Geodetic Datum

• Geodetic datums


  Define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth

  
• Hundreds of different datums have been used to frame position descriptions since the first estimates of the earth's size were made by Aristotle
• Datums have evolved from those describing a spherical earth to ellipsoidal models derived from years of astronomical observations leading up to the present satellite measurements

  
• Modern geodetic datums


  • Range from flat-earth models used for plane surveying to complex models used for international applications which completely describe the size, shape, orientation, gravity field, and angular velocity of the earth

  
• Geodetic datums are used in Geodesy, navigation, and Surveying and Cartography and Satellite navigations to translate positions indicated on maps to real locality positions on the earth's surface by given coordinates based on specific datum definition

  
• WGS84


  The latest of geodetic datum definition that was first produced by the Transit Doppler system and continuously refined by world-wide GPS tracking stations with other spatial satellite geodesy techniques

  
• The Earth is not a sphere, but an ellipsoid, flattened slightly at the poles and bulging somewhat at the Equator
• The ellipsoid is used as a surface of reference for the mathematical reduction of geodetic and cartographic data
• Modern Geodetic System


  Based on GPS satellite positioning

  
• GPS positioning


  1. High precision GPS receivers around the globe determine their positions from the group of satellites in space orbiting the universe continuously

  2. Measurements are taken simultaneously from minimum four satellites to maximum 12 with GPS only or up to 22 satellites with other GNSS satellite constellations to solve for the three dimensional positions (latitude, longitude, and altitude) and time

  
• Position measurements are in the worldwide WGS-84 geodetic reference system, and time is with respect to a worldwide common U.S. Naval Observatory Time (USNO) reference

  
• Referencing geodetic coordinates to wrong geodetic datum can result in position errors of hundreds of meters
• Different nations and agencies use different datums as the basis for coordinate systems used to identify positions in geographic information systems, precise positioning systems, and navigation systems
• The diversity of datums in use today and the technological advancements that have made possible global positioning measurements with sub-meter accuracies requires careful datum selection and careful conversion between coordinates from different datums
• Flat-earth models


  Still used for plane surveying, over distances short enough so that earth curvature is insignificant (less than 10 kms)
• Spherical earth models


  Represented as the shape of the earth with a sphere (a regular radius), often used for short range navigation (VOR-DME) and for global distance approximations

  
• Ellipsoidal earth models


  The accepted model that is required for accurate range and bearing calculations over long distances, used by Loran-C, and GPS navigation receivers

  
• Reference ellipsoids


  Usually defined by semi-major (equatorial radius) and flattening (the relationship between equatorial and polar radii)

  
• Parameters for conversion from WGS-84 to other datums


  • Delta a (WGS-84 Equatorial radius minus specified datum Equatorial radius in meters)
  • Delta f (WGS-84 flattening minus specified datum flattening multiplied by 10^4)
• The topographical surface of the earth is the actual surface of the land and sea at some moment in time
• Sea level is the average (methods and temporal spans vary) surface of the oceans, which varies over the globe by hundreds of meters due to tidal forces and gravity differences
• Gravity models attempt to describe in detail the variations in the gravity field, which is important for leveling in plane and geodetic surveying
• Geoid models attempt to represent the surface of the entire earth over both land and ocean as though the surface resulted from gravity alone
• The WGS-84 Geoid defines geoid heights for the entire earth, and the U.S. National Imagery and Mapping Agency publishes a ten by ten degree grid of geoid heights for the WGS-84 geoid

  
• Datum types


  Common types include horizontal and vertical, with the ellipsoid from GPS defining the vertical heights and the horizontal on the geographic reference system latitude, longitude and the projected coordinates in UTM eastings and northings
• Coordinate values resulting from interpreting latitude, longitude, and height values based on one datum as though they were based in another datum can cause position errors in three dimensions of up to one kilometer
• Datum conversions


  1. Accomplished by various methods, including complete datum conversion based on seven parameter transformations that include three translation parameters, three rotation parameters and a scale parameter

  2. Simple three parameter conversion between latitude, longitude, and height in different datums can be accomplished by 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

  3. The Standard Molodensky formulas can be used to convert latitude, longitude, and ellipsoid height in one datum to another datum if the Delta XYZ constants for that conversion are available and ECEF XYZ coordinates are not required