Vertical Datums and Heights Daniel J Martin National

Vertical Datums and Heights Daniel J. Martin National Geodetic Survey VT Geodetic Advisor VTrans Monthly Survey Meeting October 06, 2008

Can You Answer These Questions? • What is the current official vertical datum of the United States? • What’s the difference between ellipsoid, orthometric and geoid and dynamic heights? • The difference between NGVD 29 and NAVD 88 in most of Vermont is? • A point with a geoid height of -28. 86 m means what?

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 CLASSICAL Horizontal – 2 D (Latitude and Longitude) (e. g. NAD 27, NAD 83 (1986)) Vertical – 1 D (Orthometric Height) (e. g. NGVD 29, NAVD 88) Contemporary PRACTICAL – 3 D (Latitude, Longitude and Ellipsoid Height) Fixed and Stable – Coordinates seldom change (e. g. NAD 83 (1992) or NAD 83 (NSRS 2007)) SCIENTIFIC – 4 D (Latitude, Longitude, Ellipsoid Height, Velocity) – Coordinates change with time (e. g. ITRF 00, ITRF 05)

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, MHW, MHHW etc. ) Geodetic – Either directly or loosely based on Mean Sea Level at one or more points at some epoch (NGVD 29, NAVD 88, IGLD 85 etc. )

TYPES OF HEIGHTS ORTHOMETRIC The distance between the geoid and a point on the Earth’s surface measured along the plumb line. GEOID The distance along a perpendicular from the ellipsoid of reference to the geoid ELLIPSOID The distance along a perpendicular from the ellipsoid to a point on the Earth’s surface. DYNAMIC The distance between the geoid and a point on Earth’s sruface measured along the plumb line at a latitude of 45 degrees

Orthometric Heights • Using Optical or Digital/Bar Code Leveling B A • Adjusted to Vertical Datum using existing control • Achieve 3 -10 mm relative accuracy Topography C

VERTICAL DATUMS OF THE UNITED STATES First General Adjustment – 1899 (a. k. a. – Sandy Hook Datum) Second General Adjustment - 1903 Third General Adjustment - 1907 Fourth General Adjustment - 1912 Mean Sea Level 1929 National Geodetic Vertical Datum of 1929 (NGVD 29) North American Vertical Datum of 1988 (NAVD 88)

NGVD 29 TIDE CONTROL

Orthometric Heights Comparison of Vertical Datum Elements NGVD 29 DATUM DEFINITION TIDAL EPOCH 26 TIDE GAUGES IN THE U. S. & CANADA Varies from point-to-point NAVD 88 FATHER’SPOINT/RIMOUSKI QUEBEC, CANADA (BM 1250 -G) 1970 -1988 BENCH MARKS 100, 000 450, 000 LEVELING (Km) 106, 724 1, 001, 500 GEOID FITTING Model Distorted to Fit MSL Gauges Best Continental

3 -D Coordinates derived from GNSS X 1 Y 1 Z 1 X 2 Y 2 Z 2 X 3 Y 3 Z 3 X 4 Y 4 Z XA YA ZA Gr e Me enw rid ich ian A Earth Mass Center +ZA -X XA X Equator -Z NA EA h. A + GEOID 03 + -Y YA A A h. A Y A A HA NA EA HA

What is the GEOID? • “The equipotential surface of the Earth’s gravity field which best fits, in the least squares sense, mean sea level. ”* • Can’t see the surface or measure it directly. • Modeled from gravity data. *Definition from the Geodetic Glossary, September 1986

Relationships • Geoid = global MSL – Average height of ocean globally – Where it would be without any disturbing forces (wind, currents, etc. ). • Local MSL is where the average ocean surface is with the all the disturbing forces (i. e. , what is seen at tide gauges). • Dynamic ocean topography (DOT) is the difference between MSL and LMSL: N Tide gauge height LMSL = MSL + DOT Ellipsoid LMSL DOT Geoid

ELLIPSOID - GEOID RELATIONSHIP H = Orthometric Height (NAVD 88) h = Ellipsoidal Height (NAD 83) H N = Geoid Height (GEOID 03) =h-N H h TOPOGRAPHIC SURFACE N Geoid GEOID 03 Ellipsoid GRS 80

Level Surfaces and Orthometric Heights Level Surfaces P h’se t r Eaurfac S WP Plumb Line Mean Sea Level PO Ocean “Geoid” WO Level Surface = Equipotential Surface (W) Geopotential Number (CP) = WP -WO H (Orthometric Height) = Distance along plumb line (PO to P)

Leveled Height vs. Orthometric Height h = local leveled differences H = relative orthometric heights rfaces u S l a i t n e Equipot B A HA Topography h. AB = h. BC C HAC h. AB + h. BC HC Reference Surface (Geoid) Observed difference in orthometric height, H, depends on the leveling route.

Tectonic Motions

PRELIMENARY Vertical Velocities: CORS w/ <2. 5 yrs data

PRELIMENARY North American Vertical Velocities

High Resolution Geoid Models GEOID 03 (vs. Geoid 99) i Begin with USGG 2003 model i i i 14, 185 NAD 83 GPS heights on NAVD 88 leveled benchmarks (vs 6169) Determine national bias and trend relative to GPS/BMs Create grid to model local (state-wide) remaining differences i ITRF 00/NAD 83 transformation (vs. ITRF 97) i Compute and remove conversion surface from G 99 SSS

High Resolution Geoid Models GEOID 03 (vs. Geoid 99) i i Relative to non-geocentric GRS-80 ellipsoid 2. 4 cm RMS nationally when compared to BM data (vs. 4. 6 cm) RMS 50% improvement over GEOID 99 (Geoid 96 to 99 was 16%) GEOID 06 ~ By end of FY 07

H=h-N 131. 448 m = - 102. 456 m - (- 29. 01 m) 131. 448 m ≠ 131. 466 m (0. 18 m/0. 06 ft) H h N

VERTCON - Vertical Datum Transformations Published = 330. 894 m Difference = 0. 002 m / 0. 005 ft

Available “On-Line” at the NGS Web Site: www. ngs. noaa. gov

Using the Differential Form • Using the difference eliminates bias • Assumes the geoidal slopes “shape” is well modeled in the area. • “Valid” Orthometric constraints along with “valid” transformation parameters removes additional unmodeled changes in slope or bias (fitted plane)

Two Days/Same Time -10. 254 > -10. 253 -10. 251 Difference = 0. 3 cm “Truth” = -10. 276 Difference = 2. 3 cm Two Days/ Different Times -10. 254 -10. 295 > -10. 275 Difference = 4. 1 cm “Truth” = -10. 276 Difference = 0. 1 cm

What is OPUS? • On-Line Positioning User Service • Processes Dual-Frequency GPS data • Global availability (masked) • 3 goals: – Simplicity – Consistency – Reliability

How Does OPUS Compute Position? NGS-PAGES software used L 3 -fixed solution w/ tropo adjusted 3 “best” CORS selected 3 separate baselines computed 3 separate positions averaged Position differences also include any errors in CORS coordinates

HOW GOOD ARE OPUS ORTHOMETRIC HEIGHTS? To enhance vertical accuracy use rapid orbits available in 24 hours IT DEPENDS! PUBLISHED Broadcast ~ 5 -m (real (0. 009 time) m) 32 05 Orbits 24. 91710. 00029 ORTHOMETRIC HEIGHT 0. 02 0. 04 mm) Ultrarapid Orbits ~ 0. 02 - -0. ~. 00019 04 m –(12 hours) 87 23 30. 50447 (0. 005 GEOID 03 0. 048 ~ m (2 sigma – 95% Rapid~Orbits 0. 01 –m 0. 02 m (24 confidence) hours) 10. 443 -. 035 Error ~ 0. 03– +0. 01 0. 05 m (two weeks) Precise Orbits ~ 0. 005 ~ 0. 08 m 156. 308

Gravity Recovery And Climate Experiment (GRACE)

Gravity Recovery And Climate Experiment (GRACE)

Absolute gravimeter: Example: Micro-g Solutions FG 5 • Ballistic (free-fall) of retroreflector in vacuum chamber, tracked by laser beam • Instrument accuracy and precision: ± 1. 1 m. Gals • Used for temporal change of g 7

Spring-based relative gravimeters Example: La. Coste & Romberg land meter • A mass at end of a moment arm is suspended by spring • Number of screw turns necessary to null position of mass gives change in g from reference sta. • Accuracy: ± 3 to 50 m. Gals 5

Changes for the Better Improve Gravity Field Modeling • NGS will compute a pole-to-equator, Alaska-to. Newfoundland geoid model, preferably in conjunction with Mexico and Canada as well as other interested governments, with an accuracy of 1 cm in as many locations as possible • NGS redefines the vertical datum based on GNSS and a gravimetric geoid • NGS redefines the national horizontal datum to remove gross disagreements with the ITRF