Datums and Datum Transformations Geomatics Industry Association of America December 4, 2008 Dave Doyle NGS Chief Geodetic Surveyor

GEODETIC DATUMS HORIZONTAL 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 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 Second General Adjustment Sea Level Datum of 1929 National Geodetic Vertical Datum of 1929 (NGVD 29) First General Adjustment Third General Adjustment Fourth General Adjustment Guam 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 STATES Current 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 “Affirmation of Vertical Datum for Surveying and Mapping Activities” Federal Register Notices for American Samoa, Guam and Northern Marians are ready for publication

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)

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

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 “Notice to Adopt Standard Method for Mathematical Horizontal Datum Transformation” Federal Register Notice: Vol. 72, No. 132, July 11, 2007, pg “Notice to Adopt a Standard Model fro Mathematical Vertical Datum Transformations”

3065 Projects included:  67,693 total stations  Typical shifts 1-3 cm in both horizontal/ellipsoid height  No national transformation model (e.g. NADCON) NAD 83 National Readjustment

HISTORICAL HORIZONTAL DATUMS OF THE UNITED STATES New England Datum North American Datum of 1927 Bessel Ellipsoid U.S. Standard Datum North American Datum Puerto Rico Datum Old Hawaiian Datum UnAlaska Datum SE Alaska Datum Point Barrow Datum St. Paul Island Datum St. Lawrence Island Datum Barter Island Datum Flaxman Island Datum Valdez Datum American Samoa Datum 1962 Guam Datum 1963 Golofnin Bay Datum Kripniyuk Datum Port Clarence Datum Pribilof Islands Datum St. Michael Datum Yakutat Datum Yukon Datum St. George Island Datum

HORIZONTAL DATUM OF THE UNITED STATES Current Reference System North American Datum of 1983 NAD 83 (1986) – 2D & passive NAD 83 (199x) – 3D & passive NAD 83 (CORS96) – 4D & active NAD 83 (2007) – 3D & passive Federal Register Notice: Vol. 54, No. 113, June 14, 1989, pg “Affirmation of Datum for Surveying and Mapping Activities”

ARE NAD 83 & WGS 84 THE SAME? Federal Register Notice: Vol. 60, No. 157, August 15, 1995, pg “Use of NAD 83/WGS 84 Datum Tag on Mapping Products” IT DEPENDS If requirements are greater than 3m then Yes If 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 ) 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 ) DATUM = WGS 84 RELEASED - SEPTEMBER 1987 BASED ON OBSERVATIONS AT MORE THAN 1900 DOPPLER STATIONS 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) HOW MANY WGS 84s HAVE THERE BEEN???? WORLD GEODETIC SYSTEM 1984

ARE NAD 83 & WGS 84 THE SAME? NAD 83 to ITRF00 dX = m dY = m dZ = m S = 0.62 x rX = mas rY = mas rZ = mas

MY SOFTWARE SAYS I’M WORKING 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? Unless you are doing autonomous positioning (point positioning +/ meters) you’re probably NOT in WGS-84

EARLY NAD 83 NETWORK PROBLEMS NOT “GPSABLE” POOR STATION ACCESSIBILITY IRREGULARLY SPACED POSITIONAL ACCURACY

HIGH ACCURACY REFERENCE NETWORKS (HARN) “GPSABLE” Clear Horizons for Satellite Signal Acquisition EASY ACCESSIBILITY Few Special Vehicle or Property Entrance Requirements REGULARLY SPACED Always within Km HIGH ACCURACY A-Order (5 mm + 1:10,000,000) (3 5.5 hr sessions) B-Order (8mm + 1:1,000,000) (2 5.5 hr sessions)

FEDERAL & COOPERATIVE BSE NETWORKS (FBN/CBN) MORE STATE PARTNERSHIPS REMOVE DISTORTIONS IN EARLY HARNS (3-10 CM) ENSURE CONNETIONS TO CORS IMPROVE ELLIPSOID HEIGHT ACCURACY (Not more than 2 cm)

HPGN – HARN FBN - CBN

National Geodetic Survey, Retrieval Date = DECEMBER 1, 2008 HV7843 *********************************************************************** HV7843 DESIGNATION - OBSERVATORY HV7843 PID - HV7843 HV7843 STATE/COUNTY- VA/CAROLINE HV7843 USGS QUAD - HV7843 HV7843 *CURRENT SURVEY CONTROL HV7843 ___________________________________________________________________ HV7843* NAD 83(1993) (N) (W) ADJUSTED HV7843* NAVD (meters) (feet) ADJUSTED HV7843 ___________________________________________________________________ HV7843 LAPLACE CORR (seconds) DEFLEC99 HV7843 GEOID HEIGHT (meters) GEOID03 HV7843 DYNAMIC HT (meters) (feet) COMP HV7843 MODELED GRAV- 980,023.3 (mgal) NAVD 88 HV7843 HV7843 HORZ ORDER - FIRST HV7843 VERT ORDER - FIRST CLASS I HV7843 HV7843.The horizontal coordinates were established by classical geodetic methods HV7843.and adjusted by the National Geodetic Survey in November HV7843 HV7843.The orthometric height was determined by differential leveling HV7843.and adjusted in June HV7843 HV7843.The Laplace correction was computed from DEFLEC99 derived deflections. HV7843 HV7843.The geoid height was determined by GEOID03.

HV7843 SUPERSEDED SURVEY CONTROL HV7843 HV7843 NAD 83(1993) (N) (W) AD( ) 1 HV7843 NAD 83(1986) (N) (W) AD( ) 1 HV7843 NAD (N) (W) AD( ) 1 HV7843 NAVD 88 (09/21/92) (m) (f) LEVELING 3 HV7843 NGVD 29 (02/12/90) (m) (f) ADJUSTED 1 1

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).

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  = dλ = d  = dλ =  = λ = d  = dλ = d  = dλ = d  = dλ = d  = dλ = d  = dλ = d  = dλ = d  = dλ = d  = dλ = d  = dλ =

COORDINATE COMPARISON NAD 27 to NAD 83(1993) MOLODENSKY ADJUSTED vs. TRANSFORMED Station: OBSERVATORY (HV7843) LATITUDE LONGITUDE PUBLISHED MOLODENSKY.20828”.00844” m m THIS CORRESPONDS TO A POSITIONAL DIFFERENCE OF m (21.08 ft)

COORDINATE COMPARISON NAD 27 to NAD 83(1993) NADCON ADJUSTED vs. TRANSFORMED Station: OBSERVATORY (HV7843) LATITUDE LONGITUDE PUBLISHED NADCON.00052”.00244” m m THIS CORRESPONDS TO A POSITIONAL DIFFERENCE OF m (0.20 ft)

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