Montana

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Montana Height Modernization Primer
GPS-Derived Heights
Curt Smith National Geodetic Survey Idaho Phone
208-332-7197 Montana Phone [phone] Curt.Smit
h_at_noaa.gov
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BM 100
BM

• Conventional Leveling
• Very Precise
• Labor Intensive
• Max Distance 140 M
• Between Rods Per Setup
• About 22 Setups Per Mile

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GRACE Gravity Model 01 - Released July 2003
Image credit University of Texas Center for
Space Research and NASA
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Geopotential Surfaces
The Geoid
Gravity Vector
The relationships between the various
geopotential surfaces (dashed blue), and the
geoid (solid blue). The geoid exists
approximately at mean sea level (MSL). Not shown
is the actual surface of the earth, which
coincides with MSL but is generally above the
geoid.
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Level Surfaces and Orthometric Heights
Earths
Surface
WP
Level Surfaces
P
Plumb
Line
Mean Sea Level
Geoid
WO
PO
Level Surface Equipotential Surface (W)
Ocean
Geopotential Number (CP) WP -WO
H (Orthometric Height) Distance along plumb
line (PO to P)
Area of Low Density Rock
Area of High Density Rock
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Vertical Datums

• Local/Regional
• Assumed
• City, County
• International Great Lakes Datum 1955 (IGLD55)
• International Great Lakes Datum 1985 (IGLD85)
• Tidal Datums
• National
• National Geodetic Vertical Datum of 1929
  (NGVD29)
• North American Vertical Datum of 1988 (NAVD88)

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NGVD 29 Versus NAVD 88

• Datum Considerations NGVD 29 NAVD
  88
• Defining Height(s) 26 Local MSL 1
  Local MSL
• Tidal Epoch Various
  1960-78
• 
  (18.6 years)

• Treatment of Leveling Data
• Gravity Correction Ortho Correction
  Geopotential Nos.
• (normal gravity) (observed
  gravity)
• Other Corrections Level, Rod, Temp.
  Level, Rod, Astro,
• Temp, Magnetic,
• and Refraction

• Adjustments Considerations
• Method Least-squares
  Least-squares
• Technique Condition Eq.
  Observation Eq.
• Units of Measure Meters
  Geopotential Units
• Observation Type Links Between
  Height Differences
• Junction Points
  Between Adjacent BMs

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NGVD 29 Versus NAVD 88 (continued)

• Adjustments Statistics NGVD 29
  NAVD 88
• No. of Bench Marks 100,000 (est)
  450,000 (US only)
• Km of Leveling Data 75,159 (US)
  1,001,500
• 31,565 (Canada)

• Published Information
• Orthometric Height Type Normal Helmert
  
• Orthometric Height Units Meters
  Meters
• Gravity Value Normal Actual

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Height Differences Between NAVD 88 and NGVD 29
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Tidal Datums

• Heights Measured Above Local Mean Sea Level
• National Tidal Datum epoch 19 year series
• Encompasses all significant tidal periods
  including 18.6 year period for regression of
  Moons nodes
• Averages out nearly all meteorological,
  hydrological, and oceanographic variability
• Leveling is used to determine relationship
  between bench marks and tidal gauges

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Global Positioning System
27 Satellites 6 Planes, 55 Rotation 4/5
Satellites /Plane 20,183 km Orbit 1 Revolution
/12 Hrs
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The Ellipsoid
N
a Semi major axis
b Semi minor axis
f a-b Flattening a
b
a
Geodetic Reference System 1980
S
a 6,378,137 meters (semi-major axis)
b 6,356,752.3141403 m (semi-minor axis)
1/f 298.25722210088 (flattening)
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GPS - Derived Ellipsoid Heights
Z Axis
(X,Y,Z) P (?,?,h)
P
h
Earths
Surface
Zero
Meridian
Reference Ellipsoid
Y Axis
?
?
Mean Equatorial Plane
X Axis
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Geopotential Surfaces
The Geoid
Gravity Vector
The relationships between the ellipsoid surface
(solid red), various geopotential surfaces
(dashed blue), and the geoid (solid blue). The
geoid exists approximately at mean sea level
(MSL). Not shown is the actual surface of the
earth, which coincides with MSL but is generally
above the geoid.
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Ellipsoid, Geoid, and Orthometric Heights
h H N
Earths
Surface
P
Plumb Line
Ellipsoid
h
Q
N
Mean
Sea
Geoid
Level
PO
Ocean
h (Ellipsoid Height) Distance along ellipsoid
normal (Q to P)
N (Geoid Height) Distance along ellipsoid
normal (Q to PO)
H (Orthometric Height) Distance along plumb
line (PO to P)
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Horizontal Datums

• 8 Constants
• 3 specify location of the origin of the
  coordinate system
• 3 specify the orientation of the coordinate
  system
• 2 specify the dimensions of the reference
  ellipsoid
• Geodetic Reference System 1980 - (GRS 80)
• a 6,378,137 m 1/f 298.257222101
• World Geodetic System 1984 - (WGS 84)
• a 6,378,137 m 1/f 298.257223563

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Comparison of Horizontal Datum Elements

• 
  NAD 27 NAD 83
• ELLIPSOID CLARKE 1866 GRS80
• a 6,378,206.4 m
  a 6,378,137. M
• 1/f 294.9786982
  1/f 298.257222101
• DATUM POINT Triangulation
  Station
  NONE
• MEADES RANCH, KANSAS
  EARTH MASS CENTER
• ADJUSTMENT 25k STATIONS
  250k STATIONS
• Several Hundred Base Lines
  Appox. 30k EDMI Base Lines
• Several Hundred Astro Azimuths
  5k Astro Azimuths
• 
  Doppler Point Positions
• 
  VLBI Vectors
• BEST FITTING North
  America
  World-Wide

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NAD 27 and NAD 83
NAD27 and NAD83
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NAD27, NAD83, WGS84
NAD27
WGS84
NAD83
Approximately 2 meters
Approximately 236 meters
Earth Mass Center
GEOID
WGS84 and NAD83 share similar shaped ellipsoids
but their origins differ by about 2m NAD27 uses
the Clark spheroid of 1866, the origin is 236 m
from WGS84
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In Search of the Geoid
Courtesy of Natural Resources Canada
www.geod.nrcan.gc.ca/index_e/geodesy_e/geoid03_e.h
tml
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High Resolution Geoid ModelsUSGG2003 (Scientific
Model)

• 2.6 million terrestrial, ship, and altimetric
  gravity measurements
• offshore altimetry from GSFC00.1 instead of KMS98
• 30 arc second Digital Elevation Data
• 3 arc second DEM for the Northwest USA
• Decimated from 1 arc second NGSDEM99
• Earth Gravity Model of 1996 (EGM96)
• Computed on 1 x 1 arc minute grid spacing
• GRS-80 ellipsoid centered at ITRF00 origin

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Earth Gravity Model 1996 (EGM96)
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Gravity Coverage for GEOID03
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NGSDEM99 is a 1 x 1 arc-second Digital Elevation
Model (DEM) of the Northwest United States,
covering the region 39 - 49N latitude, and 234 -
265E longitude.
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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)
• Remove national bias (55 cm) and 1st order trend
  (slope) relative to GPS/BMs
• Generate grid by the multi-matrix Least Squares
  Collocation (vs. single Gaussian matrix)
• ITRF00/NAD83 transformation (vs. ITRF97)
• Compute and remove conversion surface from
  USGG2003

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High Resolution Geoid ModelsGEOID03 (vs. Geoid99)

• Relative to non-geocentric GRS-80 ellipsoid
• Fits NAD83 coordinates
• Relative differences typically less than 1 cm in
  10 km
• 2.4 cm RMS nationally when compared to BM data
  (vs. 4.6 cm)
• RMS ? 50 improvement over GEOID99
• (GEOID96 to GEOID99 was 16)

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Composite Geoids

• Gravity Geoid systematic misfit with bench marks

Composite Geoid warped to fit local bench marks
Earths Surface
Ellipsoid
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Vertical Datum Relationships
3-D Datums
Orthometric Datums
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Guidelines for Establishing GPS-Derived Ellipsoid
Heights (Standards 2 cm and 5 cm)
www.ngs.noaa.gov
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Height Modernization Layout
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Guidelines for Establishing GPS-Derived
Orthometric Heights (Standards 2 cm and 5 cm)
Draft
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DATABASE Sybase ,PROGRAM datasheet, VERSION
7.121 National Geodetic Survey, Retrieval Date
JANUARY 25, 2005OM1256
OM1256
HT_MOD - This is a Height Modernization Survey
Station.OM1256 CBN - This is a Cooperative Base
Network Control Station.OM1256 DESIGNATION -
CAMBRIA GPSOM1256 PID - OM1256OM1256
STATE/COUNTY- WI/COLUMBIAOM1256 USGS QUAD -
RANDOLPH (1980)OM1256OM1256 CURRENT SURVEY
CONTROLOM1256 ___________________________________
________________________________OM1256 NAD
83(1997)- 43 34 10.47581(N) 089 06 09.35995(W)
ADJUSTED OM1256 NAVD 88 - 303.84
(meters) 996.8 (feet) GPS OBS OM1256
__________________________________________________
_________________OM1256 X - 72,495.418 (meters)
COMPOM1256 Y - -4,628,194.515 (meters)
COMPOM1256 Z - 4,373,750.772 (meters)
COMPOM1256 LAPLACE CORR- 1.49 (seconds)
DEFLEC99OM1256 ELLIP HEIGHT- 268.36 (meters)
(04/28/99) GPS OBSOM1256 GEOID HEIGHT- -35.46
(meters) GEOID03OM1256OM1256 HORZ ORDER -
AOM1256 ELLP ORDER - THIRD CLASS
IOM1256OM1256.The horizontal coordinates were
established by GPS observationsOM1256.and
adjusted by the National Geodetic Survey in April
1999.OM1256OM1256.The orthometric height was
determined by GPS observations and
aOM1256.high-resolution geoid model using
precise GPS observation andOM1256.processing
techniques.OM1256OM1256.The X, Y, and Z were
computed from the position and ellipsoidal
ht.OM1256OM1256.The Laplace correction computed
from DEFLEC99 derived deflections.OM1256OM1256.T
he ellipsoidal height was determined by GPS
observationsOM1256.and is referenced to NAD
83.OM1256OM1256.The geoid height was determined
by GEOID03.OM1256
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Obstruction Visibility Diagram
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A Stability First Order Class II NAVD88 Bench
Mark Its Gotta be Good!
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Bench Mark G 506
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www.ngs.noaa.gov
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OPUS - Multiple CORS Providing Position to Base
Receiver
CORS Base Receiver Rover Receiver
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www.wsrn.org
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Height Modernization Program
LIDAR and its Products