Geoid Modeling and GRAV-D: Gravity for the Redefinition of the American Vertical Datum Beaumont, Texas June 8-9, 2009 Renee Shields Height Modernization Manager

Define the NSRS –“The NSRS must be more accurate than all activities which build upon it, while still being practicably achievable.” Maintain the NSRS –“NGS must track all of the temporal changes to the defining points of the NSRS in such a way as to always maintain the accuracy in the NSRS definition.” Provide Access to the NSRS –“NGS must develop and maintain guidelines for users to access the NSRS at a variety of accuracies.” –“NGS will publish all coordinates of defining points of the NSRS with an epoch tag and will furthermore publish velocities relative to that epoch-tagged set of coordinates” From the NGS 10-Year Plan

The official national coordinate system of the U.S. federal government which includes: –G–Geodetic latitude, longitude and height –S–Scale, gravity, and orientation –H–How these values change with time Components include: –N–National and Cooperative CORS –N–Network of passive monuments –O–Official national shoreline –P–Precise orbits of GNSS satellites used to define NSRS –M–Models and tools to describe how all of these quantities change over time. Mission – The NSRS is…

Science of Height mod – 3 kinds of Heights Orthometric Heights (NAVD88): Traditionally leveling Ellipsoid Heights (NAD83): GNSS Geoid Heights (NAD83): gravity and modeling

(NAVD88) H H = Orthometric Height (leveling) H = h - N TOPOGRAPHIC SURFACE h = Ellipsoidal Height (GPS) N = Geoid Height (model) h (NAD83) Ellipsoid N Geoid Geoid Height (GEOID03/09) Ellipsoid, Geoid, and Orthometric Heights

NAVD88 Heights - Conventional Leveling BM 100’ BacksightForesight ROD 2 INSTR Backsight ROD 1 Foresight ROD 1 INSTR 5’ 6’ 105’ HI 99’ 7.5’ 4.5’ 96’

enter GNSS… Can we get accurate heights with GNSS?

Guidelines to obtain accurate heights through GNSS Equipment requirements Field Procedures/Data Collection Parameters Basic Control Requirements Processing/Analysis Procedures

Equipment Requirements Dual-frequency, full-wavelength GPS receiver –Required - observations > 10 km –Preferred - 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

“Fixed” Height Tripod Equipment Requirements

Data Collection Parameters VDOP < 6 for 90% or longer of 30 minute session Session lengths and sampling rate Track satellites down to 10° elevation angle Repeat Baselines –Different days –Different times of day Detect, remove, reduce effects due to multipath and similar satellite geometry between sessions

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 >

Station pairs with large repeat base line differences also result in large residuals. NGS guidelines for estimating GPS-derived ellipsoid heights require user to re-observe these base lines.

Four Basic Control Requirements Occupy stations with known NAVD 88 orthometric heights, evenly distributed throughout project Project areas < 20 km on a side, surround project with at least 4 NAVD 88 bench marks Project areas > 20 km on a side, keep distances between GPS-occupied NAVD 88 bench marks to less than 20 km Projects located in mountainous regions, occupy bench marks at base and summit of mountains, even if distance is less than 20 km

Perform 3-D minimally constrained (free) adjustment Analyze adjustment results Compute differences between GPS-derived orthometric heights from free adjustment and published NAVD88 BMs Evaluate differences to determine which BMs have valid NAVD88 height values Perform constrained adjustment with results from previous step Processing: Five Basic Procedures

Sample Project Area: East San Francisco Bay Project – Latitude 37° 50” N to 38° 10” N –Longitude 121° 45” W to 122° 25” W Receivers Available: 5 Standards: 2 cm GPS-Derived Heights

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

GPS-Usable Stations Spacing Station Primary Base Station 8.2km CORS HARN NAVD’88 BM New Station

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 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

Texas Primary Control – CORS TXAN – San Antonio RRP2, TX TXBM – Beaumont, TX TXME – Memphis, TX

Primary Control - Texas High Accuracy Reference Network (1993)

HARN/Control Stations (75 km) 5.5 hr 3 days different times Primary Base (40 km) 5.5 hr 3 days different times Secondary Base (15 km) 0.5 hr 2 days different times Local Network Stations (7 to 10 km) 0.5 hr 2 days different times GPS Ellipsoid Height Hierarchy

Height Modernization Project = Existing NGS Level line = New HMP Level line = HARN = Primary Base Network = Secondary Base Network = Local Base Network HARN - Average 50km, max 75km Primary – 20-25km, max 40km Secondary - Average 12-15km, max 15km Local – Average 6-8 km, max 10km

1 National Geodetic Survey, Retrieval Date = JUNE 6, 2009 AC6323 *********************************************************************** AC6323 DESIGNATION - BEA5 B AC6323 PID - AC6323 AC6323 STATE/COUNTY- TX/JEFFERSON AC6323 USGS QUAD - VOTH (1993) AC6323 AC6323 *CURRENT SURVEY CONTROL AC6323 ___________________________________________________________________ AC6323* NAD 83(2007) (N) (W) ADJUSTED AC6323* NAVD (meters) (feet) ADJUSTED AC6323 ___________________________________________________________________ AC6323 EPOCH DATE AC6323 X , (meters) COMP AC6323 Y - -5,504, (meters) COMP AC6323 Z - 3,185, (meters) COMP AC6323 LAPLACE CORR (seconds) DEFLEC99 AC6323 ELLIP HEIGHT (meters) (02/10/07) ADJUSTED AC6323 GEOID HEIGHT (meters) GEOID03 AC6323 DYNAMIC HT (meters) (feet) COMP AC6323 AC Accuracy Estimates (at 95% Confidence Level in cm) AC6323 Type PID Designation North East Ellip AC AC6323 NETWORK AC6323 BEA5 B AC AC6323 MODELED GRAV- 979,314.4 (mgal) NAVD 88 AC6323 AC6323 VERT ORDER - FIRST CLASS II NGS Datasheet – Leveling

AC6323.This is a reference station for the BEAUMONT RRP AC6323.National Continuously Operating Reference Station (BEA5). AC6323 AC6323.The horizontal coordinates were established by GPS observations AC6323.and adjusted by the National Geodetic Survey in February AC6323 AC6323.The datum tag of NAD 83(2007) is equivalent to NAD 83(NSRS2007). AC6323.See National for more information. AC6323.The horizontal coordinates are valid at the epoch date displayed above. AC6323.The epoch date for horizontal control is a decimal equivalence AC6323.of Year/Month/Day. AC6323 AC6323.The orthometric height was determined by differential leveling AC6323.and adjusted in July AC6323 AC6323.Photographs are available for this station. AC6323 AC6323.The X, Y, and Z were computed from the position and the ellipsoidal ht. AC6323 AC6323.The Laplace correction was computed from DEFLEC99 derived deflections. AC6323 AC6323.The ellipsoidal height was determined by GPS observations AC6323.and is referenced to NAD 83. AC6323 AC6323.The geoid height was determined by GEOID03. AC6323.The dynamic height is computed by dividing the NAVD 88 AC6323.geopotential number by the normal gravity value computed on the AC6323.Geodetic Reference System of 1980 (GRS 80) ellipsoid at 45 AC6323.degrees latitude (g = gals.). NGS Datasheet – Leveling

AC6323.The modeled gravity was interpolated from observed gravity values. AC6323 AC6323; North East Units Scale Factor Converg. AC6323;SPC TXSC - 4,266, ,064, MT AC6323;SPC TXSC -13,998, ,491, sFT AC6323;UTM ,336, , MT AC6323 AC6323! - Elev Factor x Scale Factor = Combined Factor AC6323!SPC TXSC x = AC6323!UTM x = AC6323 AC6323 SUPERSEDED SURVEY CONTROL AC6323 AC6323 ELLIP H (10/23/00) (m) GP( ) 4 2 AC6323 NAD 83(1993) (N) (W) AD( ) B AC6323 ELLIP H (08/21/98) (m) GP( ) 5 2 AC6323 NAD 83(1993) (N) (W) AD( ) B AC6323 ELLIP H (01/23/98) (m) GP( ) 3 2 AC6323 NAVD 88 (08/21/98) (m) 43.0 (f) LEVELING 3 AC6323 NAVD 88 (01/23/98) (m) 43.5 (f) LEVELING 3 AC6323 AC6323.Superseded values are not recommended for survey control. AC6323.NGS no longer adjusts projects to the NAD 27 or NGVD 29 datums. AC6323.See file dsdata.txt to determine how the superseded data were derived. AC6323 NGS Datasheet – Leveling

AC6323_U.S. NATIONAL GRID SPATIAL ADDRESS: 15RUP (NAD 83) AC6323_MARKER: I = METAL ROD AC6323_SETTING: 59 = STAINLESS STEEL ROD IN SLEEVE (10 FT.+) AC6323_STAMPING: BEA5 B 1996 AC6323_MARK LOGO: NGS AC6323_PROJECTION: FLUSH AC6323_MAGNETIC: I = MARKER IS A STEEL ROD AC6323_STABILITY: A = MOST RELIABLE AND EXPECTED TO HOLD AC6323+STABILITY: POSITION/ELEVATION WELL AC6323_SATELLITE: THE SITE LOCATION WAS REPORTED AS SUITABLE FOR AC6323+SATELLITE: SATELLITE OBSERVATIONS - January 27, 2005 AC6323_ROD/PIPE-DEPTH: 9.9 meters AC6323_SLEEVE-DEPTH : 0.9 meters AC6323 AC6323 HISTORY - Date Condition Report By AC6323 HISTORY MONUMENTED NGS AC6323 HISTORY GOOD NGS AC6323 HISTORY GOOD JCLS AC6323 HISTORY GOOD USPSQD AC6323 AC6323 STATION DESCRIPTION AC6323 AC6323'DESCRIBED BY NATIONAL GEODETIC SURVEY 1996 (GAS) AC6323'IN BEAUMONT, AT THE INTERSECTION OF HIGHWAYS 69, 96, 287, AND CHINN AC6323'LANE, 70.6 M (231.6 FT) NORTH OF BENCH MARK W 1496, 8.3 M (27.2 FT) AC6323'EAST OF THE CENTERLINE OF THE NORTHBOUND LANES OF THE HIGHWAY, 0.7 M AC6323'(2.3 FT) NORTHEAST OF A WITNESS POST, 0.5 M (1.6 FT) EAST OF THE NORTH AC6323'END OF A GUARDRAIL, AND 0.4 M (1.3 FT) BELOW THE LEVEL OF THE HIGHWAY. NGS Datasheet – Leveling

BL0243; North East Units Scale Factor Converg. BL0243;SPC TXSC - 4,258, ,072, MT BL0243;SPC TXSC -13,972, ,519, sFT BL0243;UTM ,327, , MT BL0243 BL0243! - Elev Factor x Scale Factor = Combined Factor BL0243!SPC TXSC x = BL0243!UTM x = BL0243 BL0243 SUPERSEDED SURVEY CONTROL BL0243 BL0243 NAD 83(1993) (N) (W) AD( ) 1 BL0243 ELLIP H (03/11/02) (m) GP( ) 4 1 BL0243 NAVD 88 (03/11/02) 6.22 (m) 20.4 (f) LEVELING 3 BL0243 NGVD 29 (??/??/??) (m) (f) ADJUSTED 1 1 BL0243 BL0243.Superseded values are not recommended for survey control. BL0243.NGS no longer adjusts projects to the NAD 27 or NGVD 29 datums. BL0243.See file dsdata.txt to determine how the superseded data were derived. BL0243 BL0243 HISTORY - Date Condition Report By BL0243 HISTORY MONUMENTED NGS BL0243 HISTORY GOOD NGS BL0243 HISTORY GOOD USPSQD BL0243 HISTORY MARK NOT FOUND USPSQD BL0243 HISTORY GOOD USPSQD BL0243 HISTORY GOOD USPSQD NGS Datasheet – Leveling

1 National Geodetic Survey, Retrieval Date = APRIL 30, National Geodetic Survey, Retrieval Date = JUNE 7, 2009 AC6388 *********************************************************************** AC6388 DESIGNATION - BPT AP STA B2 AC6388 PID - AC6388 AC6388 STATE/COUNTY- TX/JEFFERSON AC6388 USGS QUAD - PORT ACRES (1993) AC6388 AC6388 *CURRENT SURVEY CONTROL AC6388 ___________________________________________________________________ AC6388* NAD 83(2007) (N) (W) ADJUSTED AC6388* NAVD (meters) 5. (feet) GPS OBS AC6388 ___________________________________________________________________ AC6388 EPOCH DATE AC6388 X , (meters) COMP AC6388 Y - -5,517, (meters) COMP AC6388 Z - 3,165, (meters) COMP AC AC6388.The orthometric height was determined by GPS observations and a AC6388.high-resolution geoid model. AC6388 AC6388.The X, Y, and Z were computed from the position and the ellipsoidal ht. AC6388 AC6388.The Laplace correction was computed from DEFLEC99 derived deflections. AC6388 NGS Datasheet - GPS Height

1 National Geodetic Survey, Retrieval Date = JUNE 6, 2009 AJ8222 *********************************************************************** AJ8222 HT_MOD - This is a Height Modernization Survey Station. AJ8222 DESIGNATION - BASELINE AJ8222 PID - AJ8222 AJ8222 STATE/COUNTY- TX/JEFFERSON AJ8222 USGS QUAD - BEAUMONT WEST (1994) AJ8222 AJ8222 *CURRENT SURVEY CONTROL AJ8222 ___________________________________________________________________ AJ8222* NAD 83(2007) (N) (W) ADJUSTED AJ8222* NAVD (meters) 36.5 (feet) GPS OBS AJ8222 ___________________________________________________________________ AJ8222 EPOCH DATE AJ8222 X , (meters) COMP AJ AJ8222 The epoch date for horizontal control is a decimal equivalence AJ8222 of Year/Month/Day. AJ8222 AJ8222.The orthometric height was determined by GPS observations and a AJ8222.high-resolution geoid model using precise GPS observation and AJ8222.processing techniques. AJ8222 AJ8222.The X, Y, and Z were computed from the position and the ellipsoidal ht. AJ8222 AJ8222.The Laplace correction was computed from DEFLEC99 derived deflections. NGS Datasheet - Height Mod GPS

1 National Geodetic Survey, Retrieval Date = JUNE 6, 2009 AC6323 *********************************************************************** AC6323 DESIGNATION - BEA5 B AC6323 PID - AC6323 AC6323 STATE/COUNTY- TX/JEFFERSON AC6323 USGS QUAD - VOTH (1993) AC6323 AC6323 *CURRENT SURVEY CONTROL AC6323 ___________________________________________________________________ AC6323* NAD 83(2007) (N) (W) ADJUSTED AC6323* NAVD (meters) (feet) ADJUSTED AC6323 ___________________________________________________________________ AC6323 EPOCH DATE AC6323 X , (meters) COMP AC6323 Y - -5,504, (meters) COMP AC6323 Z - 3,185, (meters) COMP AC6323 LAPLACE CORR (seconds) DEFLEC99 AC6323 ELLIP HEIGHT (meters) (02/10/07) ADJUSTED AC6323 GEOID HEIGHT (meters) GEOID03 AC6323 DYNAMIC HT (meters) (feet) COMP AC6323 AC Accuracy Estimates (at 95% Confidence Level in cm) AC6323 Type PID Designation North East Ellip AC AC6323 NETWORK AC6323 BEA5 B AC AC6323 MODELED GRAV- 979,314.4 (mgal) NAVD 88 AC6323 NGS Datasheet – Leveling N H h NAVD88 – Ellipsoid Ht + Geoid Ht = … – ( ) – = USGG – ( ) – = GEOID03

How accurate is a GPS-derived Orthometric Height? Relative (local) accuracy in ellipsoid heights between adjacent points will be better than 2 cm, at 95% confidence level Network accuracy (relative to NSRS) in ellipsoid and orthometric heights will be better than 5 cm, at 95% confidence level Accuracy of orthometric height is dependent on accuracy of the geoid model – Currently NGS is improving the geoid model with more data, i.e. Gravity and GPS observations on leveled bench marks from Height Mod projects

(NAVD88) H H = Orthometric Height (leveling) H = h - N TOPOGRAPHIC SURFACE h = Ellipsoidal Height (GPS) N = Geoid Height (model) h (NAD83) Ellipsoid N Geoid Geoid Height (GEOID03/09) Ellipsoid, Geoid, and Orthometric Heights ?

In Search of the Geoid… Courtesy of Natural Resources Canada Dr. Dan Roman Dr. Yan Wang

Definitions: GEOIDS versus GEOID HEIGHTS “The equipotential surface of the Earth’s gravity field which best fits, in the least squares sense, (global) mean sea level.”* Can’t see the surface or measure it directly. Can be modeled from gravity data as they are mathematically related. Note that the geoid is a vertical datum surface. A geoid height is the ellipsoidal height from an ellipsoidal datum to a geoid. Hence, geoid height models are directly tied to the geoid and ellipsoid that define them (i.e., geoid height models are not interchangeable). *Definition from the Geodetic Glossary, September 1986

LEVEL SURFACES AND ORTHOMETRIC HEIGHTS Level Surfaces Plumb Line “Geoid” POPO P Level Surface = Equipotential Surface (W) H (Orthometric Height) = Distance along plumb line (P O to P) Earth’s Surface Ocean Mean Sea Level WOWO WPWP

High Resolution Geoid Models Start with gravity measurements Add Digital Elevation Data (Continental) Add a Global Earth Gravity Model (EGM96, EGM08) Result – A purely Gravitational geoid model – good for scientific applications … But is this what we need?

To use GNSS you need a good geoid model NGS makes 2 geoid models Gravitational model: is good for scientific applications uses gravity data collected from a variety of sources “Hybrid” model: starts with gravitational model uses GPS on bench marks to enable a fit to NAVD88 GRACE Satellite Gravity

GGPSBM2003: 14,185 total 579 Canada STDEV 4.8 cm (2 σ ) GGPSBM1999: 6,169 total 0 Canada STDEV 9.2 cm (2σ)

0.876 M in Beaumont, TX– 1999 model M in Beaumont, TX – 2003 model Gravimetric Geoid systematic misfit to BM’s but best fits “true” heights Hybrid Geoid “converted” to fit local BM’s, so best fits NAVD 88 heights Conversion Surface model of systematic misfit derived from BM’s in IDB Earth’s Surface h h h h h H H H H H N N N N N Ellipsoid Hybrid Geoid Geoid Gravimetric Geoid N NN N N Gravimetric vs. Hybrid Geoid surface Note use of GPS on BMs 1.065M in Beaumont, TX– 2009 Beta model

Access to accurate, reliable heights nationally Standards that are consistent across the nation Data, technology, and tools that yield consistent results regardless of terrain and circumstances A system/process that will stand the test of time – “Maintain-able” Goal of NHMP

That was then…. In the early years of Height Mod NGS felt the Gravimetric geoid was adequate as the base for the Hybrid geoid What’s changed? Better accuracy from GNSS-derived heights – can use GNSS to monitor changes in heights Better understanding of poor condition of vertical network Gravity holdings at NGS evaluated

NGS Gravity Holdings Most of the historical NGS data is terrestrial Multiple observers, multiple processors over the past 60 years Numerous corrections and datums over time Metadata maintained in paper records Very limited aerogravity Deficit in near-shore gravity data

Ship gravity Terrestrial gravity New Orleans km gravity gaps along coast

Gravity Coverage for USGG2003/USGG2008

Is NAVD 88 “Maintainable”? NAVD88 defined through leveling network Not practical to re-leveling the country –At $3000 / km, re-leveling NAVD 88 would cost $2.25 Billion –Does not include densifying poorly covered areas in Western CONUS, Alaska –Does not include leveling needed for separate vertical datums on island states and territories Leveling yields cross-country error build-up; problems in the mountains Leveling requires leaving behind marks –Bulldozers and crustal motion do their worst

Official NGS policy as of Nov 14, 2007 –$38.5M over 10 years Airborne Gravity Snapshot Absolute Gravity Tracking Re-define the Vertical Datum of the USA by 2017 Transition to the Future – GRAV-D Gravity for the Redefinition of the American Vertical Datum

GRAV-D is the most ambitious project within the National Height Mod Program National Height Modernization needs to support the NAVD 88 while transitioning (via GRAV-D) to a new vertical datum in 10 years All National Height Mod funds (internal or grants) should support access to accurate heights, in general, but: –With emphasis on NAVD 88 today –With emphasis on the new vertical datum in 5 years

From NGS’ 10-Year Plan NGS Mission: “Modernize the Geopotential (“Vertical”) Datum “The gravimetric geoid, long used as the foundation for hybrid geoid models, becomes the most critical model produced by NGS.”

Questions Renee Shields Height Modernization Manager , x116 Dan Roman Research Geodesist , x161