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Geodesy NYSAPLS Conference January 2013

Joseph V.R. Paiva

Geodesy — …the scientific discipline that deals with the measurement and representation of the earth, including its gravitational field, in a three- dimensional time-varying space.

— Geodesists also study geodynamical phenomena such as crustal motion, tides and polar motion. — For this they design global and national surveying networks, using space and terrestrial techniques while relying on datums and coordinate systems.

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Warning! — This is not Geodesy 101 in three hours — It is ABOUT geodesy, with goals to… — Understand its relevance to your practice — Be more familiar with geodetic terms — Understand how work done by geodesists is important to your work — Help you to not ignore it

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Thanks — To hardworking NGS professionals — Many of the information, and slides are used as is or modified from work they have done

• Doyle • Childers • Martin • Shields • Diehl • Ikehara • Fromhertz • Schenewerk • Smith • Mader • Roman …and many more!

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Outline 1. Some history 2. Why you cannot ignore geodesy 3. Datums, datums and more datums 4. Why the geoid is important to your professional life 5. Time…who has the time? 6. Integrating geodesy into your practice [get it before it gets you]

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1. Historical earth views — Flat — Flat disk (Homer) — Sphere (Pythagoras, Aristotle)

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Size — Eratosthenes (276-195 BC) — Looked in a well at Aswan during summer solstice — Measured deviation of sun from zenith on same day at Alexandria — Calculated sphere circumference to be 25,000 mi — Around equator, we measure 24,902 mi today — Around poles 24,860 mi

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Others — Aryabhata (India, in AD 476-550) calculated circumference within 1%

— Muslim scholars AD 830…similar results — Persians (AD 873-1048), Biruni at age 17 computed circumference with >99% accuracy

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A little bit closer in time… — 18th century: French Academy of Sciences sent expeditions to Lapland and Ecuador for purpose of calculating “geodesic arc” — The measurements showed 1:210 flattening, introducing concept of oblate spheroid or ellipsoid

— 19th century work of Everest and others showed deviation of the vertical, introducing term: “undulation of the geoid”

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2. Geodesy for you? — You just cannot ignore it — GPS requires you to understand it — Not understanding it dooms you to errors, liability exposure, MISTAKES — State plane coordinates — UTM — GIS — Like everything else, survey areas get progressively bigger 9

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Yes…it isn’t an option — Especially if you — use GPS — publish or use state plane coordinates, UTM, etc. — do surveys that have long length or large area — are tasked with higher order surveys for special purposes

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It’s like with instruments — How do you know you got it right? — An expert needs to be conversant in all aspects of his/her scientific body of knowledge, customs, the art of practicing it

— And yet, many surveyors have trouble staying in the conversation as soon as geodesy, geodetic, etc. comes up in the conversation

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If you use CORS — You need to understand some geodetic concepts

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If you set up base stations on national control — You need to at least be conversant with what appears on an NGS datasheet

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If you use or publish — Stuff in NAD83, NGVD88, etc. you better know what you’re getting into

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In these days especially… — Geodetic illiteracy could mean the barrier to financial health

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A good test — Present a 10-15 monologue on geodetic concepts without long pauses

— Must be accurate!

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Some necessary background — How instrumentation works — Theory of errors — Propagation — How to apply theory to measurement analysis — www.ngs.noaa.gov

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3. Datums — Terms: datum, realization, ellipsoid, epoch, projection — The many flavors of NAD83 — Future datums — Datasheets, shapefiles — NGS support, including geodetic advisor program — Website: www.ngs.noaa.gov — Dan Martin (VT)

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What is a datum? — …set of constants specifying the coordinate system used for geodetic control, i.e., for calculating the coordinates of points on the Earth

— …plus, together with the coordinate system and the set of all points and lines whose coordinates, lengths, and directions have been determined by measurement or calculation.

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NAD 27 — …horizontal control datum defined by (a) location and azimuth on the Clarke spheroid of 1866, with origin at (the survey station) Meades Ranch.

— ... The geoidal height at Meades Ranch (was) assumed to be zero.

— Geodetic positions on NAD27 were derived from the (coordinates of and an azimuth at Meades Ranch) through a readjustment of the existent triangulation

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NAD 83 — …horizontal control datum for U.S., Canada, Mexico, and Central America, based on a geocentric origin and the Geodetic Reference System 1980.

— …designated as NAD 83, is the new geodetic reference system. — …NAD 83 is based on the adjustment of 250,000 points including 600 satellite Doppler stations which constrain the system to a geocentric origin.

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Official U.S. Datums

REGION CONUS Alaska American Guam CNMI Puerto US Virgin Samoa Rico Islands

Ellipsoidal NAD83 NAD83 NAD83 NAD83 NAD83 NAD83 NAD83 Reference (NSRS (CORS96) (PACP00) (MARP00) (MARP00) (CORS96) (CORS96) Frame 2007) Vertical NAVD88 NAVD88 ASVD02 GUVD04 NMVD03 PRVD02 VIVD09 Datum

NAVD88 - NORTH AMERICAN VERTICAL DATUM OF 1988 ASVD02 - AMERICAN SAMOA VERTICAL DATUM OF 2002 GUVD04 - GUAM VERTICAL DATUM OF 2004 NMVD03 - NORTHERN MARIANAS VERTICAL DATUM OF 2003 PRVD02 – PUERTO RICO VERTICAL DATUM OF 2002 VIVD09 – VIRGIN ISLANDS VERTICAL DATUM OF 2009 –pending adoption

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Horizontal datums — Only! — NAD 27 — NAD 83

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Vertical Datums — NGVD 29 — 26 tide gages, U.S. & Canada

— NAVD 88 — Fixed on one point: Father Point/Rimouski, Quebec, Canada — VERTCON can be used to convert — ±2 cm, one sigma

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WGS 84 — World Geodetic System of 1984 — Reference frame used by (DoD); defined by National Geospatial-Intelligence Agency (NGA), (formerly the National Imagery and Mapping Agency) (formerly the Defense Mapping Agency) — WGS 84 is used by DoD for all its mapping, charting, surveying, and navigation needs, including its GPS "broadcast" and "precise" orbits — WGS 84 was defined in Jan 1987 using Doppler satellite surveying techniques. It was used as the reference frame for broadcast GPS Ephemerides (orbits) beginning January 23, 1987.

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WGS 84 / 2 — At 0000 GMT Jan 2, 1994, it was upgraded in accuracy using GPS measurements. The formal name then became WGS 84 (G730) since the upgrade date coincided with the start of GPS Week 730. It became the reference frame for broadcast orbits on June 28, 1994. — At 0000 GMT Sep 30, 1996 (start of GPS Week 873), WGS 84 was redefined again and was more closely aligned with International Earth Rotation Service (IERS) Terrestrial Reference Frame (ITRF) 94. Now called WGS 84 (G1150)

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Changing the Datum

The Grid shifts Uniformly (mathematically) in any one region 1927 Everything gets a New coordinate!

1927-1983: up to 100’s of meters

1983 1983-2022: 1-2 meters 27

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Adjusting Coordinates within the Datum is a new Realization 1 cm

Modifying each point for its ”issues”: change is not uniform/constant everywhere

1) Actual Motion/Velocity 2) Error correction/Old data 3) New Information/Obs

On the order of centimeters Done regularly: Next 2012 1983 28

Realizations

1. (86) –original, pre-GPS data 2. (92) for California; for other states (9#) 3. (CORS96) 4. (98) in CA 5. (NSRS2007) or (2007) 6. (2011) All on same datum 7. Future: ~2022 29

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What’s the same, what’s different? — Same reference ellipsoid: GRS80 for each datum NAD83, WGS84, and ITRF## or IGS##

— Difference in datums is location of origin (center) — NAD83(#) is the datum tag, represents an adjustment, either national or by state

— Difference is the dataset of which geodetic control points used as constraints

— Difference could be epoch date of coordinates

NAD83(2007) 2007.00 or NAD83(2007) 2008.00 30

What’s in a name? — Coordinate system as used in geodesy: “coordinate system” (ISO terminology). — International geodetic organizations like the IERS (International Earth Rotation and Reference Systems Service) speak of a “reference system.” — When these coordinates are realized by choosing datum points and fixing a geodetic datum, ISO uses “coordinate reference system,” while IERS speaks of a “reference frame.” — A “datum transformation” is referred to by ISO as a “coordinate transformation.”

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The Celestial Frame The celestial frame describes the Earth as it looks from far above. From this frame we watch our world rotate as it orbits around the Sun. The Moon travels with the Earth and completes its orbit in a little less than a month. Likewise, the GNSS satellites travel with the Earth orbiting it twice per day. The equations describing the motions and interactions of these bodies are much simpler in this frame.

nssdc.gsfc.nasa.gov/image/planetary/earth/gal_earth_moon.jpg

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The Terrestrial Frame The terrestrial frame describes the Earth as looks to an observer on the Earth’s surface. In this frame, the Earth appears stationary while the Sun, Moon and satellites pass overhead. This is in the frame that we “see” every day. And it is in this frame we ask questions like what are the coordinates of this point? What are the distances and directions to other points? How fast is this point moving relative to other points?

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Celestial and Terrestrial Link

The connection between these two frames is dominated by stable processes. The Sun, Earth, Moon and satellites seem to move in the same way day after day. But if we look more closely, other processes are involved too. Our irregular, slightly flattened Earth suffers ● Precession. ● Nutation. ● Changes in its rate of spin. ● Changes in the orientation of its spin axis.

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Precession — The gravitational attraction of the Sun, Moon and planets cause the spinning top that is the Earth to precess, or slowly wobble, just as a toy top does under the influence of the Earth's gravity. The magnitude of this change is about 20 arcsec (620 meters) per year, but very stable and very accurately modelled.

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Nutation — The gravitational attraction of the Sun also slowly precesses the Moon's orbit. This variation in the Moon's orbit in turn causes a variation in the orientation of the rotation axis of the Earth. This variation is called nutation and has an amplitude of about 9 arcsec (270 meters). Nutation is very accurately modelled.

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LOD/UTC — The Earth's rate of spin, the largest of these effects, is slowing down because of tidal friction. Think about this for a moment and you’ll realize this implies our Length Of Day (LOD) is slowly increasing, but the effect is so small that, at worst, we might notice the occasional news stories about leap seconds inserted into Universal Coordinated Time (UTC). Broadly, the rate of change is a constant, but slight and unpredictable variations occur (the definition of mathematical chaos).

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EOP — Terms describing other variations in the orientation of the spin axis of the Earth are called Earth Orientation Parameters (EOP). EOP is now known to be a "catch all" for several physical phenomena including ocean and atmospheric currents, seasonal movement of water between the northern and southern hemispheres, changes in surface water reservoirs, etc.. These variations are typically about 0.5 arcsec (15 meters) or less, but change chaotically from day to day.

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Where do we get this information? The International Astronomical Union (IAU) defines the connection between the celestial and terrestrial frames. For GNSS processing, the IAU precession and nutation models are more than adequate, but because of those pesky chaotic variations, the EOP and LOD require actual measurements.

Formally, the U.S. Naval Observatory (USNO) is responsible for EOP and LOD measurements for the United States. In turn, the USNO collaborates with a global community represented by the International Earth Rotation and Reference Systems Service (IERS). The IERS and its contributing members provide “first look” EOP and LOD daily, and refined parameters several times per week.

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Terrestrial Reference Frames As we all know, there are many terrestrial reference frame definitions. Although each is valid in its context, accuracies can vary and there may be inconsistencies between frame definitions. We’ll briefly discuss five: ITRF and IGS, WGS 84, PZ-90 and NAD 83.

One point to keep in mind is that the definition of any terrestrial frame is inherently a bootstrapping process. Repeated observations from a point are necessary for accurate coordinates and years of observations from a point are necessary to determine a velocity comparable in accuracy to the coordinates.

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International Terrestrial Reference Frame The ITRF, produced by the IERS, is the “gold standard” of terrestrial reference frames. It is the most internally consistent and accurate. As we’ll see, it also is effectively the reference frame of GNSS.

Contributing sources include: ● Very Long Baseline Interferometry (VLBI) ● Satellite Laser Ranging (SLR) ● GNSS ● DORIS ● Conventional surveys for connections between techniques. ● Historically, others have been included. The latest realization, the ITRF2008, was released in May 2011.

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The ITRF And The IGS

The sources contributing to the IERS products are communities unto themselves

The International GNSS Service (IGS) is the organization for the GNSS community. The IGS operates mail and informational services, format standards, models, etc. The IGS has also organized a global GNSS tracking network. From this, it produces satellite ephemerides, EOP and reference frames.

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Tides What causes tides?

They are created by the gravitational attraction of the Moon and Sun, because the gravitational pull of, say, the Moon is greater on the side of the Earth nearer the Moon than that on the far side further from the Moon.

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Tides

View from celestial frame of gravitational forces exerted by Moon on Earth

To view from terrestrial frame subtract the acceleration felt at the center of the Earth from all other points (gray arrows).

Forces combined from above act to stretch the Earth along the Earth-Moon line, and compressing the Earth perpendicular to that line. 44

Tides On a global scale, the solid Earth is viscous enough to respond like a fluid. The result is bulges that respond quickly and follow the sub-lunar or -solar point closely.

The oceans and atmosphere respond similarly, but are affected by the topography of the Earth, large scale patterns and weather.

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Earth Tide Effects Upon Positions

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Ocean Tide Loading Correction

As the ocean tide swells and ebbs, the changing weight of water pressing on the Earth’s crust causing it to deform in sympathy with the tide. Called ocean tide loading (OTL), this effect can be as large as several centimeters.

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OTL Effects Upon Positions Computed vertical OTL

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Atmospheric Loading Correction The weight of the air above a site will deform the supporting crust of the Earth. Atmospheric loading (AL) is a more subtle effect that OTL which, in turn, is more subtle than the solid Earth tide. Nonetheless, it is measurable in the very highest accuracy surveys. It is rarely implemented in common GNSS processing software. The current standard model is the inverted barometer.

delta = -0.35 × Pr − 0.55 × Pr where: delta is the vertical deformation in millimeters. Pr is the barometric pressure at the site in millibars Pr is the pressure averaged over a 2000 km circular region around the site, also in millibars.

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Hydrological Loading

Hydrological loading by surface water is actually a "hot" topic in some academic circles now. The basic concept is that weight of stored surface water depresses the supporting crust. This water may be store in lakes and reservoirs, snow packs, soil moisture and in other ways I'm sure. Cases of real significance are known most of which are associated with new dam and reservoir construction.

Because it this is such a localized phenomena, no model for hydrological loading although its effects may be expressed in the velocity of a site.

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Other subsidence causes — Post-glacial rebound — Fluid extraction — Sinkholes — Vulcanism — Tectonics

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Projections — Tool to ‘translate’ geodetic locations—those that take into account the earth’s curvature-- to ‘show’ them on a flat, 2-dimensional plane

— Independent of datum — On NGS main page, select Geodetic TOOLKIT — State Plane Coordinates

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Get ready for the Future

— Move from NGVD 29 to NAVD 88 — Understand the accuracy of VERTCON in your area — Move away from passive marks to CGPS — Especially move off of classical (non GPS) passive geodetic control

— Require/provide complete metadata for all surveying and mapping work — What realization? Just “NAD83” is not enough. What EPOCH? — How did they (you) get the positions/heights? DOCUMENT!! 54

POSITIONING TECHNOLOGY- A CARTOON GRAPH 0.5' SAT IMAGERY, TERR. LASER SCANNING, 0.10' “Human knowledge is doubling every GNSS- GLONASS, AERIAL MAPPING, GALILEO, COMPASS/ 10 years. …scientific knowledge INTERNATIONAL BEIDOU, produced between 1987 and 1997 is NETWORKS, INDOOR greater than that produced in all POSITIONING, 3-D GIS mankind’s history.” Michio Kaku- renowned theoretical physicist RTN TECHNOLOGY RTK THE CHANGE FROM LABOR GIS INTENSIVE TO TECHNOLOGY! GPS

THEODOLITE TOTAL STATION STICKS AND COMPASS STRINGS

0 YEAR 500 750 -500 -500 1000 1250 1500 1700 1750 1850 1900 1977 1989 2000 2010 2017 2030 -2700 -2700 -2500 -1500 -1000 55

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SOME DATUM DEFINITIONS IN THE USA

HORIZONTAL/ GEOMETRIC: VERTICAL/GEOPOTENTIAL: — NAD 83 — NGVD 29

— ITRS — NAVD 88

— WGS 84 — NAVD 22 (?)

— NRS 22 (?)

NAD 83, NAVD 88

HORIZONTAL 2 D (Latitude and Longitude) [e.g. NAD 27, NAD 83 (1986)]

VERTICAL 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 (1991, 1999), NAD 83 (2007))

also 4 D (Latitude, Longitude, Ellipsoid Height, Velocities) Coordinates change with time NAD 83(CORS96) Epoch 2002 to: NAD 83(2011) Epoch 2010.0

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Z Zero DATUM= Meridian • SURFACE -X • ORIENTATION -Y - • SCALE • ORIGIN + GRAVITY

X Mean Equatorial Plane Y AUTONOMOUSGN SS POSITIONS ARE ECEF, XYZ IN WGS 84 (~ITRF)

-Z 58

Some definitions BESSEL 1841 (1848 – 1879) a = 6,377,397.155 m 1/f = 299.1528128

CLARKE 1866 (1879 – 1986) a = 6,378,206.4 m 1/f = 294.97869821

GEODETIC REFERENCE SYSTEM 1980 - (GRS 80) (1986 - Present) a = 6,378,137 m 1/f = 298.257222101

WORLD GEODETIC SYSTEM 1984 - (WGS 84) a = 6,378,137 m 1/f = 298.257223563 59

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Conventional Earth- Z Axis Terrestrial Pole Centered- P (X,Y,Z) Earth-Fixed Earth’s Coordinates Surface

Zero Meridian Z

Origin (0,0,0) Y Axis Center of Mass

X Y

X Axis Mean Equatorial Plane 60

Z Axis X,Y,Z TO φ,λ,h P (X,Y,Z) = P (φ,λ,h) h Earth’s Surface Ellipsoid height component Zero produced from Meridian GPS

Reference Ellipsoid

Y Axis φ

λ

X Axis Mean Equatorial Plane 61

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THE REALIZATION OF NAD 83 HAS ITS ORIGIN 2.2 M FROM THE SCIENTIFIC ITRS DATUM REALIZED AS ITRF XX

h83 h00 Earth’s Surface

ITRF 00 ORIGIN (WGS 84 IS WITHIN A COUPLE OF CENTIMETERS IN REALIZATION) 2.2 meters

NAD 83 Origin 62

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 63

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4. Geoid, gravity and the vertical — Vertical is basic to most measurements done by local surveyors

— What is the basis for “vertical”? — Vertical relates to geoid, not the ellipsoid — What’s the difference? — What is deflection of the vertical

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Geoid vs. Ellipsoid

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Vertical Datums — NGVD 29 — 26 tide gages, U.S. & Canada

— NAVD 88 — Fixed on one point: Father Point/Rimouski, Quebec, Canada — VERTCON can be used to convert — ±2 cm, one sigma

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Altitude Reference

• Ellipsoid: A smooth, mathematically defined model of the earth's surface. • Geoid: A surface of equal gravitational pull (equipotential) best fitting the average sea surface over the whole globe. Earth's Surface

MSLE HAE Ellipsoid

Geoid 67

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Geometric Relationships

Topographic Surface

H h e

Geoid N

H = Ellipsoid Height Ellipsoid h = Orthometric Height N = Geoid Undulation H = h + N e = Deflection of the vertical 68

Time — Time is a dimension in which events can be ordered from the past through the present into the future

— Measure of durations of events and the intervals between them.

— relatively uncontroversial definitions of time include "time is what clocks measure” and — "time is what keeps everything from happening at once”

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Connection to geodesy? — Necessary for determination of longitude — [Read Longitude by Dava Sobel] — The more precise the time, the more precise the longitude determination

— Essential for GPS (it is the standard for space and time). For it to work, it relies on atomic clocks inside each satellite

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GPS — Would not work without precise time — That is, the space segment, the ground segment and the user segment

— Now…GPS is used for time: — Cell towers — Networks (the internet) — Power generation and distribution — Radio and TV — Many more

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Keep up with the Lightsquared issue — Could make GPS for all of us not so effective — Would change our life as we know it today

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What time is it?

System Description UT1 UTC TT TAI GPS

UT1 Mean Solar UT1 UTC = UT1 TT = UT1 + TAI = UT1 - GPS = UT1 Time - DUT1 32.184 s + DUT1 + LS - DUT1 + LS - DUT1 LS - 19 s

UTC Civil Time UT1 = UTC UTC TT = UTC + TAI = UTC GPS = UTC + DUT1 32.184 s + + LS + LS – 19 s LS

TAI Atomic UT1 = TAI + UTC = TAI - TT = TAI + TAI GPS = TAI - Time DUT1 - LS LS 32.184 s 19 s

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Second — Length of a second in the tropics in 1900 — Formalized into the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom

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6. Integrating geodesy — For the local surveyor, GPS, SPCs alone create the need for a background in geodesy basics

— Large surveys, whether land based, airborne or satellite-based requires it

— The biggest reason, in my opinion, for knowing something about surveying? …because we are surveyors

— If we don’t, who?

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GNSS TO ANY DATUM

— GNSS ECEF X,Y,Z (WGS 84 & PZ90) NAD 83 (φ,λ,h) SPC N,E,h

+ GEOID XX = SPC N,E,H

OR

CALIBRATE TO 4-5 SITE POINTS IN THE DESIRED DATUM. THIS IS USED TO LOCK TO PASSIVE MONUMENTATION IN THE PROJECT AREA. 76

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ECEF Coordinate System +Z

ECEF X = – 2691542.5437 m Y = – 4301026.4260 m Z = 3851926.3688 m

Z Y X

-Y

+X 78

Projections — Tool to ‘translate’ geodetic locations—those that take into account the earth’s curvature-- to ‘show’ them on a flat, 2-dimensional plane

— Independent of datum — On NGS main page, select Geodetic TOOLKIT — State Plane Coordinates

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Problems — meridians converge

Parallel is curved except at equator

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Problems — On the Earth, “straight lines” are not straight except for meridians (or the equator) and the difference gets larger as you extend them

N

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Problems — Changes in elevation cannot be ignored, that is why all geodetic distances are at “sea level”

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Projections — To have a plane coordinate system, it is necessary to distort the curved surface of the earth to a fit on a plane — Orange peel analogy — This process of flattening must be systematic in order to have accuracy — In surveying this process is called a projection

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Projections / 2 — Systematic way to portray (curved) surface of the earth on a flat surface

— Distortions inevitable — Different projections are used because each minimizes distortion in some properties at the expense of others

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General classes — Cylindrical

Tangent

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Transverse Mercator

A C

B D

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Transverse Mercator edge view

Cylinder

Sphere 87

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General classes — Conic

Secant

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Lambert conformal

— Varying central apex angle of cone changes section of ellipsoid that is intersected

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Feet!

— U.S. Survey foot = [m] x 3937/1200 — International foot = [m] / 0.3048 — 2 PPM! — [0.01 ft in a mile] — [but with a coord value of 500,000 m, difference is 1 m!]

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…or

Scale greater than true Cylinder

Scale less than true View perpendicular to axis of cylinder

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Ellipsoid, Geoid, Topography

Mass Excess Local Topography

Ellipsoid

Geoid Mass Deficiency

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Central Meridian « «

γ Geodetic Geodetic γ azimuth azimuth

Grid Grid azimuth azimuth

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Coordinates

Translation (2D) 94

Coordinates

Translation and rotation (2D) 95

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Coordinates

Translation, rotation & scale (2D) 96

Transformations

Y Y’ N B

A

X

X’ E Given: A and B in N/E reference frame and X/Y reference frame. Determine the transformation equation to convert any point from the X/Y to N/E system 97

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Transformation / 2 Y Y’ N B A X

X’ E Three parts to the transformation: 1. Rotation 2. Scale 3. Translation

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Transformation / 3 Y Y’ N B A X

X’ E Rotation: 1. Determine azimuth of AB in XY and NE systems 2. Rotation = azimuth in XY minus azimuth in NE = θ

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Transformation / 4 Y Y’ N B A X

X’ E Scale: 1. Determine length of AB in XY and NE systems 2. Scale = length in NE system divided by length in XY system = s

10 0

Transformation / 5 Y Y’ N B A X

X’ E Translation is done in two steps: 1. Calculate coordinates of A and B in X’Y’ system 2. Then determine translation by subtracting coordinates in X’Y’ system from coordinates in NE system

3. Result is Tx and TY 10 1

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Determining coordinates in X’Y’ frame

X 'A = sX A cosθ − sYA sinθ

Y'A = sX A sinθ + sX A cosθ Transforms from XY to X’Y’ coordinates

Y Y’ N B TX = EA − X 'A A X TY = N A −Y'A X’ E 10 2

Final equations for transformation

E = sX cosθ − sY sinθ +TX

N = sX sinθ + sY cosθ +TY

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Reference Ellipsoid a = semi-major axis b = semi-minor axis (a −b) Flattening f = a H

φ ≡ latitude λ ≡ longitude b H ≡ ellipsoidal height φ WGS-84 Ellipsoid a λ a = 6378137.000000 m b = 6356752.314245 m 1/f = 298.2572235630 104

Datum Transformation

Z Z Three Parameter Datum Transformation (Translation in X, Y, Z) X Seven Parameter Datum Transformation X adds 3 Rotations (Rotation X, Y, Z) Plus Scaling Y Y 105

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OPUS Reference Frame Choices

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NA2011 project for passive geodetic stations — Optimally align passive control with CORS — >1000 projects submitted since 2007 national readjustment

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NA2011 CONUS 1983-2011 (29 yrs): 426,977 vectors

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NGS Datasheets — Geometric elements, e.g., ellipsoid height and epoch date

— Information on geoid model usage, including for superseded ortho height data

— Started publishing superseded GPS-derived ortho heights — Hyperlinks to Local Ties & Accuracies — Shapefile content now identifies Ht Mod (GPS observations of the vertical

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Datasheet Format

— NA0174 CBN - This is a Cooperative — NA0174 NAD 83(2011) Z - 4,295,406.534 Base Network Control Station. (meters) COMP — NA0174 DESIGNATION - N 296 — NA0174 LAPLACE CORR - -4.77 — NA0174 PID - NA0174 (seconds) DEFLEC12A — NA0174 STATE/COUNTY- NY/ALBANY — NA0174 GEOID HEIGHT - -30.93 (meters) GEOID12A — NA0174 USGS QUAD - WESTERLO (1980) — NA0174 DYNAMIC HEIGHT - 434.513 — NA0174 *CURRENT SURVEY (meters) 1425.56 (feet) COMP CONTROL — NA0174 MODELED GRAVITY - 980,268.4 — NA0174* NAD 83(2011) POSITION- 42 36 (mgal) NAVD 88 10.35074(N) 074 02 04.52519(W) ADJUSTED — NA0174 VERT ORDER - SECOND CLASS 0 — NA0174* NAD 83(2011) ELLIP HT- 403.729 (meters) (06/27/12) ADJUSTED — NA0174 FGDC Geospatial Positioning Accuracy Standards (95% confidence, cm) — NA0174* NAD 83(2011) EPOCH - 2010.00 — NA0174 Type Horiz Ellip — NA0174* NAVD 88 ORTHO HEIGHT - 434.661 Dist(km) (meters) 1426.05 (feet) ADJUSTED — NA0174 NETWORK — NA0174 NA0174 NAD 83(2011) X - 1.08 1.84 1,293,379.951 (meters) COMP — NA0174 MEDIAN LOCAL ACCURACY AND DIST — NA0174 NAD 83(2011) Y - -4,520,850.977 (078 points) 1.15 2.05 126.07 (meters) COMP — NA0174 NOTE: Click here for information on individual local accuracy — NA0174 values and other accuracy information. 111

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Suggested GPS Test Network 1

2

C

A

B 112

GPS mistakes (& good technique)

0 miles 5 10 15 Project Area 113

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Consider…

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Resources — NGS Toolkit page: http://www.ngs.noaa.gov/TOOLS/

— LOCUS: Leveling Online Computations User Service — OPUS: Online Positioning User Service

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Thank you

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