Geodesy, Datums, and Coordinate Systems Dr. Stephen Crabtree January 30, 2017
Geodesy : • The science of measuring the size and shape of the Earth Datum : a reference surface • Example: a site datum - a reference height against which elevations are measured – Site plan for a subdivision – Establish datum as a fixed elevation at the lowest point on the property. – All heights are measured relative to this site datum
Defining Coordinate Systems • Display of Earth’s curvature necessarily complicated for three reasons – Most people see geography as a Cartesian set of planar, 90° x , y , and z coordinates – Earth is not truly spherical, but is a more distorted form – Measurements are rarely perfect, and add error margins • Result: Multiple coordinate sets and standards to report identical locations
Different Ellipsoids in Different Countries There are locally “best fit” ellipsoids Ellipsoid A Ellipsoid B
The Earth has irregularities in it - deviations from a perfectly ellipsoidal shape These deviations are due to differences in the Earth’s density and gravitational pull Deviations are NOT the surface topography The Earth is NOT an Ellipsoid (only very close in shape)
The Earth’s True Shape is Best Described as a GEOID
Definition of the Geoid A Geoid is the surface perpendicular to a plumb line, and for which the pull of gravity is a given constant – essentially, sea level
Separation between the Geoid and best- fitting global ellipsoid averages about 30 meters – this “undulation” is always below 100 meters
Geoid takes into account measurements for local ellipsoids There are locally “best fit” ellipsoids geoid Ellipsoid A Ellipsoid B
Local or Regional Ellipsoids: Origin, R 1 , and R 2 of ellipsoid specified such that separation between ellipsoid and Geoid is small Global Ellipsoid: Selected so that is has the best fit to sets of geoid measurements taken across the globe.
Three surfaces to keep track of at each point on Earth • The Ellipsoid • The Geoid • The Physical Surface surface ellipsoid geoid
Conversions Can transform positions from one ellipsoid to another via mathematical operations e.g., an origin shift, and mapping from one surface to the next
Geocentric Ellipsoid and Coordinate System • 3-D Cartesian system • Origin (0,0,0) at the Earth center of mass • Best globally fit spheroid, e.g., WGS84, used for global coordinate systems Y Z X
Geocentric Ellipsoid and Coordinate System • Lines of Latitude – Run East-to-West parallel to the equator – Values range ± 90° • Line of Longitude – Run North-to-South perpendicular to equator – Values range ± 180° 45 67.5 22.5 90 -67.5 -45 -22.5 0 -45 -67.5 22.5 45 67.5 longitude meridians parallels equator Greenwich meridian 90 - north pole south pole
Datum : a reference surface A Geodetic Datum consists of two major components: • An ellipsoid with a spherical or
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- Spring '17
- Stephan C.
- Geodesy, Map projection, Geographic coordinate system, Universal Transverse Mercator coordinate system, Coordinate systems, Datums