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(GIS) Softwares. Geographic Information System Geographic Information System (GIS) Outline: I. Spatial reference systems and projections. II. Geographic Information System (GIS) softwares. Datum How to locate a position on Earth ? - Cartesian coordinates XYZ → relatively inconvenient except in a few cases. - Geographic reference system → longitude, latitude (+altitude). Z - XYZ depend on the origin and axis directions. - Lon,Lat depend on the origin, axis directions + the shape of the ellipsoid Y → a clear and precise definition is required. X To define a geographic reference system or datum: - Origin (position with respect to the Earth gravity center) and directions of the axes (one is the pole axis and one crosses the central/origin meridian). Or - Fundamental point on Earth surface; azimuth of the North direction; and central meridian. + Ellipsoid shape defined by the semi-major axis and flattening Datum For a global reference system: Position of For a local reference system: the origin + definition of the ellipsoid that Position of the fundamental point + best approximates the geoid at global azimuth + definition of the ellipsoid scale. that best approximates the geoid near the fundamental point. Tangent at the fundamental point Ellipsoid point Gravity centre Geoid Exemples of Datum Example of ellipsoid: - WGS84: used by the GPS system - IAG-GRS80: used in France and Europe. Very similar to WGS 84 (same semi-major axis and flattening) - NAD83: used in North America. Example of datum: - Nouvelle triangulation de la France (NTF) : official in France until Dec 2000 ; most IGN maps are still in this old system based on Clarke 1880 IGN's ellipsoid. The fundamental point is the Panthéon in Paris. - Réseau géodésique français (RGF) 1993 : Official in France, based on IAG-GRS80 ellipsoid - European Datum (ED) 50 : widely used in Europe based on Hayford 1909 ellipsoid. It is obsolete. - ETRS89: based on IAG-GRS80. Now official in Europe. - World Geodetic System (WGS84) : global datum used for GPS, based on WGS84 ellipsoid. The precision is adequate for conventional GPS but is insufficient for geodesic applications. ITRS datum is the accurate equivalent of WGS84 to use for geodesy. RGF 1993, ETRS89 and WGS84 can be assumed equivalent for most conventional applications. Examples of Datum Latitudes and longitudes are different in all these systems, differences up to hundreds of meters between « old » data (e.g. NTF) and the new generation of data (WGS84 and equivalent). Be carefull when using « old » datum. Detailled information for converting between data: http://www.crs-geo.eu/ In addition, these systems move respectively to each other due to continent drift. For instance, ETRS89 uses the same ellipsoid as WGS84 but it is attached to a point in UK while WGS84 is not attached to any particular point on Earth (it is defined by Earth rotation angular speed). For a precision better than 1m, differences between ETRS89 and WGS84 may be significant. Remark: this course is insufficient for geodesic applications. Conclusion: Spatial data are/have to be associated to a well-defined datum. Altitudes Measuring the altitude is a complex subject. In short, the minimum that you should know: Attitude can be measured with respect to: - geoid (equipotential near the mean sea level): Orthometric Altitude and normal Altitude. - ellipsoid (altitude given by GPS for instance): Ellipsoid Altitude Altitude of geoid with respect to ellipsoid is up to 140m at global scale. To work with altitude data, it is necessary to Simplified scheme know: - the kind of reference surface (ellipsoid or geoid). - the characteristics of the particular geoid or ellipsoid used as reference. → vertical datum Schéma simplifié Map projections Projections allow to represent the sphere or ellipsoid surface onto a surface that can be directly a plane or a surface that can be unambiguously unwrapped onto a plane (i.e. cylinder or cone). Mathematical transformation: (lon,lat) → (x,y) Northing y Easting O x x and y are in meters and defined with respect to the origin of the map. The interest of a particular projection for a given usage depends upon the mathematical properties of the projection. Map projections Numerous types of projection. They all causes distortions somewhere. Criteria to consider when choosing a projection for a given application: - scale of the map: In general, the coarser the scale, the more significant the distortions are. However, fine-scale maps are usually used for applications that require high precision... - usage of the map: in statistics: preserve surface area, in navigation: preserve angles (bearing, direction), … - region of the Earth (e.g. polar or not) - legal or historical reasons. - Use the common projection to most of your data to avoid re-projection that may degrade information (in the case of raster data, see further). The projections can be classified with respect to the surface used for the projection. - cylindrical projections. - conic projections. - azimuthal projections (onto a plane). - unique projections: all the other cases. Some of these projections are not associated to any surface. Additional attributes: normal, transverse, oblique Remark: These classification and attributes are insufficient to fully define a projection (see further). Map projections Important properties: - equal-area projections (projection équivalente en Francais) locally preserve surface areas. - conformal projections (projection conforme en Francais) locally preserve angles and shapes. - other projections are called aphylactic. No projection can be 100% equal-area and conformal. Another property: Equidistant: the distance is preserved along some lines. These lines are called “standard lines”. Examples of projection types Examples of projection types: Azimuthal Equidistant Projection Gnomonic Projection Orthographic Projection Geostationary Projection Near-Sided Perspective Projection Mollweide Projection Robinson Projection Sinusoidal Projection Equidistant Cylindrical Projection Cassini Projection Mercator Projection Transverse Mercator Projection Oblique Mercator Projection Polyconic Projection Miller Cylindrical Projection Gall Stereographic Projection Lambert Conformal Projection Lambert Azimuthal Equal Area Projection Stereographic Projection Equidistant Conic Projection http://www.progonos.com/furuti/MapProj/CartIndex/cartIndex.html Albers Equal Area Projection Polar Stereographic Projection Polar Lambert Azimuthal Projection Polar Azimuthal Equidistant Projection McBryde-Thomas Flat Polar Quartic van der Grinten Projection http://matplotlib.sourceforge.net/basemap/doc/html/ Examples of projection types Credits: Basemap site Conformal: useful in navigation. Often use for global maps but it does not fairly represent the world. The surface area on the map of countries near the equator are smaller than at higher latitudes. Examples of projection types Lambert conformal conic. Abbreviation: lcc Official projection in France (see further) Tissot's Indicatrice Examples of projection types The most simple projection as: x=longitude, y=latitude Meridians are standard lines Examples of projection types Equidistant: the shortest path from the centre point toward any point on the map is the straight line. Examples of projection types Equal-area: useful in statistics because two countries/regions having the same surface area on Earth are represented with the same surface area on the map. Statistics are simple to calculated. Examples of projection types Conformal: projection used for the UTM system (see later). Coordinate reference system A projection is well-defined by: - the type/family of projection. - the parameters (origin meridian, true latitude, primary standard parallel, ...). The lists of required parameters depends on the type of projection. E.g: - polar stereographic projection: Origin latitude, true latitude, origin meridian, ... - Lambert Conical Conformal: Primary, secondary and origin latitudes, origin meridian, ... Coordinate reference system (CRS) or spatial reference system (SRS): - the projection and its parameters. - the datum. The CRS is a comprehensive set of data needed to project points or to produce maps. In GIS softwares, the CRS of any spatial data to be imported must be known. UTM system Universal Transverse Mercator: - a projection type adequate for small-scale areas (fine resolution): Transverse Mercator - projection parameters depend on the location on Earth and are defined for ~1200 zones. UTM system - 20 bands in latitude (entre 84°N – 80°S) and 60 bands in longitude (→ 1200 zones). - most zones are regular, some exceptions... Coordinates (x,y) gives the position . “y” is in meter from the equator. “x” from the central meridian of the zone. However, in order to avoid negative numbers, a “false easting” of 500000m is added to x. For the points in the Southern hemisphere a “false northing” of 10000000 m (10000km) is added. UTM coordinates are uniquely defined by: - Zone Number - The hemisphere (N, S) or the letter of the zone - x,y coordinates in meter. Lambert's projections in France Since 2000: In metropolitan France: Lambert 93 ( Lambert Conformal Conic) with the RTF93 datum (close to WGS84 datum and GPS system). http://lambert93.ign.fr/ Since 2006: To improve the accuracy of the Lambert 93 system: 9 zones with specific parameters are defined (CC42 to CC50). In practice, the “old” Lambert I, II, III, IV and Lambert étendue are still used. Be careful, old Lambert projections use the NTF datum which is significantly different from the RTF93 datum and GPS coordinates. Projections
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