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

The State Plane Coordinate System. December 8, 2010. David Doyle Chief Geodetic Surveyor National Geodetic Survey dave.doyle@noaa.gov, (301) 713-3178. So What Is A Projection. NORTHING. EASTING. MAP PROJECTIONS. Lambert Conformal Conic. Transverse Mercator.

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

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  1. The State Plane Coordinate System December 8, 2010 David Doyle Chief Geodetic Surveyor National Geodetic Survey dave.doyle@noaa.gov, (301) 713-3178

  2. So What Is A Projection NORTHING EASTING

  3. MAP PROJECTIONS Lambert Conformal Conic Transverse Mercator

  4. STATE PLANE COORDINATE SYSTEMNAD 27 • 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)

  5. 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

  6. NAD 83 STATE PLANE ZONES

  7. SPCS PUBLICATIONS http://www.ngs.noaa.gov/PUBS_LIB/publication235.pdf http://www.ngs.noaa.gov/PUBS_LIB/FundSPCSys.pdf http://www.ngs.noaa.gov/PUBS_LIB/UnderstandingSPC.pdf

  8. SPCS PUBLICATIONS http://www.ngs.noaa.gov/PUBS_LIB/publication62-4.pdf http:// http://pubs.er.usgs.gov/djvu/PP/PP_1395.pdf http://www.ngs.noaa.gov/PUBS_LIB/ManualNOSNGS5.pdf

  9. FEDERAL CONVERSION UTILITIES GPPCGP and SPCS83 National Geodetic Survey No Datum Transformation (e.g. NAD 27 – NAD 83) Values in meters only for NAD 83 http://www.ngs.noaa.gov/TOOLS/program_descriptions.html#SPCZ CORPSCON U.S. Army Corps of Engineers Both horizontal and vertical datum transformations Values in meters, U.S. Survey Foot or International Foot http://crunch.tec.army.mil/software/corpscon/corpscon.html

  10. NATIONAL SPATIAL REFERENCE SYSTEM(NSRS) Consistent National Coordinate System • Latitude • Longitude • Height • Scale • Gravity • Orientation and how these values change with time

  11. National Shoreline - Consistent, accurate, and up-to-date • National and Cooperative CORS • Tools • Tools - A network of GPS Continuously Operating Reference Stations • Models of geophysical effects on spatial measurements • e.g., NADCON, INVERSE, SPCS83, UTMS, FORWARD • Models of geophysical effects on spatial measurements • e.g., NADCON, INVERSE, SPCS83, UTMS, FORWARD • Networks of geodetic control points - Permanently marked passive survey monuments NSRS COMPONENTS

  12. METADATA?? Horizontal Datum?? Plane Coordinate Zone ?? Units of Measure ?? How Accurate ??

  13. 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)

  14. 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

  15. THE ELLIPSOIDA MATHEMATICAL MODEL OF THE EARTH N b a a = Semi major axis b = Semi minor axis f = a-b = Flattening a S

  16. UNITED STATESELLIPSOID DEFINITIONS BESSEL 1841 a = 6,377,397.155 m 1/f = 299.1528128 1848 - 1879 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

  17. ELLIPSOID - GEOID RELATIONSHIP H = Orthometric Height (NAVD 88) h = Ellipsoidal Height [NAD 83 (1996) or NAD 83(2007)/NAD 83 (CORS96)] N = Geoid Height (GEOID 09) H=h– (N) h H N GEOID09 Geoid Ellipsoid GRS80

  18. 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.

  19. 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|---------------------------------------------------------------------|

  20. 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

  21. 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

  22. Continuously Operating Reference Stations (CORS)

  23. Continuously Operating Reference Stations (CORS)

  24. 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 = 0.917m DEHt = 1.256m = NAD 83(NSRS 2007)

  25. What is OPUS? • On-Line Positioning User Service • Processes GPS data • Global availability (masked) • 3 goals: • Simplicity • Consistency • Reliability

  26. You’ve got mail! OPUS solution

  27. OPUS – DB Simple Shared Data NGS Archived

  28. FLAVORS OF OPUS OPUS-Projects $$ Receivers 2-4 Hours of data Multiple Receivers Network Solution Results shared or not OPUS-S $$ Receivers 2 Hours of data Results not shared OPUS-RS $$ Receivers 15 Minutes of data Results not shared OPUS LOCUS (Leveling Online Computing User Service) Digital Bar-Code Leveling Integration with OPUS? Results shared or not? OPUS-DB $$ Receivers 4 Hours of data Results shared

  29. 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

  30. 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

  31. DEFINITIONS • GRID SCALE Factor • Multiplier to change geodetic distances based on the Earth model (ellipsoid) to the grid plane. • ELEVATIONFactor (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

  32. Normal to ellipsoid

  33. 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 (g) applied • Grid Azimuth – Derived from the inverse between two points defined in northing & easting, or from a geodetic azimuth - the mapping angle (g) • (e.g. State Plane, UTM, local grid coordinates)

  34. ELLIPSOID - GEOID RELATIONSHIP LaPlace Correction +/- 0 ~ 25” Lower 48 states NGS Tool – DEFLEC09 Geoid Ellipsoid GRS80

  35. STANDARD PARALLELS N Approximately 154 miles S λO CENTRAL MERIDIAN LAMBERT CONFORMAL CONICWITH 2 STANDARD PARALLELS

  36. CONVERGENCE ANGLE(Mapping Angle) The Convention of the Sign of the Convergence Angle is Always From Grid To Geodetic Convergence angles () always positive (+) East Convergence angles () always negative (-) West λO CENTRAL MERIDIAN

  37. SCALE < 1 SCALE > 1 SCALE > 1 SCALE EXACT SCALE EXACT CENTRAL MERIDIAN TRANSVERSE MERCATOR λO

  38. Pennsylvania State Plane Coordinate System – NAD 83 Geometric Parameters remain the same As NAD 27 Zone Boundaries Central Meridian North/South Standard Parallels Latitude/Longitude of Origin False Northing and Easting Changed and defined in meters Conversion to Feet left up to individual states U.S. Survey or International Feet

  39. ORIGIN 39o 20’ 00” 77o 45’ 00” N = 0 m E = 600,000 m GRID Dist > GEODETIC Dist GRID SCALE FACTOR > 1 GRID CONVERGENCE ANGLE + NORTH STANDARD PARALLEL CENTRAL MERIDIAN GRID CONVERGENCE ANGLE - GRID Dist < GEODETIC Dist 1 < GRID SCALE FACTOR GRID Dist > GEODETIC Dist GRID SCALE FACTOR > 1 SOUTH STANDARD PARALLEL

  40. COORDINATE CHANGES(STATE PLANE) • STATION: STRAUSS (pid KW0527) • PENNSYLVANIA SOUTH ZONE (NAD 27/NAD 83) • NorthingEastingConverg AngleScale Factor • 428,352.11 ft. 2,433,279.72 ft. +1o 00’ 39.0” 0.99995985 • 130,575.318m. 732,088.384m. +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.

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

  42. 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 (g) = + 1o 00’ 39.8” • Observed Astro Azimuth (aA) = 253o 26’ 14.9” • Horizontal Distance (D) = 3,314.91 Feet

  43. STATE PLANE COORDINATE COMPUTATION • N1 = N + (Sg x cos ag) • E1 = E + (Sg x sin ag) • Where: • N = Starting Northing Coordinate • E = Starting Easting Coordinates • Sg = Grid Distance • ag = Grid Azimuth

  44. ___R___ S = D * R + H + (N) REDUCTION TO THE ELLIPSOID D h H S N R Earth Radius 6,372,200 m 20,906,000 ft. S = D * ___R__ R + h Where: h = H + [N]

  45. _____________ N R = 1 – e’2cos2 f cos2a a _____________ N = (1 – e’2 cos2 f)1/2 REDUCTION TO THE ELLIPSOID(The correct method) N = Radius of Curvature in Azimuth a = Ellipsoid semi-major axis b = Ellipsoid semi-minor axis • = Azimuth of the line f = Latitude of the Station WHERE e’2 = (a2 – b2) / b2

  46. 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

  47. 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 • Sgeodetic = 3,314.91 [20,906,000 / 20,906,000 + 529] • Sgeodetic = 3,314.91 x 0.99997470 • Sgeodetic = 3,314.83 ft • Sgeodetic = 3,314.91 [20,936,382 / 20,936,282 + 529] • Sgeodetic = 3,314.91 x 0.99997473 • Sgeodetic = 3,314.83 ft • Diff = 0.00 ft

  48. GRID SCALE FACTOR (k) OF A POINTGRID CONVERGENCE ANGLE () OF A POINT • Easiest to obtain by using • NGS SPCs tool kit utility • or • CORPSCON

  49. 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

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