# Geographic Datums & Coordinates

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1 Geographic Datums & Coordinates What is the shape of the earth? Why is it relevant for GIS? GEO327G/386G, UT Austin 2-1

2 From Conceptual to Pragmatic Dividing a sphere into a stack of pancakes (latitude) and segments of an orange (longitude) is useful for navigation (relative to Polaris) and keeping time on a rotating sphere (15 o long.=1 hr). How can we make graphs (= paper or digital maps) in units that can be measured (e.g. meters, feet) relative to this concept? CONVERT DEGREES TO OTHER UNITS GEO327G/386G, UT Austin 2-2

3 Make a Map, Graph the World What determines spacing of 30 o increments of Lat. & Lon.? Dimensions and shape ( figure ) of earth Map Projection Map Scale Austin: (-97.75, 30.30) X-axis Y-axis Graph shows 30 o increments of Lat. & Lon GEO327G/386G, UT Austin 2-3

4 The Figure of the Earth Models Sphere with radius of ~6378 km Ellipsoid (or Spheroid) with equatorial radius (semimajor axis) of ~6378 km and polar radius (semiminor axis) of ~6357 km Difference of ~21 km usually expressed as flattening (f ) ratio of the ellipsoid: f = difference/major axis = ~1/300 for earth GEO327G/386G, UT Austin 2-4

5 Ellipsoid / Spheroid Rotate an ellipse around an axis (c.f. Oblate indicatrix of optical mineralogy) a = Semimajor axis b = Semiminor axis X, Y, Z = Reference frame Rotation axis GEO327G/386G, UT Austin 2-5

6 Standard Earth Ellipsoids Ellipsoid Clark (1886) Major Axis a (km) Minor Axis b (km) Flattening (1/f) 6, , GRS 80 6, , At least 40 other ellipsoids in use globally GEO327G/386G, UT Austin 2-6

7 Earth Ellipsoids Distances Ellipsoid Clark (1886) GRS of Latitude ~110,591 meters ~110,598 meters ~ 7 meter difference is significant with modern software, but the real difference is the Datums with which they are typically associated GEO327G/386G, UT Austin 2-7

8 Horizontal Control Datums Datum = shape of ellipsoid AND location of origin for axis of rotation relative to center of mass of earth. Common North American datums: NAD27 (1927 North American Datum) Clarke (1866) ellipsoid, non-geocentric (local) origin for axis of rotation* NAD83 (1983 North American Datum) GRS80 ellipsoid, geocentric origin for axis of rotation WGS84 (1984 World Geodetic System) WGS84 ellipsoid; geocentric, nearly identical to NAD83 Other datums in use globally GEO327G/386G, UT Austin 2-8

9 Datum Rotation Axes and the Geocenter Geocenter = center of mass of earth Local Datum vs. Geocentric Datum ESRI GCS =Geographic Coordinate System=Datum Local Datum, e.g. NAD27 Point of tangency Geocenter Earth s Surface WGS84 datum NAD27 datum Geocentric GCS, e.g. WGS84 or NAD GEO327G/386G, UT Austin 2-9

10 NGS Geodetic Datum A set of constants specifying the coordinate system used for geodetic control Used for calculating the coordinates of points on Earth NAD83 is the modern (legal) horizontal control datum for US, Canada, Mexico and Central America GEO327G/386G, UT Austin 2-10

11 Adjustments to NAD83 HARN (or HPGN) High Accuracy Reference Network = Empirical corrections to NAD83 Cooperative initiative between N.G.S. and states using GPS to refine NAD83 network of control points Network of 16,000 stations surveyed from , allowing network accuracy of 5mm GEO327G/386G, UT Austin 2-11

12 Datum shifts Coordinate shift by application of wrong 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 GEO327G/386G, UT Austin 2-12

14 Datum Transformations -Theoretical Equations relating Lat. & Lon. in one datum to the same in another: 1) Convert Lat., Lon. and elevation to X, Y, Z Using known X, Y, Z offsets of datums, transform from X, Y, Z of old to X, Y, Z of new Convert new X, Y, Z to Lat., Lon. and elevation of new datum E.g. Molodensky, Geocentric Translation, Coordinate Frame Methods GEO327G/386G, UT Austin 2-14

15 Datum Transformations - Emperical 2) Use Grid of differences to convert values directly from one datum to another E.g. NADCON (US), NTv2 (Canada) Emperical; potentially most accurate (NAD27 to NAD83 accurate to ~0.15 m for Cont. US) HARN and HPGS values used for grid to update NAD83 Stand-alone programs are available to do conversions by most methods; also done within ArcGIS ArcMap &Toolbox See Digital Book on Map Projections for more info GEO327G/386G, UT Austin 2-15

16 Latitude and Longitude Historical Development Coordinates on an ellipsoidal earth +30 o (North) Latitude -30 o (West) Longitude GEO327G/386G, UT Austin 2-16

17 Coordinates have roots in marine navigation Latitude: measured by vertical angle to polaris (N. Hemisphere) or to other stars and constellations (S. Hemisphere) Longitude: determined by local time of day vs. standard time (e.g. GMT) requires accurate clocks; 1 hour difference = 15 o of Longitude* GEO327G/386G, UT Austin 2-17

18 Latitude(f) on Ellipsoidal Earth Latitude of point U calculated by: 1) Defining the tangent plane (fg) to the ellipsoid at U. 2) Defining the line perpendicular to the tangent plane (cd) passing through U. 3) Latitude (f) is the angle that the perpendicular in 2) makes with the equatorial plane (angle cde) GEO327G/386G, UT Austin 2-18

19 Latitude facts: Lines of latitude (parallels) are evenly spaced (small circles) from 0 o at equator (a great circle) to 90 o at poles. 60 nautical miles (~ 110 km)/1 o, ~1.8 km/minute and ~ 30 m/second of latitude. N. latitudes are positive (+f), S. latitudes are negative (-f) GEO327G/386G, UT Austin 2-19

20 Longitude (l) Longitude is the angle (l) between the plane of the prime meridian and the meridianal plane containing the point of interest (P). Prime Meridian Equator Meridian GEO327G/386G, UT Austin 2-20

21 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 180 o (Greenwich) Meridian (PM); longitude is measured from o east and west of the PM. East longitudes are positive (+l), west longitudes are negative (-l). P.M GEO327G/386G, UT Austin 2-21

22 Units of Measure Decimal degrees (DD), e.g o, o order by long., then lat. Format used by ArcGIS software Degrees, Minutes, Seconds (DMS), e.g. 90 o 30 00, 35 o 24, 00 Degrees, Decimal Minutes (DDM) e.g. 90 o 30.0, 35 o GEO327G/386G, UT Austin 2-22

23 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 GEO327G/386G, UT Austin 2-23

24 Vertical Datums Can t directly observe Geoid or Ellipsoid So traditionally MSL heights found by level line surveys away from coasts. Use plumb bob to establish horizontal Plumb bob Normal to Ellipsoid Deflection of the vertical Normal to Geoid GEO327G/386G, UT Austin 2-24

25 Sea Level (MSL), Geoid Measure ht. of sea surface (via satellites) and connect with costal surveys on land to get geoid. Earth Surface Ellipsoid Sea Level (geoid) not level; as much as 85 to m of relief globally. Geoid GEO327G/386G, UT Austin 2-25

26 Geoid, Ellipsoid and Elevation (H) h = H + N or H = h - N Geoid Height = N Ht. above MSL (ORTHOMETRIC HEIGHT) = H H.A.E.= h Earth Surface Geoid (~MSL) Geoid (~MSL) Ellipsoid GEO327G/386G, UT Austin 2-26

27 Geoid of the conterminous US GEOID99 heights (= Geoid Ellipsoid) range from a low of m (magenta) in the Atlantic Ocean to a high of 3.23 m (red) in the Labrador Strait. Source: NGS at GEO327G/386G, UT Austin 2-27

28 Geoid of the World (EGM96) Source: GEO327G/386G, UT Austin 2-28

29 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 GEO327G/386G, UT Austin 2-29

30 N. American Vertical Datums National Geodetic Vertical Datum 1929 (NGVD29) ~mean sea level height based on 26 tide gauges and 1000 s of bench marks. Not MSL, not Geoid, not an equipotential surface Failed to account for sea surface topography (unknown at the time) GEO327G/386G, UT Austin 2-30

31 N. American Vertical Datums North American Vertical Datum 1988 (NAVD88) Established 1991 Fixed to 1 tidal benchmark in Quebec Based on best fit to vertical obs. of US, Canada and Mexico benchmarks GEO327G/386G, UT Austin 2-31

32 Next time: 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 GEO327G/386G, UT Austin 2-32

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