GPS-Derived Orthometric Heights

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Height Determination Methods In Subsidence Areas

• NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION
• National Geodetic Survey

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• Subsidence
• Areas

• Questionable
• Elevation Data

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Hurricane Ike - 2008
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No Reference Marks!
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• DIFFERENCE OF 3.1 FEET !!

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Difference of 0.9 meter (2.95 feet) !
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DSWorld in Google Earth
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GPS Derived Heights Planning And Evaluating a GPS
Vertical Survey

• NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION
• National Geodetic Survey

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Topics To Be Discussed

• Review of heights and accuracies
• A Guide for Establishing GPS-derived Orthometric
  Heights
• Sample project following NGS guidelines
• Discussion on base line processing and analysis
  of repeat base line results
• Discussion of adjustment procedures and analysis
  of results
• NGS web site and services

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Ellipsoid, Geoid, and Orthometric Heights
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GPS - Derived Ellipsoid Heights
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GEOID2009 (BETA)
GEOID2003
For the conterminous United States (CONUS),
GEOID2003 heights range from a low of -52
meters (magenta) in the Atlantic Ocean to a high
of -5 meters (red) in northwest Wyoming.
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Expected Accuracies

• GPS-Derived Ellipsoid Heights
• 2 centimeters (following the guidelines)
• Geoid Heights (GEOID99)
• 2.5 cm correlated error (randomizing at 40 km)
• Relative differences typically less than 1 cm in
  10 km
• 4.6 cm RMS about the mean
• Leveling-Derived Heights
• Less than 1 cm in 10 km for third-order leveling

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Recommendations to Guidelines Based on Tests and
Sample Projects

• 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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Table 1. -- Summary of Guidelines
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Sample Project Showing Connections
CS2
CS1
LN4
LN3
LN1
LN2
PB2
PB1
SB2
LN5
SB1
LN7
LN6
SB3
SB5
SB4
PB4
PB3
CS3
CS4
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A Guide for Establishing GPS-Derived
Orthometric Heights (Standards 2 cm and 5 cm)
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A Guide for Establishing GPS-Derived Orthometric
Heights(Standards 2 cm and 5 cm)
3-4-5 System

• Three Basic Rules
• Four Basic Control Requirements
• Five Basic Procedures

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Three Basic Rules

• Rule 1
• Follow NGS guidelines for establishing
  GPS-derived ellipsoid heights (Standards 2 cm
  and 5 cm)
• Rule 2
• Use latest National Geoid Model, i.e., GEOID99
• Rule 3
• Use latest National Vertical Datum, i.e., NAVD 88

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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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BCR Example
BCR1 Sketch indicates that the 20 km rule was
met.
BCR2 This requirement is not applicable because
the project is greater than 20 km on a side.
BCR3 Circled bench marks are mandatory.
Analysis must indicate bench marks have
valid NAVD 88 heights. Other BMs can be
substituted but user must adhere to 20 km
requirement.
BCR4 This requirement is not applicable because
project is not in a mountainous region.
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Five Basic Procedures

• BP-1 Perform 3-D minimum-constraint least
  squares adjustment of GPS survey project
• Constrain 1 latitude, 1 longitude, 1 orthometric
  height
• BP-2 Analyze adjustment results from BP-1
• Detect and remove all data outliers

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BP2 After performing minimum constraint
adjustment, plot ellipsoid height residuals (or
dU residuals) and investigate all residuals
greater than 2 cm.
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BP2 Station pairs with large residuals, i.e.,
greater than 2.5 cm, also have large repeat base
line differences. NGS guidelines for estimating
GPS-derived ellipsoid heights require user to
re-observe these base lines. Following NGS
guidelines provides enough redundancy for
adjustment process to detect outliers and apply
residual on appropriate observation, i.e., the
bad vector.
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Five Basic Procedures(continued)

• BP-3 Compute differences between GPS-derived
  orthometric heights from minimum-constraint
  adjustment in BP-2 and published NAVD88 BMs

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BP3 All height differences are under 5 cm and
most are less than 2 cm. Almost all relative
height differences between adjacent station pairs
are less than 2 cm. However, most of the height
differences appear to be positive relative to the
southwest corner of the project.
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Five Basic Procedures(continued)

• BP-4 Determine which BMs have valid NAVD88
  height values from results from BP-3
• Differences need to agree 2 cm for 2 cm survey
• Differences need to agree 5 cm for 5 cm survey
• May detect systematic tilt over large areas
• Solve for geoidal slope and scale
• BP-5 Perform constrained adjustment with results
  from BP-4
• Constrain 1 latitude, 1 longitude, all valid
  orthometric height values
• Ensure final heights not distorted in adjustment

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BP4 To detect and remove any systematic trend, a
tilted plane is best fit to the height
differences (Vincenty 1987, Zilkoski and Hothem
1989). After a trend has been removed, all the
differences are less than /- 2 cm except for one
and almost all relative differences between
adjacent station are less than 2 cm.
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BP5 After rejecting the largest height
difference (-2.4 cm), of all the closely spaced
station pairs only 3 are greater than 2 cm, 1 is
greater than 2.5 cm and none are greater than 3
cm.
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GPS-Derived Orthometric Heights

• Recent Articles in ACSM SALIS Vol. 58, No.1
  (March 1998) and SALIS Vol. 58, No. 2 (June
  1998)
• Accuracy of GPS-derived Orthometric Heights in
  San Diego County, California by Wesley Parks
• An Evaluation of GPS-derived Orthometric Heights
  for First-Order Horizontal Control Surveys by
  Daniel J. Martin
• Baltimore County, Maryland, NAVD 88 GPS-Derived
  Orthometric Height Project by William E. Henning,
  Edward E. Carlson, and David B. Zilkoski
• NAVD88 GPS-derived Orthometric Heights, Parts 1
  to 4
• by David B. Zilkoski, P.O.B. Magazine, Mar.
  to Sept. 2001

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• Data Processing and Analysis
• of Repeat Base Line Results

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Vector Processing Controls

• Elevation Mask - 15 degrees
• Ephemeris - Precise
• Tropospheric Correction Model
• Iono Corrections - All baselines longer than 5
  km.
• Fix Integers
• Baselines less than 5 km L1 fixed solution
• Baselines greater than 5 km Iono free (L3)
  solution
• Looking for RMS - Less than 1.5 cm

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Analysis of the Data Processing

• Fixed solutions / low RMS
• Repeatability of measurements
• Analysis of loop misclosures
• Be aware that repeatability and loop misclosures
  do not disclose all problems

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Repeat Vector Analysis
From To Session dh Diff
Dist RMS Solution

Station Station
Meters cm Meters Type BR13
BR14 0780-0780 45.974 1628
0.016 L1 float double
0770-0770 46.004 -3.0 0.017 L1
fixed double 0761-0762
46.009 -3.5 0.015 L1 fixed double
BR13 K251 0780-0780 -12.397
673 0.006 L1 fixed double
0770-0770 -12.400 0.3 0.006 L1
fixed double 0762-0761
-12.408 1.1 0.006 L1 fixed double
BR14 GR15 0780-0780 43.680
1133 0.022 L1 fixed double
0770-0770 43.654 2.6 0.024 L1
fixed double 0762-0765
43.607 7.3 0.020 L1 fixed double
BR19 CL20 0781-0781 54.703
365 0.047 L1 fixed double
0771-0771 55.031 -32.8 0.022 L1
fixed double 0762-0763
55.007 -30.4 0.019 L1 fixed double
BR20 BR30 0782-0782 28.939
9850 0.014 Iono free fixed
0772-0772 28.947 -0.8 0.014 Iono
free fixed 0760-0763 28.940
-0.1 0.020 Iono free fixed BR20
VINT HILL 0782-0782 33.045 11967
0.011 Iono free fixed
0772-0772 33.051 -0.6 0.009 Iono
free fixed 0760-0763 33.063
-1.8 0.013 Iono free fixed NOTE -
Reprocess all vectors which have difference
greater than 2 cm.
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Repeat Vector Analysis After Re-Processing
From To Session dh Diff
Dist RMS Solution

Station Station
Meters cm Meters Type BR13
BR14 0761-0762 46.009 1628
0.015 L1 fixed double
0770-0770 46.004 0.5 0.017 L1
fixed double 0780-0780
46.007 0.2 0.015 L1 fixed double
BR13 K251 0770-0770 -12.400
673 0.006 L1 fixed double
0780-0780 -12.397 -0.3 0.006 L1
fixed double 0762-0761
-12.408 0.8 0.006 L1 fixed double
BR14 GR15 0780-0780 43.680
1133 0.022 L1 fixed double
0765-0762 43.658 2.2 0.020 L1
fixed double 0770-0770
43.654 2.6 0.024 L1 fixed double
BR19 CL20 0771-0771 55.031
365 0.022 L1 fixed double
0781-0781 55.027 0.4 0.023 L1
fixed double 0762-0763
55.019 1.2 0.018 L1 fixed double
BR20 BR30 0782-0782 28.939
9850 0.014 Iono free fixed
0772-0772 28.947 -0.8 0.014 Iono
free fixed 0760-0763 28.940
-0.1 0.020 Iono free fixed BR20
VINT HILL 0782-0782 33.045 11967
0.011 Iono free fixed
0760-0763 33.063 -1.8 0.013 Iono
free fixed 0772-0772 33.051
-0.6 0.009 Iono free fixed
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• Adjustment Procedures to Obtain
• GPS-Derived NAVD88
• Orthometric Heights

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Adjustment of 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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Adjustment ProceduresControl and Primary Base
Stations

• Horizontal Adjustment
• (Latitude, Longitude, Ellipsoid Heights)
• Minimum Constrained One fixed station
• Fix latitude, longitude and ellipsoid height at
  one station
• Resolve all blunders and large residuals
• Determine which published coordinates should be
  fixed
• Partially Constrained All suitable stations
  fixed
• Fix latitude, longitude, and ellipsoid heights at
  suitable stations
• Make sure the constraints did not distort the
  project
• NOTE - Geoid model NOT applied

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Adjustment of Local Network Stations
CORS HARN NAVD88 BM New Station Spacing Station
3816N
Primary Base Station
LATITUDE
8.2km
3755N
12140W
12220W
LONGITUDE
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Adjustment ProceduresLocal Network Stations

• Horizontal Adjustment
• (Latitude, Longitude, Ellipsoid Heights)
• Minimum Constrained One fixed station
• Fix latitude, longitude and ellipsoid height at
  one station
• Resolve all blunders and large residuals
• Determine which control and primary base station
  coordinates should be fixed
• Partially Constrained All suitable stations
  fixed
• Fix latitude, longitude, and ellipsoid heights at
  suitable stations
• Make sure the constraints did not distort the
  project
• NOTE - Geoid model NOT applied

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Adjustment ProceduresCombined Network Horizontal
Adjustment

• Perform combined adjustment
• Control and primary base network along with local
  network
• Latitude, longitude, and ellipsoid height
• Use GEOID model to obtain geoid heights
• Make sure combined adjustment did not distort the
  project

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Adjustment ProceduresCombined Network Vertical
Adjustment

• 3-D Vertical Adjustment
• (Orthometric Heights)
• Minimum Constrained One fixed station
• Fix latitude, longitude, and orthometric height
  at one station
• Resolve all blunders and large residuals
• Determine which NAVD 88 bench marks should be
  fixed
• Partially Constrained All suitable orthometric
  heights fixed
• Fix latitude, longitude at one station
• Fix orthometric heights at all suitable stations
• Make sure the constraints did not distort the
  project

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Real World
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Mapping World
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GPS Site Calibration

• Four parameter coordinate transformations
• Perform scaling, translation, and rotation of
  coordinate axes
• Transformation from one system to another
• x? s cos?x s sin?y tx
• y? s sin?x s cos?y ty
• Where s is scale factor
• x and y are coordinates from original system
• x? and y? are coordinates of point in transformed
  system
• ? is rotation angle from original to transformed
  system
• tx and ty are components of translation from
  original to transformed system

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GPS Site Calibration

• GPS leveling by the two-plane method
• Provides reasonable accuracy over limited areas
• Assumes the ellipsoid and geoid as plane surfaces
• Relation of geoid with respect to ellipsoid
• (Hi hi) ?E(Ni No) ?N(Ei Eo) tZ
• (Hi hi) is vertical shift form ellipsoid to
  geoid at point i
• ?E and ?N are rotations about north and east
  axes, respectively, of the geoid plane with
  respect to the ellipsoid plane
• No and Eo are approximate coordinates of centroid
  of project area
• Ni and Ei are plane coordinates about point i
• tZ is vertical shift at centroid

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GPS Site Calibration

• Surround project with at least four stations
• Each with known ellipsoid and orthometric
• Bound project area, ideally in corners
• Rough terrain may require additional control
• Initialize and calibrate GPS on known control
• Calibration requirements are equipment specific
• Compute best fit model for project area

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Existing GPS-Usable Stations
GABB
HARN2
HARN1
CORS HARN NAVD88 BM
HARN3
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GPS-Usable and New Stations
GABB
HARN2
HARN1
CORS HARN NAVD88 BM Project Control (new)
HARN3
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Project Control (Base) Stations
Project Control
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Rapid Static Survey
BASE2
BASE1
Project Control (base station)
Stop and Go Point
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Calibrated Real Time Survey
BASE1
Project Control (base station)
Stop and Go Calibration Point
Stop and Go Point
Continuous Point
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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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• Importance of Shoreline

• AL, AK, CA, CT, FL, GA, LA, MD, MS, NJ, NY, NC,
  OR, RI, SC, WA and TX (post-1836)

• Territorial Seas

• Privately Owned
• Uplands

• State Owned
• Tidelands

• Contiguous Zone

• Exclusive Economic Zone

• State Submerged Lands

• Federal Submerged Lands

• High Seas

• 3 n. mi.

• 12 n. mi.

• MHHW

• 200 n. mi.

• MHW

• MLLW

• Chart Datum

• Privately
• Owned

• State
• Owned

• Privately
• Owned

• State
• Owned

• TX pre--1836

• DE, MA, ME, NH, PA, VA

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Precise Digital Leveling
National Oceanic and Atmospheric
Administration National Geodetic Survey
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• Rigid Leg Tripod
• With Thermister
• Equipment

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• Single-Piece, Bar-Coded Invar, Calibrated Rod
  with Brace Poles

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• Leveling rods must be one piece.

• According to at least one manufacturer's
  specifications, the electronic digital leveling
  instrument should not be exposed to direct
  sunlight. The manufacturer recommends using an
  umbrella in bright sunlight.

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Leveling Tips

• Always practice SAFETY FIRST!!!!
• Apparent Heat Waves reduce sight lengths
• Wind effects block wind with body place a
  light hand on tripod leg - reduce sight lengths
• Difficult to obtain standard deviation reduce
  SL
• Carry instrument upright between setups
• Check rods and instruments circular levels once
  a week to ensure theyre in adjustment
• Transfer elevation to instrument when foresight
  is ready minimize settlement
• Do not leave the instrument setup unattended
• Do not let thermistors or level get wet

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Leveling Tips (continued)

• Cross pavement (roadway) at right angles to
  minimize uneven sight conditions
• Clearly focus level instrument before measurement
• Stabilize both turning points and tripod every
  setup
• Never read below 0.5 meters on rod
• Ensure upper stadia crosshair is not above Invar
  when reading near the top of the rod
• Maintain tight setup imbalances
• Dont point the instrument into the sun
• Orchestrate setups so instrument is not pointing
  into low sun angle

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Leveling Tips (continued)

• DO NOT DROP RODS!!
• Keep one hand on rod at all times
• Keep rod faces clean do not touch Invar
• Always protect base of rod keep off ground
• Never setup rod or instrument on asphalt
• Turn rod to change shadows if measurement fails
• Rod person calls out BM designation for check
• Start and end with the same rod on mark
• Backsight rod person does not move until
  foresight has been recorded and observer directs

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Leveling Tips (continued)

• Make sure base of rod is directly on the turning
  point or BM not on centering guide
• Be aware of your surroundings carrying rod
• Spacer must have a backsight and a foresight
• Do not forget to retrieve spacer after setup
• Double run all sections
• Plan reverse leveling during a different time of
  day from the first level run
• Place visible mark on rod to indicate 0.5 m

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• FGCS Specifications and Procedures to Incorporate
  Electronic Digital/Bar-Code Leveling Systems

• NGS analysis of the data will be the final
  determination if the data meet the desired FGCS
  order and class standards

• http//www.ngs.noaa.gov/FGCS/tech_pub/Fgcsvert.v41
  .specs.pdf