So What Is A Projection NORTHING EASTING.

The State Plane Coordinate System
December 8, 2010 David Doyle Chief Geodetic Surveyor National Geodetic Survey (301)

So What Is A Projection NORTHING EASTING

MAP PROJECTIONS Lambert Conformal Conic Transverse Mercator

STATE PLANE COORDINATE SYSTEM NAD 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) State Plane Coordinates by Automatic Data Processing (USC&GS 62-4)

STATE PLANE COORDINATE SYSTEM NAD 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 = U.S. Survey Feet 1 m = International Feet

NAD 83 STATE PLANE ZONES

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

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

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 CORPSCON U.S. Army Corps of Engineers Both horizontal and vertical datum transformations Values in meters, U.S. Survey Foot or International Foot

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

Networks of geodetic control points
NSRS COMPONENTS National Shoreline - Consistent, accurate, and up-to-date Networks of geodetic control points - Permanently marked passive survey monuments a consistent, accurate, up-to-date National Shoreline; .the National CORS, a set of Global Positioning System (GPS) Continuously Operating Reference Stations meeting NOAA geodetic standards for installation, operation, and data distribution; .a network of permanently marked geodetic control points; and .a set of accurate models describing dynamic geophysical processes affecting spatial measurements. National and Cooperative CORS - A network of GPS Continuously Operating Reference Stations Tools Models of geophysical effects on spatial measurements e.g., NADCON, INVERSE, SPCS83, UTMS, FORWARD 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
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)

8 Constants HORIZONTAL DATUMS
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 ELLIPSOID A MATHEMATICAL MODEL OF THE EARTH
N b a a = Semi major axis b = Semi minor axis f = a-b = Flattening a S

UNITED STATES ELLIPSOID DEFINITIONS
BESSEL 1841 a = 6,377, m 1/f = CLARKE 1866 a = 6,378,206.4 m 1/f = GEODETIC REFERENCE SYSTEM (GRS 80) a = 6,378,137 m /f = Present WORLD GEODETIC SYSTEM (WGS 84) a = 6,378,137 m /f = Present

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

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 KW *CURRENT SURVEY CONTROL KW0527 ___________________________________________________________________ KW0527* NAD 83(2007) (N) (W) ADJUSTED KW0527* NAVD (meters) (feet) ADJUSTED KW0527 EPOCH DATE KW0527 X ,159, (meters) COMP KW0527 Y ,716, (meters) COMP KW0527 Z ,120, (meters) COMP KW0527 LAPLACE CORR (seconds) DEFLEC09 KW0527 ELLIP HEIGHT (meters) (02/10/07) ADJUSTED KW0527 GEOID HEIGHT (meters) GEOID09 KW0527 DYNAMIC HT (meters) (feet) COMP KW Accuracy Estimates (at 95% Confidence Level in cm) KW0527 Type PID Designation North East Ellip KW KW0527 NETWORK KW0527 STRAUSS KW0527 MODELED GRAV , (mgal) NAVD 88 KW0527 VERT ORDER - SECOND CLASS 0 KW0527.The horizontal coordinates were established by GPS observations KW0527.and adjusted by the National Geodetic Survey in February 2007. 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.The Laplace correction was computed from DEFLEC09 derived deflections. KW0527.The ellipsoidal height was determined by GPS observations KW0527.and is referenced to NAD 83. KW0527.The geoid height was determined by GEOID09. KW0527; North East Units Scale Factor Converg. KW0527;SPC PA S , , MT KW0527;SPC PA S , ,401, sFT KW0527;UTM ,483, , MT KW0527! Elev Factor x Scale Factor = Combined Factor KW0527!SPC PA S x = KW0527!UTM x = KW0527: Primary Azimuth Mark Grid Az KW0527:SPC PA S STRAUSS AZ MK KW0527:UTM STRAUSS AZ MK KW0527| | KW0527| PID Reference Object Distance Geod. Az | KW0527| dddmmss.s | KW0527| KW0529 STRAUSS AZ MK | KW0527| KW0528 STRAUSS RM METERS | KW0527| KW3019 STRAUSSTOWN MUNICIPAL TANK APPROX. 1.2 KM | KW0527| KW0526 STRAUSS RM METERS |

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)

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
This slide shows you the simple steps you need to access the OPUS website. Enter your data file, antenna type and height. Give us your address and upload the file.

OPUS – DB Simple Shared Data NGS Archived
Realization and unification of NAD83 in Canada and the U.S. via the ITRF. > Geodetic Survey Division > Publications > Papers

(Leveling Online Computing User Service) Digital Bar-Code Leveling
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 Database Stream-lined method for users to publish their results User registration - ID & password, Validation process, OPUS solutions can be integrated into the NGS database Data elements from OPUS , Additional metadata Submission review by user and NGS OPUS Projects Managers can define a project Process any number of stations under a project, Project can span several days to weeks, Contract work Project processing Each dataset sent to OPUS but identified with a project, Results returned to submitter a few minutes later, Manager can monitor processing and submission Final adjustment Entire project adjusted as one campaign, Review & submission to NGS OPUS Rapid Static User requests, Single frequency capability, Rapid static solutions (10 – 15 minutes of data), Will be processed with carrier phases Accurate to several centimeters, Need more accurate ionospheric and tropospheric modeling In development at OSU and NGS OPUS GIS Compute a differential pseudorange solution for less expensive GPS receivers Aimed at the GIS community who do not require cm level accuracies Allows processing in a consistent approach and “certify” their locations in the NSRS Generate rapid static solution from seconds or minutes of data Accuracies: A few decimeters to a meter horizontally Pilot project underway in Phoenix, Arizona 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

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 (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)

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

LAMBERT CONFORMAL CONIC WITH 2 STANDARD PARALLELS
Approximately 154 miles CENTRAL MERIDIAN STANDARD PARALLELS N S λO The International Earth Rotation Service (IERS) is a non-governmental agency based in Paris, France. Their goal is to produce a global reference system - ITRF that takes into account the motions of the Earth's tectonic plates. Data from a variety of techniques (listed) are provided to IERS annually by National governments (such as NGS), academic institutions and research facilities around th world. Use of ITRF is recommended for all reference frames that are designed to use space-based (e.g. GPS) measurements, with a need for international coordination at the several centimeter level.

CONVERGENCE ANGLE (Mapping Angle)
The Convention of the Sign of the Convergence Angle is Always From Grid To Geodetic The International Earth Rotation Service (IERS) is a non-governmental agency based in Paris, France. Their goal is to produce a global reference system - ITRF that takes into account the motions of the Earth's tectonic plates. Data from a variety of techniques (listed) are provided to IERS annually by National governments (such as NGS), academic institutions and research facilities around th world. Use of ITRF is recommended for all reference frames that are designed to use space-based (e.g. GPS) measurements, with a need for international coordination at the several centimeter level. Convergence angles () always positive (+) East Convergence angles () always negative (-) West λO CENTRAL MERIDIAN

TRANSVERSE MERCATOR λO CENTRAL MERIDIAN SCALE EXACT SCALE < 1
The International Earth Rotation Service (IERS) is a non-governmental agency based in Paris, France. Their goal is to produce a global reference system - ITRF that takes into account the motions of the Earth's tectonic plates. Data from a variety of techniques (listed) are provided to IERS annually by National governments (such as NGS), academic institutions and research facilities around th world. Use of ITRF is recommended for all reference frames that are designed to use space-based (e.g. GPS) measurements, with a need for international coordination at the several centimeter level. λO

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

GRID Dist > GEODETIC Dist GRID SCALE FACTOR > 1
GRID CONVERGENCE ANGLE + NORTH STANDARD PARALLEL MERIDIAN CENTRAL GRID CONVERGENCE ANGLE - GRID Dist < GEODETIC Dist 1 < GRID SCALE FACTOR GRID Dist > GEODETIC Dist GRID SCALE FACTOR > 1 SOUTH STANDARD PARALLEL 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, ft. 2,433, ft o 00’ 39.0” 130, m , m o 00’ 39.8” (428, ft)* (2,401, ft)* (428, ft)# (2,401, ft)# (0.15) (4.81) * Converted using U.S. Survey Foot, 1 M = Ft. # Converted using International Foot, 1 M = Ft.

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

STATE PLANE COORDINATE COMPUTATION
STRAUSS (pid KW0527) N = , U.S. Survey Feet E = 2,401, U.S. Survey Feet Orthometric Height (H) = Feet Geoid Height (N) = Feet Laplace Correction = ” Grid Scale Factor (k) = Meridian Convergence (g) = + 1o 00’ 39.8” Observed Astro Azimuth (aA) = 253o 26’ 14.9” Horizontal Distance (D) = 3, Feet

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

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

REDUCTION TO THE ELLIPSOID (The correct method)
_____________ N 1 – e’2 cos2 f cos2 a R = 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 _____________ a (1 – e’2 cos2 f)1/2 N = e’2 = (a2 – b2) / b2

REDUCTION TO ELLIPSOID Ellipsoid Ht /Orthometric Ht
Sgeodetic = D x [R / (R + h)] D = 3, ft (Measured Horizontal Distance) R = 20,906,000 ft (Mean Radius of the Earth) h = H + N (H = 642 ft, N = ft) = 529 ft (Ellipsoid Height) S = 3, [20,906,000 / 20,906, ] S = 3, x S = 3, ft Sgeodetic = 3, [20,906,000 / 20,906, ] Sgeodetic = 3, x Sgeodetic = 3, ft Diff = 0.02 ft or ~ 1:166,000

REDUCTION TO ELLIPSOID Mean Radius vs. Computed Earth Radius
Sgeodetic = D x [R / (R + h)] D = 3, 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, [20,906,000 / 20,906, ] Sgeodetic = 3, x Sgeodetic = 3, ft Sgeodetic = 3, [20,936,382 / 20,936, ] Sgeodetic = 3, x Diff = 0.00 ft

GRID SCALE FACTOR (k) OF A POINT GRID 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

Sgrid = Sgeodetic * k (Grid Scale Factor)
REDUCTION TO GRID Sgrid = Sgeodetic * k (Grid Scale Factor) Sgrid = 3, x Sgrid = 3, meters

COMBINED FACTOR (CF) CF = Ellipsoidal Reduction x Grid Scale Factor (k) = x = CF x D = Sgrid x 3, = 3, ft

GRID AZIMUTH COMPUTATION
agrid = aAstro + Laplace Correction – Convergence Angle (g) = 253o 26’ 14.9” (Observed Astro Azimuth) - 2.6” (Laplace Correction) = 253o 26’ 12.3” (Geodetic Azimuth) (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 agrid) E1 = E + (Sgrid x sin agrid) N1 = 428, (3, x Cos 252o 25’ 32.5”) = 428, (3, x ) = 428, (-1,000.85) = 427, U.S. Survey Feet E1 = 2,401, (3, x Sin 252o 25’ 32.5”) = 2,401, (3, x ) = 2,401, (-3,159.99) = 2,398, U.S. Survey Feet

GROUND LEVEL COORDINATES SURFACE LEVEL COORDINATES PROJECT DATUM COORDINATES LOW DISTORTION PROJECTIONS “I WANT STATE PLANE COORDINATES RAISED TO GROUND LEVEL” GROUND LEVEL COORDINATES ARE NOT STATE PLANE COORDINATES!!!!!

GROUND LEVEL COORDINATES PROBLEMS
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 = , ft becomes 4,648.89 E = 26,341, ft becomes 1,246.75 AND DOCUMENT DOCUMENT DOCUMENT !!

The NSRS has evolved 1 Million Monuments 70,000 Passive Marks 
(Separate Horizontal and Vertical Systems) 70,000 Passive Marks (3-Dimensional)  Passive Marks (Limited Knowledge of Stability) 1,500+ GPS CORS (Time Dependent System Possible; 4-Dimensional)  GPS CORS  GNSS CORS

Problems with NAD 83 and NAVD 88
NAD 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 readjustment Subsurface fluid withdrawal Sediment loading Sea level rise .

The National Geodetic Survey 10 year plan Mission, Vision and Strategy
2008 – 2018 Official NGS policy as of Jan 9, 2008 Modernized agency Attention to accuracy Attention to time-changes Improved products and services Integration with other fed missions 2018 Targets: NAD 83 and NAVD 88 re-defined Cm-accuracy access to all coordinates Customer-focused agency Global scientific leadership Realization and unification of NAD83 in Canada and the U.S. via the ITRF. > Geodetic Survey Division > Publications > Papers

Simplified Concept of NAD 83 vs. ITRF00
h83 h00 Earth’s Surface ITRF (International Terrestrial Reference Frame) just has an origin; take NAD83 shaped ellipsoid centered at the ITRF origin to derive ITRF97 ellipsoid heights. Ellipsoid heights NAD83 vs. ITRF97 - Defined origins are best estimate of the center of mass; NAD83 is not geocentric. Move origin; move ellipsoid surface as illustrated. Ellipsoid height differences reflect the non-geocentricity of NAD83. ITRF 00 Origin 2.2 meters Identically shaped ellipsoids (GRS-80) a = 6,378, meters (semi-major axis) 1/f = (flattening) NAD 83 Origin

Predicted Positional Changes in 2018 Vicinity of Silver Spring, MD
Predicted Positional Changes in 2018 Vicinity of Silver Spring, MD. (Computed for HASSLER pid HV9698) HORIZONTAL = m (4.3 ft) ELLIPSOID HEIGHT = m (- 4.1 ft) Predicted with HTDP ORTHOMETRIC HEIGHT = m (- 1.5 ft) Predicted with HTDP and USGG2009 ACURRACY BUT NOT CONSISTENCY!! To summarize: This slide shows how far we’ve come since 1986, really since 1927. Unfortunately, --- Next slide ----

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 ) 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

So What Is A Projection NORTHING EASTING.

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