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Pmjecuon Type

Country

Transverse Mercaior

Oblique Mercator Lambert Conform al Conic Stereograph! t

Albania, Australia, Austria, I5enmark, Finland, Gentiany, Great Britain, Ireland, Italy, l.uxembourg, Norway, Poland, Portugal, Russia, Spain, Sweden, USA Hungary, Madagascar, Malaysia, Switzerland Belgium, France, Portugal, USA Netherlands (oblique aspect), Poland, Romania, UPS (polar regions)

Table 2.2. Selected projections used in various countries

The following general coordinate systems are commonly used in GIS:

geographic (global) coordinate system (latitude-longitude);

planar (cartesian) georeferenced coordinate system (easting, northing, elevation) which includes projection from an ellipsoid to a plane, with origin and axes tied to the Earth surface;

planar non-georeferenced coordinate system, such as image coordinate system with origin and axes defined arbitrarily (e.g. image corner) without defining its position on the Earth.

Note that for planar georeferenced systems false easting and false northing may be used. These are selected offset constants added to coordinates to ensure that all values in the given area are positive.

For mapping purposes, each country has one or more national grid systems. Information about national grid systems can be obtained from the national cartographic institutes or from the Internet ASPRS site9. A national grid system is defined by a set of parameters such as ellipsoid, datum, projection, coordinate system origin and axes, etc. Examples of worldwide and national grid systems are UTM (Universal Transverse Mercator), Gauss-Kruger, Gauss-Boaga, or State Plane, with the projections listed in the Table 2.2. Information about the grid system used to georeference digital geospatial data is a crucial component of the metadata and allows the user to integrate and combine data obtained from different sources.

2.2.2 Common coordinate systems

Geographic coordinate system: latitude-longitude. The most common coordinate system used for the global data is the spherical coordinate system which determines the location of a point on the globe using latitude and longitude. It is based on a grid of meridians and parallels, where meridians are the



longitude lines connecting the north and south poles and parallels are the latitude lines which form circles around the Earth parallel with the equator. The longitude of a point is then defined as an angle between its meridian and the prime meridian (0° east, passing through the Royal Observatory in Greenwich, near London, UK). The latitude of a point is defined as an angle between the normal to the spheroid passing through the given point and the equator plane. The longitude is measured 0-180° east from prime meridian and 0-180° west, where 180° longitude is the international date line. Latitude is measured 0-90° north and 0-90° south from equator.

Geographic coordinates can be expressed in two notations:

decimal degree;

sexagesimal degree.

Decimal values of W and S are expressed as negative numbers, N and E as positive numbers (e.g. Murcia, Spain: -1.167°, 38.0°). Values given in sexagesimal system always use positive numbers together with N, S, E, W (Murcia, Spain: 1:10:00W, 38:00:00N). It is not difficult to convert between these notations.

Universal Transverse Mercator Grid System. The Universal Transverse Mercator (UTM) Grid System is used by many national mapping agencies for topographic and thematic mapping, georeferencing of satellite imagery and in numerous geographical data servers. It applies to almost the entire globe (area between 84° N and 80° S). The pole areas are covered by the Universal Polar Stereographic (UPS) Grid System not explained here; please refer to Robinson et al., 1995 or other authors.

UTM is based on a Transverse Mercator (conformal, cylindrical) projection with strips (zones) running north-south rather than east-west as in the standard Mercator projection. UTM divides the globe into 60 zones with a width of 6° longitude, numbered 1 to 60, starting at 180° longitude (west). Each of these zones will then form the basis of a separate map projection to avoid unacceptable distortions and scale variations. Each zone is further divided into strips of 8° latitude with letters assigned to from C to X northwards, omitting the letters I and O, beginning at 80° south (Robinson et al., 1995:101).

The origin of each zone (central meridian) is assigned an easting of 500,000 m (false easting, Maling, 1992:358). For the northern hemisphere the equator has northing set to zero, while for the southern hemisphere it has northing 10,000,000 m (false northing). To minimize the distortion in each zone, the scale along the central meridian is 0.9996, leading to a secant case of the Transverse Mercator projection with two parallel lines of zero distortion. Note that UTM is used with different ellipsoids, depending on the country and time of mapping.



For GIS applications, it is important to realize that each UTM zone is a different projection using a different system of coordinates. Combining maps from different UTM zones into a single map using only one UTM zone (which can be done relatively easily using GIS map projection modules) will result in significant distortion in the location, distances and shapes of the objects that originated in a different zone map and are outside the area of the given zone. To overcome the problem, a different coordinate system should be used and the data re-projected. For a quick reference, you can find the UTM zone numbers in the Unit 013 Coordinate System Overview of the NCGIA Core

Curriculum in GIS.10

Lambert Conformal Conic Projection based systems. The Lambert Con-formal Conic (LCC) projection is one of the best and most common for middle latitudes. It uses a single secant cone, cutting the Earth along two standard parallels. The tangent cone version with a single standard parallel case is also used. When working with LCC based coordinate systems, the following parameters have to be provided: the standard parallel(s) (one or two), the longitude of the central meridian, the latitude of projection origin (central parallel), false easting and, sometimes, false northing (you may recall that false easting and northing are shifts of the origin of the coordinate system from the central meridian and parallel).

State Plane Coordinate System. The State Plane Coordinate System used by state mapping agencies in the U.S.A. is based on different projections depending on the individual state shape and location, usually LCC or a Transverse Mercator with parameters optimized for each state. Various combinations of datums (NAD27, NAD83) and units (feet, meters) have been used, so it is important to obtain all relevant coordinate system information (usually stored in the metadata file) when working with the data georeferenced in the State Plane Coordinate System. GIS projection modules often allow to define the State Plane system by providing the name of the state and the county, however, the parameters should always be checked, especially when working with older data.

Gauss-Kruger Grid System. The Gauss-Kruger Grid System is used in several European and other countries. It is based on the Transverse Mercator Projection and the Bessel ellipsoid. The zones are 3° wide, leading to 120 strips. The zone number is divided by 3 according to longitude of central meridian. Adjacent zones have a small overlapping area. The scale along the central meridian (scale factor) is 1.0.

Figure 2.4 illustrates the coordinate system, the x-axis is defined by the central meridian, the y-axis by the equator. The northing values are positive north



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