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Geographic Datums & Coordinates

Geographic Datums & Coordinates. What is the shape of the earth? Why is it relevant?. Make a Map, Graph the World. What determines spacing of 30 o increments of Lat. & Lon. ? Dimensions and shape of earth (= DATUM) Map Projection Map Scale. Austin: (-97.75, 30.30). X-axis. Y-axis.

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Geographic Datums & Coordinates

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  1. Geographic Datums & Coordinates What is the shape of the earth? Why is it relevant? GEO420k, UT Austin

  2. Make a Map, Graph the World • What determines spacing of 30o increments of Lat. & Lon. ? • Dimensions and shape of earth(= DATUM) • Map Projection • Map Scale Austin: (-97.75, 30.30) X-axis Y-axis • Graph shows 30o increments of Lat. & Lon. at ~ 1:385,000,000 GEO420k, UT Austin

  3. The Figure of the Earth • Models • Sphere with radius of ~6378 km • Ellipsoid (or Spheroid) with equatorial radius (major axis) of ~6378 km and polar radius (minor axis) of ~6357 km • Difference of ~21 km is usually expressed as the “flattening” (f) ratio of the ellipsoid: • f = difference/major axis = ~1/300 for earth GEO420k, UT Austin

  4. Ellipsoid / Spheroid • Rotate an ellipse around an axis (c.f. Uniaxial indicatrix of optical mineralogy) Rotation axis a = Major axis b = Minor axis X, Y, Z = Reference frame GEO420k, UT Austin

  5. Standard Earth Ellipsoids GEO420k, UT Austin

  6. Horizontal Datums Datum = ellipse and axis of rotation. Common North American datums: • NAD27 (1927 North American Datum) • Clarke (1866) ellipsoid, non-geocentric axis of rotation* • NAD83 (1983 North American Datum) • GRS80 ellipsoid, non-geocentric axis of rotation • WGS84 (1984 World Geodetic System) • GRS80 ellipsoid, nearly identical to NAD83 • Other datums in use globally GEO420k, UT Austin

  7. Datum “shifts” • Coordinate shift by use of improper datum can result in horizontal positioning errors as great as 800 m • An example compares the WGS84 location of the Texas state capitol dome to 13 other datums. GEO420k, UT Austin

  8. Latitude and Longitude +30o (North) Latitude -30o (West) Longitude GEO420k, UT Austin

  9. Latitude facts: • Lines of latitude (parallels) are evenly spaced (small circles) from 0o at equator (a great circle) to 90o at poles. • 60 nautical miles (~ 110 km)/1o, ~1.8 km/minute and ~ 30 m/second of latitude. • N. latitudes are positive (+f), S. latitudes are negative (-f). GEO420k, UT Austin

  10. P.M. 180o Longitude facts: • Lines of longitude (meridians) converge at the poles; the distance of a degree of longitude varies with latitude. • Zero longitude is the Prime (Grenwich) Meridian (PM); longitude is measured from 0-180o east and west of the PM. • East longitudes are positive (+l), west longitudes are negative (-l). GEO420k, UT Austin

  11. Vertical Datums • Sea Level (MSL), Geoid • Geoid = surface of constant gravitational potential that best fits MSL • governed by mass distribution of earth • Ellipsoid (HAE = Height above ellipsoid) • Geometric surface • Datum used by most GPS receivers GEO420k, UT Austin

  12. Sea Level (MSL), Geoid • Measure ht. of sea surface (via satellites) and connect with costal surveys on land to get geoid. • Sea “Level” (geoid) not level; as much as 700 m of relief globally. Earth Surface Ellipsoid Geoid GEO420k, UT Austin

  13. Geoid, Ellipsoid and Elevation (z) Height above MSL(Orthometric height) H.A.E. Geoid height = H.A.E. Earth Surface Geoid (~MSL) Ellipsoid Geoid Height GEO420k, UT Austin

  14. Geoid of the conterminous US GEOID99 heights (= Geoid – Ellipsoid) range from a low of -50.97 m (magenta) in the Atlantic Ocean to a high of 3.23 m (red) in the Labrador Strait. Source: NGS at http://www.ngs.noaa.gov/GEOID/GEOID99/geoid99.html GEO420k, UT Austin

  15. To convert HAE to orthometric (elev. above MSL) height: • Need accurate model of geoid height (e.g. N.G.S. GEOID99) • GEOID99 has 1 x 1 minute grid spacing • Compute difference between HAE and Geoid height (online here for US) • Current model allows conversions accurate to ~ 5 cm • More precise orthometric heights require local gravity survey GEO420k, UT Austin

  16. How do we get from 3D earth models to 2D maps? • Map Projections – transforming a curved surface to a flat graph • Rectangular coordinate systems for smaller regions – UTM, SPCS, PLS GEO420k, UT Austin

  17. Laying the earth flat • How? • Projections – transformation of curved earth to a flat map; systematic rendering of the lat. & lon. graticule to rectangular coordinate system. Scale1: 42,000,000 Scale Factor0.9996 (for specific line(s)) Earth Globe Map Peters Projection Globe distanceEarth distance Map distanceGlobe distance GEO420k, UT Austin

  18. Laying the earth flat • Systematic rendering of Lat. (f) & Lon. (l) to rectangular (x, y) coordinates: y 0, 0 x Geographic Coordinates(f, l) Projected Coordinates(x, y) Map Projection GEO420k, UT Austin

  19. Laying the earth flat • “Geographic” display – no projection • x , y = f , l • coords. have same scale and spacing GEO420k, UT Austin

  20. Laying the earth flat • How? Projection types: Orthographic Gnomonic Stereographic A’ a A’ A’ a a T’ T’ T’ T T T b B’ B’ b b B’ GEO420k, UT Austin

  21. Developable Surfaces • Surface for projection: • Plane (azimuthal projections) • Cylinder (cylindrical projections) • Cone (conical projections) Cylinder and cone produce a line of intersection (standard parallel) rather than at a point StandardParallel T’ GEO420k, UT Austin

  22. 3 orientations for developable surfaces GEO420k, UT Austin

  23. Tangent or Secant? • Developable surfaces can be tangent at a point or line, or secant if they penetrate globe • Secant balances distortion over wider region • Secant cone & cylinder produce two standard parallels StandardParallels GEO420k, UT Austin

  24. Projection produces distortion of: • Distance • Area • Direction • Proximity • Shape Distortions vary 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 property of interest GEO420k, UT Austin

  25. Where’s the distortion? • No distortion along standard parallels, secants or point of tangency. • For tangent projections, distortion increases away from point or line of tangency. • For secant projections, distortion increases toward and away from standard parallels. Secant line Tangent Secant GEO420k, UT Austin

  26. Horizontal Datum • Origin Coordinates • Secant Locations • Origin X, Y Values What needs to be specified? Geographic (unprojected) Lambert Conformal Conic GEO420k, UT Austin

  27. Projections in common use, US • Lambert Conformal Conic • Projection used by USGS for most maps of conterminous US (E-W extent is large) • Used by SPCS for state zones that spread E-W (Texas) • Conformal GEO420k, UT Austin

  28. Projections in common use, US • Cylindrical • Transverse Mercator – basis for UTM coordinate system and State Plane Coordinate Systems that spread N-S Standard Parallels3o apart GEO420k, UT Austin

  29. Rectangular Coordinate Systems • Universal Transverse Mercator (UTM) • US military developed for global cartesian reference frame. • State Plane Coordinate System (SPCS) • Coordinates specific to states; used for property definitions. • Public Land Survey System (PLS) • National system once used for property description • no common datum or axes, units in miles or fractional miles. GEO420k, UT Austin

  30. (Y) (x) UTM Coordinate System • T. M. secant projection is rotated about vertical axis in 6o increments to produce 60 UTM zones. Rotate in 6o increments UTM Zone is 6o wide GEO420k, UT Austin

  31. UTM Coordinate System • Zone boundaries are parallel to meridians. • Zones numbered from 180o (begins zone 1) eastward and extend from 80o S to 84o N. UTM Zones 20 9 10 19 11 12 18 13 14 15 16 17 GEO420k, UT Austin

  32. (Y) (x) UTM Coordinate System • Central meridian of each zone in US has a scale factor of 0.9996 (max. distortion). • Secants are 1.5o on either side of the central meridian. GEO420k, UT Austin

  33. y N. Hemisphereorigin is(500,000m, 0) x x S. Hemisphereorigin is(500,000m, 10,000,000m) y UTM Coordinate System • Locations are given in meters from central meridian (Easting) and equator (Northing). • (-) Eastings avoided by 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. GEO420k, UT Austin

  34. Y 99oW Zone 14 Austin Y = 3,000,000 mN Central Meridian(X = 500,000 m) UTM Coordinate System UTM Coordinates for central Austin: Zone 14 621,000 mE, 3,350,000 mN GEO420k, UT Austin

  35. State Plane Coordinate System (SPCS) • Developed in 1930’s to provide states a reference system that was tied to national datum (NAD27); units in feet. • Updated to NAD83, units in meters; some maps still show SPCS NAD27 coordinates. • Larger states divided into several zones. • X, Y coordinates are given relative to origin outside of zone; false eastings and northings different for each zone. GEO420k, UT Austin

  36. Texas NAD83 SPCS Austin:Central Zone ~ 944,000mE~ 3,077,000mN Y Austin X GEO420k, UT Austin

  37. Public Land Survey System (PLS) • System developed to survey and apportion public lands in the US, c. ~1800? • Coordinate axes are principle baselines and meridians, which are distributed among the states. • Grid system based on miles and fractional miles from baseline and meridian origin. • Not in Texas or original 13 states GEO420k, UT Austin

  38. Public Land Survey System (PLS) Step 2 Step 1 Section 33 Center Sec. 33 Step 3 T2S, R1W, Section 33 GEO420k, UT Austin

  39. Summary • Projections transform geographic coordinates (f, l) to cartesian (x, y). • Projections distort distance, area, direction and shape to greater or lesser degrees; choose projection that minimizes the distortion of the map theme. • Points of tangency, standard parallels and secants are areas of no distortion. • A conformal map has the same scale in all directions. GEO420k, UT Austin

  40. Summary (cont.) • Projection characteristics are classified by: • Light source location • Gnomonic • Stereographic • Orthographic • Developable surface • Plane (azimuthal) • Cylinder (cylindrical) • Cone (conic) • Orientation • Normal • Transverse • Oblique GEO420k, UT Austin

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