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1 Geodesy, Geoids, and Vertical Datums: A Perspective from te U.S. ational Geodetic Survey Daniel R. ROMA, Yan Ming WAG, Jarir SALEH, and Xiaopeng LI Paper 3768 ational Geodetic Survey An Office wit te ational Ocean Service in te ational Oceanic and Atmosperic Administration Responsible for maintaining elements of and access to te ational Spatial Reference System including: ort American Datum of 1983 (AD 83) ort American Vertical Datum of 1988 (AVD 88) GS developed geoid eigt models for easier access GEOID90 - te earliest regional gravimetric geoid eigts USGG2009 most recent gravimetric eigts (ITRF00) GEOID09 ybrid geoid eigts (AD 83 to AVD 88) Model development paralleled evolution of GSS 2, April
2 Definitions: GEOIDS versus GEOID HEIGHTS Te equipotential surface of te Eart s gravity field wic best fits, in te least squares sense, (global) mean sea level. * Can t see te surface or measure it directly. Can be modeled from gravity data as tey are matematically related. ote tat te geoid is a vertical datum surface. A geoid eigt is te ellipsoidal eigt from an ellipsoidal datum to a geoid. Hence, geoid eigt models are directly tied to te geoid and ellipsoid tat define tem (i.e., geoid eigt models are not intercangeable). *Definition from te Geodetic Glossary, September Relationsip between ellipsoid, geoid and ortometric eigts. Mean Sea Level Ellipsoid + H DoV GEOID HEIGHT OR UDULATIO P Q P O Plumb Line Geoid Ocean (Ellipsoid Heigt) = Distance along ellipsoid normal (Q to P) (Geoid Heigt) = Distance along ellipsoid normal (Q to P O ) H (Ortometric Heigt) = Distance along plumb line (P O to P) 4, April
3 Model Development USGG2009 Ellipsoid: ITRF00/GRS-80 Base Model: EGM2008 Gravity Data: 2.1 million Kernel: mod. (120/6 ex. AK) DEM: SRTM 3 (except AK) Terrain: EGM08 implicit 5 Altimetry: DSC08 Metod: R-C-R Format: 1 grid/1-line eader USGG2003 ITRF00/GRS-80 EGM million unmodified mixed 30 /3 (PW) TC s GSFC00.1 R-C-R 1 grid/1-line eader 5 GEOID09 Development Starts from USGG2009 model Convert to AD 83 (SRS2007, PAC00, MAR00) USGG2009 TOITRF00 => USGG2009* Interpolate at GPSBM locations Residual = (AD83) H(AVD88) (USGG2009*) Use MMLSC to generate mat model to fit residuals Use same mat model to predict on even grid (15 ) Interpolate grid to 1 Conv. Surf. = 1 grid + bias + trend + TOITRF00 GEOID09 = USGG2009 Conversion Surface 6, April
4 Hybrid Geoids Eart s Surface H Ellipsoid H H H H Hybrid Geoid =~ AVD 88 Gravimetric Geoid systematic misfit wit bencmarks Hybrid Geoid biased to fit local bencmarks e = H - GS Gravimetric Geoid 7 ote tat te ITRF00-AD83 transformation is not included ere Tis was neglected to igligt te significant systematic features 8, April
5 Te GS Ten Year Plan Calls for replacing bot AD 83 and AVD 88 Bot ave significant (meter level) systematic errors AD 83 replacement needs to be more geocentric AVD 88 replacement needs to be a geoid surface Bot new datums would work togeter CORS/OPUS tools to access GSS coordinates Geoid eigt model determines ortometric eigts Goal of cm-level accuracy in non-mountainous areas Targeted timeline is for end of next decade (~2018) Wy do all tis? Is tere really a need? 9 Simplified Concept of ITRF 00 vs. AD Eart s Surface ITRF 00 Origin AD 83 Origin Identically saped ellipsoids (GRS-80) a = 6,378, meters (semi-major axis) 1/f = (flattening) 10, April
6 Positional Sifts of Geocenter: AD 83 to ITRS Realizations Relative to Epoc Sift from AD83 to ITRF00 in Ellipsoid Heigts (meters) Reference Frame X Sift (m) Y Sift (m) Z Sift (m) Total Sift (m) ITRF ITRF ITRF ITRF ITRF ITRF otes: Used HTDP for transformations (ttp:// Relative cange in coordinates for last two models is at millimeter level (quasi-stable) Determination of a gravimetric geoid is made using a geocentric ellipsoid (KISS) 11 Vertical Control etwork AVD ,000 BM s over 1,001,500 km 12, April
7 GPSBM2009 (GEOID09 Control Data) total less 1003 rejected leaves 18,867 (COUS) plus 576 (Canada) 13 Wy isn t AVD 88 good enoug anymore? Approximate level of error known to exist in te AVD 88 zero elevation surface 14, April
8 Possible ways to fix AVD 88 Long term fix: Re-level some/all of AVD 88 81,500 km of 1 st order leveling at least 625,000 km of mixed 1 st and 2 nd order leveling About $3000 / km (average contract cost) Re-leveling AVD 88 would cost between $200 Million and $2 Billion Tis wouldn t fix all of te problems associated wit te use of benc marks toug 15 Possible ways to fix AVD 88 Long term fix: Replace AVD 88 Find a metod of defining a vertical datum tat seeks to fix all of te known issues wit AVD 88 Best option: Define te datum as a given geoid eigt model and realize it troug GSS tecnology GRAV-D 16, April
9 Wat is GRAV-D? Official GS policy as of ov 14, 2007 $38.5M over 10 years Airborne Gravity Snapsot Absolute Gravity Tracking Re-define te Vertical Datum of te USA by 2018 (if fully funded beginning in 2009) Part of te GS 10 year plan ( ) Target: 2 cm accuracy ortometric eigts from GSS and a geoid model 17 Geoid Power and Potential Sources Work wit many groups to obtain oter data sets as well as wat we observe satellite models (GRACE/GOCE) Variance (m 2 ) airborne and surface gravity terrain and density models Degree (n) km 10 Spectrally merge te data sources to obtain a seamless gravity field Work wit neigbors to incorporate regional data (ort American Geoid/IAG CP 2.2) Use rigorous geodetic teory and/or forward modeling to make a geoid eigt model 18, April
10 COCLUSIOS Current models are precise but not accurate AD 83 & AVD 88 ave significant systematic errors GS Ten Year Plan aims to replace bot by about 2018 Te geoid eigt model will be determined troug GRAV-D Aerogravity will be tied to satellite data (GRACE/GOCE) Combined aerogravity/satellite model will fix surface data Merged gravity data will provide seamless gravity field Improved teory will rigorously transform to geoid eigts Future vertical control accessed by GSS and geoid eigts Tim varying aspects will be incorporated Span of te model sould cover all of ort America 19 GEOID Team Daniel R. Roman, P.D. Yan Ming Wang, P.D. Jarir Sale Simon Holmes, P.D. Aerogravity Collection/Processing Vicki A. Cilders, P.D. Teresa Diel, P.D. Sandra A. Preaux Programming/IT Support William Waickman Questions? Websites ttp:// ttp:// 20 2, April
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