GOCE Gravity Field Models – Overview and Performance Analysis Th. Gruber, R. Rummel & High Level Processing Facility (HPF) Team *Institute of Astronomical.

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GOCE Gravity Field Models – Overview and Performance Analysis Th. Gruber*, R. Rummel* & High Level Processing Facility (HPF) Team *Institute of Astronomical & Physical Geodesy (IAPG) Technische Universität München 5th International GOCE User Workshop, Paris,

2. GOCE-based Gravity Field Models  Overview  Signal Characteristics 3. Performance Analysis  Estimated Errors  External Validation  Geoid Accuracy 4. Summary Outline 1. High Level Processing Facility

5th International GOCE User Workshop, Paris, High Level Processing Facility Universität Bern, Astronomisches Institut, Switzerland Politechnico di Milano, DIIAR Sezione Rilevamento Italy Technische Universität Graz, Institut für Theoretische Geodäsie und Satellitengeodäsie, Austria Universität Bonn, Institut für Geodäsie & Geoinformation, Germany Delft University of Technology, Astrodynamics and Space Missions, The Netherlands SRON Netherlands Institute for Space Research Nils Bohr Institute, University of Copenhagen, Denmark Deutsches GeoForschungsZentrum Potsdam, Dept. 1 Geodesy and Remote Sensing, Germany Centre Nationale d‘Etudes Spatiales, Toulouse, France PI & Project Management: Technische Universität München, Institut für Astronomische und Physikalische Geodäsie, Germany

5th International GOCE User Workshop, Paris, High Level Processing Facility The people behind the HPF (only some of them)

5th International GOCE User Workshop, Paris, Overview of GOCE Models ESA Rel. 5 GOCE Models

5th International GOCE User Workshop, Paris, Overview of GOCE Models GFZ/CNES Other GOCO

5th International GOCE User Workshop, Paris, Overview of GOCE Models ESA Release 5 GOCE Models Characteristics DIR5TIM5 Maximum D/O GOCE Data Volume ; ~3.5 yrs (net) Gravity GradientsV xx, V yy, V zz, V xz >400 Mio. Obs.V xx, V yy, V zz, V xz >439 Mio. Obs. Gradient FilterBand-pass filterARMA filter per segment (87) GOCE SST (GPS)-Short arc approach (d/o 150) GRACE SST (K-Band) GRGS RL03 (d/o 130) - LAGEOS 1/2 (SLR) , ~25 yrs- Regularizationspherical cap based on GRACE/LAGEOS. Kaula zero constraint (d/o > 180) Kaula zero constraint (near zonals and for d/o > 200)

5th International GOCE User Workshop, Paris, Signal Degree Variances (GOCE RL5 vs. earlier Models) Full Signal Content up to d/o Goal was d/o 200 Signal Characteristic

5th International GOCE User Workshop, Paris, Map Source: Pavlis, N. K., Holmes, S., Kenyon, S., Factor, J “The Development and Evaluation of the Earth Gravitational Model 2008 (EGM2008).” Journal of Geophysical Research 117 EGM2008 Data Coverage 12.0% of Land 42.9% of Land 45.1% of Land Signal Characteristic

5th International GOCE User Workshop, Paris, Signal Characteristic GOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200) RMS of Differences in Test Area [mgal] Gravity Anomalies Signal Rel. 1Rel. 2Rel. 3Rel. 4Rel. 5 TIM3.14 DIR1.07

5th International GOCE User Workshop, Paris, Signal Characteristic GOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200) RMS of Differences in Test Area [mgal] Rel. 1Rel. 2Rel. 3Rel. 4Rel. 5 TIM DIR Gravity Anomalies Signal

5th International GOCE User Workshop, Paris, Signal Characteristic GOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200) RMS of Differences in Test Area [mgal] Rel. 1Rel. 2Rel. 3Rel. 4Rel. 5 TIM DIR Gravity Anomalies Signal

5th International GOCE User Workshop, Paris, Signal Characteristic GOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200) RMS of Differences in Test Area [mgal] Rel. 1Rel. 2Rel. 3Rel. 4Rel. 5 TIM DIR Gravity Anomalies Signal

5th International GOCE User Workshop, Paris, Signal Characteristic GOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200) RMS of Differences in Test Area [mgal] Rel. 1Rel. 2Rel. 3Rel. 4Rel. 5 TIM DIR Gravity Anomalies Signal

5th International GOCE User Workshop, Paris, Estimated Errors Coefficient Standard Deviations (log10) GOCE-DIR4GOCE-TIM4 GOCE-TIM5 GOCE-DIR5

5th International GOCE User Workshop, Paris, Estimated Errors Cummulative Geoid Errors from Coefficient Errors 0.8 cm (d/o 200) 3.4 cm (d/o 200) 4.3 cm (d/o 220) 12.5 cm (d/o 280) 1.2 cm (d/o 220) 4.9 cm (d/o 300)

5th International GOCE User Workshop, Paris, Estimated Errors Maps of Geoid Error from VCM Propagation (Full Resolution) Degree/Order & Area TIM5 [cm] DIR5 [cm] 200 Global 200 Germany 220 Global 220 Germany Full Global Full Germany Geoid Error Comparison (Global from cum. Error Degree Variances, Germany from VCM Propagation) TIM5 DIR5

5th International GOCE User Workshop, Paris, Estimated Errors Maps of Geoid Error from VCM Propagation (Degree/Order 220) Degree/Order & Area TIM5 [cm] DIR5 [cm] 200 Global 200 Germany 220 Global Germany Full Global Full Germany Geoid Error Comparison (Global from cum. Error Degree Variances, Germany from VCM Propagation) TIM5 DIR5

5th International GOCE User Workshop, Paris, Estimated Errors Maps of Geoid Error from VCM Propagation (Degree/Order 200) Degree/Order & Area TIM5 [cm] DIR5 [cm] 200 Global Germany Global Germany Full Global Full Germany Geoid Error Comparison (Global from cum. Error Degree Variances, Germany from VCM Propagation) TIM5 DIR5

5th International GOCE User Workshop, Paris, Model Validation GPS Levelling Data for Gravity Field Validation Map Source: Pavlis, N. K., Holmes, S., Kenyon, S., Factor, J “The Development and Evaluation of the Earth Gravitational Model 2008 (EGM2008).” Journal of Geophysical Research 117 EGM2008 Data Coverage & Coverage of GPS/Levelling Data 12.0% of Land 42.9% of Land 45.1% of Land GPS/ LEVELLING POINTS

5th International GOCE User Workshop, Paris, Model Validation RMS of Geoid Differences at GPS-Levelling Points after planar Fit (Omission Error estimated from EGM2008) Germany 2.7 cm 2.9 cm Acknowledgement: GPS levelling data for have been provided for validation purposes by BKG, Frankfurt/Main

5th International GOCE User Workshop, Paris, Model Validation RMS of Geoid Differences at GPS-Levelling Points after planar Fit (Omission Error estimated from EGM2008) Germany 2.7 cm 2.9 cm Acknowledgement: GPS levelling data for have been provided for validation purposes by BKG, Frankfurt/Main

5th International GOCE User Workshop, Paris, Model Validation RMS of Geoid Differences at GPS-Levelling Points after planar Fit (Omission Error estimated from EGM2008) Acknowledgement: GPS levelling data for have been provided for validation purposes by Brazilian Institute of Geography and Statistics - IBGE, Directorate of Geosciences - DGC, Coordination of Geodesy - CGED Australia Acknowledgement: GPS levelling data for have been provided for validation purposes by AUSLIG. Brazil

5th International GOCE User Workshop, Paris, Model Validation RMS of Geoid Differences at GPS-Levelling Points after planar Fit (Omission Error estimated from EGM2008) Canada Europe (EUREF EUVN) Acknowledgement: GPS levelling data for have been provided for validation purposes by National Resources of Canada (NRCan).

5th International GOCE User Workshop, Paris, Model Validation RMS of Geoid Differences at GPS-Levelling Points after planar Fit (Omission Error estimated from EGM2008) Acknowledgement: GPS levelling data for Japan have been provided for validation purposes by the Japanese Geographical Survey Institute Greece Japan Acknowledgement: Access to GPS levelling data for GREECE has been provided by technical University Thesssaloniki.

5th International GOCE User Workshop, Paris, Model Validation RMS of Geoid Differences at GPS-Levelling Points after planar Fit (Omission Error estimated from EGM2008) Acknowledgement: GPS levelling data for have been provided for validation purposes by King Abdulaziz City for Science and Technology KACST. Saudi Arabia United Kingdom

5th International GOCE User Workshop, Paris, Model Validation RMS of Geoid Differences at GPS-Levelling Points after planar Fit (Omission Error estimated from EGM2008) USA (2009 Data Set) Finland (EUREF EUVN)

5th International GOCE User Workshop, Paris, Model Validation RMS of Geoid Differences at GPS-Levelling Points after planar Fit (Omission Error estimated from EGM2008) Areas with High Quality GPS/Levelling Data AreaRMS [cm]No. Points Germany UK Netherlands (EUREF)1.815 Sweden (EUREF)2.684 USA DC1.916 USA2009 – MD USA NH2.614 USA NJ USA RI2.229 USA MN

5th International GOCE User Workshop, Paris, What is the GOCE Geoid Accuracy ?  Estimated error from GOCE-DIR5 at D/O 200 in Germany (formal): 0.5 cm  Estimated error from GOCE-TIM5 at D/O 200 in Germany (calibrated based on gradient residuals): 1.4 cm  Differences at GPS/Levelling Stations in Germany for both models at D/O 200 (after planar fit): 2.8 cm  GPS/Levelling geoid error is composed by:  GPS height error: ≈ 1.5 cm  Normal height accuracy after planar fit: ≈ 1.5 cm  Total after error propagation: 2.1 cm  Attempt to derive a realistic error:  GOCE geoid error (reverse error propagation) → 1.8 cm

5th International GOCE User Workshop, Paris, Summary  Full signal of GOCE-based satellite-only model up to degree and order  Fit to “quiet” ocean area at a level of 0.7 mgal in terms of gravity anomaly or 2.6 cm in terms of geoid – geoid more sensitive to dynamic ocean topography.  Estimated cumulative geoid error at d/o 200 for Germany, 0.5 and 1.4 cm respectively.  GPS-leveling fits significantly improved wrt. release 4 models (now 2.8 cm RMS in Germany, about 1 cm better than rel. 4).  Estimated absolute geoid error of rel. 5 models at d/o 200 roughly 1.8 cm or better.

5th International GOCE User Workshop, Paris, Summary The GOCE Cup