This section briefly discusses and lists the design parameters for three common rectangular coordinate systems that are most useful for mapping large areas or regions, such as multiple counties or an entire state.
Due to their long established use in mapping and surveying applications, these systems are commonly used as the means to store geographic data in a variety of computer-aided design (CAD) and geographic information system (GIS) software. The overall scale accuracy of these systems tends to be lower than those of local coordinate systems, and the ground-to-grid differences are large enough to be cumbersome in applications requiring high accuracy.
State Plane Coordinates
The State Plane Coordinate (SPC) system was introduced nationally in the 1930's by the U.S. Coast & Geodetic Survey to accommodate the needs of surveying, mapping, and engineering projects. Based on both the Lambert conformal conic and transverse Mercator projections, State Plane Coordinate systems were developed for every state such that there would be no more than one foot of distortion in every 10,000 feet of distance (on the ellipsoid). The scale of the Lambert projection varies from north to south (Figure 3); therefore, it is used mostly for areas that extend in an east-west direction. The transverse Mercator projection varies in scale in an east-west direction (Figure 3), making it most suitable for areas primarily extending north and south.
Wisconsin is covered by three Lambert projections one for each of its State Plane Coordinate zones: South, Central, and North. Each zone has a false origin located at the southwest corner of the zone, so that the entire area covered will have positive coordinate values. The approximate north-south width of each zone (158 miles) was selected so that the maximum scale difference between the ellipsoid and projection distances would not exceed one part in 10,000.
SPC zone boundaries follow county lines because the coordinate systems are designed to support local surveying and mapping needs. Similarly, the standard unit selected for SPC was the U.S. Survey Foot rather than the international foot (S.I.) in keeping with local use and legal precedent. The original SPC was based on a horizontal geodetic datum called the North American Datum of 1927 (NAD 27). This set of coordinate systems is now called SPC 27.
A more recent horizontal datum, the North American Datum of 1983 (NAD 83), was developed by the National Geodetic Survey in the 1980's. As a result, the SPC was redefined based upon the new NAD 83 datum. SPC 83 utilizes meters, rather than feet, as the unit of measure (in Wisconsin, Chapter 236 of State statutes continues the U.S. Survey Foot definition for SPC 83.) In addition, SPC 83 was assigned a different false easting than SPC 27 so that coordinate values in the two systems could easily be distinguished.
It is important to understand that the SPC 27 and SPC 83 systems cannot be related simply by converting the units and adjusting the false easting value. This is because the datum conversion is not exact. (The NAD 83 datum represents both a redefinition and readjustment, as well as the removal of geodetic network errors built up over the years). For more information on the topic, refer to the SCO's publication, Wisconsin Geodetic Control.
Universal Transverse Mercator
The Universal Transverse Mercator (UTM) projection and coordinate system was developed by the Department of Defense for military purposes and is a global coordinate system. The UTM projection has 60 north south zones arranged edge-to-edge around the equator. The zone width (6 degrees wide) was chosen to maintain a scale difference of no more than 1 part in 2,500. Zones in the UTM system are numbered from west to east starting at the 180th meridian. Wisconsin lies about equally in zones 15 and 16. The origin for each zone is at the intersection of the zone central meridian and the equator. A false coordinate easting value of 500,000 meters is assigned to the central meridian to avoid negative coordinate values.
With the introduction of NAD 83, the specific parameters of the UTM system were not redefined. However, the user should be aware that this datum difference causes a shift in coordinate values. The differences in Wisconsin amount to roughly 200 meters of northing, and 10 meters of easting, and are traceable to use of a different ellipsoid and datum definition plus the removal of geodetic network errors.
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Mercator (UTM) Coordinate System
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Figure 9: Wisconsin Transverse Mercator (WTM)
Coordinate System |
The Wisconsin Department of Natural Resources developed the Wisconsin Transverse Mercator (WTM) projection and coordinate system to avoid splitting the state into two UTM zones. This system centers a UTM-like zone on the 90th meridian (west) thereby covering the state with one zone, sometimes referred to as zone "15-1/2." The distortion in the projection increases from the center toward both the east and west edges of the state. A false easting of 500,000 and a false northing of –4,500,000 are used to produce more convenient coordinate values for Wisconsin. WTM is an example of a coordinate system designed and created to satisfy a particular need and to avoid problems caused by these of two UTM zones.
Unlike UTM, WTM 27 has been redefined for the NAD 83 datum. WTM 83 has a different false easting and northing than WTM 27. WTM83 coordinates are based on a false easting of 520,000 and a false northing of –4,480,000. Together with the 200 meter and 10 meter "shifts" discussed above (see UTM), the total difference in coordinate values between WTM 27 and WTM83 is slightly more than 200,000 meters (in both northing and easting).
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