1. Astronomical Institute University of Bern Astronomical Institute, University of Bern Swarm Gravity Field Results with the CMA Adrian Jäggi, Daniel Arnold, Ulrich Meyer Christoph Dahle GFZ, German Research Centre for Geosciences, Potsdam

2. Slide 2 Astronomical Institute University of Bern CMA – Celestial Mechanics Approach The CMA is a generalized orbit determination procedure. Kinematic LEO positions derived from GPS are taken as pseudo-observations (weighted according to covariance information from kinematic PPP) Orbit, gravity field and stochastic parameters are estimated simultaneously. CMA is applied to Swarm as well as to GRACE kinematic orbits

3. Slide 3 Astronomical Institute University of Bern Data used for gravity field solutions Swarm A, B & C: 01 Dec 2013 – 25 Sept 2014 (10 months) Kinematic orbits (based on original/screened GPS data) GRACE A & B: 01 Dec 2013 - 31 March 2014 (4 months) Kinematic orbits

4. Slide 4 Astronomical Institute University of Bern Description of gravity field solutions Models  EGM2008 120x120  FES2004 Estimated parameters per 24-hour orbit arc  initial state  constant empirical accelerations  15-minute piecewise constant empirical accelerations (constrained) spherical harmonic gravity field coefficients up to degree/order 60x60 (coefficients 61 to 120 fixed to EGM2008)

5. Slide 5 Astronomical Institute University of Bern Gravity field solutions – two months of data Experimental setup: Data: 2013/12 – 2014/01 Swarm A, B, C still all at the same orbital height Results: Solutions very similar Formal errors identical Confirmation of results from Copenhagen workshop when using GPS data with PCVs from RUAG adopted for RINEX generation.

6. Slide 6 Astronomical Institute University of Bern Gravity field solutions – two months of data Experimental setup: Data: 2013/12 – 2014/01 Comparison of recoveries from kinematic orbits used for Copenhagen workshop and from new orbits Results: Solutions improved Formal errors improved Adopted PCVs were not optimal for the the Copenhagen workshop. PCV information crucial, especially for long-wavelength gravity recovery.

7. Slide 7 Astronomical Institute University of Bern Gravity field solutions – two months of data Experimental setup: Data: 2013/12 – 2014/01 Comparison of recoveries from kinematic orbits used for Copenhagen workshop and from new orbits Results: Solutions improved Formal errors improved Adopted PCVs were not optimal for the Copenhagen workshop. PCV information crucial, especially for long-wavelength gravity recovery.

8. Slide 8 Astronomical Institute University of Bern Gravity field solutions – two months of data Experimental setup: Data: 2013/12 – 2014/01 Comparison of recoveries from kinematic orbits used for Copenhagen workshop and from new orbits Results: Solutions improved Formal errors improved Adopted PCVs were not optimal for the the Copenhagen workshop. PCV information crucial, especially for long-wavelength gravity recovery.

9. Slide 9 Astronomical Institute University of Bern Gravity field solutions – eight months of data Experimental setup: Data: 2013/12 – 2014/07 Swarm A, B, C at varying altitudes Combination seems to only slightly improve the solutions. Needs to be investigated what is preventing the further noise reduction. Results: Solutions very similar, no effect due to varying heights Small impact visible on formal errors

10. Slide 10 Astronomical Institute University of Bern Screening of GPS observations Screening of GPS data at RINEX level by colleagues of TU Delft: Remove observations where the ionosphere change is large.  Computation of new kinematic orbits  Repetition of gravity field recovory

11. Slide 11 Astronomical Institute University of Bern Gravity field solutions – GPS data screening Experimental setup: Data: 2013/12 – 2014/07 Comparison of recoveries from kinematic orbits based on original/screened GPS data Results: Solutions very similar Formal errors improved No large impact is seen on the level of difference degree amplitudes. Improvement of formal errors is due to the use of 1Hz data since mid of July for the solution based on screened data.

12. Slide 12 Astronomical Institute University of Bern Gravity field solutions – GPS data screening (Differences wrt EGM2008, 400 km Gauss smoothing adopted) Systematic signatures along the geomagnetic equator seem to be notably reduced when adopting the screening to the raw RINEX GPS data files, but there is also noise magnification. Needs to be further investigated … Original GPS Data Screened GPS Data

13. Slide 13 Astronomical Institute University of Bern Gravity field solutions – GPS data screening Experimental setup: Data: 2013/12 – 2014/09 Addition of two months based on 1 Hz screened data (from 16/07/2014) Results: Solutions very similar Formal errors improved Completely unclear why the solutions do not improve at all. => Needs to be investigated … Most probably a processing artefact …

14. Slide 14 Astronomical Institute University of Bern Gravity field solutions – GPS data screening (Differences wrt EGM2008, 400 km Gauss smoothing adopted) Most probably something went wrong in this experiment … Following slides show a couple of experiments to shed further light on this 8 months of screened data 10 months of screened data

15. Slide 15 Astronomical Institute University of Bern Gravity field solutions – 0.1 Hz vs. 1 Hz Experimental setup: Data: 07/16 – 08/07 Comparison of 1-sec and 10-sec solutions Results: Solutions only slightly improved Formal errors improved Slight noise reduction is in accordance with experience from other missions (e.g. GOCE).

16. Slide 16 Astronomical Institute University of Bern Gravity field solutions – 0.1 Hz vs. 1 Hz (Differences wrt EGM2008, 400 km Gauss smoothing adopted) Very similar performance when using 1-sec or 10-sec kinematic orbits for gravity field recovery. Everything seems to be fine for these 23 days … 0.1 Hz kinematic orbits 1 Hz kinematic orbits

17. Slide 17 Astronomical Institute University of Bern Gravity field solutions – Comparison with GRACE Experimental setup: Data: 2013/12 – 2014/01 Comparison with GPS-only GRACE A+B solutions Results: Similar performance for long wavelengths Worse performance for high degrees Worse performance for high degrees is to be expected due to the different heights. The good agreement at the low degrees is very encouraging.

18. Slide 18 Astronomical Institute University of Bern Gravity field solutions – Comparison with GRACE (Differences wrt EGM2008, 400 km Gauss smoothing adopted) Swarm is still a bit worse, but this might be explained by the different high frequency noise? It is interesting to note that GRACE also seems to show (?) traces of the geomagnetic equator (was not noted so far!). GRACE Swarm

19. Slide 19 Astronomical Institute University of Bern Gravity field solutions – monthly solutions Visual inspection of monthly solutions

20. Slide 20 Astronomical Institute University of Bern Gravity field solutions – 2013/12 (Differences wrt EGM2008, 500 km Gauss smoothing adopted) Slight reduction of the geomagnetic equator observed. original GPS data Screened GPS data

21. Slide 21 Astronomical Institute University of Bern Gravity field solutions – 2014/01 (Differences wrt EGM2008, 500 km Gauss smoothing adopted) No change wrt geomagnetic equator. original GPS data Screened GPS data

22. Slide 22 Astronomical Institute University of Bern Gravity field solutions – 2014/02 (Differences wrt EGM2008, 500 km Gauss smoothing adopted) Slight reduction of the geomagnetic equator observed, signature generally very strong. original GPS data Screened GPS data

23. Slide 23 Astronomical Institute University of Bern Gravity field solutions – 2014/03 (Differences wrt EGM2008, 500 km Gauss smoothing adopted) Slight reduction of the geomagnetic equator observed. original GPS data Screened GPS data

24. Slide 24 Astronomical Institute University of Bern Gravity field solutions – 2014/01-2014/03

25. Slide 25 Astronomical Institute University of Bern Gravity field solutions – 2014/04 (Differences wrt EGM2008, 500 km Gauss smoothing adopted) Slight reduction of the geomagnetic equator observed. original GPS data Screened GPS data

26. Slide 26 Astronomical Institute University of Bern Gravity field solutions – 2014/05 (Differences wrt EGM2008, 500 km Gauss smoothing adopted) No change wrt geomagnetic equator, signature generally rather weak. original GPS data Screened GPS data

27. Slide 27 Astronomical Institute University of Bern Gravity field solutions – 2014/06 (Differences wrt EGM2008, 500 km Gauss smoothing adopted) No change wrt geomagnetic equator, signature almost not present. original GPS data Screened GPS data

28. Slide 28 Astronomical Institute University of Bern Gravity field solutions – 2014/04-2014/06

29. Slide 29 Astronomical Institute University of Bern Gravity field solutions – 2014/07 (Differences wrt EGM2008, 500 km Gauss smoothing adopted) Slight reduction of the geomagnetic equator observed, signature very weak. original GPS data Screened GPS data

30. Slide 30 Astronomical Institute University of Bern Gravity field solutions – 2014/07-2014/09

31. Slide 31 Astronomical Institute University of Bern Gravity field solutions – monthly solutions Comparison with GRACE

32. Slide 32 Astronomical Institute University of Bern Gravity field solutions – 2013/12 (Differences wrt EGM2008, 500 km Gauss smoothing adopted) Swarm is more noisy, geomagnetic equator also visible (?) for GRACE. GRACE Swarm

33. Slide 33 Astronomical Institute University of Bern Gravity field solutions – 2014/01 (Differences wrt EGM2008, 500 km Gauss smoothing adopted) Swarm is more noisy, geomagnetic equator also visible (?) for GRACE. GRACE Swarm

34. Slide 34 Astronomical Institute University of Bern Gravity field solutions – 2014/03 (Differences wrt EGM2008, 500 km Gauss smoothing adopted) Swarm is more noisy, geomagnetic equator also visible (?) for GRACE. GRACE Swarm

35. Slide 35 Astronomical Institute University of Bern Summary and Conclusions Swarm gravity field solutions improved wrt earlier solutions (good PCVs are crucial). Low degree coefficients are of comparable quality as for GRACE. Geomagnetic signatures are clearly visible in Swarm solutions (different strength for different months). GPS data screening for large ionosphere changes helps to reduce the geomagnetic signatures. Solutions based on 1 Hz data do not seem to be significantly better.