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Datums and Projections Demystifying the Reference Frame

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Datums and ProjectionsDemystifying the Reference Frame

Georgia Geospatial Conference 2012

Where We Are Now

Presentation by Lonnie Sears, LS

Originator ; Dave Doyle

NGS Chief Geodetic Surveyor

[email protected], 301-713-3178

1807President Thomas Jefferson signs legislationestablishing 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 Ocean Service

National Geodetic Survey

1970 - National Geodetic Survey (NOS geodetic

functions)

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

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 ELLIPSOIDMATHEMATICAL 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

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

GRS80

NAD83

- b = 6,356,752.31414 m

Squash the sphere to fit at the poles

- a= 637813.000007 meters
- b= 6356752.31414 meters
- f= 1/((a-b)/a) = 298.2572220972

- 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

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.)

National Shoreline

- Consistent, accurate, and up-to-date

- National CORS Network

- 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

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
- 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

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 STATESCurrent 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 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

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

SE Alaska Datum

Old Hawaiian Datum

American Samoa Datum 1962

St. George Island Datum

Wake Island Astro 1952

St. Lawrence Island Datum

Guam Datum 1963

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)

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)

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”

WORLD GEODETIC SYSTEM 1984

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(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

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)

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 SYSTEM1927

- 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 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

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

CORPSCON (Both NAD 27 & NAD 83)

http://crunch.tec.army.mil/software/corpscon/corpscon.html

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

d= +0.12438

dλ = -1.86547

d= +0.12354

dλ = -1.8594

d= +0.12431

dλ = -1.86291

d= +0.12441

dλ = -1.83879

NADCONd= +0.12344

dλ = -1.87842

d= +0.12249

dλ = -1.88963

d= +0.12396

dλ = -1.85209

= +0.12423

λ = -1.81246

d= +0.12568

dλ = -1.83364

d= +0.12449

dλ = -1.88905

d= +0.12640

dλ = -1.85407

d= +0.12499

dλ = -1.86543

COORDINATE COMPARISONNAD 27 to NAD 83(1993)

- MOLODENSKY
- ADJUSTED vs. TRANSFORMED
- Station: OBSERVATORY (HV7843)
- LATITUDELONGITUDE
- 38-12-06.79868 077-22-22.35067 - PUBLISHED
- 38-12-06.59040077-22-22.34223 - MOLODENSKY
- .20828” .00844”
- 6.422 m 0.205 m
- THIS CORRESPONDS TO A POSITIONAL
- DIFFERENCE OF 6.425 m (21.08 ft)

COORDINATE COMPARISONNAD 27 to NAD 83(1993)

- NADCON
- ADJUSTED vs. TRANSFORMED
- Station: OBSERVATORY (HV7843)
- LATITUDELONGITUDE
- 38-12-06.79868 077-22-22.35067 - PUBLISHED
- 38-12-06.79920077-22-22.34823 - NADCON
- .00052” .00244”
- 0.016 m 0.059 m
- THIS CORRESPONDS TO A POSITIONAL
- DIFFERENCE OF 0.061 m (0.20 ft)

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