As discussed in the previous section, regional coordinate systems, such as the State Plane (SPC), Universal Transverse Mercator (UTM), and Wisconsin Transverse Mercator (WTM) provide effective reference systems for large areas. This standardized referencing supports registration and integration between different data sets covering common areas.
However, other systems may be more appropriate where a closer correspondence between ground values and grid values is needed. One approach that meets this need a is mathematically derived local coordinate system.
Mathematically derived coordinate systems, including the regional systems discussed earlier, are based on the principles of map projections--i.e., the systematic plane (flat) representation of all or part of the surface of the earth. Local projections are developed over smaller areas than regional projections to minimize projection distortion. When a local coordinate system is properly designed, its coordinates can be converted to any other mathematically-based coordinate system. In this way, precise data sharing is preserved between local and regional systems.
One limitation of regional coordinate systems is that distances computed on the grid surface are not equivalent to atual ground distances. To relate the two distances, scale and elevation factors must be applied. Proper use of these factors can be confusing and cumbersome in local surveying, mapping, and GIS/LIS projects.
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a rectangular coordinate system's
origin, by false easting
and false northing,
to produce a false origin.
A common method used to minimize the ground-to-grid differences has been to develop localized "project" elevation and scale factors, applying these universally to ground distance in the area. Another method has been to compute the average elevation and scale factor for a project area. However, since these practices are based on averages over an area, they do not maintain a mathematically precise relationship between the ground and the coordinate systems related to it.
A mathematically derived local projection and coordinate system is a plane coordinate system developed from a known ellipsoid and designed to minimize grid/ground differences in a local region. The origin for a local coordinate system is selected to optimize the projection and is generally near the geographic center. It is also common to assign a false easting and/or false northing to the origin to assure that coordinates have positive values throughout the local area (Figure 6). In addition to the origin the local coordinate system must have a defined axis, a unit of measure, and a projection.
Axes are lines of either constant x or constant y values, and are typically the north and east lines running through the origin. The unit of measure is the increment of the coordinate system. Rectangular systems typically use the U.S. Survey foot, the international foot or the meter. The State Plane Coordinate system based on the NAD 27 datum was defined using the U.S. Survey Foot. For applications based upon deeds, land conveyances, or other cadastral information, the U.S. Survey Foot is the preferred unit of measure.
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and coordinate systems
A projection is defined in terms of a horizontal datum, a vertical reference surface, and a map projection surface. The horizontal datum definition includes the ellipsoid and its parameters and constants describing measurement origins. Conversions between coordinate systems on the same datum are accomplished easily. However, datum to datum conversions, such as between NAD 27 SPC and NAD 83 SPC coordinates, must be approximated because of datum development and definition issues. Local projection and coordinate systems cannot resolve datum-to-datum conversion issues (Figure 4).
Projections can be based on a vertical reference surface other than mean sea level. By basing the projection surface other than mean sea level. By basing the projection on an average or median elevation, coordinate system grid distances can more closely match ground distances. This aspect of a local coordinate system's design minimizes the grid-to-ground distance differences.
Three common projection surfaces used for local system are the Lambert conformal conic, the transverse Mercator, and the tangent plane. The specific projection chose for a local coordinate system is selected to minimize distortion and optimize the projection.
Local projection and coordinate systems are most often developed on a county basis. In 1993, the Wisconsin Department of Transportation developed a statewide set of local coordinate systems based upon counties, called the Wisconsin County Coordinate System. (Minnesota preceded Wisconsin in developing county coordinate systems and has successfully used them for several years.) The Wisconsin County Coordinate system is described in the next section of this handbook. Return to Top
