Datums and ProjectionsDemystifying the Reference FrameNOAA Enterprise GIS Seminar SeriesNovember 16, 2009Dave DoyleNGS Chief Geodetic Surveyordave.doyle@noaa.gov, 301-713-3178

1807President Thomas Jefferson signs legislationestablishing the Survey of the Coast

Our Positioning History1807 - Survey of the CoastWhats In a Name?1970 - National Geodetic Survey (NOS geodetic functions)1970 - National Ocean Service National Geodetic Survey 1878 - US Coast and Geodetic Survey1836 - Coast Survey

GLOBAL NAVIGATION SATELLITE SYSTEMS(GNSS)POTENTIAL CONSTELLATION DEVELOPMENTS(10 Years??)

GPS MODERNIZATION BLOCK IIR-M & IIIGLONASS ENHANCEMENTS EUROPEAN UNION - GALILEOCHINA - COMPASS

100+ SatellitesSecond and Third Civil Frequency GPSMore Robust Signal TransmissionsReal-Time Unaugmented 1 Meter (or better!) Accuracy

Image credit: University of Texas Center for Space Research and NASA GRACE Gravity Model 01 - Released July 2003 Orthometric Heights are related to the Geoid

THE ELLIPSOIDMATHEMATICAL MODEL OF THE EARTH

a = Semi major axis b = Semi minor axis f = a-b = Flattening abaNSHorizontal Coordinates and Ellipsoid Heights are related to the Ellipsoid

a= 637813.000007 metersb= 6356752.31414 metersf= 1/((a-b)/a) = 298.2572220972a = 6,378,137.00000 mb = 6,356,752.31414 mSquash the sphere to fit at the poles An ellipsoid of revolution is the figure which would be obtained by rotating an ellipse about its shorter axis. An ellipsoid of revolution describing the figure of the Earth is called a reference ellipsoid.

ELLIPSOID - GEOID RELATIONSHIP

H = Orthometric Height (NAVD 88) H = h [N] h = Ellipsoidal Height [NAD 83 (2007) or (CORS96)]N = Geoid Height (GEOID 09)HhEllipsoidGRS80NGeoid GEOID09

National Spatial Reference System (NSRS)Consistent National Coordinate System

Latitude Longitude Height Scale Gravity Orientation

and how these values change with time

NATIONAL SPATIAL REFERENCE SYSTEMACCURATE -- cm accuracy on a global scale

MULTIPURPOSE -- Supports Geodesy, Geophysics, Land Surveying, Navigation, Mapping, Charting and GIS activities

ACTIVE -- Accessible through Continuously Operating Reference Stations (CORS) and derived products

INTEGRATED -- Related to International services and standards (e.g. International Earth Rotation and Reference Systems Service, International GNSS Service etc.)

NSRS COMPONENTS

GEODETIC DATUMSA set of constants specifying the coordinate system used for geodetic control, i.e., for calculating coordinates of points on the Earth. Specific geodetic datums are usually given distinctive names. (e.g., North American Datum of 1983, European Datum 1950, National Geodetic Vertical Datum of 1929)Characterized by: A set of physical monuments, related by survey measurements and resulting coordinates (horizontal and/or vertical) for those monuments

GEODETIC DATUMSHORIZONTAL 2-D (Latitude and Longitude) (e.g. NAD 27, NAD 83 (1986))

VERTICAL/GEOPOTENTIAL 1-D (Orthometric Height) (e.g. NGVD 29, NAVD 88, Local Tidal)

GEOMETRIC 3-D (Latitude, Longitude and Ellipsoid Height) Fixed and Stable(?) - Coordinates seldom change (e.g. NAD 83 (1993), NAD 83 (2007))

also

4-D (Latitude, Longitude, Ellipsoid Height, Velocities) Coordinates change with time (e.g. ITRF00, ITRF05)

HORIZONTAL DATUMS8 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

VERTICAL DATUMSA set of fundamental elevations to which other elevations are referred.

Datum Types

Tidal Defined by observation of tidal variations over some period of time (MSL, MLLW, MLW, MHW, MHHW etc.)(NOS Center for Operational Oceanographic Products and Services) (CO-OPS)

Geodetic Tided to Local Mean Sea Level at one or more points at some epoch(NAVD 88, IGLD85)

HISTORICAL VERTICAL DATUMS OF THE UNITED STATES

Second General Adjustment - 1903Sea Level Datum of 1929National Geodetic Vertical Datum of 1929 (NGVD 29)First General Adjustment - 1899Third General Adjustment - 1907Fourth General Adjustment - 1912Guam 1963

The National Geodetic Vertical Datum of 1929 is referenced to 26 tide gauges in the US and Canada

The North American Vertical Datum of 1988 is referenced to a single tide gauge in Canada

VERTICAL DATUMS OF THE UNITED STATESCurrent Reference Systems

North American Vertical Datum of 1988 (NAVD 88)American Samoa Vertical Datum of 2002 (ASVD 02)Northern Marians Vertical Datum of 2003 (NMVD 03)Guam Vertical Datum of 2004 (GUVD 04)Federal Register Notice: Vol. 58, No. 120, June 24, 1993, pg. 34245Affirmation of Vertical Datum for Surveying and Mapping ActivitiesFederal Register Notices for American Samoa, Guam and Northern Marians: Vol. 74, No. 13, January 22, 2009, pgs 3990 - 3991

VERTICAL DATUMS OF THE UNITED STATESWorks in Progress

Puerto Rico Vertical Datum of 2002 (PRVD 02)Virgin Island Vertical Datum of 2009 (VIVD 09)Hawaiian Islands Vertical Datum (HIVD)

HISTORICAL HORIZONTAL DATUMS OF THE UNITED STATES

New England Datum North American Datum of 1927Bessel Ellipsoid U.S. Standard Datum North American Datum Puerto Rico Datum Old Hawaiian Datum UnAlaska Datum SE Alaska Datum Kripniyuk DatumSt. Paul Island Datum St. Lawrence Island Datum Barter Island Datum Camp Colonna Datum Valdez Datum American Samoa Datum 1962Guam Datum 1963Flaxman Island DatumGolofnin Bay DatumPoint Barrow DatumPort Clarence DatumSt. Michael Datum Yakutat Datum Yukon Datum St. George Island Datum Johnson Island 1961 Midway Astro 1961 Wake Island Astro 1952

NORTH AMERICAN DATUM OF 1983

NAD 83 (1986) 2D & passive ~ 1m national integrity(1986 1990)

NAD 83 (199x) 3D & passive ~ 10 cm national integrity(1990 1997)

NAD 83 (CORS96) 4D & active ~ 2 cm national integrity(1994 Present)

NAD 83 (2007) 3D & passive ~ 2 cm relative to CORS(2007 Present)

Federal Register Notice: Vol. 54, No. 113, June 14, 1989, pg. 25318Affirmation of Datum for Surveying and Mapping Activities

Tectonic Motions

International Earth Rotation and Reference System Service (IERS) (http://www.iers.org)The International Terrestrial Reference System (ITRS) constitutes a set of prescriptions and conventions together with the modeling required to define origin, scale, orientation and time evolution

ITRS is realized by the International Terrestrial Reference Frame (ITRF) based upon estimated coordinates and velocities of a set of stations observed by Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging ( SLR), Global Positioning System and GLONASS (GNSS), and Doppler Orbitography and Radio- positioning Integrated by Satellite ( DORIS).

ITRF89, ITRF90, ITRF91, ITRF92, ITRF93, ITRF94, ITRF95, ITRF96, ITRF97, ITRF2000, ITRF2005, ITRF2008 (soon)

International Global Navigation Satellite Systems Service (IGS)International Laser Ranging Service (ILRS)International Very Long Baseline Service (IVS)International DORIS Service (IDS)International Terrestrial Reference Frame4 Global Independent Positioning Technologies

ARE NAD 83 & WGS 84 THE SAME?

Federal Register Notice: Vol. 60, No. 157, August 15, 1995, pg. 42146Use of NAD 83/WGS 84 Datum Tag on Mapping ProductsIT DEPENDSIf requirements are greater than 3m then YesIf requirements are less than 3m then No

DATUM = WGS 84(G730)Datum redefined with respect to the International Terrestrial Reference Frame of 1992 (ITRF92) +/- 20 cm in each component (Proceedings of the ION GPS-94 pgs 285-292)DATUM = WGS 84(G873)Datum redefined with respect to the International Terrestrial Reference Frame of 1994 (ITRF94) +/- 10 cm in each component (Proceedings of the ION GPS-97 pgs 841-850)DATUM = WGS 84RELEASED - SEPTEMBER 1987BASED ON OBSERVATIONS AT MORE THAN 1900 DOPPLER STATIONSDATUM = WGS 84(G1150)Datum redefined with respect to the International Terrestrial Reference Frame of 2000 (ITRF00) +/- 2 cm in each component (Proceedings of the ION GPS-02) http://earth-info.nima.mil/GandG/sathtml/IONReport8-20-02.pdf HOW MANY WGS 84s HAVE THERE BEEN????WORLD GEODETIC SYSTEM 1984

ARE NAD 83 & WGS 84 THE SAME?

NAD 83 to ITRF00dX = 0.9956 mdY = - 1.9013 mdZ = - 0.5215 mS = 0.62 x 10-9rX = 25.915 masrY = 9.426 masrZ = 11.599 mas

MY SOFTWARE SAYS IM WORKING IN WGS-84

Project tied to WGS-84 control points obtained from the Defense Department -- Good Luck!Youre really working in the same reference frame as your control points -- NAD 83?Unless you are doing autonomous positioning (point positioning +/- 6-10 meters) youre probably NOT in WGS-84

PLANE COORDINATE SYSTEMS

STATE PLANE AND UNIVERSAL TRANSVERSE MERCATOR GRID COORDINATES ARE A DIRECT MATHEMATICAL CONVERSION FROM LATITUDE AND LONGITUDE TO A CARTESIAN NORTHING AND EASTING (Y & X) COORDINATE SYSTEM, AND MUST MAINTAIN THE SAME DATUM TAG [e.g. NAD 27 or NAD 83] AS THE LATITUDE AND LONGITUDE)

NORTHINGEASTINGSo What Is A Projection

MAP PROJECTIONSCONIC AND CLYNRIDCAL

UTM ZONES

STATE PLANE COORDINATE ZONES

What Are State Plane CoordinatesState plane coordinates are the projection of latitudes and longitudes from the GRS80 ellipsoidTo:A flat mapping surface that is usually defined by state law

Developed by U.S. Coast and Geodetic Survey from a request in 1933 from the North Carolina Department of Transportation

Two basic map projections used:

Lambert Conformal Conic States or parts of states that have a more East-West orientationTransverse 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 calculated using tables (e.g. USC&GS Special Publication. 316 Plane Coordinate Projections Tables New Jersey)

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

STATE PLANE COORDINATE SYSTEM 1927

STATE PLANE COORDINATE SYSTEM1983

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

Utah is now a U.S. Survey Foot State(Blue)

PLANE COORDINATE CONVERSION TOOLS

UTM

UTMS (Both NAD 27 & NAD 83)http://www.ngs.noaa.gov/TOOLS/utm.shtml

CORPSCON (Both NAD 27 & NAD 83)http://crunch.tec.army.mil/software/corpscon/corpscon.html

STATE PLANE COORDINATESGPPCGP (NAD 27 only)SPCS83 (NAD 83 only)http://www.ngs.noaa.gov/TOOLS/spc.shtml

CORPSCON (Both NAD 27 & NAD 83)http://crunch.tec.army.mil/software/corpscon/corpscon.html

DATUM TRANSFORMATIONS1. WHAT DATUM ARE THE EXISTING COORDINATES/HEIGHTS ON?2. WHAT DATUM DO I WANT THE NEW COORDINATES/HEIGHTS ON?3. HOW LARGE A GEOGRAPHICAL AREA DO I WANT TO CONVERT AT ONE TIME?4. HOW MANY POINTS ARE COMMON TO BOTH DATUMS?5. WHAT IS THE DISTRIBUTION OF THE COMMON POINTS?6. HOW ACCURATE ARE THE EXISTING COORDINATES/HEIGHTS?

0.01 Meter0.1 Meter1.0 Meter

7. HOW ACCURATE DO I WANT THE NEW COORDINATES/HEIGHTS?

DATUM TRANSFORMATION IDEAL METHOD SATISFIES ALL USERS REQUIREMENTS

CAPABLE OF TRANSFORMING LARGE DATASETS

NEAR-REAL TIME APPLICATIONS

SIMPLE - METHOD SHOULD NOT REQUIRE AN EXPERT OR DECISIONS TO BE MADE

ACCURATE

DATUM TRANSFORMATIONSMOLODENSKY

For continental regions accuracy can be +/- 8 to 10 meters

Does not model network distortions very well.

Assumes heights in both systems are ellipsoidal (NAD 27 did not have ellipsoidal heights).

NGS DATUM TRANSFORMATION MODELS

VERTCON(NGVD 29 only)

NADCON(NAD 27, OLD HAWAIIAN, PUERTO RICO, 3 ALASKA ISLANDS)(HPGN/HARN)Federal Register Notice: Vol. 55, No. 155, August 10, 1990, pg. 32681Notice to Adopt Standard Method for Mathematical Horizontal Datum TransformationFederal Register Notice: Vol. 72, No. 132, July 11, 2007, pg. 37732Notice to Adopt a Standard Model fro Mathematical Vertical Datum Transformations

DATUM TRANSFORMATIONSMOLODENSKY

Converts latitude, longitude and ellipsoidal height to X,Y,Z Earth-Centered Coordinates.

Applies a 3-dimensional change in the origin (dX, dY,dZ)

Applies a change in the size and shape of the reference ellipsoid

Converts new X,Y,Z Earth-Centered Coordinates back to latitude, longitude and ellipsoidal height

MOLODENSKY TRANSFORMATION

NADCONd = +0.12344d = -1.87842d = +0.12249d = -1.88963 = +0.12423 = -1.81246d = +0.12568d = -1.83364d = +0.12449d = -1.88905d = +0.12499d = -1.86543d = +0.12640d = -1.85407d = +0.12396d = -1.85209

COORDINATE COMPARISONNAD 27 to NAD 83(1993)MOLODENSKY

ADJUSTED vs. TRANSFORMED

Station: OBSERVATORY (HV7843)

LATITUDE LONGITUDE 38-12-06.79868 077-22-22.35067 - PUBLISHED 38-12-06.59040 077-22-22.34223 - MOLODENSKY .20828 .00844 6.422 m 0.205 m THIS CORRESPONDS TO A POSITIONALDIFFERENCE OF 6.425 m (21.08 ft)

COORDINATE COMPARISONNAD 27 to NAD 83(1993)NADCON

ADJUSTED vs. TRANSFORMED

Station: OBSERVATORY (HV7843)

LATITUDE LONGITUDE 38-12-06.79868 077-22-22.35067 - PUBLISHED 38-12-06.79920 077-22-22.34823 - NADCON .00052 .00244 0.016 m 0.059 m

THIS CORRESPONDS TO A POSITIONALDIFFERENCE OF 0.061 m (0.20 ft)

GOOD COORDINATION BEGINS WITH GOOD COORDINATESGEOGRAPHY WITHOUT GEODESY IS A FELONY

******This shape is what we reference NAD83 and the GPS system to. Both the horizontal and vertical coordinates originate with this surface. The Pythagorean concept of a spherical Earth offers a simple surface which is mathematically easy to deal with. Many astronomical and navigational computations use it as a surface representing the Earth. While the sphere is a close approximation of the true figure of the Earth and satisfactory for many purposes, to the geodesists interested in the measurement of long distancesspanning continents and oceansa more exact figure is necessary. Closer approximations range from modelling the shape of the entire Earth as an oblate spheroid or an oblate ellipsoid to the use of spherical harmonics or local approximations in terms of local reference ellipsoids. The idea of a planar or flat surface for Earth, however, is still acceptable for surveys of small areas as local topography is more important than the curvature. Plane-table surveys are made for relatively small areas and no account is taken of the curvature of the Earth. A survey of a city would likely be computed as though the Earth were a plane surface the size of the city. For such small areas, exact positions can be determined relative to each other without considering the size and shape of the total Earth.Earth - Lumpy Bumpy rock that is difficult if not impossible to describe with an equation. ClickLet's take a sphere and put its center at the earth's center of massThen resize the sphere to best fit the earth - radius of 6,378137.0 meters (later to become the semi-major axis)This is a pretty good fit but we are out a little at the poles.ClickNow we can squash the sphere at the poles for a better fit. This creates an oblate spheroid.Now the diameter along the polar (semi-minor) axis is 6,356,752 meters.We can now describe the earth's shape with an equation.a= 637813.000007 metersb= 6356752.31414 metersf= 1/(a-b)/a = 298.2572220972ClickWe now have an ellipsoid - Since the Earth is in fact flattened slightly at the poles and bulges somewhat at the equator, the geometrical figure used in geodesy to most nearly approximate the shape of the Earth is an ellipsoid of revolution. The ellipsoid of revolution is the figure which would be obtained by rotating an ellipse about its shorter axis. An ellipsoid of revolution describing the figure of the Earth is called a reference ellipsoid.Definition:NAD83 The North American Datum of 1983 the earth centered, earth fixed reference system that uses the GRS80 ellipsoidThe rotation of the Earth creates the equatorial bulge so that the equatorial diameter is 43km larger than the pole to pole diameter.[37] The largest local deviations in the rocky surface of the Earth are Mount Everest (8,848m above local sea level) and the Mariana Trench (10,911m below local sea level). Hence compared to a perfect ellipsoid, the Earth has a tolerance of about one part in about 584, or 0.17%, which is less than the 0.22% tolerance allowed in billiard balls.[38] Because of the bulge, the feature farthest from the center of the Earth is actually Mount Chimborazo in Ecuador.[39]

****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.

***************************************