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? - PowerPoint PPT PresentationTRANSCRIPT
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Vertical Datums and Heights
Daniel J. MartinNational Geodetic Survey
VT Geodetic Advisor
VTrans Monthly Survey Meeting October 06, 2008
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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?
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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
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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)
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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.)
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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
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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
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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
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NGVD 29 TIDE CONTROL
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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
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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
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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
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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
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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
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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
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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
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Tectonic Motions
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PRELIMENARYVertical Velocities: CORS w/ <2.5 yrs data
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PRELIMENARY North American Vertical Velocities
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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
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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
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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)
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VERTCON - Vertical Datum Transformations
Published = 330.894 mDifference = 0.002 m / 0.005 ft
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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
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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
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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
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What is OPUS?• On-Line Positioning User Service
• Processes Dual-Frequency GPS data• Global availability (masked)• 3 goals:
– Simplicity– Consistency– Reliability
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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
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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
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Gravity Recovery And Climate Experiment (GRACE)
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Gravity Recovery And Climate Experiment (GRACE)
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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
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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
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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