Chapter 2. Position on the Earth

1. Chapter 2. Position on the Earth

3. Contents • The Importance of position • Basic coordinate systems • Reference systems • Geodetic datums

4. The Importance of position • Accurate referencing of geographic location is fundamental to all geo-information • Many different coordinate systems are used to record location • global systems, latitude and longitude • regional or local • postal codes • Combining data referred to different systems requires that positions be carefully converted, transformed, or projected from one system to another

5. Geographic position is related to the shape of the Earth • Sphere => ellipsoid • the Earth shape, geodetic datums • Phenomena whose positions are recorded by street address or postal code can also referenced using geographic coordinates • The process of matching street addresses and postal codes to geographic coordinate systems is called discrete georeferencing

6. Basic Coordinate Systems • represent points in two-dimensional or three-dimensional space • Cartesian systems • polar systems

12. Reference Systems • Reference systems and map projections extend the ideas of coordinate systems over the Earth • are based on various models for the size and shape of the Earth (sphere; ellipsoidal + gravity models ) • Ellipsoidal earth models are required for precise distance and direction measurement over long distances. • semi-major (equatorial radius) and semi-minor (polar radius) axes

15. Global systems • Latitude, Longitude, Height • The Prime Meridian and the Equator are the reference planes used to define latitude and longitude

18. Earth Centered, Earth Fixed (ECEF) Cartesian coordinates • with respect to the center of mass of the reference ellipsoid

20. Universal Transverse Mercator (UTM) coordinates • define two dimensional, horizontal, positions • Each UTM zone is identified by a number - 6 degrees wide longitudinal strips extending from 80 South latitude to 84 North latitude • central meridian given a false easting of 500 km (so that only positive eastings are measured anywhere in the zone) • Northings increase northward from the equator • for Southern Hemisphere locations, the Equator is given a false northing of 10,000 km

24. Regional systems • different systems are used regionally to identify geographic location • Some of these are true coordinate systems, such as those based on UTM • Others, such as the metes and bounds and Public Land Survey systems describe below, simply partition space

25. Transverse Mercator Grid Systems • the British National Grid (BNG), administered by the British Ordnance Survey (http://www.ordsvy.gov.uk/) • the Ordnance Survey of Great Britain Datum 1936 • The true origin of the system is at 49? north latitude and 2 degrees west longitude • Scale factor at the central meridian is 0.9996012717

27. Universal Polar Stereographic (UPS) • defined above 84° north latitude and south of 80° south latitude • eastings and northings are computed using a polar aspect stereographic projection

30. Metes and Bounds • lengths and directions of a sequence of lines forming the property boundary • Line lengths are measured along a horizontal level plane • Directions are bearing angles measured with respect to the previous line in the survey

32. Geodetic Datums • Hundreds of geodetic datums are in use around the world • North American Datum of 1983 is used for United States marine, aviation, and topographic maps (based in the past on NAD 1927) • The Global Positioning system is based on the World Geodetic System 1984 (WGS-84) • Horizontal (NAD27), Vertical (NAVD88 ), complete (World Geodetic System 1984 )

33. account for irregularities in the earth's surface due to factors in addition to polar flattening • Topographic and sea-level models (the average surface of the oceans) attempt to model the physical variations of the surface • gravity models and geoids are used to represent local variations in gravity that change the local definition of a level surface • levelling

34. Gravity models and geoids are used to represent local variations in gravity that change the local definition of a level surface • Local variations in gravity: caused by variations in the earth's core and surface materials • Geoid models attempt to represent the surface of the entire earth over both land and ocean as though the surface resulted from gravity alone • In the United States, this work is the responsibility of the National Geodetic Survey (http://www.ngs.noaa.gov/)

36. The WGS-84 Geoid defines geoid heights for the entire earth

37. National Geodetic Survey Geoid-96

38. Datum conversions • seven parameter transformations: • 3 for translation, 3 rotation, and 1 scale • Simple three parameter conversion between latitude, longitude, and height in different datums • conversion through Earth-Centered, Earth Fixed XYZ Cartesian coordinates in one reference datum and three origin offsets that approximate differences in rotation, translation and scale.

42. References • Bomford, G. 1980. Geodesy. Oxford: Clarendon Press. • Maling, D.H. 1992. Coordinate systems and map projections.  2nd ed. New York: Pergamon Press. • Schwarz, Charles R. 1989. North American Datum of 1983. Rockville, MD: National Geodetic Survey. • Torge, Wolfgang. 1991 Geodesy, 2nd Edition, New York: deGruyter

43. Questions 1. In what ways does the existence of hundreds of local and regional geodeitc datums limit the possibility of for international cooperation in GIS projects? 2. To what extent is the problem of georeferencing a major obstacle to the creation of global GIS?