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Vertical Datums and Heights

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### 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

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)

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

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

RelationshipsELLIPSOID - 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.

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

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)

-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

Absolute gravimeter: 24 hoursExample: 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 gravimeters 24 hoursExample: 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 Better 24 hoursImprove 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

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