Map Projections & Coordinate Systems 9/10/2013. Why? M. Helper GEO327G/386G, UT Austin 2. M. Helper GEO327G/386G, UT Austin 4

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1 Map Projections & Coordinates Laing the earth flat Wh? Need convenient means of measuring and comparing distances, directions, areas, shapes. Traditional surveing instruments measure in meters or feet, not degrees of lat. & lon. Globes are bulk and can t show detail. 1:24,000 globe would have diameter of ~ 13 m Tpical globe has scale of ~ 1:42,000,000 Distance & area computations more comple on a sphere GEO327G/386G, UT Austin GEO327G/386G, UT Austin 2 Laing the earth flat How? Projections transformation of curved earth to a flat map; sstematic rendering of the lat. & lon. graticule to rectangular coordinate sstem. Laing the earth flat Sstematic rendering of Lat. (f) & Lon. (l) to cartesian (, ) coordinates: Scale 1: 42,000,000 Scale Factor (for areas) , 0 Earth Globe Map Globe distance Earth distance Peters Projection Map distance Globe distance GEO327G/386G, UT Austin 3 Geographic Coordinates Projected Coordinates (f, l) (, ) Map Projection GEO327G/386G, UT Austin 4 GEO327G/386G, UT Austin 1

2 Map Projections & Coordinate Sstems 9/10/2013 Laing the earth flat Geographic Displa Geographic displa no projection Distance and areas distorted b varing amounts (scale not true ); e.g. high latitudes = l, = f Grid lines have same scale and spacing f f l l GEO327G/386G, UT Austin Projected Displa E.g. Mercator projection: =l = ln [tan f + sec f] 6 GEO327G/386G, UT Austin Laing the earth flat How? Projection tpes: 90 f Orthographic a Gnomonic A Stereographic A a A a f T T T l B b b GEO327G/386G, UT Austin GEO327G/386G, UT Austin GEO327G/386G, UT Austin B b B 8 2

3 Light Bulb at Center (Gnomic) Gnomonic Grid Lines out of focus awa from point of tangenc All great circles are straight lines Same as image produced b spherical lens GEO327G/386G, UT Austin GEO327G/386G, UT Austin 10 Orthographic Light source at infinit; neither area or angles are preserved, ecept locall Stereographic Projection is conformal, preserves angles and shapes for small areas near point of tangenc, larger areas awa from point are distorted. Great circles are circles. 90 o GEO327G/386G, UT Austin GEO327G/386G, UT Austin 12 GEO327G/386G, UT Austin 3

4 Developable Surfaces 3 orientations for developable surfaces Surface for projection: Plane (azimuthal projections) Clinder (clindrical projections) Cone (conical projections) Clinder and cone produce a line of intersection (standard parallel) rather than at a point Standard Parallel Normal Transverse Oblique GEO327G/386G, UT Austin GEO327G/386G, UT Austin 14 Tangent or Secant? Tangent or Secant? Developable surfaces can be tangent at a point or line, or secant if the penetrate globe Secant balances distortion over wider region Secant cone & clinder produce two standard parallels Standard Parallels GEO327G/386G, UT Austin GEO327G/386G, UT Austin 16 GEO327G/386G, UT Austin 4

5 Projection produces distortion of: Where s the distortion? Distance Area Angle Shape Distortions var with scale; minute for large-scale maps (e.g. 1:24,000), gross for small-scale maps (e.g. 1: 5,000,000) Goal: find a projection that minimizes distortion of propert of interest GEO327G/386G, UT Austin 17 No distortion along standard parallels, secants or point of tangenc. For tangent projections, distortion increases awa from point or line of tangenc. For secant projections, distortion increases toward and awa from standard parallels. Secant line Tangent Secant GEO327G/386G, UT Austin 18 Distortions Azimuthal Clindrical Conic GEO327G/386G, UT Austin 19 How do I select a projection? Scale is critical projection tpe makes ver little difference at large scales For large regions or continents consider: Latitude of area Low latitudes normal clindrical Middle latitudes conical projection High latitudes normal azimuthal Etent Broad E-W area (e.g. US) conical Broad N-S area (e.g. S. America) transverse clindrical Theme e.g. Equal area vs. conformal (scale same in all directions) GEO327G/386G, UT Austin 20 GEO327G/386G, UT Austin 5

6 What needs to be specified? Projections in common use, US Geographic (unprojected) Teas Albers (Equal Area Conic) Albers Equal Area Conic Standard parallels at 29 o 30 and 45 o 30 for conterminous US. Latitude range should not eceed o Preserves area, distorts scale and distance (ecept on standard parallels!). Areas are proportional and directions true in limited areas. Origin X, Y Values Origin Longitude ( ais) Secant Locations Origin Latitude ( ais) Units of measure Ellipsoid Model Horizontal Datum GEO327G/386G, UT Austin GEO327G/386G, UT Austin 22 Projections in common use, US Lambert Conformal Conic Projection used b USGS for most maps of conterminous US (E-W etent is large) Used b SPCS for state zones that spread E-W (Teas) Conformal Projections in common use, US Clindrical Transverse Mercator basis for UTM coordinate sstem and State Plane Coordinate Sstems that spread N-S Standard Parallels 3 o apart GEO327G/386G, UT Austin GEO327G/386G, UT Austin 24 GEO327G/386G, UT Austin 6

7 Rectangular Coordinate Sstems UTM Coordinate Sstem Universal Transverse Mercator (UTM) US militar developed for global cartesian reference frame. State Plane Coordinate Sstem (SPCS) Coordinates specific to states; used for propert definitions. Public Land Surve Sstem (PLS) National sstem once used for propert description no common datum or aes, units in miles or fractional miles GEO327G/386G, UT Austin 25 T. M. secant projection is rotated about vertical ais in 6 o increments to produce 60 UTM zones. Rotate in 6 o increments UTM Zone is 6 o wide GEO327G/386G, UT Austin 26 () () UTM Coordinate Sstem T. M. secant projection is rotated about vertical ais in 6 o increments to produce 60 UTM zones. Zone boundaries are parallel to meridians. Zones numbered from 180 o (begins zone 1) eastward and etend from 80 o S to 84 o N. Each zone has a central meridian with a scale factor in US of (central meridian is farthest from secants, meaning scale distortion is greatest here). Secants are 1.5 o on either side of the central meridian. UTM Coordinate Sstem Zone boundaries are parallel to meridians. Zones numbered from 180 o (begins zone 1) eastward and etend from 80 o S to 84 o N UTM Zones GEO327G/386G, UT Austin GEO327G/386G, UT Austin 28 GEO327G/386G, UT Austin 7

8 UTM Coordinate Sstem UTM Coordinate Sstem Central meridian of each zone in US has a scale factor of (ma. distortion). Secants are 1.5 o on either side of the central meridian. (Y) () Locations are given in meters from central meridian (Easting) and equator (Northing). (-) Eastings avoided b giving X value of 500,000 m ( false easting ) to the Central Meridian In S. hemisphere, equator is given false northing of 10,000,000 m to avoid (-) Northings. N. Hemisphere origin is (500,000m, 0) S. Hemisphere origin is (500,000m, 10,000,000m) GEO327G/386G, UT Austin GEO327G/386G, UT Austin 30 UTM Coordinate Sstem UTM Coordinates for central Austin: Zone ,000 me, 3,350,000 mn Central Meridian (X = 500,000 m) GEO327G/386G, UT Austin 31 Y 99 o W Zone 14 Austin Y = 3,000,000 mn State Plane Coordinate Sstem (SPCS) Developed in 1930 s to provide states a reference sstem that was tied to national datum (NAD27); units in feet. Updated to NAD83, units in meters; some maps still show SPCS NAD27 coordinates. Some larger states are divided into zones. X, Y coordinates are given relative to origin outside of zone; false eastings and northings different for each zone GEO327G/386G, UT Austin 32 GEO327G/386G, UT Austin 8

9 Teas NAD83 SPCS (meters) Public Land Surve Sstem (PLS) Zone Code 4201 North 4202 N. Cent Central 4204 S. Cent South Stand. Parallels Origin F. Easting F. Northing 200,000 1,000, ,000 2,000, ,000 3,000, ,000 4,000, ,000 5,000,000 Austin: Central Zone ~ 944,000mE ~ 3,077,000mN Austin GEO327G/386G, UT Austin 33 Y X Sstem developed to surve and apportion public lands in the US, c Coordinate aes are principal baselines and meridians, which are distributed among the states. Grid sstem based on miles and fractional miles from baseline and meridian origin. Not in Teas, nor 19 other states Units are miles and fractional miles; feet and ards are also in use GEO327G/386G, UT Austin 34 Principal Baselines & Meridians Public Land Surve Sstem (PLS) Meridian Step 1 Step 2 Baseline Section 33 P.L.S. No P.L.S. Principal Meridian Baseline T2S, R1W, Section 33 Step 3 Center Sec GEO327G/386G, UT Austin GEO327G/386G, UT Austin 36 GEO327G/386G, UT Austin 9

10 Summar Summar (cont.) Projections transform geographic coordinates (f, l) to cartesian (, ). Projections distort distance, area, direction and shape to greater or lesser degrees; choose projection that minimizes the distortion of the map theme. Points of tangenc, standard parallels and secants are points or lines of no distortion. A conformal map has the same scale in all directions GEO327G/386G, UT Austin 37 Projection characteristics are classified b: Light source location Gnomonic Stereographic Orthographic Developable surface Plane (azimuthal) Clinder (clindrical) Cone (conic) Orientation Normal Transverse Oblique GEO327G/386G, UT Austin 38 Summar (cont.) Modern coordinate sstems are based on projections that minimize distortion within narrow, conformal zones. UTM is a global sstem using WGS84/NAD83; others are local with varing datums GEO327G/386G, UT Austin 39 GEO327G/386G, UT Austin 10