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EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 EIGEN-6 A new combined global gravity field model including GOCE data from.

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Presentation on theme: "EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 EIGEN-6 A new combined global gravity field model including GOCE data from."— Presentation transcript:

1 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 EIGEN-6 A new combined global gravity field model including GOCE data from the collaboration of GFZ-Potsdam and GRGS- Toulouse Christoph Förste 1, Sean Bruinsma 3, Richard Shako 1, Jean-Charles Marty 3, Frank Flechtner 2, Oleh Abrikosov 1, Christoph Dahle 2, Jean-Michel Lemoine 3, Hans Neumayer 2, Richard Biancale 3, Franz Barthelmes 1, Rolf König 2, Georges Balmino 3 1 GeoForschungsZentrum Potsdam, Dept. 1 ‘Geodesy and Remote Sensing’,Telegrafenberg, D-14473 Potsdam, Germany, e-mail: foer@gfz-potsdam.de, fax: ++49 331 288 1169 2 GeoForschungsZentrum Potsdam, Department 1 ‘Geodesy and Remote Sensing’, c/o DLR Oberpfaffenhofen, D-82234 Weßling, Germany, e-mail: flechtne@gfz-potsdam.de, fax: ++49 331 288 1169 3 Groupe de Recherche de Geodesie Spatiale (18, avenue Edouard Belin, F-31055 Toulouse, France, e-mail: richard.biancale@cnes.fr, fax: ++33 5 61 253098)

2 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Data used for EIGEN-6C/S LAGEOS-1/2 SLR dat GRACE GPS-SST and K-band range-rate data: - January 2003 … June 2009 (6.5 years) - within the GRGS RL02 GRACE processing - normal equations including 5 time variable parameters for each spher. harm. coeff. up to d/o 50: G(t)=G(t 0 )+DOT*(t-t0 )+C1A*cos(ωa*(t-t0))+S1A*sin(ωa*(t-t0)) +C2A*cos(ωsa*(t-t0))+S2A*sin(ωsa*(t-t0)) with t 0 =2005.0 = reference epoch where:DOT=drift C1A, S1A=annual terms C2A, S2A=semi-annual terms The combination of the different satellite and surface parts has been done done by a band-limited combination of normal equations, which are obtained from observation equations for the spherical harmonic coefficients. GOCE: - GOCE SGG data: Txx, Tyy and Tzz - processed by the direct approach (GFZ/GRGS within GOCE-HPF) - individual normal equations for each SGG component - application of a (100 – 8) sec band pass filter for all three SGG components  The SGG signal is filtered-out below degree ~ 50 Terrestrial data: DTU10 global gravity anomaly grid (Andersen, Knudsen and Berry 2010 & Anderson 2010)  This is obtained from altimetry over the oceans and EGM2008 over land

3 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 The satellite-only model EIGEN-6S

4 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 contribution to the solution: kept separately: GRACE degree/order 2402 130160 Combination scheme of EIGEN-6S (satellite-only) GOCE SGG Txx + Tyy + Tzz Polar gap regularization Application of external gravity field information over the polar gaps For EIGEN-6S: GRACE/LAGEOS to d/o 130 + zero coefficients to d/o 240 Algorithm: Spherical cap regularization (Metzler & Pail 2005) LAGEOS 30

5 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 EIGEN-6S: GOCE Polar Gap stabilization for GRACE + GOCE The effect of the stabilization in the spectral domain EGM-2008 GOCE-only non-stabilized GRACE/LAGEOS + GOCE non-stabilized EIGEN-6S - stabilized for comparison: GOCO01S GRACE

6 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 The effect of the stabilization of GRACE on GOCE: GOCE-only vs. GRACE+GOCE, both non-stabilized Max degree of GRACE

7 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 The effect of the stabilization on the spherical hermonic coefficients: GRACE+GOCE-only non-stabilized vs. EIGEN-6S

8 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 The effect of the stabilization on the spherical hermonic coefficients: GOCE-only non-stabilized vs. EIGEN-6S

9 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 The combined model EIGEN-6C

10 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 GRACE degree/order 240 2 130160 LAGEOS 30 370 Combination scheme of EIGEN-6C Accumulation of a full normal matrix up to d/o 370: ~200.000 parameters, ~ 250 GByte GOCE SGG Txx + Tyy + Tzz 1420 Spherical harmonic degree 260 contribution to the solution: kept separately: Separate block diagonal solution: DTU10, block diagonal DTU10 gravity anomaly data

11 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 GRACE/LAGEOS GOCE SGG DTU10 in the Full normal equ. EIGEN-6C spectral behavior (1)

12 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Coeff. of the block diagonal normal equ. Full normal equ. EIGEN-6C spectral behavior (2)

13 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Evaluation Results

14 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Evaluation by computation of residuals RMS of filtered SGG residuals: GOCE measurements (cycle 1) - model GOCE models - Improvement with GOCE compared to GRACE

15 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Gravity field model / max. d/o120x120150x150180x180 EGM20084.02.92.8 GGM03C3.62.42.3 EIGEN-5C3.42.32.2 EIGEN-51C3.22.01.8 ITG-GRACE2010S3.31.81.7 GO_CONS_GCF_2_DIR3.92.62.4 GOCO01S3.31.81.6 EIGEN-6S (epoch 01.12.2009)3.21.61.5 EIGEN-6C (epoch 01.12.2009)3.21.61.5 1) Orbit computation with different spher. harm. max. degree GOCE Orbit adjustment tests Observations: GO_CONS_SST_PKI_2I (kinematic GOCE orbit positions) Dybamic orbit computation 60 arcs (01.11. – 31.12.2009), Arclength = 1.25 days Parametrization: - Accelerometer biases: 2/rev for cross track / radial / along track - Accelerometer scaling factor: along track fixed (set to 1.0), 1/arc for cross track / radial Rms values [cm] of the orbit fit residuals (mean values from the 60 arcs)  The best orbit fits for max deg. 180 for all models

16 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Gravity field model / max. d/o180x180 EGM20082.8 GGM03C2.3 EIGEN-5C2.2 EIGEN-51C1.8 ITG-GRACE2010S1.7 2) Obit fits without and with GOCE-contaning models GOCE Orbit adjustment tests Observations: GO_CONS_SST_PKI_2I (kinematic GOCE orbit positions) Dybamic orbit computation 60 arcs (01.11. – 31.12.2009), Arclength = 1.25 days Parametrization: - Accelerometer biases: 2/rev for cross track / radial / along track - Accelerometer scaling factor: along track fixed (set to 1.0), 1/arc for cross track / radial Rms values [cm] of the orbit fit residuals (mean values from the 60 arcs)  GOCE-only models are not better than most of the GRACE models GOCE TIM-24.2 GOCE DIR-22.4 GOCO01S1.6 EIGEN-6S (epoch 01.12.2009)1.5 EIGEN-6C (epoch 01.12.2009)1.5 GRACE GOCE-only GOCE+GRACE GOCE-GRACE models give better results than GRACE models

17 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Europe (1234) Germany (675) Canada (1930) USA (6169) Australia (201) Comparison with geoid heights determined point-wise by GPS positioning and levelling: Root mean square (cm) about mean of GPS-Levelling minus model-derived geoid heights (number of points in brackets). GGM03C 33.3 18.8 27.8 34.5 25.8 EIGEN- GL04C 33.6 17.8 25.3 33.9 24.4 EIGEN- 5C 30.2 15.2 25.1 33.9 24.3 EGM2008 (till d/o 360) 26.9 14.2 22.9 31.8 23.6 GPS/Levelling test with EIGEN-6C EIGEN-6C 27.5 15.4 22.9 31.6 23.6 Used GPS/Leveling data sets: - USA: (Milbert, 1998) - Canada: (M. Véronneau, personal communication 2003, Natural Resources Canada) - Europe/Germany: (Ihde et al., 2002) - Australia: (G. Johnston, Geoscience Australia and W. Featherstone, Curtin University of Technology, personal communication 2007) Maximum d/o 360  EIGEN- 51C 28.8 14.8 24.4 33.3 23.3

18 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Comparison of independend GRACE time series and the time variable coefficients from EIGEN-6C (max d/o 50) 10-day modelMean model EIGEN-6C atinterpolated to April 2007 Geoidheight differences between the time variable gravity field at the epoch and the corresponding mean field expressed in equivalent water heights (meter)

19 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Comparison of independend GRACE time series and the time variable coefficients from EIGEN-6C (max d/o 50) 10-day modelMean model EIGEN-6C atinterpolated to July 2007 Geoidheight differences between the time variable gravity field at the epoch and the corresponding mean field expressed in equivalent water heights (meter)

20 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Comparison of independend GRACE time series and the time variable coefficients from EIGEN-6C (max d/o 50) 10-day modelMean model EIGEN-6C atinterpolated to October 2007 Geoidheight differences between the time variable gravity field at the epoch and the corresponding mean field expressed in equivalent water heights (meter)

21 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Comparison of independend GRACE time series and the time variable coefficients from EIGEN-6C (max d/o 50) 10-day modelMean model EIGEN-6C atinterpolated to January 2008 Geoidheight differences between the time variable gravity field at the epoch and the corresponding mean field expressed in equivalent water heights (meter)

22 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Comparison of independend GRACE time series and the time variable coefficients from EIGEN-6C (max d/o 50) 10-day modelMean model EIGEN-6C atinterpolated to January 2007 Geoidheight differences between the time variable gravity field at the epoch and the corresponding mean field expressed in equivalent water heights (meter)

23 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Gravity field model / max. d/o150x150 GRACE 2003-2010 (static) 2.1  0.7 GRACE 2003-2010 (at epoch 20091201) 1.8  0.7 GRACE 2003-2009.5 (static) 2.0  0.7 GRACE 2003-2009.5 (at epoch 20091201) 1.7  0.7 EIGEN-6C (static) 1.8  0.8 EIGEN-6C (at epoch 01.12.2009) 1.6  0.7 The impect of time variable models in satellite orbit computation: GOCE orbit adjustment fit: Static vs. Time variable Gravity model Dynamic orbit computation Observations: GO_CONS_SST_PKI_2I (kinematic GOCE orbit positions) 60 arcs (01.11. – 31.12.2009), Arclength = 1.25 days Rms values [cm] of the orbit fit residuals (mean values from the 60 arcs) Parametrization: Accelerometer biases: 2/rev for cross track / radial / along track Accelerometer scaling factor: along track fixed (set to 1.0), 1/arc for cross track / radial

24 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 - EIGEN-6C/S will be published on the ICGEM data base at GFZ Potsdam within the next weeks http://icgem.gfz-potsdam.de Summary / Conclusion - EIGEN-6S is new satellite-only model from the combination of LAGEOS/GRACE & GOCE. - EIGEN-6C is a new combined gravity field model from the EIGEN-6S satellite data and the DTU10 global gravity anomaly grid of a maximum degree 1420. - Over land and beyond degree 240, EIGEN-6C is in principle a reconstruction of EGM2008 (Due to the inclusion of DTU10) - EIGEN-6C/S contain time variable parameters for all spher. harm. coeff. up to degree 50 (drift, annual and semiannual terms). - GOCE-only models are not as good as GRACE models for GOCE orbit computation. The best GOCE orbit fit results are obtained with combined GRACE+GOCE models. Thereby, the maximum degree should be taken up to 180. - The application of time variable gravity field components in GOCE orbit computations gives a futher improvement in the orbit fit results (best results with EIGEN-6C). - Thus, time variable gravity field components should be used in satellite orbit computations generally - GPS/Leveling comparisons show an improvement of EIGEN-6C compared to the previous EIGEN-models. The EIGEN-6C results are comparable with EGM2008 - Meanwhile the generation and inversion of normal equations > 300 Gbyte of more than 200.000 parameters is technically feasible

25 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 Thank you for your attention

26 EGU General Assembly 2011, 3 rd – 8 th April 2011, Vienna, Austria EGU2011-3242 GRACE 240 2 130160 LAGEOS 30 370 Combination scheme of EIGEN-6C (incl. Spherical Cal Regularization) Accumulation of a full normal matrix up to d/o 370: ~200.000 parameters, ~ 250 GByte 1420 Spherical harmonic degree 260 contribution to the solution: kept separately: Separate block diagonal solution: Spher. Cap stabilizer* GOCE SGG Txx + Tyy + Tzz DTU10 gravity anomaly data DTU10, block diagonal * based on an internal combined model LAGEOS/GRACE + DTU10 (EIGEN-52C)

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