2016/07/25. GIS 211 Map Projections & Coordinate Systems Chang Chapter 2. Why is this important to YOU? Dr W Britz

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1 GIS 211 Map Projections & Coordinate Systems Chang Chapter 2 Dr W Britz Every map user and maker should have a basic understanding of projections no matter how much computers seem to have automated the process. - John P. Snyder Why is this important to YOU? Creating spatial data (collecting GPS data) Import into GIS and overlay with other layers Acquiring spatial data from other sources Display your GPS data using maps 1

2 Map projections Define the spatial relationship between locations on earth and their relative locations on a flat map Are mathematical expressions Cause the distortion of one or more map properties (scale, distance, direction, shape) Map Projection A map projection is a systematic arrangement of parallels and meridians on a plane surface. Cartographers group map projections by the preserved property into conformal, equal area or equivalent, equidistant, and azimuthal or true direction. Cartographers also use a geometric object (a cylinder, cone, or plane) and a globe (i.e., a sphere) to illustrate how to construct a map projection. Types of Projections created from different surfaces Conic (Albers Equal Area, Lambert Conformal Conic) - good for East-West land areas Cylindrical (Transverse Mercator) - good for North-South land areas Azimuthal (Lambert Azimuthal Equal Area) - good for global views Case and projection. Scale distortion Scale near intersections with surface are accurate Scale between intersections is too small Scale outside of intersections is too large and gets excessively large the further one goes beyond the intersections 2

3 Why project data? Data often comes in geographic, or spherical coordinates (latitude and longitude) and can t be used for area calculations in most GIS software applications Some projections work better for different parts of the globe giving more accurate calculations Some projection parameters Map projection parameters include standard lines (standard parallels and standard meridians), principal scale, scale factor, central lines, false easting, and false northing. Standard parallels and meridians the place where the projected surface intersects the earth there is no scale distortion Central meridian on conic projects, the center of the map (balances the projection, visually) How to choose projections Generally, follow the lead of people who make maps of the area you are interested in. Look at maps! Transvers Mercator is a popular projection in SA UTM is commonly used and is a good choice when the east-west width of area does not exceed 6 degrees 3

4 Projections Preserve Some Earth Properties Area - correct earth surface area (Albers Equal Area) important for mass balances Shape - local angles are shown correctly (Lambert Conformal Conic) Direction - all directions are shown correctly relative to the center (Lambert Azimuthal Equal Area) Distance - preserved along particular lines Some projections preserve two properties Commonly Used Map Projections Transverse Mercator Lambert conformal conic Albers equal-area conic Equidistant conic The central parallel and the central meridian divide a map projection into four quadrants. Points within the NE quadrant have positive x- and y-coordinates, points within the NW quadrant have negative x-coordinates and positive y-coordinates, points within the SE quadrant have positive x-coordinates and negative y-coordinates, and points within the SW quadrant have negative x- and y-coordinates. The purpose of having a false origin is to place all points within the NE quadrant. Datum A datum is a mathematical model of the Earth, which serves as the reference or base for calculating the geographic coordinates of a location. A shift of the datum will result in the shift of positions of points. Datums/ Spheroids A National geodetic coordinate system is defined by a Geodetic Datum This Datum consists of two parts: 1. A defined geodetic reference ellipsoid, in terms of the a,b or a,f parameters (f=flatning) 2. A defined orientation, position and scale of the Geodetic system in space From this, it can be deduced that a specific ellipsoid can be used to define an infinite amount of datums. 4

5 Coordinate Systems There are 2 types of coordinate systems: s Projected Coordinate Systems A reference system using latitude and longitude to define the location of points on the surface of a sphere or spheroid decimal degrees (DD) degrees/minutes/seconds (DMS) W Spheroid approximates the shape of the earth Model of the earth Essentially when surveyors get together and all agree to be wrong Also called an ellipsoid A datum defines the position of the spheroid relative to the center of the earth Origin and orientation of latitude and longitude lines are determined by the datum Hundreds of datums customized for different parts of the world Universal Coordinate System (lat/lon) Lat/lon good for locating positions on surface of a globe Lat/lon is not efficient for measuring distances and areas! Latitude and longitude are not uniform units of measure One degree of longitude at equator = km (Clarke 1866 spheroid) One degree of longitude at 60 latitude = km (Clarke 1866 spheroid) Projected Coordinate Systems The Universal Transverse Mercator (UTM) grid system Longitude of Origin (Lo System) The Universal Polar Stereographic (UPS) grid system The Public Land Survey System (PLSS) 5

6 Projected Coordinate Systems A map projection is the systematic transformation of locations on the earth (latitude/longitude) to planar coordinates The basis for this transformation is the geographic coordinate system (which references a datum) Map projections are designed for specific purposes This process of flattening the earth will cause distortions in one or more of the following spatial properties: Shape Conformal map projections preserve shape Area Equal area map projections preserve area Distance/Scale Equidistant map projections preserve distance Direction/Angle Azimuthal map projections preserve true direction Universal Transverse Mercator (UTM) Developed by military Grid system Earth divided into 60 zones Great for small areas minimal map distortion distortion greater at edge of zones Most common map projection used by NWRs Coordinate Systems Universal Transverse Mercator (UTM) - a global system developed by the US Military Services Longitude of origin (Lo System) a system developed and used for South Africa The following simple conversion is applicable only where the Lo. of the South African system and the central meridian of the UTM system coincide ie. 15ºE 21ºE 27ºE and 33ºE Y(Lo.)=( E(UTM))/ X(Lo.)=( N(UTM))/ The UTM system incorporates a scale distortion of at the Lo. to reduce distortion at the edges of the belt. Universal Transverse Mercator (projected coordinate system) Uses the Transverse Mercator projection Each zone has a Central Meridian (l o ), zones are 6 wide, and go from pole to pole 60 zones cover the earth from East to West Reference Latitude (f o ), is the equator (Xshift, Yshift) = (x o,-y o ) = (500000, 0) in the Northern Hemisphere, units are meters The Universal Transverce Mercator coordinate system The UTM system divides the earth into 60 zones, each 6 degrees of longitude wide. These zones define the reference point for UTM grid coordinates within the zone. UTM zones extend from a latitude of 80 degrees South to 84 degrees North. UTM zones are numbered 1 to 60, starting at the international date line, longitude 180, and proceeding east. Zone extends from 180 W to 174 W and is centered on 177 W. Each zone is divided into horizontal bands spanning 8 degrees of latitude. 6

7 These bands are lettered, south to north, beginning at 80 S with the letter C and ending with the letter X at 84 N. The letters I and O are skipped The band lettered X spans 12 of latitude. A square grid is superimposed on each zone. It s aligned so that vertical grid lines are parallel to the center of the zone, called the central meridian. UTM grid coordinates are expressed as a distance in meters to the east, referred to as the eastings, and a distance in meters to the north, referred to as the northings. Eastings: o UTM easting coordinates are referenced to the center line of the zone known as the central meridian. o The central meridian is assigned an easting value of meters East. o Since this m value is arbitrarily assigned, eastings are sometimes reffered to as false eastings. o An easting of zero will never occur, since a 6 wide zone is never more than meters wide Northings: o UTM northing coordinates are measured relative to the equator. o For locations north of the equator the equator is assigned the northing value of 0 meters North. o To avoid negative numbers, locations south of the equator are made with the equator assigned a value of meters North. o Some UTM northing values are valid both north and south of the equator. o In order to avoid confusion the full coordinate needs to specify if the location is north or south of the equator. o Usually this is done by including the letter for the latitude band. When GPS points don t align with GIS Data Most likely a projection issue if: There are huge errors data points do not overlay Features could be displayed in wrong state or hemisphere! When GPS points don t align with GIS Data Possibly a datum issue if: GPS data overlays with GIS data, but off by several hundred feet Differences between NAD27 and NAD83 can be as much as 500 feet This creates problems when doing analysis 7