**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. ITRF00, ITRF05)

**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.) • Geodetic– Either directly or loosely based on Mean Sea Level at one or more points at some epoch • (NGVD 29, NAVD 88, IGLD85 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

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

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

**A** A hA A A HA 3-D Coordinates derived from GNSS X1 Y1 Z1 X2 Y2 Z2 X3 Y3 Z3 X4 Y4 Z4 Z XA YA ZA NA EA hA A Greenwich Meridian Earth Mass Center +ZA + GEOID03 + - Y NA EA HA YA - X XA Y X Equator - Z

**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

**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: LMSL = MSL + DOT Ellipsoid N Tide gauge height LMSL DOT Geoid Relationships

**ELLIPSOID - GEOID RELATIONSHIP** H = Orthometric Height(NAVD 88) h = Ellipsoidal Height (NAD 83) H = h - N N = Geoid Height (GEOID 03) H TOPOGRAPHIC SURFACE h N GEOID 03 Geoid Ellipsoid GRS80

**Level Surfaces and Orthometric Heights** Earth’s Surface WP Level Surfaces P Plumb Line Mean “Geoid” Sea Level WO PO Level Surface = Equipotential Surface (W) Ocean 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 Equipotential Surfaces B Topography hAB = hBC A C HA HC HAChAB + hBC Reference Surface (Geoid) Observed difference in orthometric height, H, depends on the leveling route.

**Tectonic Motions**

**PRELIMENARYVertical Velocities: CORS w/ <2.5 yrs data**

**PRELIMENARY North American Vertical Velocities**

**High Resolution Geoid ModelsGEOID03 (vs. Geoid99)** • Begin with USGG2003 model • 14,185 NAD83 GPS heights on NAVD88 leveled benchmarks (vs 6169) • Determine national bias and trend relative to GPS/BMs • Create grid to model local (state-wide) remaining differences • ITRF00/NAD83 transformation (vs. ITRF97) • Compute and remove conversion surface from G99SSS

**High Resolution Geoid ModelsGEOID03 (vs. Geoid99)** • 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 GEOID99 (Geoid96 to 99 was 16%) • GEOID06 ~ By end of FY07

**H** h N H = h - N 131.448 m = - 102.456 m - (- 29.01 m) 131.448 m ≠ 131.466 m (0.18 m/0.06 ft)

**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 un-modeled changes in slope or bias (fitted plane)

**Two Days/Same Time** -10.254 -10.251 > -10.253 Difference = 0.3 cm “Truth” = -10.276 Difference = 2.3 cm Two Days/ Different Times -10.254 > -10.275 -10.295 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 L3-fixed solution w/ tropo adjusted 3 “best” CORS selected3 separate baselines computed3 separate positions averaged Position differences also include any errors in CORS coordinates

**To enhance vertical accuracy use rapid orbits available in** 24 hours Broadcast Orbits ~ 5 m (real time) Ultrarapid Orbits ~ 0.02- 0. 04 m (12 hours) Rapid Orbits ~ 0.01 – 0.02 m (24 hours) Precise Orbits ~ 0.005 – 0.01 m (two weeks) PUBLISHED 32 05 24.91710 - .00029 (0.009 m) 87 23 30.50447 - .00019 (0.005 m) 10.443 m - .035 HOW GOOD ARE OPUS ORTHOMETRIC HEIGHTS? IT DEPENDS! ORTHOMETRIC HEIGHT ~ 0.02 – 0.04 m GEOID03 ~ 0.048 m (2 sigma – 95% confidence) Error ~ 0.03 + 0.05 ~ 0.08 m 156.308

**Gravity Recovery And Climate Experiment (GRACE)**

**Gravity Recovery And Climate Experiment (GRACE)**

**Absolute gravimeter:Example: Micro-g Solutions FG5** • Ballistic (free-fall) of retro- reflector in vacuum chamber, tracked by laser beam • Instrument accuracy and precision: ± 1.1 mGals • Used for temporal change of g 7

**Spring-based relative gravimetersExample: LaCoste & 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 mGals 5

**Changes for the BetterImprove 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