Wisconsin County Coordinate Systems: WLIA Task Force ... · Why a Local Coordinate System? Regional...
Transcript of Wisconsin County Coordinate Systems: WLIA Task Force ... · Why a Local Coordinate System? Regional...
Wisconsin County Coordinate Systems: WLIA Task Force Report on the Issues
WSLS Annual InstituteJanuary 27, 2005
Ted Koch - State CartographerDiann Danielsen – LIO Manager, Dane CountyJerry Mahun – Civil & Environmental Engineering Technology, MATCAl Vonderohe – Dept. of Civil & Environmental Engineering, UW-Madison
Today’s Presentation
Diann - WCCS: Why & What + Concerns
Jerry - Wisconsin Coordinate Systems: The Technical Foundation
Al - WCCS: Emerging Issues and Solutions
Ted - Summary: Where are we headed?
WI Coordinate Systems Task Force
Mission:Analyze and document the foundations of the WCCSInvestigate, analyze and document software implementations of WCCSInvestigate the redesign of the WCCSRegister WCCS with standards setting organizationDocument WCCS proceedingsDevelop user-focused documentationEvaluate and make recommendations regarding statutory changes Present TF recommendations to WLIA Board
Task Force MembersBrett Budrow St Croix CountyTom Bushy ESRIDiann Danielsen Dane CountyJohn Ellingson Jackson CountyBob Gurda State Cartographer’s Office (ended 4/30/04)Pat Ford Brown CountyGene Hafermann WI Dept of TransportationDavid Hart UW-Madison Sea GrantTed Koch State Cartographer, ChairMike Koutnik ESRIJohn Laedlein WI Dept of Natural ResourcesTim Lehmann Buffalo CountyGerald Mahun Madison Area Technical CollegeDavid Moyer, Acting State Advisor Nat’l Geodetic SurveyKent Pena USDA-Natural Resources Conservation ServiceKarl Sandsness yres AssociatesGlen Schaefer WI Dept of TransportationJerry Sullivan WI Dept of AdministrationPeter Thum GeoAnalytics. Inc.Al Vonderohe UW-Madison, Dep’t of Civil & Environmental EngineeringJay Yearwood City of AppletonAJ Wortley State Cartographer’s Office
Task Force Accomplishments9 meetings in the past 12 monthsDocuments:
Equations & Parameters for WI Coordinate Systems, (Jerry Mahun)WCCS Test Point DataProducts matrixProposal to redesign the WCCS
WTM parameters registered with ESPGPresenting TF work and conclusions to the professional community
Next: Local coordinate systems and the WCCS: Why and What + Concerns
Diann Danielsen
Why a Local Coordinate System?Regional coordinate systems require ground-to-grid conversions to relate field surveyed coordinates to projected mapping coordinates
Earth’s Surface
Geoid
Ellipsoid Map Projection Surface
Distances on property maps and construction stakeout are measured here.
GIS spatial databases and design drawings are developed here.
Three SurfacesEasy for staff to misapply or forget conversionsHuge conversion effort for historic records
Property maps have tens of thousands of ground-level distances on them. Too difficult to convert to map projections for GIS.Design drawings have tens of thousands of map projection distances on them. Too difficult to convert to ground distances for construction stakeout.
Wisconsin Local Coordinate SystemsOld WisDOT county coordinate system used an average elevation and scale factor for each county to ease conversion between grid and ground values
• Typical project-based approach; does not preserve a precise mathematical relationship with other coordinate systems.
Several Wisconsin counties began defining and adopting coordinate systems for local useWisDOT desired a unified set of county coordinate systems for the agency’s large-scale mapping and roadway design activities that would be:
• Standardized and mathematically relatable to other systems • Incorporate existing local county coordinate systems
Solution….Develop map projections that are even more localized than state plane coordinate projections
• No significant differences between ground distances and map projection distances
• Ground distances can be used directly in spatial databases and grid (design) distances can be used directly for stakeout.
Wisconsin County Coordinate System
Fairview Industries was hired by WisDOT in 1993 to develop a consistent statewide set of county based coordinate systems
This design raised the ellipsoid surface to near ground level to minimize ground and grid differences
Geoid
Ellipsoid
Enlarged Local Ellipsoid Surface
Local Map Projection Surface (Secant)
Earth’s Surface
Wisconsin County Coordinate System
59 separate map projections (Lambert and Transverse Mercator)
72 counties – some share a projection
Use and Adoption of the WCCS
Not officially adopted in statute (no current statutory home for coordinate system definition outside of a platting context)Chapter 236 updates were crafted to recognize and allow the use of WCCS for platting purposesWLIP & Task Force surveys indicate the WCCS has been adopted for use in ¾’s of Wisconsin counties
Use and Adoption of the WCCSWCCS has become a key component of the WLIP, recognized as a voluntary or de facto standard, and supported by a number of educational resources
Statewide educational rollout in mid-1990’sHardcopy and online resources
http://www.geography.wisc.edu/sco/pubs/wiscoord/wiscoord.php
Emerging IssuesMultiple county coordinate systems
• Jackson County Official Coordinate System (county adopted)• Jackson County Coordinate System (WisDOT developed)
Different naming conventions• Badger County Coordinate System; Badger County Geodetic
Grid; Badger County Coordinate Grid; WCCS – Badger County; WCCS for Badger County; WCCS – Badger Zone
Questionable use of datums• WCCS designed specifically for use with NAD83(1991)• WisDOT plats being filed using WCCS – Badger Zone;
NAD83(1997)
Variations create confusion when communicating and trying to convert data
Other ConcernsVendor Implementation
Difficult because of the WCCS’s unconventional design; mathematically correct, but less understoodVendor implementation methodology differs, resulting in different coordinate values for the same feature
Lack of Formal RegistrationSome local systems adopted in ordinance; most are notNot registered with European Petroleum Survey Group/EPSG
• Aids consistent interpretation and implementation
Lack of State Custodian/OversightNo designated entity responsible for Wisconsin coordinate systems or other spatial reference parameters (land and water datums, geoid models, ellipsoids, etc)No single point of contact for assistance
Defining ConceptsCoordinate System Development
Two-Dimensional Rectangular Coordinate SystemsFormal Coordinate Systems in Wisconsin
Jerry MahunMadison Area Technical College
Defining Concepts
To develop a coordinate system:• Relate non mathematical three dimensional earth to a mathematical 3D model.
• Project 3D model into a 2D plane
• Define coordinate axes and units
East
North
(N ,E )p p
Defining Concepts
Earth Models
Earth Physical Earth; Terrain
Entity on which measurements are made. A surface on which gravity and centrifugal forces are balanced.
Geoid An equipotential surface
Directions of gravity
Earth
Geoid
Defining Concepts
Earth Models
Earth
Geoid
Ellipsoid
EllipsoidThe ellipsoid is a mathematical surface used to approximate the geoid.
a = semimajor axisb = semiminor axisf = flatteninge = eccentricity
b
a -ba2 2
e =
Defining Concepts
Ellipse Parameters
b
f = a-b
a
Defining Concepts
Ellipsoid
b
a
Typical Ellipsoids
Ellipsoid a (meters) b (meters) 1/fClarke 1866 6,378,206.4* 6,356,583.8* 1/294.9786982GRS 80 6,378,137.0* 6,356,752.31414 1/298.257222101*WGS 84 6,378,137.0* 6,356,752.31424 1/298.257223563*
*defining parameters
Defining Concepts
Fitting an Ellipsoid
Regional Fitting
Geoid
Ellipsoid 2 fit
Ellipsoid 1 fit
Defining Concepts
Fitting an Ellipsoid
Global Fitting
Geoid
Defining Concepts
Fitting an Ellipsoid
Earth
Geoid
Ellipsoid
Deflection ofthe Vertical
Nor
mal
to e
llipso
idN
orm
al to
geo
id(g
ravi
ty)
Defining Concepts
Fitting an Ellipsoid
Earth
Geoid
Ellipsoid
H
hH: orthometric heightN: geoid height
(+) if geoid is above ellipsoid(-) if geoid is below ellipsoidN
h: ellipsoidal (geodetic) heighth = H + N
Defining Concepts
Datum
datum
Any quantity or set of such quantities that may serve as a reference or basis for calculations of other quantities.
datum, geodetic
A set of constants specifying the coordinate system used for geodetic control, i.e., for calculating coordinates of points on the Earth.
A datum consists of the ellipsoid and its geoid fit.
Defining Concepts
DatumDatum
Ellipsoid
Fit to
Criteria
NAD 27
Clarke 1866
North America
Origin at Meades Ranch, KS; no geoid separation.Azimuth to Waldo fixed.
NAD 83
GRS 80
World
Ellipsoid centroid coincideswith earth's mass center.
Semiminor axis setparallel with polar axis
Approx Number ofControl Stations 25,000 272,000
NAD 83 has been adjusted three times in Wis:NAD 83 (1986) - Original national adjustmentNAD 83 (1991) - WI HARN incorporatedNAD 83 (1997) - Re-observed GPS stations
Coordinate System Development
Three-Dimensional Reference System
Spherical Coordinates
W Long
N Lat
Equator
North PoleLat 90° N
eeG
wi ch
dn
irM
i an
er
Long 180° ELong 180° W Long 0°
South PoleLat 90° S
Coordinate System Development
Three-Dimensional Reference System
Spherical CoordinatesMeri
dian
EquatorialPlane
Pol
ar A
xis
: Astronomic latitude: Geocentric latitude: Geodetic latitude
Types of Latitude
Coordinate System Development
Three-Dimensional Reference System
Geodetic Coordinates
Greenwich
Equator
Normal to
MeridianEllipsoid
Three dimensional position of a point is expressed by:
geodetic latitudegeodetic longitude
Coordinate System Development
Three-Dimensional Reference System
Rectangular Coordinates
Gre
enwi
chM
erid
ian
EquatorX
Z
Y
Earth Centered Earth Fixed (ECEF)Rectangular Coordinate System
Three dimensional position of a point is expressed by x, y, and z
Two-Dimensional Rectangular Coordinate Systems
Building a Two-Dimensional Coordinate System
Projecting a 3-D surface into a 2-D surface causes distortions:Linear and Angular
Y
90 degree angles
Same point, different X coordinates
X“Orange Peel” Map of the World
Two-Dimensional Rectangular Coordinate Systems
Building a Two-Dimensional Coordinate System
Length distortion occurs when projecting from:- ground (Earth) to ellipsoid- ellipsoid to projection surface
Ellipsoid
Projection Surface
AB
A'
B'
A"
B"
Earth
Two-Dimensional Rectangular Coordinate Systems
Building a Two-Dimensional Coordinate System
Direction distortion occurs because true north lines converge to a point (North Pole)
True NGrid N
A
B
Two-Dimensional Rectangular Coordinate Systems
“Developable” Surface and Projections
A developable surface along with fit criteria becomes a projection that can be used to define a coordinate system.
Three commonly used surfaces:PlaneCylinderCone
The developable surface is placed tangent or secant to the ellipsoid.
Points are projected from the ellipsoid to the developable surface.
The surface is rolled out flat without “tearing” the surface.
Because a projection is mathematical, distortions introduced can be compensated for mathematically.
Selecting the type, size, and orientation of the projection allows us to control “maximum” distortions.
Two-Dimensional Rectangular Coordinate Systems
Developable SurfacePlane Projection Scale:
>1 =1 >1
A A
B
B'
C
C'
D
D'
E
E'
Scale distortionsTangent plane
Scale
varie
s
North
Lines of Constant Scale
EastCoordinate system
Two-Dimensional Rectangular Coordinate Systems
Developable SurfaceCylindrical Projection
AB
A'C
C' D
E
E'
Scale:> 1> 1 = 1 = 1< 1
Scale distortionsTransverse cylinder
Scal
e =
1
Scal
e C
onst
ant
Scal
e =
1
NorthScale < 1
Scale> 1
Scale > 1
Scale varies
East
Coordinate system
Two-Dimensional Rectangular Coordinate Systems
Developable SurfaceConic Projection
A
B
A'
CC'
D
E
E'Scale:
> 1
> 1 = 1
= 1
< 1
DistortionsCone
Scale < 1
Scale > 1
Scale > 1
Scale va
ries
Scale = 1
Scale = 1
Scale constant
Standard
North
Parallels
East
Coordinate system
Two-Dimensional Rectangular Coordinate Systems
Transverse Mercator Cylindrical Projection
Eo
Cen
tral M
erid
ian
Grid
Nor
th
No
Np
Ep
P
North
East
North Pole
convergence
Two-Dimensional Rectangular Coordinate Systems
Transverse Mercator Cylindrical Projection
Computing Zone/System ConstantsDesign parameters are used to compute constants for each zone or system.
( )( )2 4
2
a b fna b 2 f
9n 225nr a 1 n 1 n 14 64
−= =
+ −
= − − + +
3
2
2 4
4
3
6
4
8
3n 9nu2 16
15n 15nu16 3235nu48
315nu512
= − +
= −
= −
=
( )( )
( )
0 2 4 6 8
2 4 6 8
4 6 8
6 8
U 2 u 2u 3u 4u
U 8 u 4u 10u
U 32 u 6uU 128u
= − + −
= − +
= −
=
( )( )
( )
0 2 4 6 8
2 4 6 8
4 6 8
6 8
V 2 v 2v 3v 4v
V 8 v 4v 10v
V 32 v 6vV 128v
= − + −
= − +
= −
=
3
2
2 4
4
3
6
4
8
3n 27nv2 3221n 55nv16 32
151nv96
1097nv512
= −
= −
=
=
( )2 4 6o o o o 0 2 o 4 o 6 o
o o o
sin cos U U cos U cos U cos
S k r
ω = φ + φ φ + φ + φ + φ
= ω
Two-Dimensional Rectangular Coordinate Systems
Transverse Mercator Cylindrical Projection
Direct Conversion Geodetic to grid coordinates
( )( )
o
2 4 60 2 4 6
L cos
sin cos U U cos U cos U cos
= λ − λ φ
ω = φ + φ φ + φ + φ + φ( )
( )( )
2 2 2o o 2 4 6
2 2 2o 1 3 5 7
N S S N A L 1 L A A L
E E A L 1 L A L A A L
= − + + + + = + + + +
( )
o
2 2 2
o1/ 22 2
S k rt tan
e' cosk a
R1 e sin
= ω
= φ
η = φ
=− φ
( )
( )
1
2 43
25
C t1C 1 3 231C 2 t
15
= −
= + η + η
= −
( )
( )
( )
( )
( )
1
2
2 23
2 2 24
2 4 2 25
2 4 2 26
2 4 67
A R1A Rt21A 1 t61A 5 t 9 4
121A 5 18t t 14 58t
1201A 61 58t t 270 330t
3601A 61 479t 179t t
5040
= −
=
= − + η
= − + η + η
= − + + η −
= − + + η −
= − + −
( )
( )
22
2 2 24
1F 121F 5 4t 9 24t
12
= + η
= − + η −
( )( )
2 21 3 5
2 2o 2 4
C L 1 L C C L
k k 1 F L 1 F L
γ = + + = + +
Two-Dimensional Rectangular Coordinate Systems
Transverse Mercator Cylindrical Projection
Inverse Conversion Grid to geodetic coordinates.
( )
( )( )
( )( )
o o
o
2 4 6f 0 2 4 6
f f2 2 2
f f
of 1/ 22 2
f
o
f
N N Sk r
sin cos V V cos V cos V cos
t tan
e' cosk a
R1 e sin
E EQ
R
− +ω =
φ = ω + ω ω + ω + ω + ω
= φ
η = φ
=− φ
−=
( )( )( )
2 2 23 5 7
2 2 2f 2 4 6
of
L Q 1 Q B Q B B Q
B Q 1 Q B B Q
Lcos
= + + + φ = φ + + +
λ = λ −φ
( )
( )
1 f
2 2 43 f f f
2 45 f f
D t1D 1 t 23
1D 2 5t 3t15
=
= − + − η − η
= + +
( )
( )
( )
( )
( )
( )
22 f f
2 23 f f
2 2 2 44 f f f f
2 4 2 25 f f f f
2 4 2 2 46 f f f f f
2 4 67 f f f
1B t 121B 1 2t61B 5 3t 1 9t 4
121B 5 28t 24t 6 8t
1201B 61 90t 45t 46 252t 90t
3601B 61 662t 1320t 720t
5040
= − + η
= − + + η
= − + + η − − η
= + + + η +
= + + + η − −
= − + + +
( )
( )
22 f
24 f
1G 121G 1 5
12
= + η
= + η
( )( )
2 21 3 5
2 2o 2 4
D Q 1 Q D D Q
k k 1 G Q 1 G Q
γ = + + = + +
Two-Dimensional Rectangular Coordinate Systems
Cen
tral M
erid
ian
Grid
Nor
th
EO
Nb
Np
EP
P
North
East
Rb
North Pole
convergence
Lambert Conic Projection
Two-Dimensional Rectangular Coordinate Systems
Lambert Conic Projection
Computing Zone/System ConstantsDesign parameters are used to compute constants for each zone or system.
( )
s ss
s s
1/ 22 2s s
1 sin 1 e sin1Q e2 1 sin 1 e sin
W 1 e sin
+ φ + φ= −
− φ − φ
= − φ
ln ln
( ) ( )
n s
s no
n s
s s o n n o
s o n o
W cosW cos
sinQ Q
a cos exp Q sin a cos exp Q sinK
W sin W sin
φ φ φ =
−
φ φ φ φ= =
φ φ
ln
( )
( )( )
bb o
0o o
o o oo
o b b o
KRexp Q sin
KRexp Q sin
W tan Rk
aN R N R
=φ
=φ
φ=
= + −
Two-Dimensional Rectangular Coordinate Systems
Lambert Conic Projection
Direct Conversion Geodetic to grid coordinates
1 1 sin 1 e sinQ e2 1 sin 1 e sin
+ φ + φ= − − φ − φ
ln ln
( )( )
o
o o
KRexp Q sin
sin
=φ
γ = λ − λ φ
( ) ( )( )
b b
o
1/ 2 o2 2
N R N R cosE E R sin
R sink 1 e sin
a cos
= + − γ
= + γ
φ= − φ
φ
Two-Dimensional Rectangular Coordinate Systems
Lambert Conic Projection
Inverse Conversion Grid to geodetic coordinates.
( )
( )( )
b b
o
1
oo
1/ 22 2
o
R ' R N NE' E E
E'tan R'
sin
R R' E'
KRQ
sin
−
= − +
= −
γ =
γλ = λ − φ
= +
=φ
ln
1
2
2 2 2 2
1 1 sin 1 e sinf e Q2 1 sin 1 e sin
1 ef1 sin 1 e sin
+ φ + φ= − − − φ − φ
= − − φ − φ
ln ln
( )( )
exp 2Q 1sin
exp 2Q 1−
φ =+ ( ) ( )
( )1/ 2 o2 2 R sin
k 1 e sina cos
φ= − φ
φ
Formal Coordinate Systems in Wisconsin
Wisconsin State Plane Coordinate (SPC) ZonesNAD 27 and NAD 83
North
Central
South
Three Lambert Conic Projection Zones
Maximum scale distortion (ellipsoid to projection): 1/10,000
Formal Coordinate Systems in Wisconsin
Wisconsin State Plane Coordinate (SPC) ZonesNAD 27
North
Central
South
Datum: NAD 27Ellipsoid: Clarke 1866
Zone North Central SouthCode 4801 4802 4803
South Std Par 45°34' N 44°15' N 42°44' NNorth Std Par 46°46' N 45°30' N 44°04' N
Central Meridian 90°00' W 90°00' W 90°00' WLatitude of Origin 45°10' N 43°50' N 42°00' N
Nb Origin Northing 0 ft 0 ft 0 ftEo Origin Easting 2,000,000 ft 2,000,000 ft 2,000,000 ft
NAD 27 uses the US Survey foot (39.37 inches = 1 meter, exact) as thedefining linear unit.
Datum: NAD 27Ellipsoid: Clarke 1866
Zone North Central SouthCode 4801 4802 4803
South Std Par 45°34' N 44°15' N 42°44' NNorth Std Par 46°46' N 45°30' N 44°04' N
Central Meridian 90°00' W 90°00' W 90°00' WLatitude of Origin 45°10' N 43°50' N 42°00' N
Nb Origin Northing 0 ft 0 ft 0 ftEo Origin Easting 2,000,000 ft 2,000,000 ft 2,000,000 ft
NAD 27 uses the US Survey foot (39.37 inches = 1 meter, exact) as thedefining linear unit.
Formal Coordinate Systems in Wisconsin
Wisconsin State Plane Coordinate (SPC) ZonesNAD 83
North
Central
South
Datum: NAD 83Ellipsoid: GRS 80
Zone North Central SouthCode 4801 4802 4803
South Std Par 45°34' N 44°15' N 42°44' NNorth Std Par 46°46' N 45°30' N 44°04' N
Central Meridian 90°00' W 90°00' W 90°00' WLatitude of Origin 45°10' N 43°50' N 42°00' N
Nb Origin Northing 0 m 0 m 0 mEo Origin Easting 600,000 m 600,000 m 600,000 m
NAD 83 datums use the meter as the defining linear unit.
Datum: NAD 83Ellipsoid: GRS 80
Zone North Central SouthCode 4801 4802 4803
South Std Par 45°34' N 44°15' N 42°44' NNorth Std Par 46°46' N 45°30' N 44°04' N
Central Meridian 90°00' W 90°00' W 90°00' WLatitude of Origin 45°10' N 43°50' N 42°00' N
Nb Origin Northing 0 m 0 m 0 mEo Origin Easting 600,000 m 600,000 m 600,000 m
NAD 83 datums use the meter as the defining linear unit.
Formal Coordinate Systems in Wisconsin
Universal Transverse Mercator (UTM) ZonesNAD 27 and NAD 83
UTM Zone 15 UTM Zone 16
90°0
0' W
est
96°0
0' W
est
Maximum scale distortion (ellipsoid to projection): 1/2,500
Two 6° wide transverse cylindrical zones
84°0
0' W
est
UTM Zones are defined using the same parameters for both NAD 27 and NAD 83 datums:
UTM Zone UTM 15N UTM 16NCentral Meridian 93°00' W 87°00' W
Latitude of Origin 0°00' N 0°00' NNo Origin Northing 0 m 0 mEo Origin Easting 500,000 m 500,000 mko Scale at Cen Mer 0.9996 0.9996
UTM systems use the meter as the defining linear unit.
UTM Zones are defined using the same parameters for both NAD 27 and NAD 83 datums:
UTM Zone UTM 15N UTM 16NCentral Meridian 93°00' W 87°00' W
Latitude of Origin 0°00' N 0°00' NNo Origin Northing 0 m 0 mEo Origin Easting 500,000 m 500,000 mko Scale at Cen Mer 0.9996 0.9996
UTM systems use the meter as the defining linear unit.
Formal Coordinate Systems in Wisconsin
Wisconsin Transverse Mercator (WTM) ZoneNAD 27 and NAD 83
87°0
0' W
est
90°0
0' W
est
93°0
0' W
est
WTM
Maximum scale distortion (ellipsoid to projection): 1/2,500
One 6° wide transverse cylindrical zone
WTM is defined for NAD 27 and NAD 83. A distinct "shift" of approximately 13 miles in northing andeasting was introduced to the NAD 83 parameters to moreeasily distinguish the coordinate values:
NAD 27 NAD 83Central Meridian 90°00' W 90°00' WLatitude of Origin 0°00' N 0°00' N
No Origin Northing -4,500,000 m -4,480,000 mEo Origin Easting 500,000 m 520,000 mko Scale at Cen Mer 0.9996 0.9996
The WTM system uses the meter as the defining linear unit.
WTM is defined for NAD 27 and NAD 83. A distinct "shift" of approximately 13 miles in northing andeasting was introduced to the NAD 83 parameters to moreeasily distinguish the coordinate values:
NAD 27 NAD 83Central Meridian 90°00' W 90°00' WLatitude of Origin 0°00' N 0°00' N
No Origin Northing -4,500,000 m -4,480,000 mEo Origin Easting 500,000 m 520,000 mko Scale at Cen Mer 0.9996 0.9996
The WTM system uses the meter as the defining linear unit.
Formal Coordinate Systems in Wisconsin
Wisconsin County Coordinate SystemNAD 83 (1991)
59 systems covering 72 counties
Conic or cylindrical projection
Each uses a “raised” ellipsoid
Maximum ratio: (grid to ground)1/30,000 rural1/50,000 urban
Hd
Nd
Geoid
GRS 80 Ellipsoid
Raised Ellipsoid Earth Grid
Formal Coordinate Systems in Wisconsin
Wisconsin County Coordinate SystemNAD 83 (1991)
Conic projections
Formal Coordinate Systems in Wisconsin
Wisconsin County Coordinate SystemNAD 83 (1991)
Conic projections
Formal Coordinate Systems in Wisconsin
Wisconsin County Coordinate SystemNAD 83 (1991)
The Jackson County Official Projection does not use a raised enlarged ellipsoid and is instead referenced to the GRS 80 ellipsoid. It is based on a transverse cylindric projection:
Central Meridian 90°50'39.46747" W
Latitude of Origin 44°15'12.00646" NNo Origin Northing 25,000.000 mEo Origin Easting 27,000.000 mko Scale at Cen Mer 1.00003 53000
The Jackson County Official Projection does not use a raised enlarged ellipsoid and is instead referenced to the GRS 80 ellipsoid. It is based on a transverse cylindric projection:
Central Meridian 90°50'39.46747" W
Latitude of Origin 44°15'12.00646" NNo Origin Northing 25,000.000 mEo Origin Easting 27,000.000 mko Scale at Cen Mer 1.00003 53000
Formal Coordinate Systems in Wisconsin
Wisconsin County Coordinate SystemNAD 83 (1991)
Cylindrical projections
Formal Coordinate Systems in Wisconsin
Wisconsin County Coordinate SystemNAD 83 (1991)
Cylindrical projections
WCCS: Emerging Issues & WCCS: Emerging Issues & SolutionsSolutions
Al Vonderohe
Emerging IssueEmerging Issue
Enlarging the ellipsoid has the mathematical effect of modifying the underlying geodetic datum.This has caused difficulties in both the vendor and user communities.– Vendors want to support WCCS, but there
is complexity.– Most of the user community doesn’t have a
clue about datums and map projections.
WLIA Task ForceWLIA Task ForceThe WLIA Task Force on Wisconsin Coordinate Systems was formed early this year to address this and other issues associated with location referencing in Wisconsin.A question that emerged:Can the WCCS be re-designed so that:
1. There is no need to change the ellipsoid from GRS 80. That is, there will be one datum for all projections.
2. Coordinate differences between the existing and re-designed systems will be within negligible bounds. In this way, legacy databases and records will not have to be modified.
Leave the ellipsoid where it is and enlarge only the map projection surface. This way, the ellipsoid factor and the scale factor are nearly inverses of one another and their product = 1.
Map Projection SurfaceGeoid
Ellipsoid
Local Map Projection Surface
Earth’s Surface
Approach to Lambert ReApproach to Lambert Re--DesignDesignTwo strategies:
1. Make the original and re-designed map projection surfaces be identical in three-dimensional space.– This will cause the latitude of the central parallel
(φ0) to change.– Challenge: Finding φ0.
2. Hold φ0 constant.– This will cause the original and re-designed map
projection surfaces to be dissimilar.– Challenge: Finding k0.
Approach to Strategy 1Approach to Strategy 1
Work in geocentric coordinates (3D rectangular).Use analytical geometry.Find equations of the line that is the projection of the central meridian.Find the point of tangency between GRS 80 ellipsoid and a line parallel with the above line.Convert X,Y,Z of this point to φ,λ,h. φ is the latitude of the central parallel.
Geocentric / Geodetic CoordinatesGeocentric / Geodetic Coordinates
Equator
Gre
enwi
ch
λP
φP
P
Y
X
Z
YP
ZP
XP
hP
Geocentric coordinates are based upon a 3D right-handed system with origin at ellipsoid center, XY plane is the equatorial plane, +X axis passes through λ = 08, +Y axis passes through λ = 908E.For any point, there are direct and inverse transformations between X,Y,Z and φ,λ,h.
Approach to Strategy 1Approach to Strategy 1Profile through GRS80, enlarged ellipsoid, and original map projection surface at λ0:
GRS 80 Enlarged ellipsoid
Map projection surface
Geodetic coords = φ1, λ0, 0; Compute X,Y,Z
Geodetic coords = φ2, λ0, 0; Compute X,Y,Z
Compute equations for this line.
Parallel
Find X,Y,Z of point of tangency. Transform to φ0, λ0, h.
NOTE: Two sets of geodetic coordinates; one set of geocentric coordinates.
Approach to Strategy 1Approach to Strategy 1To find k0:
GRS 80 Enlarged ellipsoid
Map projection surface
Compute perpendicular distance between these two lines.
D
RDRk +
=0
where R is the radius in the meridian of GRS 80 at φ0.
Ellipsoid Normal
Minor Axis
R
Approach to Strategy 1Approach to Strategy 1
There will be discrepancies because the two ellipsoids do not have the same shape.Compute best fit translation in Y (change in false northing) and scale from sets of coordinates of points in both the original and re-designed systems.
– Points should be well-distributed across geographic extent.
Apply these best fits to final re-designed parameters.
Dane County Test of Lambert Dane County Test of Lambert Methodology (Strategy 1)Methodology (Strategy 1)
∆X = -0.003m;∆Y = 0.000m
∆X = +0.003m;∆Y = +0.001m
∆X = +0.001m;∆Y = -0.001m
∆X = -0.001m;∆Y = -0.001m
∆X = +0.002m;∆Y = 0.000m
Approach to Transverse Approach to Transverse MercatorMercatorReRe--DesignDesign
Hold all parameters initially constant except k0.Compute new k0 in manner similar to that for Lambert re-design.Compute best fits for translation in Y (false northing) and scale.Apply best fits to final parameters.NOTE: Cannot hold map projection surface identical because the 2 cylinders have different shapes.
Lincoln County Test of Transverse Lincoln County Test of Transverse MercatorMercator MethodologyMethodology
∆X = -0.002m;∆Y = -0.002m
∆X = +0.002m;∆Y = +0.002m
ConclusionsConclusions
Under the re-design, all WCCS would have a single, common datum based upon the GRS 80 ellipsoid.Initial tests indicate that WCCS can be re-designed to within 5mm or better.The WLIA Task Force has deemed 5mm to be a negligible difference.The WLIA Task Force is recommending re-design.
SummarySummary
Where are we headed?– Ted Koch
SummarySummary
Where are we headed?– WCCS redesign proposal approved by
WLIA – October ’04– WCCS redesign proposal approved by
WLIB – November ’04– WLIB approves $35 K for redesign costs– Contract for redesign through a single
county using WLIB Strategic Initiative Grant
SummarySummary
Where are we headed? (Continued)– WCCS redesign completed by Sept. ’05– WCCS redesign documentation completed
by Dec. ’05– During ’05, TF will continue to address
issues of registration, legislation and use
– Prepare a TF final report– Continue to inform the community
Thank YouThank You
Questions???Questions???