David Doyle Chief Geodetic Surveyor National Geodetic Survey dave.doyle@noaa, (301) 713-3178

David DoyleChief Geodetic SurveyorNational Geodetic Survey

[email protected], (301) 713-3178

The State Plane Coordinate System

December 8, 2010

NORTHING

EASTING

So What Is A Projection

MAP PROJECTIONS

Lambert ConformalConic

TransverseMercator

Developed from a request in 1933 from the North Carolina Department of Transportation

Zones designed by U.S. Coast and Geodetic Survey (Oscar Adams and Charles Claire)

Two basic map projections used:

Lambert Conformal Conic – States or parts of states that have a more East-West orientation

Transverse Mercator – States or parts of states that have a more North-South orientation

Zone boundaries along International, State and county boundaries

Zones typically 154 miles wide – this limits the maximum geodetic to grid distance distortion to 1:10,000

All coordinate values in U.S. Survey Feet

Conversions to/from latitude & longitude originally calculated using tables (S.P. 267 Plane Coordinate Projections Tables – Pennsylvania)

1968 - State Plane Coordinates by Automatic Data Processing (USC&GS 62-4)

STATE PLANE COORDINATE SYSTEMNAD 27

STATE PLANE COORDINATE SYSTEMNAD 83

(SPCs are NOT defined relative to WGS 84/ITRF)

Geometric parameters of original SPC zones left unchanged unless requested by “the State”

All states get new false northing and false easting defined in meters.

All values in meters – conversions to feet defined by individual state legislation or Federal Register Notice:

1 m = 3.2808333333 U.S. Survey Feet 1 m = 3.2808398950 International Feet

NAD 83 STATE PLANE ZONES

http://www.ngs.noaa.gov/PUBS_LIB/UnderstandingSPC.pdf

http://www.ngs.noaa.gov/PUBS_LIB/publication235.pdf

http://www.ngs.noaa.gov/PUBS_LIB/FundSPCSys.pdf

SPCS PUBLICATIONS

http://www.ngs.noaa.gov/PUBS_LIB/publication62-4.pdf

http://www.ngs.noaa.gov/PUBS_LIB/ManualNOSNGS5.pdf

http:// http://pubs.er.usgs.gov/djvu/PP/PP_1395.pdf

SPCS PUBLICATIONS

GPPCGP and SPCS83National Geodetic Survey

No Datum Transformation (e.g. NAD 27 – NAD 83)Values in meters only for NAD 83http://www.ngs.noaa.gov/TOOLS/program_descriptions.html#SPCZ

CORPSCONU.S. Army Corps of Engineers

Both horizontal and vertical datum transformationsValues in meters, U.S. Survey Foot or International Foot

http://crunch.tec.army.mil/software/corpscon/corpscon.html

FEDERAL CONVERSION UTILITIES

NATIONAL SPATIAL REFERENCE SYSTEM(NSRS)

Consistent National Coordinate System

• Latitude • Longitude

• Height • Scale

• Gravity• Orientation

and how these values change with time

• National Shoreline- Consistent, accurate, and up-to-date

• National and Cooperative CORS- A network of GPS Continuously Operating Reference Stations

• Networks of geodetic control points- Permanently marked passive survey monuments

• Tools-Models of geophysical effects on spatial measurements-e.g., NADCON, INVERSE, SPCS83, UTMS, FORWARD

NSRS COMPONENTS

• Tools-Models of geophysical effects on spatial measurements-e.g., NADCON, INVERSE, SPCS83, UTMS, FORWARD

METADATA??Horizontal Datum??

Plane Coordinate Zone ??

Units of Measure ??

How Accurate ??

HORIZONTALGEODETIC DATUMS

HORIZONTAL 2 D (Latitude and Longitude) (e.g. NAD 27, NAD 83 (1986))

GEOMETRIC 3 D (Latitude, Longitude and Ellipsoid Height)

Fixed and Stable - Coordinates seldom change (e.g. NAD 83 (1996), NAD 83 (2007), NAD 83 (CORS96))

also

4 D (Latitude, Longitude, Ellipsoid Height, Velocities) Coordinates change with time

(e.g. ITRF00, ITRF08)

HORIZONTAL DATUMS

8 Constants 3 – specify the location of the origin of the

coordinate system.

3– specify the orientation of the coordinate system.

2 – specify the dimensions of the reference ellipsoid

THE ELLIPSOIDA MATHEMATICAL MODEL OF THE EARTH

a = Semi major axis b = Semi minor axis f = a-b = Flattening a

b

a

N

S

UNITED STATESELLIPSOID DEFINITIONS

CLARKE 1866 a = 6,378,206.4 m 1/f = 294.97869821

1879 - 1986

GEODETIC REFERENCE SYSTEM 1980 - (GRS 80) a = 6,378,137 m 1/f = 298.257222101

1986 - Present

WORLD GEODETIC SYSTEM 1984 - (WGS 84) a = 6,378,137 m 1/f = 298.257223563

1987 - Present

BESSEL 1841 a = 6,377,397.155 m 1/f = 299.1528128

1848 - 1879

ELLIPSOID - GEOID RELATIONSHIP

H = Orthometric Height (NAVD 88)

H = h – (N)

h = Ellipsoidal Height [NAD 83 (1996) or NAD 83(2007)/NAD 83 (CORS96)]

N = Geoid Height (GEOID 09)

H h

EllipsoidGRS80

N

Geoid

GEOID09

National Geodetic Survey, Retrieval Date = NOVEMBER 5, 2010 KW0527 *********************************************************************** KW0527 CBN - This is a Cooperative Base Network Control Station. KW0527 DESIGNATION - STRAUSS KW0527 PID - KW0527 KW0527 STATE/COUNTY- PA/BERKS KW0527 USGS QUAD - STRAUSSTOWN (1974) KW0527 KW0527 *CURRENT SURVEY CONTROL KW0527 ___________________________________________________________________ KW0527* NAD 83(2007)- 40 29 55.74517(N) 076 11 29.92386(W) ADJUSTED KW0527* NAVD 88 - 195.756 (meters) 642.24 (feet) ADJUSTED KW0527 ___________________________________________________________________ KW0527 EPOCH DATE - 2002.00 KW0527 X - 1,159,255.008 (meters) COMP KW0527 Y - -4,716,671.900 (meters) COMP KW0527 Z - 4,120,364.800 (meters) COMP KW0527 LAPLACE CORR- -2.65 (seconds) DEFLEC09 KW0527 ELLIP HEIGHT- 161.232 (meters) (02/10/07) ADJUSTED KW0527 GEOID HEIGHT- -34.54 (meters) GEOID09 KW0527 DYNAMIC HT - 195.655 (meters) 641.91 (feet) COMP KW0527 KW0527 ------- Accuracy Estimates (at 95% Confidence Level in cm) -------- KW0527 Type PID Designation North East Ellip KW0527 ------------------------------------------------------------------- KW0527 NETWORK KW0527 STRAUSS 0.51 0.39 1.25 KW0527 ------------------------------------------------------------------- KW0527 MODELED GRAV- 980,104.4 (mgal) NAVD 88 KW0527 KW0527 VERT ORDER - SECOND CLASS 0 KW0527 KW0527.The horizontal coordinates were established by GPS observations KW0527.and adjusted by the National Geodetic Survey in February 2007. KW0527 KW0527.The datum tag of NAD 83(2007) is equivalent to NAD 83(NSRS2007). KW0527.See National Readjustment for more information. KW0527.The horizontal coordinates are valid at the epoch date displayed above. KW0527.The epoch date for horizontal control is a decimal equivalence KW0527.of Year/Month/Day.

KW0527.The orthometric height was determined by differential leveling and KW0527.adjusted in June 1991. KW0527 KW0527.The X, Y, and Z were computed from the position and the ellipsoidal ht. KW0527 KW0527.The Laplace correction was computed from DEFLEC09 derived deflections. KW0527 KW0527.The ellipsoidal height was determined by GPS observations KW0527.and is referenced to NAD 83. KW0527 KW0527.The geoid height was determined by GEOID09. KW0527 KW0527; North East Units Scale Factor Converg. KW0527;SPC PA S - 130,575.318 732,088.384 MT 0.99995985 +1 00 39.8 KW0527;SPC PA S - 428,395.86 2,401,859.97 sFT 0.99995985 +1 00 39.8 KW0527;UTM 18 - 4,483,805.533 399,024.353 MT 0.99972550 -0 46 26.3 KW0527 KW0527! - Elev Factor x Scale Factor = Combined Factor KW0527!SPC PA S - 0.99997471 x 0.99995985 = 0.99993456 KW0527!UTM 18 - 0.99997471 x 0.99972550 = 0.99970022 KW0527 KW0527: Primary Azimuth Mark Grid Az KW0527:SPC PA S - STRAUSS AZ MK 075 40 15.0 KW0527:UTM 18 - STRAUSS AZ MK 077 27 21.1 KW0527 KW0527|---------------------------------------------------------------------| KW0527| PID Reference Object Distance Geod. Az | KW0527| dddmmss.s | KW0527| KW0529 STRAUSS AZ MK 0764054.8 | KW0527| KW0528 STRAUSS RM 1 21.824 METERS 08830 | KW0527| KW3019 STRAUSSTOWN MUNICIPAL TANK APPROX. 1.2 KM 1393323.8 | KW0527| KW0526 STRAUSS RM 2 21.520 METERS 23922 | KW0527|---------------------------------------------------------------------|

CONTINUOUSLY OPERATING REFERENCE STATIONS (CORS)

1500+ Installed and operated by more than 200

Federal-State-Local gov and private partners

NOAA/National Geodetic Survey

NOAA/OAR Global Systems Division

U.S. Coast Guard - DGPS/NDGPS

Corps of Engineers - DGPS

FAA - WAAS/LAAS

State DOTs

County and City

Academia

Private Companies

CONTINUOUSLY OPERATING REFERENCE STATIONS (CORS)

NGS PROVIDES

Horizontal and Vertical NSRS Connections

NAD 83 and ITRF00 Coordinates

Network Data Collection - Hourly & Daily

Daily 3D Network Integrity Adjustment

Public Data Distribution - Internet 16 Year On-Line Data Holding

Continuously Operating Reference Stations (CORS)

Continuously Operating Reference Stations (CORS)

= NAD 83(NSRS 2007)

HARRISBURG (GTS1), PENNSYLVANIA ____________________________________________________________________________ | || Antenna Reference Point(ARP): HARRISBURG CORS ARP || ------------------------------------------------- || PID = DF5874 || || || ITRF00 POSITION (EPOCH 1997.0) || Computed in Jun., 2003 using 14 days of data. || X = 1110966.251 m latitude = 40 15 07.81645 N || Y = -4746445.044 m longitude = 076 49 34.84696 W || Z = 4099452.309 m ellipsoid height = 88.059 m || || ITRF00 VELOCITY || Predicted with HTDP_2.7 May 2003. || VX = -0.0167 m/yr northward = 0.0035 m/yr || VY = -0.0018 m/yr eastward = -0.0167 m/yr || VZ = 0.0028 m/yr upward = 0.0002 m/yr || || || NAD_83 POSITION (EPOCH 2002.0) || Transformed from ITRF00 (epoch 1997.0) position in Jun., 2003. || X = 1110966.793 m latitude = 40 15 07.78742 N || Y = -4746446.496 m longitude = 076 49 34.83862 W || Z = 4099452.437 m ellipsoid height = 89.315 m || || NAD_83 VELOCITY || Transformed from ITRF00 velocity in Jun., 2003. || VX = 0.0000 m/yr northward = 0.0000 m/yr || VY = 0.0000 m/yr eastward = 0.0000 m/yr || VZ = 0.0000 m/yr upward = 0.0000 m/yr ||____________________________________________________________________________|

ITRF00 – NAD 83(CORS96)

DHoriz = 0.917mDEHt = 1.256m

What is OPUS?

• On-Line Positioning User Service

• Processes GPS data• Global availability (masked)• 3 goals:

– Simplicity– Consistency– Reliability

You’ve got mail!

OPUS solution

OPUS – DB

SimpleShared Data

NGS Archived

OPUS

OPUS-Projects$$ Receivers

2-4 Hours of dataMultiple ReceiversNetwork Solution

Results shared or not

OPUS-RS$$ Receivers

15 Minutes of dataResults not shared

OPUS-DB$$ Receivers

4 Hours of dataResults shared

OPUS-S$$ Receivers

2 Hours of dataResults not shared

LOCUS(Leveling Online Computing User Service)

Digital Bar-Code LevelingIntegration with OPUS?Results shared or not?

FLAVORS OF OPUS

WHAT YOU NEED TO USE THE STATE PLANE COORDINATE SYSTEMS

N & E State Plane Coordinates for Control Points

AZIMUTHS - True, Geodetic, or Grid - Conversion from Astronomic to Geodetic (LaPlace Correction) - Conversion from Geodetic to Grid (Mapping Angle)

DISTANCES - Reduction from Horizontal to Ellipsoid “Sea-Level Reduction Factor” - Correction for Grid Scale Factor - Combined Factor

THREE DISTANCES:

• “GROUND” DISTANCE = NORMAL TO GRAVITY BETWEEN TWO POINTS

• “GEODETIC” DISTANCE = ALONG THE ELLIPSOID

• “GRID” DISTANCE = ALONG THE MAP PROJECTION SURFACE ------------------------------------------------------------------

• PROJECTED COORDINATES ARE ALWAYS DISTORTED

DEFINITIONS• GRID SCALE Factor

– Multiplier to change geodetic distances based on the Earth model (ellipsoid) to the grid plane.

• ELEVATION Factor (a.k.a. Sea Level Reduction or Ellipsoid Reduction Factor)– Multiplier to change horizontal ground distances to

geodetic (ellipsoid) distances

• GRID-ELEVATION or COMBINED Factor– Gird Scale Factor times the Elevation Factor

• This factor changes horizontal ground distances to grid distances

Normal to ellipsoid

AZIMUTH RELATIONSHIP “True” Azimuth – Derived from astronomic observations (e.g.

Solar/Polaris) –this can usually be considered the same as a geodetic azimuth.

Geodetic Azimuth – Derived from the inverse between two points of known latitude and longitude, or from a LaPlace corrected astronomic azimuth or a grid azimuth with the mapping angle () applied

Grid Azimuth – Derived from the inverse between two points defined in northing & easting, or from a geodetic azimuth - the mapping angle ()

(e.g. State Plane, UTM, local grid coordinates)

ELLIPSOID - GEOID RELATIONSHIP

EllipsoidGRS80

Geoid

LaPlace Correction+/- 0 ~ 25” Lower 48 states

NGS Tool – DEFLEC09

LAMBERT CONFORMAL CONICWITH 2 STANDARD PARALLELS

Approximately 154 miles

CENTRAL MERIDIAN

STANDARD PARALLELS

N

S

λO

CONVERGENCE ANGLE(Mapping Angle)

CENTRAL MERIDIANλO

Convergence angles () always positive (+) East

Convergence angles () always negative (-) West

The Convention of the Sign of the Convergence Angle is Always From Grid To Geodetic

TRANSVERSE MERCATOR

CENTRAL MERIDIAN

SC

AL

E E

XA

CT

SC

AL

E E

XA

CT

SCALE < 1 SCALE > 1SCALE > 1

λO

Pennsylvania State Plane Coordinate System – NAD 83

False Northing and Easting Changedand defined in meters

Conversion to Feet left up to individual states

U.S. Survey or International Feet

Geometric Parameters remain the sameAs NAD 27

Zone BoundariesCentral Meridian

North/South Standard ParallelsLatitude/Longitude of Origin

CE

NT

RA

L

ME

RID

IAN

NORTH STANDARD PARALLEL

SOUTH STANDARD PARALLEL

GRID Dist <

GEODETIC Dis

t

1 < GRID SCA

LE FACTOR

GRID Dist >

GEODETIC Dis

t

GRID SCALE F

ACTOR > 1

GRID Dist >

GEODETIC Dis

t

GRID SCALE F

ACTOR > 1

GRID CONVERGENCE

ANGLE +

GRID CONVERGENCE

ANGLE -

ORIGIN 39o 20’ 00” 77o 45’ 00”

N = 0 m E = 600,000 m

COORDINATE CHANGES(STATE PLANE)

STATION: STRAUSS (pid KW0527)

PENNSYLVANIA SOUTH ZONE (NAD 27/NAD 83)

Northing Easting Converg Angle Scale Factor

428,352.11 ft. 2,433,279.72 ft. +1o 00’ 39.0” 0.99995985 130,575.318 m. 732,088.384 m. +1o 00’ 39.8” 0.99995985

(428,395.86 ft)* (2,401,859.97 ft)* (428,396.71 ft)# (2,401,864.78 ft)# (0.15) (4.81)

* Converted using U.S. Survey Foot, 1 M = 3.2808333333 Ft. # Converted using International Foot, 1 M = 3.2808398950 Ft.

Michigan Compiled Laws, Public Act 9 of 1964, Sections 54.231- .239,

STATE PLANE COORDINATE COMPUTATION

STRAUSS (pid KW0527) N = 428,395.86 U.S. Survey Feet E = 2,401,859.97 U.S. Survey Feet Orthometric Height (H) = 642.24 Feet Geoid Height (N) = - 113.32 Feet Laplace Correction = - 2.6” Grid Scale Factor (k) = 0.99995985 Meridian Convergence () = + 1o 00’ 39.8”

Observed Astro Azimuth (A) = 253o 26’ 14.9”

Horizontal Distance (D) = 3,314.91 Feet


N1 = N + (Sg x cos g)

E1 = E + (Sg x sin g)

Where: N = Starting Northing Coordinate E = Starting Easting Coordinates

Sg = Grid Distance

g = Grid Azimuth

REDUCTION TO THE ELLIPSOID

h

N

H

R Earth Radius 6,372,200 m

20,906,000 ft.

S

D

S = D * ___R__ R + h

Where: h = H + [N]

S = D * R + H + (N)

___R___

REDUCTION TO THE ELLIPSOID(The correct method)

WHERE

_____________N

1 – e’2 cos2cos2 R =

_____________a

(1 – e’2 cos2)1/2

N =

e’2 = (a2 – b2) / b2

N = Radius of Curvature in Azimutha = Ellipsoid semi-major axisb = Ellipsoid semi-minor axisAzimuth of the lineLatitude of the Station

REDUCTION TO ELLIPSOIDEllipsoid Ht /Orthometric Ht

Sgeodetic = D x [R / (R + h)] D = 3,314.91 ft (Measured Horizontal Distance) R = 20,906,000 ft (Mean Radius of the Earth) h = H + N (H = 642 ft, N = - 113 ft) = 529 ft (Ellipsoid Height)

S = 3,314.91 [20,906,000 / 20,906,000 + 529] S = 3,314.91 x 0.99997470 S = 3,314.83 ft

Sgeodetic = 3,314.91 [20,906,000 / 20,906,000 + 642] Sgeodetic = 3,314.91 x 0.99996929 Sgeodetic = 3,314.81 ft

Diff = 0.02 ft or ~ 1:166,000

REDUCTION TO ELLIPSOIDMean Radius vs. Computed Earth Radius

Sgeodetic = D x [R / (R + h)] D = 3,314.91 ft (Measured Horizontal Distance) R = 20,906,000 ft (Mean Radius of the Earth) R = 20,936,382 ft (Computed Radius of the Earth) h = 529



Diff = 0.00 ft

GRID SCALE FACTOR (k) OF A POINTGRID CONVERGENCE ANGLE () OF A POINT

Easiest to obtain by using

NGS SPCs tool kit utility or

CORPSCON

GRID SCALE FACTOR (k) OF A LINE

k 12 = (k1 + 4km + k2) / 6

(m = mean of k1 & k2)

Typically the Average Value Works Fine

k 12 = (k1 + k2) / 2

REDUCTION TO GRID

Sgrid = Sgeodetic * k (Grid Scale Factor)

Sgrid = 3,314.83 x 0.99995985

Sgrid = 3,314.70 meters

COMBINED FACTOR (CF)

CF = Ellipsoidal Reduction x Grid Scale Factor (k)

= 0. 0.99997470 x 0.99995985

= 0.99993455

CF x D = Sgrid

0.99993455 x 3,314.91 = 3,314.69 ft

GRID AZIMUTH COMPUTATION

grid = Astro + Laplace Correction – Convergence Angle (

= 253o 26’ 14.9” (Observed Astro Azimuth) - 2.6” (Laplace Correction) = 253o 26’ 12.3” (Geodetic Azimuth) - 1 00 39.8 (Convergence Angle) = 252o 25’ 32.5” (Grid Azimuth)

The convention of the sign of the convergence angle is always from Grid to Geodetic


N1 = N + (Sgrid x cos grid) E1 = E + (Sgrid x sin grid)

N1 = 428,395.86 + (3,314.70 x Cos 252o 25’ 32.5”) = 428,395.86 + (3,314.70 x -0.301942400) = 428,395.86 + (-1,000.85) = 427,395.01 U.S. Survey Feet

E1 = 2,401,859.97 + (3,314.70 x Sin 252o 25’ 32.5”) = 2,401,859.97 + (3,314.70 x -0.953326170) = 2,401,859.97 + (-3,159.99) = 2,398,699.98 U.S. Survey Feet

GROUND LEVEL COORDINATESSURFACE LEVEL COORDINATESPROJECT DATUM COORDINATESLOW DISTORTION PROJECTIONS

“I WANT STATE PLANE COORDINATES RAISED TO GROUND LEVEL”

GROUND LEVEL COORDINATES ARE

NOT STATE PLANE COORDINATES!!!!!

GROUND LEVEL COORDINATESPROBLEMS

RAPID DISTORTIONS*

PROJECTS DIFFICULT TO TIE TOGETHER*

CONFUSION OF COORDINATE SYSTEMS

LACK OF DOCUMENTATION

* Can be minimized with LDP

GROUND LEVEL COORDINATES“IF YOU DO”

TRUNCATE COORDINATE VALUES SUCH AS:

N = 404,648.89 ft becomes 4,648.89 E = 26,341,246.75 ft becomes 1,246.75

AND

The NSRS has evolved

1 Million Monuments

(Separate Horizontal and

Vertical Systems)

Passive Marks(Limited

Knowledge of Stability)

GPS CORS GNSS CORS

70,000 Passive Marks

(3-Dimensional)

1,500+ GPS CORS

(Time Dependent System Possible; 4-Dimensional)

Problems with NAD 83 and NAVD 88NAD 83 is not as geocentric as it could be (approx 1-2 m).

Data users don’t see this – Yet

NAD 83 is not well defined with positional velocities.

Most users still think of NAD 83 as 2-dimensional (lat/long, N/E)

NAVD 88 is realized by passive control (bench marks) most of which have not been releveled in 40 years.

NAVD 88 does not account for local vertical velocities (subsidence and uplift) Post glacial isostatic readjustmentSubsurface fluid withdrawalSediment loadingSea level rise

.

The National Geodetic Survey 10 year planMission, Vision and Strategy

2008 – 2018http://www.ngs.noaa.gov/INFO/NGS10yearplan.pdf

Official NGS policy as of Jan 9, 2008Modernized agencyAttention to accuracyAttention to time-changesImproved products and servicesIntegration with other fed missions

2018 Targets:NAD 83 and NAVD 88 re-definedCm-accuracy access to all coordinatesCustomer-focused agencyGlobal scientific leadership

Simplified Concept of NAD 83 vs. ITRF00

2.2 meters

NAD 83Origin

ITRF 00Origin

Earth’s

Surface

h83

h00

Identically shaped ellipsoids (GRS-80)a = 6,378,137.000 meters (semi-major axis)1/f = 298.25722210088 (flattening)

Predicted Positional Changes in 2018Vicinity of Silver Spring, MD.

(Computed for HASSLER pid HV9698)

HORIZONTAL = 1.31 m (4.3 ft)ELLIPSOID HEIGHT = - 1.25 m (- 4.1 ft)

Predicted with HTDP

ORTHOMETRIC HEIGHT = - 0.47 m (- 1.5 ft)Predicted with HTDP and USGG2009

2020 GEOMETRIC DATUM OPTIONS

Option 1: Adopt ITRF20xx and compute new coordinates based on the best available

Velocity model(Coordinates du Jour)

Option 2: Adopt a reference frame that agrees with ITRF20xx at some instant of time,

(e.g. Epoch 2020.00)but does not move relative to “stable” North

American tectonic plate similar to NAD 83

GOOD COORDINATION BEGINS WITH GOOD COORDINATES

GEOGRAPHY WITHOUT GEODESY IS A FELONY

Documents

David Doyle Chief Geodetic Surveyor National Geodetic Survey dave.doyle@noaa, (301) 713-3178