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GPS-Derived Orthometric Heights Part1

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					GPS Heights Primer


 •Chris Pearson1

 •1National Geodetic Survey
 2300 South Dirksen Pkwy
 Springfield IL
   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?
             Ellipsoid, Geoid, and Orthometric Heights
                                “h = H + N”
                                                            P
        Ellipsoid                                                    Plumb Line
                                                           h



Mean                                                            N
Sea                                                                    “Geoid”
Level
                                                                PO



                     h (Ellipsoid Height) N (Geoid Height) H (Orthometric Height)
   Ocean




                    Mass excess                          Mass deficiency
                In Search of the Geoid…




Courtesy of Natural Resources Canada www.geod.nrcan.gc.ca/index_e/geodesy_e/geoid03_e.html
    Leveled Height Differences




               B                     Topography


A
                                 C
 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

               P


            0
                g dn  W            0    WP  C P
   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

                                 b
              ΔCb-a   h i g i
                                 a
   Heights Based on Geopotential Number (C)

• Normal Height (NGVD 29)                         H* = C / 
       = Average normal gravity along plumb line
                                                      dyn
• Dynamic Height (IGLD 55, 85)                    H         = 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)
           GPS - Derived Ellipsoid Heights
               Z Axis
                                         P    (X,Y,Z) = P (,,h)
                                   h
                                             Earth’s
                                             Surface

 Zero
Meridian

                                                          Reference Ellipsoid


                                                        Y Axis
                            

                        




X Axis                          Mean Equatorial Plane
       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 earth’s 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
Simplified Concept of ITRF 00 vs. NAD 83


                                            h83
                                                   h00         Earth’s
                                                               Surface




            ITRF 00
            Origin



   NAD 83             Identically shaped ellipsoids (GRS-80)
   Origin
                      a = 6,378,137.000 meters (semi-major axis)
                      1/f = 298.25722210088 (flattening)
      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
Vertical Control Network NAVD 88
                    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,
Adjustments Considerations:                          and Refraction
•       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
      GPS-Derived Ellipsoid Height
              Guidelines

• Basic concepts

• GPS Related Error Sources

• NOAA Technical Memorandum NOS NGS-58
San Francisco Bay Demonstration Project
                                                 R 1393




  941 4873 TIDAL 17            MOLATE

                                      941 4863 TIDAL 5        BRIONE

              RV 223
                                                                                CORS
                               PT. BLUNT
  941 4819 TIDAL 32                           YACHT                             GPS Site

                941 4290 N                 941 4779 ASFB                    0    5     10
                                                    PORT 1
                             S 1320                                             KM
                                                    941 4750 TIDAL 7

                                                   M 554           CHABOT
                       U 1320
                                                           M 148
                         L 1241                                    N 1197

                                                               WINTON
Comparison of 30 Minute Solutions - Precise Orbit; Hopfield (0); IONOFREE
(30 Minute solutions computed on the hour and the half hour)
                                                                                              Two Days/Same Time
                                                                                               -10.254 > -10.253
MOLA to RV22 10.8 Km                                                                           -10.251
                                                                                               Difference = 0.3 cm
                                                          Day 264 *             Mean dh *
                 dh      Hours                    dh       minus diff Mean dh    minus diff   “Truth” = -10.276
 Day 264                          Day 265
                (m)       Diff.                  (m)      Day 265 >2    (m)      "Truth" >2   Difference = 2.3 cm
                                                           (cm) cm                (cm) cm

 14:00-14:30   -10.281   27hrs    17:00-17:30   -10.279    -0.2       -10.280     -0.5   Two Days/Different Times
 14:30-15:00   -10.278   27hrs    17:30-18:00   -10.270    -0.8       -10.274      0.2
 15:00-15:30   -10.281   27hrs    18:00-18:30   -10.278    -0.3       -10.280     -0.4       -10.254 > -10.275
 15:30-16:00   -10.291   27hrs    18:30-19:00   -10.274    -1.7       -10.283     -0.7        -10.295
 16:00-16:30   -10.274   27hrs    19:00-19:30   -10.274     0.0       -10.274      0.2       Difference = 4.1 cm
 16:30-17:00   -10.287   27hrs    19:30-20:00   -10.276    -1.1       -10.282     -0.6
 17:00-17:30   -10.279   27hrs    20:00-20:30   -10.261    -1.8       -10.270      0.6         “Truth” = -10.276
 17:30-18:00   -10.270   27hrs    20:30-21:00   -10.251    -1.9       -10.261      1.5
                                                                                               Difference = 0.1 cm
 18:00-18:30   -10.277   21hrs    15:00-15:30   -10.270    -0.7       -10.274      0.2
 18:30-19:00   -10.271   21hrs    15:30-16:00   -10.276     0.5       -10.274      0.2
 19:00-19:30   -10.277   21hrs    16:00-16:30   -10.278     0.1       -10.278     -0.2
 19:30-20:00   -10.271   21hrs    16:30-17:00   -10.286     1.5       -10.279     -0.3
 20:00-20:30   -10.259   18hrs    14:00-14:30   -10.278     1.9       -10.269      0.7
 20:30-21:00   -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
             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)
             Up rms Relative to Distance
                     Mean rms - 10 Days of Observation
           0.030




                                                                      ( m e te r s )
rm s U p




           0.020


           0.010


           0.000
                25    50    75 100 125 150 175 200 225 250 275 300
                              Baseline Length (kilometers)


                   4 Hrs.     6 Hrs.    8 Hrs.    12 Hrs.    24 Hrs
        Recommendations to Guidelines
            Based 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., < 1.5 cm
NOAA Technical Memorandum NOS NGS-58                                                    Available On-Line at
GUIDELINES FOR ESTABLISHING GPS-DERIVED ELLIPSOID HEIGHTS
(STANDARDS: 2 CM AND 5 CM)
                                                                                         the NGS Web Site:
VERSION 4.3

                                                                                         www.ngs.noaa.gov
David B. Zilkoski
Joseph D. D'Onofrio
Stephen J. Frakes




Silver Spring, MD

November 1997




U.S. DEPARTMENT OF    National Oceanic and         National Ocean   National Geodetic
COMMERCE              Atmospheric Administration   Service          Survey
                 Primary or Secondary
                Station 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
                      Physically Monumented
                               Points




Stainless steel rod
driven to refusal




                              Poured in place
Disk in outcrop
                               concrete post
             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
             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
             Data Collection Parameters

• VDOP < 6 for 90% or longer of 30 minute session
    Shorter session lengths stay < 6 always
    Schedule travel during periods of higher VDOP


• Session lengths > 30 minutes collect 15 second data
      Session lengths < 30 minutes collect 5 second data

• Track satellites down to 10° elevation angle
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)
                    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
                    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
                       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
      Sample Project Showing Connections
                                                             CS2
CS1
                                                 LN4
             LN1                     LN3
                         LN2                           PB2
       PB1

             SB1               LN5         SB2




                               SB3


                                       SB5
                   SB4
       PB3                                             PB4


CS3                                                          CS4
                                  East Bay Project Points
38°16’N
          CORS
          HARN                                    TIDD             D191
          NAVD’88 BM
          New Station             10LC
          Spacing Station
           Primary Base Station
                                                          MONT            X469        Z190
                                                                                                   DROU
                                          BM20
                                                                        Q555

                                         04KU
                                                                               CATT             TOLA
                                     TIDE          5144

                                          ZINC
                            PT14                                          R100
                                                                 P371
                                                                                                04HK

                                           MART                                          LAKE

    122°20’W                                        LONGITUDE                                     121°40’W
                               Primary Base Stations
38°20’N
               CORS
               HARN
               NAVD’88 BM                              D191
               New Station               10CC

               Primary Base Station




                                                              LAKE
                                                MART
                         MOLA




    122°35’W                           LONGITUDE                     121°40’W
                                    Observation Sessions
38°16’N
          CORS          Session F
                                                             Session E
          HARN
          NAVD’88 BM                                                     Session D
          New Station
          Spacing Station
           Primary Base Station




                Session G




                  Session A
                                                                         Session C
                                                 Session B
    122°20’W                               LONGITUDE                          121°40’W
                                  Independent Base Lines
38°16’N                                                               F
          CORS
                                              F
          HARN
                                                                                  E
          NAVD’88 BM                                          F
          New Station
          Spacing Station                                                                     E
                                          G                                                               D
           Primary Base Station
                                                      F                   E           E



                                                                                                                  D
                                                                                          D
                                      G
                                                                                                      D
                                              G
                                      G
                                                                                              C
                                                                  B
                                  A           A                                                               C

                                      A
                                                  B
                                                                              B
                                      A                                                           C
                                                                                                          C
                                                          B



    122°20’W                                              LONGITUDE                                               121°40’W
Observation Schedule
           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
 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
 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
  CORS
 Network
 February
   2010


~1445 Stations

So far added
~50 (green dots)

CORS
reprocessing
on track.
All data back to
1995 re-
processed
  CORS
 Network
 February
   2010


Another 17 PBO
sites will be added
next week
                              Horizontal Velocity Map
                                HTDP Version 3.0




NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION
National Ocean Service
                            aaaaaaaaaa
National Geodetic Survey
                                            Positioning America for the Future
      Test of Alaska secular
               field




Measurements Freymuller 2008
             New Alaska data for HTDP, v 3.0
includes 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, doi:10.1029/2006JB004428.
Multi-year CORS reprocessing
           Vertical
IGA Crustal deformation for the midwest
                                           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

				
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