properties Source tab. View projection information of a data frame: View Data Frame Properties

21 ArcGIS and Coordinate Systems On-the-fly Projections Permanent Layer Projections What if you don t know the Coordinate System of a layer? Search for layer metadata or other documentation. What is projection of other data from the same agency? Load layer into ArcMap, view location reference numbers. Ex. Does it look like a geographic coordinate system (DMS) or UTM (6 or 7 numbers)?