Wisconsin County Coordinate Systems: WLIA Task Force ... · Why a Local Coordinate System? Regional coordinate systems require ground-to-grid conversions to relate field surveyed

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


Global Fitting

Geoid

Defining Concepts


Earth

Geoid

Ellipsoid

Deflection ofthe Vertical

Nor

mal

to e

llipso

idN

orm

al to

geo

id(g

ravi

ty)

Defining Concepts


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



Spherical CoordinatesMeri

dian

EquatorialPlane

Pol

ar A

xis

: Astronomic latitude: Geocentric latitude: Geodetic latitude

Types of Latitude



Geodetic Coordinates

Greenwich

Equator

Normal to

MeridianEllipsoid

Three dimensional position of a point is expressed by:

geodetic latitudegeodetic longitude



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



Length distortion occurs when projecting from:- ground (Earth) to ellipsoid- ellipsoid to projection surface

Ellipsoid

Projection Surface

AB

A'

B'

A"

B"

Earth



Direction distortion occurs because true north lines converge to a point (North Pole)

True NGrid N

A

B


“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.


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


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


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


Transverse Mercator Cylindrical Projection

Eo

Cen

tral M

erid

ian

Grid

Nor

th

No

Np

Ep

P

North

East

North Pole

convergence



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



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 = + + = + +



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 = + + = + +


Cen

tral M

erid

ian

Grid

Nor

th

EO

Nb

Np

EP

P

North

East

Rb

North Pole

convergence

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=

= + −



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



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


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




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.


Wisconsin State Plane Coordinate (SPC) ZonesNAD 83

North

Central

South

Datum: NAD 83Ellipsoid: GRS 80




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




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.


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


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.


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


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.


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



Conic projections



Conic projections



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



Cylindrical projections



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???