Height System Unificationand GOCE. Reiner Rummel, Michael Sideris, Phil Woodworth

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1 Height System Unificationand GOCE Reiner Rummel, Michael Sideris, Phil Woodworth 14th Canadian Geoid Workshop, Banff/Alberta, June 5, 2012

2 GOCE basic facts Gravity andsteady stateoceancirculationexplorer launched on March 17, 2009 (now 2½ years in orbit) first mission of ESA s Living Planet programme (followed by SMOS and CRYOSAT) mission goals: gravity with 1 ppm (1 mgal) accuracy geoid with 1 to 2 cm accuracy spatial resolution 100km (equivalent to degree/order = 200 in spherical harmonics) orbit characteristics inclination 96.5 (sun synchronous) polar data gaps circular altitude 265km! mission duration: medium monthsdata processed

3 GOCE gravity gradiometry measurement principle: acceleration differences GOCE: firstgravitationalgradiometer

4 GOCE gravity gradiometry 2 2 Vxx Vxy Vxz ω y ωz ωω x y ωxωz 0 ωz ωy 2 2 Vyx Vyy Vyz + ωω y x ωz ωx ωω y z + ωz 0 ωx 2 2 Vzx Vzy V zz ωω z x ωzωy ωx ω y ωy ωx 0 Y GRF Y A A Y 2 6 O 6 X X O2 6 2 Z 6 6 Z 2 2 A Y X X A 4 O4 Y 1 O1 X 1 Z 1 1 O 4 GRF GRF Z 4 4 A Y A Y 5 3 O O3 X 5 X 5 3 Z 5 5 Z 3 3 Z GRF Basic facts: 1.Measurementstaken in a rotatingframe 2. Eachaccelerometer withtwo ultra precise andone robust axis 3. Noise is white onlyinside themeasurement band (MB) from 5mHz to 0.1Hz (belowincreaseas 1/f) skew symmetric

5 GOCEsensorsystem ion thrusters xenon tank nitrogen tank power supply star sensor gravitational gradiometer GPS receiver source: ESA ion thruster control unit magneto torquers control unit an orbiting gravitational laboratory high performance of all sensors very different from typical remote sensing satellites

6 GOCE gravitymodels Global GOCE Gravity Field Models Model Data D/O Characteristics DIR1 2 Months 240 Direct Approach: Prior model (combined) plus GOCE orbits & gradiometry DIR2 6 Months 240 Direct Approach: Prior model (GRACE-only) plus GOCE orbits & gradiometry DIR3 1 Year 240 Direct Approach: Prior model (GRACE-only normals) plus GOCE gradiometry TIM1 2 Months 224 Time-wise Approach: Pure GOCE (kin. orbits & gradiometry) TIM2 6 Months 250 Time-wise Approach: Pure GOCE (kin. orbits & gradiometry) TIM3 1 Year 250 Time-wise Approach: Pure GOCE (kin. orbits & gradiometry) SPW1 2 Months 210 Space-wise Approach: GRACE low d/o plus GOCE gradiometry SPW2 6 Months 240 Space-wise Approach: Pure GOCE (kin. Orbits &gradiometry) GOCO01s 2 Months 224 Time wiseand ITG Grace2010s (d/o 180) GOCO02s 8 Months 250 Time wiseand ITG Grace2010s (d/o 180) + CHAMP+SLR

7 GOCE reprocessing Combinedprocessingof all threestartrackers Optimizedattitudedetermination Optimized angular rate reconstruction Interpolation ofcalibrationmatrices Brockmann, Schuh, Krasbutter, 2012 Technical Note

8 GOCE reprocessing GPS leveling vs. GOCE & EGM2008 Canada USA Th Gruber, 2012

9 Status of GOCE Launch in March 2009; sciencedatasince November 2009 GOCE combines (fouraccurate) gradiometercomponentsv xx, V yy, V zz andv xz andorbittrackingby GPS Itsstrengthareprimarilytheshorterspatialscales, say> d/o 80 Approximatelyonefullyearofdataprocessedby HPF Currently level 1b re processing (combinationof 3 STRs, improved angular rate reconstruction, interpolationofcalibrationmatrices) mainimprovementsexpectedatlongspatialscales Commissionerrordecreaseswiththesqrtoffullorbitcycles (each 31 days)

10 GOCE and GRACE 10-6 SLR GRACE GOCE Mean Signal per Degree / Degree Error Median Mean Signal QL GOCE Model Mean Signal Kaula Rule ErrorMedianQLGOCEModel Error Median EIGEN-5S Error Median EIGEN-5C temporal variations GRACE GOCE Degree 400km 200km 100km degreevariances (median) ofsignalandnoise

11 GOCE and GRACE Yi W, 2011 Contribution anylysis of a GOCE GRACE combination

12 GOCE versus EGM in cm RMS geoiddifferencesbetween EGM2008 and GOCE release 3 wellsurveyedregions (black), problematicregions (red) andantarctica (green)

13 GOCE versus EGM2008 Yi & Rummel, 2012 Geoid differences GOGRA vs. EGM08

14 GOCE versus EGM2008 EGM arc minute areameangravityanomalies datasources Pavlis et al., 2012)

15 GOCE overview GOCE special issue of Journal of Geodesy Volume 85, no.11, 2011

16 GOCE scienceandapplication point of departure solid earth ocean ice geodesy sea level gravity anomalies seismic tomograpy geoid gravity anomalies geoid ocean altimetry ice topography positioning (GPS) tide gauges altimetry topography deformations laboratory mean ocean circulation bedrock topography levelled heights post glacial rebound unified height system mean ocean circulation anomalous density structure constraints on mass & heat transport mass balance of ice sheets gravity anomalies ice mass balance orbits unified height systems INS orbits Granada, 1999

17 GOCE andheightsystemunification ESA s Support Top Science Element (STSE) An elementofthe Earth Observation Envelope Programme 3 Theme 1: Height System Unificationwith GOCE (STSE HSU) Team: IAPG, Technical University Munich (coordination) University of Calgary BKG, Frankfurt/Main NOC Liverpool andconsultants

18 GOCE andheightsystemunification The nineitemsofthisstudy: 1. State-of-the-art in heightsystemsandtheirunification 2. Quantificationofknowndifferences 3. Review, evaluationandimprovementofmethodology 4. Attemptof global height (andtidegauge) unification 5. Selectionoftwotestregions effectof GOCE 6. Effectofunification on localgravityandtopographicheights 7. Geophysicalinterpretation: dynamicoceantopography, currents, 8. Involvementoflocal/ national authorities 9. Roadmap forfutureworkusing GOCE: worldheightsystem andverticaldatum

19 GOCE andheightsystemunification Perspective With GOCE gravity models a significant improvement of the global geoid can be reached. Models based on 1 year of data reach a global geoid error of 4.6 cm at 100 km resolution. With a successful extended mission of GOCE this can be further improved to better than 2.9 cm after *) from: R. Pail, IAPG

20 Structureandstatusof STSE GOCE HSU WP200: Preliminary Analysis Existing methods (210) Review ( ) VC propagation (220) GBVP approach (230) Optimal combination (280) Regional studies: North America North Atlantic Europe/Germany WP500: Impact Assessment Quality analysis of global simulation (540) GOCE regional impact assessment ( , 550) WP100: Requirements Consolidation WP400: Development & Validation Global unification simulator and error propagation (410) Regional unification and error assessment ( ) WP300: Data Collection & Promo. Web page (310, 320) Data collection ( ) Promotion (350) WP600: Scientific Roadmap Geodetic application (620) Roadmap regional unification and application (610, 630, 640) Roadmap global unification GGOS, IAG, WHS (650)

21 GOCE andheightsystemunification Vertical Reference Frame Definition The realization of a system for elevations that supports physical and geometric heights globally with ppb relative accuracy Vertical Datum A level, zero-height surface with a conventional value W o A W o value does not imply knowledge of the level surface itself Realization and Unification Data: GNSS/SLR, geodetic & ocean leveling, TGs, altimetry, gravity, GGMs Zero-tide system (BVP solution requirement) Convert C to H or H*, or vice versa Select/determine global W o value Determine local W oj values and connect W oj to W o C P = W o W P = dw = gdh P P o P P o

22 GOCE andheightsystemunification Vertical Reference Frame W o can be obtained from, e.g., ellipsoidal parameters (W o = U o ), or computed/assigned to a tide gauge or from a GGM and/or altimetry and/or MSL fit or from the solution of a (generalized) geodetic BVP W P can be obtained either from the BVP solution for T P W P = U P + T P or from levelling plus gravity (given W o ) C P = W o W P = gδn or from GNSS/SLRand geodetic/ocean levelling T P = gn P =g(h P H P ) Consistent use of standards, theory and data is essential

23 GOCE andheightsystemunification Solution of the height datum problem North America North Atlantic Europe

24 GOCE andheightsystemunification The GBVP approach Global offset No δ ( GM ) ΔWo ( h H j ) N = + Rγ γ C γ jo Geoid from GPS/levelling Geoid from solution of GBVP Regional offset Njo Gravimetric geoid with biased gravity anomalies R 2 N = S( ψ ) Δg j + C jo dω, 4πγ Ω R g Δg j = g H j γ h

25 GOCE andheightsystemunification GOCEgeoid: Limited resolution Omission error 30 cm Commission error 1 2 cm The GBVP approach N GOCE = GM Rγ L max l P (cosθ )( ΔC cos mλ +ΔS lm l= 2 m= 0 lm lm sin mλ) GOCE N = N + N res N res = R res res S ( ψ ) Δg j dω + 4πγ Ω 1 S 2πγ Ω res ( ψ ) C jo dω Biased residual geoid Indirect bias term

26 GOCE andheightsystemunification functionalpart adjustmentmodel stochasticpart land topography 8000m A O c C B H c h(c) H b h(b) N(C) N(B) O b mean dynamic ocean topography (MDT) ±1 to 2m O a h(a) H a N(A) geoid reference ellipsoid

27 GOCE andheightsystemunification Variance covariance propagation for GOCE Comparable precision of h, H, N, or ζ and proper stochastic models GOCEVCM, d/o 250 for the first orders m=0,1,2,3 HSU simulator for error analysis and impact assessment GOCO2s up to d/o 200: Geoid height error Full Error VCM m block approximation

28 GOCE andheightsystemunification Geometric and Gravimetric Coordinate System consistency The N1 term in the geoid height should be added if GOCE is not geo localized in a geocentric reference frame Center of mass in a geocentric reference system

29 GOCE andheightsystemunification Evaluation of the Indirect Bias Term All offsets are computed with respect to the global level surface defined by 2 2 W o = m / s

30 GOCE andheightsystemunification Evaluation of the Indirect Bias Term Stokes kernel

31 GOCE andheightsystemunification Evaluation of the Indirect Bias Term Truncated Stokes kernel: Lmax= 150

32 GOCE andheightsystemunification Evaluation of the Indirect Bias Term

33 GOCE andheightsystemunification Effect of the Omission Error Mean differences between the regional GPS/levelling geoid heights and GOCEgeoid heights computed by means of TIM_R3, d/o=200

34 GOCE andheightsystemunification Effect of the Omission Error North America: Datum offsets computed with EGM2008 truncated to different d/o (of the available satellite only and combined global gravity models)

35 GOCE andheightsystemunification Effect of the Omission Error A simulation study: minimum size of the averaging area with GPS/levelling stations for which the mean omission error is few centimeters neglect res the N term.

36 GOCE andheightsystemunification Effect of the Omission Error Average Area Point (1) The mean omission error is at a cm level (2) In all cases, the difference between area and point averages is below 2cm (exception: Switzerland) (3) Larger differences between observed and simulated mean omission error might indicate systematic effects

37 GOCE andheightsystemunification Height Unification Using Ocean Information NOCL Objectives: (1)Collect tide gauge, GPS, altimeter, ocean model and geoid information so as to compare MSL differences (adjusted by the models) to geoid differences over a given epoch at and near the coast (in the case of tide gauges and altimetry respectively) (2)Thereby both validate the new geoid models, and obtain confidence in the use of ocean models to relate MSL (and so datums) in one country to that in another. PSMSLRLR Stations (> 40 Years of Data)

38 MSL above National Datums North Atlantic Nova Scotia

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40 MSL above National Datums North Pacific USA MSL approximately 1 metre above datum on the Pacific coast

41 MSL minus Geoid (GOCO03Sp) N America Atlantic Outlier Reedy Point

42 MSL minus Geoid (Extended Model) N America Atlantic Outliers Reedy Point and Portland (maybe Fernandina Beach)

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44 GOCE andheightsystemunification Project Website

45 GOCE andheightsystemunification Outlook (1) Development of global height system unification simulator and error propagation (2) Implementation of the least squares adjustment model (3) Regional unification of height systems in Europe and North America (4) Connecting Europe and North America using (i) the GBVP approach and (ii) using ocean information (5) Quality analysis and interpretation of height unification results with the GBVP approach (6) Assessment of improvement in height unification with and without the GOCEgeoid (7) Assessment of improvement in consistency between geodetic and oceanographic insights into spatial variation in sea level on regional and basin scales. (8) Developing a roadmap for regional and global height system unification