GPS-Derived Orthometric Heights Part1

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GPS Heights Primer

• Chris Pearson1

• 1National Geodetic Survey 2300 South Dirksen Pkwy
  Springfield IL

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To understand how to achieve GPS-derived
orthometric heights at centimeter-level accuracy,
three questions must be answered

• 1) What types of heights are involved?
• Orthometric heights
• Ellipsoid heights
• Geoid heights
• 2) How are these heights defined and related?
• 3) How accurately can these heights be
  determined?

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Ellipsoid, Geoid, and Orthometric Heights
h H N
Earths
Surface
Ellipsoid
h
N
Mean
Sea
Geoid
Level
H (Orthometric Height)
N (Geoid Height)
h (Ellipsoid Height)
Ocean
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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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Leveled Height Differences
B
Topography
A
C
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All Heights Based on Geopotential Number (CP)
The geopotential number is the potential energy
difference between two points g local gravity
WO potential at datum (geoid) WP
potential at point
Why use Geopotential Number? - because if the
GPN for two points are equal they are at the
same potential and water will not flow between
them
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Heights Based on Geopotential Number (C)

• Normal Height (NGVD 29) H C / ?
• ? Average normal gravity along plumb line
• Dynamic Height (IGLD 55, 85) Hdyn C / ?45
• ?45 Normal gravity at 45 latitude
• Orthometric Height H C / g
• g Average gravity along the plumb line
• Helmert Height (NAVD 88) H C / (g 0.0424
  H0)
• g Surface gravity measurement (mgals)

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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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Ellipsoid Heights (NAD 83 vs. ITRF 00)

• NAD 83 Origin and ellipsoid (GRS-80)
• a 6,378,137.000 meters (semi-major axis)
• 1/f 298.25722210088 (flattening)
• ITRF 00 Origin (best estimate of earths C.O.M.)
• NAD 83 is non-geocentric relative to ITRF 00
  origin by 1 - 2 meters
• ITRF 00 ellipsoid heights Use a NAD 83 shaped
  ellipsoid centered at the ITRF 00 origin
• Ellipsoid height differences between NAD 83 and
  ITRF 00 reflect the non-geocentricity of NAD 83

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Simplified Concept of ITRF 00 vs. NAD 83
h83
h00
Earths
Surface
ITRF 00
Origin
2.2 meters
NAD 83
Identically shaped ellipsoids (GRS-80) a
6,378,137.000 meters (semi-major axis) 1/f
298.25722210088 (flattening)
Origin
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North American Vertical Datum 1988(NAVD 88)

• Defined by one height (Father Point/Rimouski)
• Water-level transfers connect leveling across
  Great Lakes
• Adjustment performed in Geopotential Numbers

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Vertical Control Network NAVD 88
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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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GPS-Derived Ellipsoid HeightGuidelines

• Basic concepts
• GPS Related Error Sources
• NOAA Technical Memorandum NOS NGS-58

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San Francisco Bay Demonstration Project
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Two Days/Same Time
-10.254
gt -10.253
-10.251
Difference 0.3 cm
Truth -10.276
Difference 2.3 cm
Two Days/Different Times
-10.254
gt -10.275
-10.295
Difference 4.1 cm
Truth -10.276
Difference 0.1 cm
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Precision With CORS

• How GPS positioning is affected by baseline
  length
• Varying length baselines formed from 19 CORS
• Dual Frequency Geodetic Receivers
• Post-Processed with a Precise Orbits
• Pairs of CORS sites forming 11 Baselines
• Baseline lengths ranging from 26 to 300 km
• Various Observation Session Durations (1, 2, 4,
  6, 8, 12, and 24 hours)

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Recommendations to GuidelinesBased on These Tests

• Must repeat base lines
• Different days
• Different times of day
• Detect, remove, reduce effects due to multipath
  and having almost the same satellite geometry
• Must FIX integers
• Base lines must have low RMS values, i.e., lt 1.5
  cm

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Available On-Line at the NGS Web
Site www.ngs.noaa.gov
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Primary or SecondaryStation Selection Criteria

• 1. HPGN / HARN either FBN or CBN or CORS
• Level ties to A or B stability bench marks during
  this project
• 2. Bench marks of A or B stability quality
• Or HPGN / HARN previously tied to A or B
  stability BMs
• Special guidelines for areas of subsidence or
  uplift

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Physically Monumented Points
Stainless steel rod driven to refusal
Poured in place concrete post
Disk in outcrop
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Four Basic Control Requirements

• BCR-1 Occupy stations with known NAVD 88
  orthometric heights
• Stations should be evenly distributed throughout
  project
• BCR-2 Project areas less than 20 km on a side,
  surround project with NAVD 88 bench marks
• i.e., minimum number of stations is four one in
  each corner of project
• BCR-3 Project areas greater than 20 km on a
  side, keep distances between GPS-occupied NAVD 88
  bench marks to less than 20 km
• BCR-4 Projects located in mountainous regions,
  occupy bench marks at base and summit of
  mountains, even if distance is less than 20 km

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Equipment Requirements

• Dual-frequency, full-wavelength GPS receivers
• Required for all observations greater than 10 km
• Preferred type for ALL observations regardless of
  length
• Geodetic quality antennas with ground planes
• Choke ring antennas highly recommended
• Successfully modeled L1/L2 offsets and phase
  patterns
• Use identical antenna types if possible
• Corrections must be utilized by processing
  software when mixing antenna types

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Data Collection Parameters

• VDOP lt 6 for 90 or longer of 30 minute session
• Shorter session lengths stay lt 6 always
• Schedule travel during periods of higher VDOP
• Session lengths gt 30 minutes collect 15 second
  data
• Session lengths lt 30 minutes collect 5 second
  data
• Track satellites down to 10 elevation angle

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Appendix B. - - GPS Ellipsoid Height Hierarchy
HARN or CORS Control Stations (75 km) Primary
Base (40 km) Secondary Base (15 km) Local
Network Stations (7 to 10 km)
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Primary Base Stations

• Basic Requirements
• 5 Hour Sessions / 3 Days
• Spacing between PBS cannot exceed 40 km
• Each PBS must be connected to at least its
  nearest PBS neighbor and nearest control station
• PBS must be traceable back to 2 control stations
  along independent paths i.e., base lines PB1 -
  CS1 and PB1 - PB2 plus PB2 - CS2, or PB1 - CS1
  and PB1 - PB3 plus PB3 - CS3

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Secondary Base Stations

• Basic Requirements
• 30 Minute Sessions / 2 Days /Different times of
  day
• Spacing between SBS (or between primary and SBS)
  cannot exceed 15 km
• All base stations (primary and secondary) must
  be connected to at least its 2 nearest primary or
  secondary base station neighbors
• SBS must be traceable back to 2 PBS along
  independent paths i.e., base lines SB1 - PB1
  and SB1 - SB3 plus SB3 - PB2, or SB1 - PB1 and
  SB1 - SB4 plus SB4 - PB3
• SBS need not be established in surveys of small
  area extent

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Local Network Stations

• Basic Requirements
• 30 Minute Sessions / 2 Days / Different times of
  the day
• Spacing between LNS (or between base stations and
  local network stations) cannot exceed 10 km
• All LNS must be connected to at least its two
  nearest neighbors
• LNS must be traceable back to 2 primary base
  stations along independent paths i.e., base
  lines LN1 - PB1 and LN1 - LN2 plus LN2 - SB1 plus
  SB1 - SB3 plus SB3 - PB2, or LN1 - PB1 and LN1 -
  LN3 plus LN3 - SB2 plus SB2 - SB4 plus SB4 - PB3

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Sample Project Showing Connections
CS2
CS1
LN4
LN3
LN1
LN2
PB2
PB1
SB2
LN5
SB1
SB3
SB5
SB4
PB4
PB3
CS3
CS4
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East Bay Project Points
3816N
CORS HARN NAVD88 BM New Station Spacing Station
D191
TIDD
10LC
X469
Primary Base Station
MONT
Z190
DROU
BM20
Q555
LATITUDE
04KU
CATT
TOLA
TIDE
5144
ZINC
8.2km
PT14
R100
P371
04HK
LAKE
MART
3755N
12140W
12220W
LONGITUDE
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Primary Base Stations
3820N
CORS HARN NAVD88 BM New Station
D191
10CC
19.0km
Primary Base Station
28.7km
25.7km
LATITUDE
38.3km
31.6km
38.7km
25.8km
LAKE
MART
29.6km
MOLA
3750N
12235W
12140W
LONGITUDE
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Observation Sessions
3816N
Session F
Session E
CORS HARN NAVD88 BM New Station Spacing Station
Session D
Primary Base Station
Session G
LATITUDE
Session A
Session C
Session B
3755N
12140W
12220W
LONGITUDE
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Independent Base Lines
3816N
F
CORS HARN NAVD88 BM New Station Spacing Station
F
E
F
E
G
D
Primary Base Station
E
F
E
D
LATITUDE
D
G
D
G
G
C
B
A
C
A
A
B
8.2km
B
A
C
C
B
3755N
12140W
12220W
LONGITUDE
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Observation Schedule
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Basic Concept of Guidelines

• Stations in local 3-dimensional network connected
  to NSRS to at least 5 cm uncertainty
• Stations within a local 3-dimensional network
  connected to each other to at least 2 cm
  uncertainty
• Stations established following guidelines are
  published to centimeters by NGS

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NSRS benchmarks in Illinois
13,515 benchmarks remain in NGS database
28 reported as good in last 10 years
About 50 are probably still usable
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Benchmark availability

• There are 3881 Benchmarks in the NGSIDB for
  Alaska
• 663,268 sq mi
• Compared to 13,515 for Illinois
• 57,918 SQ. MI

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CORSNetwork February 2010
1445 Stations So far added 50 (green
dots) CORS reprocessing on track. All data back
to 1995 re-processed
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CORSNetwork February 2010
Another 17 PBO sites will be added next week
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Horizontal Velocity Map HTDP Version 3.0
aaaaaaaaaa
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Test of Alaska secular field
Measurements Freymuller 2008
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New Alaska data for HTDP, v 3.0includes
dislocation model for the 2002 Denali earthquake
Source Elliott, J. L., Freymueller J. T., and
Rabus B. (2007), Coseismic deformation of the
2002 Denali fault earthquake Contributions from
synthetic aperture radar range offsets, J.
Geophys. Res., 112, B06421, doi10.1029/2006JB0044
28.
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Multi-year CORS reprocessing Vertical
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IGA Crustal deformation for the midwest
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Crustal motion in Central Alaska
Alaska is subject to tectonic forces Causing
horizontal and vertical changes with time The
vertical changes particularly are a challenge for
height modernization activities in the
state Crustal motion data from Freymuller
2009 Uplift data Larsen Pers .Com . 2009