Reference Coordinate Systems

Two basic types of coordinate systems exist for geographic data: geodetic coordinate systems based on map projections and geographic coordinate systems based on latitude and longitude (for details, see for example Hake et al., 2002; Longley et al., 2006). The main difference is that projected, geodetic coordinates are Cartesian coordinates with two equally scaled orthogonal axes. Distances and areas calculated in these reference units are comparable across the globe. Geographic (unprojected) coordinates, on the other hand, are polar coordinates defined by a distance (the radius of the Earth) and two angles (between a given location and the equator and between this location and the prime meridian). Because the spacing between lines of longitude decreases from the equator to the poles, they are not useful for comparing distances or areas across the globe. However, they are useful as a comprehensive global system unaffected by distortion issues associated with map projections. The following coordinate systems may be considered for georeferencing SFAP.

• The national map projection system locally used for topographic mapping, e.g., the GauB-Kriiger or ETRS89/UTM system in Germany or the state plane systems in the United States. This is most useful when the images are to be combined with other, existing data such as topographic maps or digital cadastral data, etc. It requires the connection to the national system by nearby trigonometric points or highly precise differential global positioning system (DGPS) when measuring ground control points.

• An arbitrary local coordinate system (see Chapter 9.5). This is useful when correct scale, area, and distances are required but absolute position of the study site within a national or global system is not a necessity, because no data with other spatial references have to be overlaid. Local coordinate systems subsequently may be transposed into national reference systems by rotating and shifting them, either by adjusting them visually over other referenced image data in a GIS or by mathematical transformation of the coordinates in a spreadsheet or conversion program (e.g. for Helmert transformations).

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• No pre-defined coordination system at all but image file coordinates. For some applications, not even scale, areas, or distances are of interest because relative values like percentage cover or mean normalized difference vegetation index (NDVI) value are the only output information required. If the image is not significantly distorted, it does not need to be geometrically transformed. Even time series and change analysis may be carried out when subsequent images are relatively referenced to the first by image-to-image registration.

• Geographic coordinates in decimal degrees or degrees, minutes, and seconds. This worldwide reference system (see above) is useful because of its universality and global availability, but has the already mentioned disadvantage of angular coordinates. Unless the study site is situated near the equator, images referenced in lat/lon should be projected into a geodetic coordinate system for displaying or printing, or they would appear badly stretched. Also, a coordinate precision adequate for the small ground sample distances (GSDs) of SFAP requires many decimal places: Consider that one degree of latitude equals ~ 111 km; thus, a centimeter precision for a point on Frankfurt University's Riedberg Campus requires recording a latitude coordinate as precise as 50.1794072° N.

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