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Coordinate System.pdf
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- 2. Geographic (GCS) ◦Degrees…… Projected (PCS) ◦ Meters, feet….
- 3. A GCSis a three dimensional “spherical” surface used to define a location on the earth by: ◦ Equator ◦ Prime meridian
- 4. A pointon the earth is referenced by longitude and latitude values, angles expressed in degrees LONGitude: angle measured on the sphere from the prime meridian LATitude: angle measured from the equator equator Prime meridian
- 5. Parallels: horizontallines of equal latitude The line of latitude midway between the poles of the sphere is the equator (latitude =0) The equator (latitude =0) divides the sphere in north (top) and south (bottom) latitude sides Meridians: vertical lines of equal longitude The conventional line of 0 longitude is the prime meridian The prime meridian divides the meridians in a west (left) and east (right) sides of longitude Parallels and Meridians form the geographical grid with the origin (0,0) at the intersection of the equator and the prime meridian
- 6. For most ofthe GCSs, the prime meridian is the line of longitude passing through Greenwich (UK)
- 7. Latitude andlongitude are measured in degrees, minutes and seconds (DMS) or decimal degrees (DD) Longitude ranges between -180° (or 180 west) and +180° (or 180 east) Latitude ranges between -90° (or 90° south) and +90° (or 90° north) Above and below the equator the latitude lines (circles) gradually become smaller Only along the equator one degree of latitude represents the 111.12 Kilometers)
- 8. The GCSsurface is: ◦ Ellipse defined by two radii, the longer radius is the semi major axis (a), the shorter is the semi minor axis (b) ◦ The rotation of an ellipse around its semiminor axis creates an ellipsoid ◦ An ellipsoid is defined by the two axes, a and b or by an axis and the flattening, f f= (a-b)/a a b
- 9. The earthhas been surveyed many times, by many topographers we have many ground measured ellipsoids representing the shape of the earth (International 1909, Clarke 1866, Bessel) Each of them has been chosen to better fit and cartographically represent one limited region in the world Because of gravitational and surface feature variations, the earth can not be a perfect ellipsoid; satellite technnology allowed the creation of new and more accurate ellipsoids for worldwide use the most recent and the most widely used is the one defined in the World Geodetic System of 1984 (WGS 1984 or WGS84)
- 10. A geographicposition on the earth is defined by: ◦ Latitude from the equator ◦ Longitude from a prime meridian ◦ A specific GCS A position on the earth could have different longitude and latitude if the GCS is different The difference is always around seconds or fractions of a second The error of setting a wrong GCS in a GPS system could affect the coordinates on a map even of hundred meters equator Prime meridian
- 11. An ellipsoidapproximates the shape of the earth. It is the mathematical or geometrical reference surface of the earth. A Datum ◦ defines the ellipsoid and the position of the ellipsoid relative to the center of the earth ◦ The center of the earth is defined as its center of mass as calculated by satellite measurements ◦ Provides a frame of reference for combining data from different GCS ◦ The most widely used datum is the WGS84 ◦ WGS84 it is the framework for locational measurements worldwide
- 12. A geographicposition on the earth is defined by: ◦ Latitude from the equator ◦ Longitude from a prime meridian ◦ A specific DATUM or GCS Ellipsoid Relative position according to WGS84
- 13. To preserveor measure some properties (distance, area, shape,..) on maps we need a PCS A PCS is defined on a flat two dimensional surface Locations based on x,y(,z) coordinates on a grid/cartesian plane The grid is made by a network of equally spaced lines (same distances between horizontal and vertical) Based on a GCS
- 14. The ellipsoidis transformed from a three dimensional surface to create a flat map sheet This mathematical transformation is commonly referred to as a map projection Like shining a light through the earth surface casting its shadow onto a map sheet wrapped around the earth itself Unwrapping the paper and laying it flat produces the map A map projection uses mathematical formulas to relate spherical coordinates on the globe to flat, planar coordinates. Representing the earth’s surface in two dimensions causes distortion in the shape, area,distance, or direction of the data.
- 15. Different projectionscause different distortions Projections could be: ◦ Conformal Preserve local shapes, mantaining angles Meridians and parallels intersect at 90° angles ◦ Equal area Preserve the area Meridians and parallels may not intersect at right angles ◦ Equidistant Preserve distances betweeen certain points No projection is equidistant for all points in the map
- 16. Some ofthe simplest projections are made onto developable shapes as cones, cylinders, and planes, tangent or secant to the earth ellipsoid
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- 18. Universal TransverseMercator: Central meridian as the tangent contact Developing the cylinder creates distortion: ◦ used for an area spanning 3° east and 3° west from the central meridian ◦ Used for representing lands below 80° of latitude The earth is divided into 60 zones each covering 6° of longitude
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- 21. Why consideringcoordinate systems, projections and transformations? ◦ Locating correctly a GPS point onto a map ◦ Overlaying different map data sources (a vegetation map, a soil map, etc. ) ◦ Performing spatial analysis ◦ Deriving coordinates using a topographic map in the field ◦ Specifying coordinates without errors
- 22. equipotential surfaceof the Earth gravitational field that most closely approximates the mean sea surface The geoid surface is described by geoid heights that refer to a suitable Earth reference ellipsoid Geoid heights are relative small, the minimum of some -106 meters is located at the Indian Ocean, the maximum geoid height is about 85 meters. Elevation/altitude is measured above mean sea level (AMSL)
- 25. global map withgeoid heights of the EGM96 gravity field model, computed relative to the GRS80 ellipsoid