WLIA Coordinate Systems Task Force

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WLIA Coordinate Systems Task Force

• Todays Presentation
• - Jerry Mahun WCCS Existing vs. Proposed
• - Al Vonderohe WCCS Redesign Objectives,
  Strategy, and Methodology
• - John Ellingson WCCS Testing the Redesign
• - Ted Koch Summary Questions

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WLIA Coordinate Systems Task Force

• Mission
• Analyze and document the foundations of the WCCS
• Investigate, analyze and document software
  implementations of WCCS
• Investigate the redesign of the WCCS
• Register WCCS with standards setting organization
• Document WCCS proceedings
• Develop user-focused documentation
• Evaluate and make recommendations regarding
  statutory changes
• Present TF recommendations to WLIA Board

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WLIA Coordinate Systems Task Force

• Task Force Members
• Tom Bushy ESRI
• Diann Danielsen Dane County
• John Ellingson Jackson County
• Pat Ford Brown County
• Gene Hafermann WI Dept of Transportation
• David Hart UW-Madison Sea Grant
• Ted Koch State Cartographer, Chair
• Mike Koutnik ESRI
• John Laedlein WI Dept of Natural Resources
• Gerald Mahun Madison Area Technical College
• David Moyer, Acting State Advisor Natl Geodetic
  Survey
• Karl Sandsness Ayres Associates
• Glen Schaefer WI Dept of Transportation
• Jerry Sullivan WI Dept of Administration
• Al Vonderohe UW-Madison, Dept of Civil
  Environmental Engineering
• Jay Yearwood City of Appleton
• AJ Wortley State Cartographers Office

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WLIA Coordinate Systems Task Force

• Task Force Accomplishments Past Year
• 6 meetings in past 12 months
• Task Force decision to move ahead with redesign
• WLIB directs Strategic Initiative Grant to fund
  redesign
• Jackson County administers redesign contract
• Initial redesign work is completed and tested
• Various public presentations on Task Force work
• Discussions on next steps regarding
  documentation education

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Wisconsin County Coordinate SystemExisting vs.
Proposed

• Jerry Mahun, Instructor
• Civil Environmental Engineering Technology
• Madison Area Technical College

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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
North
Purpose To express a point position by
perpendicular linear distances from two axes in a
2D planar system.
B
Eb
Nb
A
Ea
Na
East
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
North
Desirable Characteristics
Orthogonal Parallel north lines Uniform scale in
both directions
East
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
The 3D earth doesnt lend itself well to plane
coordinates over large areas.
Projecting large areas into a 2D plane distorts
the earths surface.
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
1. Earth Models
If the distortion behaviors are known, they can
be compensated for either mathematically or
procedurally. In order to control distortion we
need a mathematical model of the earth.
We have three different models of the earth -
Real earth - Geoid - Ellipsoid
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
1. Earth Models
Real earth physical entity on which
measurements are made. Highly irregular and
non-mathematical. Geoid equipotential surface
energy on it is balanced. Primary forces
gravity pulling in and centrifugal force pushing
out.
The geoid is the surface to which we orient
surveying equipment and make measurements.
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
1. Earth Models
Ellipsoid a mathematical construct used to
approximate the geoid.
Start with an ellipse
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
1. Earth Models
Ellipsoid a mathematical construct used to
approximate the geoid.
Rotate it about its semi-minor axis
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
2. Fit an Ellipsoid
Ellipsoid a mathematical construct used to
approximate the geoid.
Fit it to the geoid
A single ellipsoid cant fit perfectly everywhere
due to the irregular nature of the
geoid. Traditionally, an ellipsoid was fit
regionally. NAD 83 uses an ellipsoid which is
fit globally.
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
2. Fit an Ellipsoid
Ellipsoid a mathematical construct used to
approximate the geoid.
Fit it to the geoid
A fit parameter relates heights. H orthometric
height N geoid height h ellipsoidal height
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
2. Fit an Ellipsoid

• NAD Ellipsoid a (m)
  b (m) 1/f
  Fit
• 1927 Clarke 1866 6,378,206.4 6,356,583.8
  1/294.9786982 Regional
• 
  
  (North America)
• GRS 80 6,378,137.0
  6,356,752.31414 1/298.257222101 Global
• defining parameters

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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
3. Projections
Earth-geoid relationship can be modeled
and Geoid-ellipsoid relationship can be modeled
so Points can be transferred from the ground to
the ellipsoid.
A
A
Projections can be used to build planar
coordinate systems with controlled systematic
distortions. Points are projected from the
ellipsoid onto developable surfaces which in turn
can be rolled out flat and then form a grid.
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II. The WCCS Existing vs. Proposed A.
Coordinate Systems

• Two step process to obtain grid (map projection)
  distances from ground distances
• Or

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II. The WCCS Existing vs. Proposed A.
Coordinate Systems
Dground
Earths Surface
Dellipsoid
Ellipsoid Factor
Ellipsoid
H
Sea Level (Geoid)
N
R / (R N H) is called the ellipsoid
factor. Ellipsoid factor varies with position.
Note N is negative in the drawing.
R
Center of Earth
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
3. Projections
Developable Surfaces
Cylinder
Cone
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
3. Projections
The two primary distortions are direction
(angular), and length.
Direction distortions on a planer grid, all
meridians are parallel on the real earth they
converge to the poles.
The larger the area covered, the greater the
convergence range.
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
3. Projections
Length distortions - lines measured on the earth
must be projected thorough different heights to
get to the grid. In the process, the lines may
get slightly shorter or longer
Distortion amount depends on the total height
projected through and where the projection
surface is with respect to the ellipsoid. If
the projection is near the earths surface there
is minimal length distortion.
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
3. Projections
UTM Universal Transverse Mercator
WTM Wisconsin Transverse Mercator
SPC State Plane Coordinate
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II. The WCCS Existing vs. Proposed
A. Coordinate Systems
3. Projections
Note these are from ellipsoid to grid. There
is an additional distortion due to elevation.
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II. The WCCS Existing vs. Proposed
B. Why Local Systems?
To minimize distortions. Direction smaller
region so convergence is smaller. Length Bring
grid closer to earth surface.
Grid
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II. The WCCS Existing vs. Proposed
C. Wisconsin County Coordinate Systems
WCCS were designed in the mid 1990s. The smaller
regions were the counties and their topography
was taken into consideration.
A few counties were aggregated into a single
zone in some cases. There are a total of 59
coordinate systems in the WCCS.
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II. The WCCS Existing vs. Proposed
C. Wisconsin County Coordinate Systems
The design approach identified two heights for
each county a geoid height, and, a
representative orthometric height. These were
added to the axes of the GRS 80 ellipsoid to
bring the ellipsoid closer to the ground (raised
or enlarged ellipsoid).
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II. The WCCS Existing vs. Proposed
C. Wisconsin County Coordinate Systems
Then a projection was selected and fit then a
grid coordinate system was created. Maximum
allowed length distortions were rural
1/30,000 urban 1/50,000
Note these are from ellipsoid to grid. There
is an additional distortion due to elevation.
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II. The WCCS Existing vs. Proposed
C. Wisconsin County Coordinate Systems
All 59 local systems exceeded the 1/30,000 and
1/50,000 by quite a bit.
And since the grid was placed close to the ground
over a small region, the elevation effect was
minimized. Result ground distances and grid
distances are the same (except for exceptional
accuracy needs)
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II. The WCCS Existing vs. Proposed
D. The Redesign of the WCCS

• So if the WCCS achieved the distortion
  minimization goal and have been widely adopted by
  users, why mess with them now?
• Although referenced to GRS 80, each of the 59
  local systems uses its own ellipsoid.
• By adding a geoid height and an orthometric
  height to the axes, the geometry of the GRS 80
  ellipsoid was changed.

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II. The WCCS Existing vs. Proposed
D. The Redesign of the WCCS
Example
Most software packages when presented with
different ellipsoidal parameters use an
approximated transformation rather than a
rigorous calculation when converting coordinates
between WCCS and other conventionally defined
systems.
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II. The WCCS Existing vs. Proposed
D. The Redesign of the WCCS
Even rigorous calculations can cause small errors
to be introduced when converting between a WCCS
and other coordinate system since the GRS 80 and
raised ellipsoid are not parallel.
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II. The WCCS Existing vs. Proposed
D. The Redesign of the WCCS
To address these issues it was decided to
"redesign" the WCCS. Redesign approach use a
conventional definition of the non-conventional
systems. Rather than create a new ellipsoid, it
was decided to use the GRS 80 ellipsoid but fit
the projection differently so only the projection
was closer to the ground. Old and new
approaches would both put grid close to ground
but some differences would be introduced. Design
goal positional differences between the two
systems could not exceed 5 mm. 5 mm was
reasonably small enough would not affect mapping
and most ground survey applications.
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Wisconsin County Coordinate SystemRedesign
Objectives, Strategy, and Methodology

• Al Vonderohe, Professor
• UW-Madison Dept. of Civil Environmental
  Engineering

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Wisconsin County Coordinates

• Redesign Objectives
• Redesign the coordinate systems so there is no
  need to enlarge the ellipsoid.
• There will be only one ellipsoid (GRS80) for
  everyone.
• Redesigned (Version 2) coordinates should not
  differ by more than 5mm from the originals
  anywhere on any projection.
• Legacy data will be preserved.
• Existing and new data can be combined without
  transforming either.

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Wisconsin County Coordinates

• Redesign Strategy
• Multiply scale factor on Central Meridian
  (Transverse Mercator) or Central Parallel
  (Lambert) by (R N H) / R to obtain
  provisional scale factor.
• Causes ellipsoid factor and scale factor to be
  approximate reciprocals of one another, so when
  they are multiplied together the result is
  approximately equal to one.
• Adjust the false northing, false easting, and
  provisional scale factor to account for effects
  of the difference in eccentricities of the two
  ellipsoids (GRS80 and enlarged).

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Wisconsin County Coordinates

• Methodology
• Use DNR statewide map to obtain boundaries for
  each projection.
• Generate a 0.5-mile grid of test points within a
  2-mile buffer for each projection.

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Wisconsin County Coordinates

• Methodology
• Compute provisional scale factor for each
  projection.
• Using provisional scale factor, compute
  provisional county coordinates for each grid
  point.
• Compute original county coordinates for each grid
  point.
• Develop observation equations for each grid
  point

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Wisconsin County Coordinates

• Methodology
• Compute least squares solution of about 10,000
  equations for each projection to obtain shifts in
  false northing and false easting, and multiplier
  for provisional scale factor.
• Final Transverse Mercator parameters are
• Number of Transverse Mercator parameters is
  reduced from 7 to 5.

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Wisconsin County Coordinates

• Methodology
• Final Lambert parameters are
• Number of Lambert parameters is reduced from 8 to
  5.
• ?o(original) is computed from ?1(original) and
  ?2(original).
• Coordinate origin is shifted to ?o, ?o.
• No(original) at new coordinate origin is
  computed, not given.

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Wisconsin County Coordinates

• Methodology
• Compute differences between Version 2 and
  original coordinates at each grid point.
• Find maximum shifts in northings and eastings to
  check against 5mm tolerance.
• Prepare isoline (contour) maps of coordinate
  shifts.

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Wisconsin County Coordinates

• Results

72 Counties 59 Coordinate Systems 24
Lambert 35 Transverse Mercator
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Wisconsin County Coordinates

• Results
• All coordinate systems meet the redesign
  criterion
• All coordinate shifts are less than 5mm.
• Typical coordinate shifts range from
• 3mm to 3mm.
• Some counties have maximum shifts of less than
  1mm.
• Maximum shifts are in Oneida and Vilas (Lambert)
  and Ashland and Forest (TM).

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Coordinate Shifts
Buffalo County (Typical Transverse Mercator)
   
Shift in Northing (mm)
Shift in Easting (mm)
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Coordinate Shifts
Ashland County (Worst-Case Transverse Mercator)
 
   
Shift in Northing (mm)
Shift in Easting (mm)
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Coordinate Shifts
Forest County (Worst-Case Transverse Mercator)
 
 
   
Shift in Northing (mm)
Shift in Easting (mm)
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Coordinate Shifts
Burnett County (Typical Lambert)
 
 
   

Shift in Northing (mm)
Shift in Easting (mm)
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Coordinate Shifts
Oneida County (Worst-Case Lambert)
 
 


   

Shift in Northing (mm)
Shift in Easting (mm)
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Coordinate Shifts
Vilas County (Worst-Case Lambert)
 
 



   

Shift in Northing (mm)
Shift in Easting (mm)
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Wisconsin County Coordinates

• Validation
• Independent testing by four individuals using
  various software packages and programming
  techniques.
• All have concluded that the redesign meets the
  5mm criterion.

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Wisconsin County Coordinate
SystemTesting the Redesign

• John Ellingson, Land Information Coordinator
• Jackson County

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CONTACT INFORMATION

• EMAIL john.ellingson_at_co.jackson.wi.us
• Tele 715-284-0221
• TO VIEW COORDINATE TEST DATA
• Go To www.sco.wisc.edu
• Click on Coordinate Systems
• Click on Task Force
• Click on County Coordinate Test Point Data
• (Listed under Task Force Documents)

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Questions ?