Datums and Projections Demystifying the Reference Frame Georgia Geospatial Conference 2012 Where We Are Now Presentation by Lonnie Sears, LS Originator ; Dave Doyle NGS Chief Geodetic Surveyor dave.doyle@noaa.gov, 301-713-3178

1807 President Thomas Jefferson signs legislation establishing the Survey of the Coast

Our Positioning History What’s In a Name? 1807 - Survey of the Coast 1836 - Coast Survey 1878 - US Coast and Geodetic Survey 1970 - National Geodetic Survey (NOS geodetic functions) 1970 - National Ocean Service National Geodetic Survey

ACRONYMS US R NAD 27 GRS 80 ITRF 00 CORS WGS 84 NAVD 88 NGVD 29 NAD 83

GLOBAL NAVIGATION SATELLITE SYSTEMS (GNSS) POTENTIAL CONSTELLATION DEVELOPMENTS (10 Years??) GPS MODERNIZATION – BLOCK IIR-M & III GLONASS ENHANCEMENTS EUROPEAN UNION - GALILEO CHINA - COMPASS 100+ Satellites Second and Third Civil Frequency – GPS More Robust Signal Transmissions Real-Time Unaugmented 1 Meter (or better!) Accuracy

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

THE ELLIPSOID MATHEMATICAL MODEL OF THE EARTH N Horizontal Coordinates and Ellipsoid Heights are related to the Ellipsoid b a a = Semi major axis b = Semi minor axis f = a-b = Flattening a S

Earth - Lumpy Bumpy rock that is difficult if not impossible to describe with an equation. Click Let's take a sphere and put its center at the earth's center of mass Then 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. Now 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 meters b= 6356752.31414 meters f= 1/(a-b)/a = 298.2572220972 We 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 ellipsoid 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. Earth The rotation of the Earth creates the equatorial bulge so that the equatorial diameter is 43 km larger than the pole to pole diameter.[37] The largest local deviations in the rocky surface of the Earth are Mount Everest (8,848 m above local sea level) and the Mariana Trench (10,911 m 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] GRS80 NAD83 b = 6,356,752.31414 m 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 distances—spanning continents and oceans—a 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. a= 637813.000007 meters b= 6356752.31414 meters f= 1/((a-b)/a) = 298.2572220972 Squash the sphere to fit at the poles a = 6,378,137.00000 m

ELLIPSOID - GEOID RELATIONSHIP H = Orthometric Height (NAVD 88) h = Ellipsoidal Height [NAD 83 (2007) or (CORS96)] N = Geoid Height (GEOID 09) H = h – [N] h H N GEOID09 Geoid Ellipsoid GRS80 9

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 SYSTEM ACCURATE -- 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.)

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 CORS Network - 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

GEODETIC DATUMS A 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 DATUMS HORIZONTAL VERTICAL/GEOPOTENTIAL GEOMETRIC 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 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

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

NGVD29 The National Geodetic Vertical Datum of 1929 is referenced to 26 tide gauges in the US and Canada

NAVD88 The North American Vertical Datum of 1988 is referenced to a single tide gauge in Canada

VERTICAL DATUMS OF THE UNITED STATES Current Reference Systems North American Vertical Datum of 1988 (NAVD 88) Federal Register Notice: Vol. 58, No. 120, June 24, 1993, pg. 34245 “Affirmation of Vertical Datum for Surveying and Mapping Activities” 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 Notices for American Samoa, Guam and Northern Marians: Vol. 74, No. 13, January 22, 2009, pgs 3990 - 3991

VERTICAL DATUMS OF THE UNITED STATES Works 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 Bessel Ellipsoid Camp Colonna Datum St. Paul Island Datum New England Datum Flaxman Island Datum UnAlaska Datum U.S. Standard Datum Golofnin Bay Datum Valdez Datum North American Datum Kripniyuk Datum Yakutat Datum North American Datum of 1927 Point Barrow Datum Yukon Datum Johnson Island 1961 Puerto Rico Datum Port Clarence Datum Midway Astro 1961 Old Hawaiian Datum SE Alaska Datum American Samoa Datum 1962 St. George Island Datum Wake Island Astro 1952 Guam Datum 1963 St. Lawrence Island Datum Barter Island Datum St. Michael Datum

NORTH AMERICAN DATUM OF 1983 Federal Register Notice: Vol. 54, No. 113, June 14, 1989, pg. 25318 “Affirmation of Datum for Surveying and Mapping Activities” 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)

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, ITRF2010

International Terrestrial Reference Frame 4 Global Independent Positioning Technologies International Global Navigation Satellite Systems Service (IGS) International Laser Ranging Service (ILRS) International Very Long Baseline Service (IVS) International DORIS Service (IDS)

If requirements are greater than 3m then Yes ARE NAD 83 & WGS 84 THE SAME? IT DEPENDS If requirements are greater than 3m then Yes If requirements are less than 3m then No Federal Register Notice: Vol. 60, No. 157, August 15, 1995, pg. 42146 “Use of NAD 83/WGS 84 Datum Tag on Mapping Products”

HOW MANY WGS 84s HAVE THERE BEEN???? WORLD GEODETIC SYSTEM 1984 DATUM = 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 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 84 RELEASED - SEPTEMBER 1987 BASED ON OBSERVATIONS AT MORE THAN 1900 DOPPLER STATIONS HOW MANY WGS 84s HAVE THERE BEEN???? 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)

ARE NAD 83 & WGS 84 THE SAME? NAD 83 to ITRF00 dX = 0.9956 m dY = - 1.9013 m dZ = - 0.5215 m S = 0.62 x 10-9 rX = 25.915 mas rY = 9.426 mas rZ = 11.599 mas

MY SOFTWARE SAYS I’M WORKING IN WGS-84 Unless you are doing autonomous positioning (point positioning +/- 6-10 meters) you’re probably NOT in WGS-84 Project tied to WGS-84 control points obtained from the Defense Department -- Good Luck! You’re really working in the same reference frame as your control points -- NAD 83?

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)

So What Is A Projection NORTHING EASTING

MAP PROJECTIONS CONIC AND CLYNRIDCAL

UTM ZONES

STATE PLANE COORDINATE ZONES

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

STATE PLANE COORDINATE SYSTEM 1927 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 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 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 1983 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 COORDINATES GPPCGP (NAD 27 only) SPCS83 (NAD 83 only) http://www.ngs.noaa.gov/TOOLS/spc.shtml

DATUM TRANSFORMATIONS 1. 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 Meter 0.1 Meter 1.0 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 TRANSFORMATIONS MOLODENSKY 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. 72, No. 132, July 11, 2007, pg. 37732 “Notice to Adopt a Standard Model fro Mathematical Vertical Datum Transformations” Federal Register Notice: Vol. 55, No. 155, August 10, 1990, pg. 32681 “Notice to Adopt Standard Method for Mathematical Horizontal Datum Transformation”

DATUM TRANSFORMATIONS MOLODENSKY 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

NADCON d = +0.12344 dλ = -1.87842 d = +0.12249 dλ = -1.88963  = +0.12423 λ = -1.81246 d = +0.12568 dλ = -1.83364 d = +0.12431 dλ = -1.86291 d = +0.12441 dλ = -1.83879 d = +0.12449 dλ = -1.88905 d = +0.12640 dλ = -1.85407 d = +0.12499 dλ = -1.86543

COORDINATE COMPARISON NAD 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 POSITIONAL DIFFERENCE OF 6.425 m (21.08 ft)

COORDINATE COMPARISON NAD 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 POSITIONAL DIFFERENCE OF 0.061 m (0.20 ft)

GOOD COORDINATION BEGINS WITH GOOD COORDINATES GEOGRAPHY WITHOUT GEODESY IS A FELONY