GPS Heights Primer Chris Pearson 1 1 National Geodetic Survey 2300 South Dirksen Pkwy Springfield IL

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

Ellipsoid, Geoid, and Orthometric Heights “Geoid” Earth’s Surface Ocean Mean Sea Level POPO P Plumb Line Mass excess Mass deficiency Ellipsoid N h N “h = H + N” H (Orthometric Height) N (Geoid Height) h (Ellipsoid Height)

In Search of the Geoid… Courtesy of Natural Resources Canada

Leveled Height Differences A C B Topography

All Heights Based on Geopotential Number (C P ) The geopotential number is the potential energy difference between two points g = local gravity W O = potential at datum (geoid) W P = 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

Heights Based on Geopotential Number (C) Normal Height (NGVD 29)H* = C /    = Average normal gravity along plumb line Dynamic Height (IGLD 55, 85) H dyn = C /  45   45 = Normal gravity at 45° latitude Orthometric HeightH = C / g  g = Average gravity along the plumb line Helmert Height (NAVD 88) H = C / (g H 0 )  g = Surface gravity measurement (mgals)

GPS - Derived Ellipsoid Heights  Z Axis X Axis Y Axis (X,Y,Z) = P ( ,,h) h Earth’s Surface Zero Meridian Mean Equatorial Plane Reference Ellipsoid P

Ellipsoid Heights (NAD 83 vs. ITRF 00) NAD 83:Origin and ellipsoid (GRS-80)  a = 6,378, meters (semi-major axis)  1/f = (flattening) ITRF 00:Origin (best estimate of earth’s C.O.M.) NAD 83 is non-geocentric relative to ITRF 00 origin by 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 meters NAD 83 Origin ITRF 00 Origin Earth’s Surface h 83 h 00 Identically shaped ellipsoids (GRS-80) a = 6,378, meters (semi-major axis) 1/f = (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 (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

GPS-Derived Ellipsoid Height Guidelines Basic concepts GPS Related Error Sources NOAA Technical Memorandum NOS NGS-58

San Francisco Bay Demonstration Project CORS GPS Site BRIONE CHABOT WINTON MOLATE PT. BLUNT L 1241 U 1320 S N TIDAL 32 RV TIDAL TIDAL 5 R 1393 YACHT N 1197 M 148 M TIDAL 7 PORT ASFB KM

Two Days/Same Time > Difference = 0.3 cm “Truth” = Difference = 2.3 cm Two Days/Different Times > Difference = 4.1 cm “Truth” = Difference = 0.1 cm

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)

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

Available On-Line at the NGS Web Site:

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

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

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

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

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 CS1 PB2 SB2 LN4 LN3 LN2 LN5 LN1 SB1 SB3 SB5 SB4 PB4 PB1 PB3 CS2 CS4 CS3

38°16’N CORS HARN NAVD’88 BM New Station Spacing Station 121°40’W 122°20’W 37°55’N LATITUDE LONGITUDE Primary Base Station 8.2km 10LC TIDD D191 MONT X469 Z190 DROU BM20 04KU TIDE ZINC PT14 MART 5144 P371 R100 LAKE 04HK CATT Q555 TOLA East Bay Project Points

Primary Base Stations CORS HARN NAVD’88 BM New Station 121°40’W 122°35’W 37°50’N 38°20’N LATITUDE LONGITUDE Primary Base Station MOLA MART LAKE 10CC D km 25.8km 38.7km 19.0km 28.7km 25.7km 38.3km 31.6km

CORS HARN NAVD’88 BM New Station Spacing Station 121°40’W 122°20’W 37°55’N 38°16’N LATITUDE LONGITUDE Primary Base Station Session A Session B Session C Session D Session E Session F Session G Observation Sessions

CORS HARN NAVD’88 BM New Station Spacing Station 121°40’W 122°20’W 37°55’N 38°16’N LATITUDE LONGITUDE Primary Base Station 8.2km Independent Base Lines A A A A B B B B C C C C D D D D E E E E F F F F G G G G

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

13,515 benchmarks remain in NGS database 28 % reported as “good” in last 10 years NSRS benchmarks in Illinois 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

Positioning America for the Future NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION National Ocean Service National Geodetic Survey aaaaaaaaaa Horizontal Velocity Map HTDP Version 3.0

Test of Alaska secular field Measurements Freymuller 2008

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: /2006JB New Alaska data for HTDP, v 3.0 includes dislocation model for the 2002 Denali earthquake

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