Wisconsin County Coordinate System
Note: Red text indicates updates from the 1995 published handbook.

•  Design Considerations
•  Design Process
•  Design Results
•  Using the Wisconsin County Coordinate System

Individual Wisconsin counties began to develop and use their own coordinate systems in the 1980's. The Wisconsin Department of Transportation (WiDOT) saw the need for a statewide set of standardized and mathematically based local coordinate systems for use in large scale mapping and roadway design. In 1993, WiDOT contracted with Fairview Industries for the development of a unified set of county coordinate systems (Figure 11).

The resulting county systems were ultimately approved by the Wisconsin Secretary of Transportation, and their use within WiDOT was enacted as official agency policy on January 1, 1997. WiDOT made them available for wider public use and today most county governments are using these coordinate systems. Since the county coordinate systems are mathematically relatable to NAD 83 (1991), their use is allowed under Chapter 236 of Wisconsin Statues (Chapter 236 covers subdivision plotting and is the statutes where the use of coordinate systems and datums is mentioned).

It is important to note that these county coordinate systems are not legislatively defined or mandated for adoption. Their use at the local level is voluntary. Unless officially adopted by local ordinance or regulation, there is no mechanism for making these coordinate systems "official" or of public record.

The full summary report, prepared by Fairview Industries for WiDOT, describing the design and methodology for developing the Wisconsin County Coordinate System is available by contacting the WiDOT office of Technical Services. The following is a brief overview of their design.

Design Considerations
The Wisconsin County Coordinate System (WCCS) is designed so that each county has its own coordinate system, although two or more adjoining counties may share the same coordinate systems (i.e., they use identical design parameters).

The coordinate systems are mathematically based and related to the National Geodetic Reference System (NGRS). This maintains the benefits of the NGRS network while providing the opportunity for developing rectangular coordinate systems with minimal differences between ground and projected grid distances. The ground and grid difference is minimized by elevating a parallel local ellipsoid (the reference surface) to the median, or most commonly occurring, ground level in the country. (Figure 10).

The design considerations for the Wisconsin County Coordinate System include: reference to the NAD 83 (1991) datum adjustment, metric units, a maximum grid scale distortion of 1:30,000 in rural areas and 1:50,000 in urban areas, and a distinct numeric difference between adjacent coordinate systems to avoid confusion. The design criteria supports uses in urban areas and transportation corridors, as well as in rural areas.

Design Process
The purpose of the Wisconsin County Coordinate System is to provide a mathematically rigorous and more convenient method for relating ground measurement to geodetic control and other coordinate values.

As mentioned earlier, each county coordinate system was developed by introducing a local parallel ellipsoid that passes through the median elevation of the area. To develop each local ellipsoid, U.S. Geological Survey 1:100,000-scale topographic maps were analyzed to determine average highs, lows, and elevation profiles for each county. A minimum of fifteen points were selected from each county including the county seat and populated areas.

Using the county maximum and minimum latitude and longitude values, a rectangular geographic area was determined. Geoidal separation values for NGRS (National Geodetic Reference System) First and Second order geodetic control points in this geographic area were then averaged to determine each county's geoidal separation parameter value.

After the individual county projections were determined, the points in the county profile were run through a test program to verify the design. This step identified any computational coordinate value interpretation errors and verified the quality of the projection against the design constraints.

Opportunities combining counties were then examined regionally. For example, the Fox River Valley area, the heavily urbanized areas around Appleton and cross county boundaries were candidates for combined coordinate systems. Also counties that were known to be working on joint land records projects were combined if possible.

Design Results

•  All coordinate systems were developed for individual counties. In some cases more than one county was adequately served by a single coordinate more than one coordinate system. Figure 11 illustrates the counties that share combined coordinate systems. (there are 59 separate coordinate systems to cover the 72 counties).
•  The maximum allowable scale errors was set at one part in 50,000 for urban areas and one part in 30,000 for rural areas. All urban areas, including villages as small as 1,000 population, met the one part in 50,000 requirement, except the city of Ashland in Ashland county which is 1 part in 30,000. Three areas of the state fell below the rural 1 part in 30,000: the tops of both Rib Mountain and Mt. Whittlesey, and a low area in Northwestern Iron County. The design constraint of keeping each county on one projection system make it necessary to exceed the design criteria in these areas.
•  Compared to regional coordinate systems, these local coordinate systems improve ground-to-grid discrepancies by a factors of ten. This is more than a three-fold improvement over the average scale factor approach and is very comparable to the improvements that were obtained in the Minnesota county coordinate system.

Using the Wisconsin County Coordinate System
Using a local coordinate system requires additional considerations due to the elevated reference surface. Since the Wisconsin systems were designed using the parallel ellipsoid method, a new reference ellipsoid needs to be defined for each local system by adding the value in Wisconsin) to the semi-major and semi-minor axes of the GRS 80 ellipsoid used to define the NAD 83 datum. The local coordinate system can be defined based upon this new reference ellipsoid.

For example, the Marathon County coordinate system's design elevation is 396.24 meters and the geoidal separation is -32.64 meters. Added to the GRS 80 ellipsoid parameters, this results in a semi-major axis a of 6,378,500.60 meters (6,378,137.0 + 396.24 – 32.64) and a semi-minor axis b of 6,357,115.9141403 meters (6,356,752.3141403 + 396.24 – 32.64).

When modifying the GRS 80 ellipsoid parameters to account for the design elevation of a Wisconsin County Coordinate System, using the proper unit conversion, an appropriate number of significant Figures, and double precision numeric expression are all critical to the quality of the resulting data transformation. These and other important considerations for coordinate transformations are discussed in the coordinate and datum transformation section.
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