Projections and Coordinates - Personal Websites

1 4/11/20161 Projections and Coordinates There are many reasons for wanting to project the Earth s surface onto a plane, rather than deal with the curved surface The paper used to output GIS maps is flat Flat maps are scanned and digitized to create GIS databases Rasters are flat, it s impossible to create a raster on a curved surface The Earth has to be projected to see all of it at once It s much easier to measure distance on a planeMap Projections :the inevitability of distortion because we are trying to represent a 3 D sphere on a 2 D plane, distortion is inevitable thus,everytwo dimensional map is inaccuratewith respect to at least one of the following: area shape distance directionWe are trying to represent this amount of the earth onthis amount of map Any projection must distort the Earth in some way Two types of Projections are important in GIS Conformalproperty: Shapes of small features are preserved: anywhere on the projection the distortion is the same in all directions Equal areaproperty: Shapes are distorted, but features have the correct area Both types of Projections will generally distort distances!

2 Map Projections : classifications or How can we think about map Projections ?Property Preserved Equal area Projections preserve the area of features (popular in GIS) Conformal Projections preserve the shapeof small features (good for presentations) , and show localdirections (bearings) correctly (useful for coastalnavigation) Equidistant Projections preserve distances(scale) to places from one point, or along a one or more lines True direction Projections preserve bearings(azimuths) either locally (in which case they are also conformal) or from center of Model Used Planar/Azimuthal/Zenithal: image of spherical globe is projected onto a map planewhich is tangent to (touches) globe at single point Conical:image of spherical globe is projected onto a conewhich is tangent along a line(s) (usually a parallel of latitude) cone is then unfolded to create flat map Cylindrical:image of spherical globe is projected onto a cylinderwhich also is tangent along a line(s) again, cylinder is unfolded to create a flat map Classified by Property Preserved or by Geometrical Model 4/11/20163 Geometric ModelChoosing a Map projection Issues to Consider: Extent of area to map: city, state, country, world?

3 Location: polar, mid latitude, equatorial? Predominant extent of area to map: E W, N S, oblique? Rules of thumb Always record lat/long coordsnotprojected X,Y coords in the GIS database if possible Check project specifications; does it specify a required projection ? State Plane or UTM often specified for US gov. work. Use equal area Projections for thematic or distribution maps, and as a general choice for GIS work Use conformal Projections in presentations For navigational applications, need true distance or direction4/11/20164 Commonly Encountered Map Projections in GIS Albers Conic Equal Area often used for US base maps showing all of the lower 48 states standard parallels set at 29 1/2N and 45 1/2N Lambert Conformal Conic often used for US Base map of all 50 states (including Alaska and Hawaii), with standard parallels set at 37N and 65N also for State Base Map series, with standard parallels at 33N and 45N also used in State Plane Coordinate System (SPCS) transverse mercator used in SPCS for States with major N/S extent universal transverse mercator (UTM)

4 Used for world wide military (and other) large scale mappingMost commonly, you encounter these 3 Projections , along with the SPCS and UTM Projections systemswhich use ProjectionsNormalMercatorTransverseTrans verse MercatorObliqueOblique MercatorParallels are line of tangencyMeridians are line of tangency4/11/20165 Conformal Projections Preserve local shape Misrepresent areas Graticule lines (lat and long) on globe are perpendicular Best used for large scale reference maps Preserve angles and shapes at pointsDo not use for data distribution maps will distort area, and therefore, misrepresent densitiesBetter for showing routes and locationsLambert Conformal ConicConterminous Area Projections Preserve the area of displayed features Graticule lines (lat and long) on globe may not intersect at right angles In some instances (especially maps of smaller regions) it will not be obvious that shape has been distorted Thus, it will not be obvious that shape has been distorted and distinguishing from an equal area projection from a conformal projection is difficult (unless documented)Choose equal area when making thematic mapsRemember if you are mapping data distributions, choose an equal area projection !

5 Albers Equal Area is customized for the continental United StatesAlbers Equal Area ConicConterminous two lines of standard parallel(two lines that are true )4/11/20167 What map projection is this?What map projection is this?4/11/20168 What map projection is this?The universal transverse mercator (UTM) projection A type of cylindrical projection Implemented as an internationally standard coordinate system Initially devised as a military standard Uses a system of 60 zones Maximum distortion is TransverseMercator because the cylinder is wrapped around the Poles, not the Equator4/11/20169 Zones are each six degrees of longitude, numbered as shown at the top, from W to EUniversal transverse mercator (UTM) First adopted by US Army in 1947 for large scale maps worldwide Used from lat.

6 84 N to 80 S; universal Polar Stereographic (UPS) used for polar areas Globe divided into 60 N/S zones, each 6 wide; these are numbered from one to sixty going east from 180th meridian Each zone divided into 20 E/W belts, each 8 high lettered from the south pole using C thru X (O and I omitted) The meridian halfway between the two boundary meridians for each zone is designated as the central meridian and a cylindrical projection is done for each zone 4/11/201610 universal transverse mercator (UTM) Coordinate origins are at the intersection of the equator and the zone s central meridian; This origin given a value of 0 metersnorth, 500,000meast, thus no negative values a false origin at 10,000,000 meters south used for southern hemishere Military uses a different system for coordinate location dividing each UTM primary grid zone into 10km by 10km squares and designates each by a double letterUTM in Pennsylvania:2 zones.

7 Zone 17 (84W-78W), Zone 18 (78W-72W) universal transverse mercator (UTM)4/11/201611 Implications of the Zone System Each zone defines a different projection Two maps of adjacent zones will not fit along their common border Jurisdictions that span two zones must make special arrangements Use only one of the two Projections , and accept the greater than normal distortions in the other zone Use a third projection spanning the jurisdiction Italy is spans UTM zones 32 and 33 UTM Coordinates In the N Hemisphere define the Equator as 0 mN The central meridian of the zone is given a false easting of 500,000 mE Eastings and northings are both in meters allowing easy estimation of distance on the projection A UTM georeference consists of a zone number, a hemisphere, a six digit easting and a seven digit northing , 14, N, 468324E.

8 5362789N4/11/201612 State Plane Coordinates Defined in the US by each state Some states use multiple zones Several different types of Projections are used by the system Provides less distortion than UTM Preferred for applications needing very high accuracy, such as surveyingState Plane Coordinate System (SPCS) Began in 1930s for public works projects; popular with interstate designers States divided into 1 or more zones (~130 total for US) each zone designed to maintain scale distortion to less than 1 part per 10,000 Pennsylvania has 2 zones running E/W: north (3701), south (3702) Different Projections used: transverse mercator (conformal) for States with large N/S extent Lambert conformal conic for rest (incl. Pennsylvania) some states use both Projections (NY, FL, AK) oblique mercator used for Alaska panhandle Each zone also has: unique standard parallels (2 for Lambert) or central meridian (1 for mercator ) false coordinate origins which differ between zones, and use feet for NAD27 and meters for NAD83 (1m= in.)

9 Exact used for conversion) See Snyder, 1982 USGS Bulletin # 1532, p. 56 63 for details 4/11/201613 State Plane Coordinate System (SPCS)State Plane Coordinate System (SPCS)