Vertical Datums and Heights

Daniel J. MartinNational 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:Characterized by: A set of physical monuments, related by survey measurements and resulting A set of physical monuments, related by survey measurements and resulting

coordinates (horizontal and/or vertical) for those monumentscoordinates (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)

ContemporaryPRACTICAL – 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.

GEOIDThe 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

AC

B Topography

•Adjusted to Vertical Datum using existing control•Achieve 3-10 mm relative accuracy

•Using Optical or Digital/Bar Code Leveling

VERTICAL DATUMS OF THE UNITED STATES

Second General Adjustment - 1903

Mean Sea Level 1929National Geodetic Vertical Datum of 1929 (NGVD 29)

North American Vertical Datum of 1988 (NAVD 88)

First General Adjustment – 1899(a.k.a. – Sandy Hook Datum)

Third General Adjustment - 1907

Fourth General Adjustment - 1912

NGVD 29 TIDE CONTROL

Orthometric HeightsComparison of Vertical Datum Elements

NGVD 29 NAVD 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

3-D Coordinates derived from GNSS

YA

X

Z

Y

A

XA

+ZA

Equator

Gree

nwich

Mer

idian

EarthMass Center

- X

- Y

- Z

X1

Y1

Z1

X2

Y2

Z2

X3

Y3

Z3

X4

Y4

Z4

XA

YA

ZA

NA

EA

hA

+ GEOID03 +

NA

EA

HA

A

hA

A

A

HA

A

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: LMSL = MSL + DOT Ellipsoid

LMSL

Geoid

N Tide gauge height

DOT

ELLIPSOID - GEOID RELATIONSHIP

H h

EllipsoidGRS80

H = Orthometric Height (NAVD 88)

N

Geoid

H = h - N

TOPOGRAPHIC SURFACE

h = Ellipsoidal Height (NAD 83)N = Geoid Height (GEOID 03)

GEOID 03

Level Surfaces and Orthometric Heights

Level Surfaces

PlumbLine

“Geoid”

PO

P

Level Surface = Equipotential Surface (W)

H (Orthometric Height) = Distance along plumb line (PO to P)

Earth’s

Surface

Ocean

MeanSeaLevel

Geopotential Number (CP) = WP -WO

WO

WP

Equipotential Surfaces

HCHA

Reference Surface (Geoid)

HAC hAB + hBC

Observed difference in orthometric height, H, depends on the leveling route.

AC

B Topography

hAB

h = local leveled differences

Leveled Height vs. Orthometric Height

= hBC

H = relative orthometric heights

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

N

H

h

H = h - N131.448 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 mDifference = 0.002 m / 0.005 ft

N O A A T e c h n ic a l M e m o r a n d u m N O S N G S - 5 8

G U ID E L I N E S F O R E S T A B L I S H IN G G P S - D E R I V E D E L L IP S O I D H E IG H T S( S T A N D A R D S : 2 C M A N D 5 C M )V E R S I O N 4 . 3

D a v i d B . Z i lk o s k iJ o s e p h D . D 'O n o f r i oS t e p h e n J . F r a k e s

S i lv e r S p r i n g , M D

N o v e m b e r 1 9 9 7

U .S . D E P A R T M E N T O F N a t io n a l O c e a n ic a n d N a t io n a l O c e a n N a t io n a l G e o d e t icC O M M E R C E A t m o s p h e r ic A d m in i s t r a t io n S e r v ic e S u r v e y

Available “On-Line” atthe 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)

NhH

Comparison of 30 Minute Solutions - Precise Orbit; Hopfield (0); IONOFREE(30 Minute solutions computed on the hour and the half hour)

MOLA to RV22 10.8 Km

Day 264dh (m)

Hours Diff. Day 265

dh (m)

Day 264 minus

Day 265 (cm)

* diff >2 cm

Mean dh (m)

Mean dh minus "Truth" (cm)

* diff >2 cm

14:00-14:30 -10.281 27hrs 17:00-17:30 -10.279 -0.2 -10.280 -0.514:30-15:00 -10.278 27hrs 17:30-18:00 -10.270 -0.8 -10.274 0.215:00-15:30 -10.281 27hrs 18:00-18:30 -10.278 -0.3 -10.280 -0.415:30-16:00 -10.291 27hrs 18:30-19:00 -10.274 -1.7 -10.283 -0.716:00-16:30 -10.274 27hrs 19:00-19:30 -10.274 0.0 -10.274 0.216:30-17:00 -10.287 27hrs 19:30-20:00 -10.276 -1.1 -10.282 -0.617:00-17:30 -10.279 27hrs 20:00-20:30 -10.261 -1.8 -10.270 0.617:30-18:00 -10.270 27hrs 20:30-21:00 -10.251 -1.9 -10.261 1.518:00-18:30 -10.277 21hrs 15:00-15:30 -10.270 -0.7 -10.274 0.218:30-19:00 -10.271 21hrs 15:30-16:00 -10.276 0.5 -10.274 0.219:00-19:30 -10.277 21hrs 16:00-16:30 -10.278 0.1 -10.278 -0.219:30-20:00 -10.271 21hrs 16:30-17:00 -10.286 1.5 -10.279 -0.320:00-20:30 -10.259 18hrs 14:00-14:30 -10.278 1.9 -10.269 0.720:30-21:00 -10.254 18hrs 14:30-15:00 -10.295 4.1 * -10.275 0.1

"Truth"14:00-21:00 -10.275 14:00-21:00 -10.276 0.1 -10.276

Two Days/Same Time

-10.254 -10.251 > -10.253

Difference = 0.3 cm

“Truth” = -10.276Difference = 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

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

HOW GOOD ARE OPUS ORTHOMETRIC HEIGHTS?

IT DEPENDS!

ORTHOMETRIC HEIGHT ~ 0.02 – 0.04 mGEOID03 ~ 0.048 m (2 sigma – 95% confidence)

Error ~ 0.03 + 0.05 ~ 0.08 m

PUBLISHED32 05 24.91710 - .00029 (0.009 m)87 23 30.50447 - .00019 (0.005 m) 10.443 m - .035

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)

156.308

Gravity Recovery And Climate Experiment (GRACE)

Gravity Recovery And Climate Experiment (GRACE)

7

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 Gals

•Used for temporal change of g

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 Gals

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